Wikipedia talk:WikiProject Elements/Archive 42

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Archive 35

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Archive 40

The location and constitution of Group 3 of the periodic table

Latest comment: 4 years ago1,667 comments8 people in discussion

I’ve drafted an article for publication in an academic journal and would like to have it peer reviewed before submitting the final version.

Could you please let me know if you’re interested in providing me with a peer review and I'll send you a Dropbox link.

Abstract: The constitution of Group 3 can be pragmatically resolved on the basis of the context within which the applicable periodic table is being used, rather than an inconclusive comparison of the physical, chemical, or electronic properties of La and Lu. From an IUPAC perspective, since the periodic table is primarily the domain of chemistry, considerations of Group 3’s neighbours; predominant differentiating electrons across the four blocks of the periodic table; the periodic law; and the nature of the rare earths, support—in a chemical periodic table—Group 3 as Sc-Y-La-Ac. This is the predominant form of periodic table in the chemistry literature.

Background
The role of IUPAC
Physical, chemical, and electronic properties: inconclusive
A philosophical perspective
     Quantum mechanics
     Regularity and symmetry
     Natural kinds
Chemical, pedagogic, and designer periodic tables
The domain of chemistry
     Immediate neighbours
     Differentiating electrons
     Periodic law
     Rare earths
Conclusion
Acknowledgements
References and notes
Bibliography

Thank you! -- Sandbh (talk) 21:33, 25 December 2019 (UTC)

@Sandbh: I would be interested in providing a review, though I would like to know what exactly such a review would entail before we proceed – for example, is there a dedicated focus (copyediting, fact-checking) or is it an overall review more along the lines of a PR/FAC over here? Also, would I be correct in assuming the journal will provide a (second) review once you submit your manuscript?

Please let me know; if we proceed, I might be able to start reviewing this weekend. ComplexRational (talk) 01:12, 26 December 2019 (UTC)

@ComplexRational: It’s an informal review driven by whatever interests you, with no particular obligations. Yes, the journal will arrange for formal peer reviews once I submit the finished article. Thank you! Sandbh (talk) 08:23, 26 December 2019 (UTC)

@Sandbh: Count me interested as well! Double sharp (talk) 06:12, 26 December 2019 (UTC)

Righto! Will send a Dropbox link to your PM address shorty. Good stuff. Sandbh (talk) 08:23, 26 December 2019 (UTC)

@Sandbh: I'd be glad to give it a dekko. YBG (talk) 05:37, 27 December 2019 (UTC)

Thank you! On the way. Sandbh (talk) 22:38, 27 December 2019 (UTC)

R8R

@Sandbh: I, too, would love to help, but I am not sure if I can. By when do you want to be done with the peer review? If there is a month in hand, then I'll be sure to help you. If not, it may be harder, but I'll still try. (also, I am interested how the subtitle "Quantum mechanics" fits under "A philosophical perspective." I believe an interesting case could be made here.)--R8R (talk) 21:40, 29 December 2019 (UTC)

@R8R: The philosophical pespective section starts like this:

A further option is to step back from the minutiae of physical, chemical, and electronic properties and trends and take a philosophical approach. Such an approach seeks to understand if there is a fundamental structure or theory of physics underlying the organisation of the periodic table. If so, this may provide a perspective on Group 3. Quantum mechanics; regularity and symmetry; and natural kinds (“carving Nature at its joints”) have been inconclusively explored to this end.

I'll PM you a link to the article and see how you go. Sandbh (talk) 06:49, 30 December 2019 (UTC)

I'm sorry I haven't written anything yet. The discussion below is fascinating, a true delight to read. I overestimated myself, however, and as I am already feeling dizzy in the end of the day, I will not be able to write anything today as I thought I would. However, I have a few comments to make and I intend to write them soon enough (as afraid as I am to say this, given that there were two other instances of me wanting to say something but not writing it down last year; I hope I'll finish off all of these problem soon enough). Please assume the added subheader as the initiation of the response.

One comment about the thread below that I'll give is that it goes beyond what was written in the original article; I'll generally try to focus on the article instead.--R8R (talk) 19:37, 12 January 2020 (UTC)

@R8R: I am certainly looking forward to hearing what you think about Sandbh's article, since your comments last time were very thought-provoking and insightful! I can barely handle this flood alone and next week I shan't have much time for it. Double sharp (talk) 00:38, 26 January 2020 (UTC)

I was afraid in late December that I would only be able to respond in a month after and we are exactly there, I'm responding a month after the article has been made available for a preview by us. I'll begin later today.

For now, I've got a question for Sandbh. Did all of the wonderful discussion below result in any change in your article? Do you think something should be amended, some wording should be changed, some arguments revoked or added etc.? One reason I'd like to focus on your article rather than the general group 3 argument (though, of course, it can't be avoided at all) is to help you improve your resulting to-be-submission, and I'd like to know if the discussion has been helpful in that; if so, how, and if not, why.--R8R (talk) 10:30, 26 January 2020 (UTC)

@R8R:@Double sharp:@Droog Andrey: Subject to catching up with the rest of Double sharp’s comments, all of the arguments in the article have, as I see it, withstood the barrage. I do need to fine tune some them. My credit for Double sharp will at least thank him for indefatigable stress testing of the draft. Yes, the discussion has been tremendously helpful in refining and testing my thoughts, including my response to Droog Andrey’s 3IP argument which had me stumped for a while. I’ll be adding the 234 argument, which I’d forgotten about. I probably need to to say more about what I mean by a philosophical approach, and the place of the individual properties of the elements, per Double sharp’s criticism. And I need to say more about the nature of the n + l rule, and it’s lack of a first principles basis, and its d and f block wobbles, and the fallaciousness of arguing for double symmetry in the d and f blocks, on this basis.

It’s ironic to think that this article originated in the obsession by others as to the regularity of the LST and ADOMAH, completely overlooking the extra internal irregularities the Lu form introduces. That’s Nature’s response to glossing over the delayed start to the filling of the 4f subshell, I reckon. That doesn’t mean these tables don’t have their purpose, but not as a conventional table. Sandbh (talk) 11:11, 26 January 2020 (UTC)

@R8R:@Double sharp:@Droog Andrey: I also think the power of the conventional form to capture regularity and irregularity at the same time has been completely overlooked in the literature. Form follows function not the other way round. We need to allocate equal time to beauty/regularity/symmetry and “ugliness”/irregularity/asymmetry. Sandbh (talk) 11:19, 26 January 2020 (UTC)

If you ask me, not if the irregularity is weak and questionable for 4f, and if 5f already explains what is going on quite regularly. The block still ends at the same place (viz. No vs. Lr); it's just that its initial filling is delayed, which is something common throughout he table. But I'll stop, because this is not my section. ^_^ Double sharp (talk) 11:24, 26 January 2020 (UTC)

As far as I am concerned, I don't think of this section as of "mine"; or if it is mine, be my guest (and the same goes to everyone else).

the two options are effectively indistinguishable -- this is probably not a very big deal given that this is the opinion of the taskforce leader, but I think this argument could use elaboration in general, because the reader is thrown a few graphs at which they have to analyze all by themselves. Different thinking yields different results.

More recently, Labarca and Gonzále (2019)13 argued that quantum mechanics are inconclusive(!) when it comes to the Group 3 question. -- that's not very accurate because that's not what they said. Instead, they make a more general argument that quantum physics can help describe an element but not series of elements, and they say so in the context of H and He, not group 3. Also notable is that they make an argument for a -Lu-Lr group 3, which is based on electron configurations, triads, and electronegativity. The latter two make the bulk of their argument but they received very little to no coverage in the article.

@R8R: L & G's paper is called, "About the elements belonging to group 3 from the periodic table: a new approach".

In section 2 of their paper, which is about the position of H and He, they write:

"The standard periodic table, of 18 columns or of medium length, usually includes the elements through scandium (Sc), yttrium (Y), lanthanum (La) and actinium (Ac) integrating group 3. Agree with Jensen (1982), this grouping was progressively established from the decade of 1940, when the quantum mechanical criterion - that is, the use of orbitals and configurations electronic popularized in the representations of the periodic system by LM Simmons and VM Klechkovskii (Mazurs, 1974) - it was crystallized as the moderno to explain the chemical periodicity (for example, Luder 1943)."

Then they say, "the quantum conic has not satisfactorily resolved the position of these elements".

Could it be that you are reading a translation and I'm reading a machine translation of the orinigal paper and that's where our differences come from? I presume that you are specifically referring with that last sentence to this part:

En este sentido, la mecánica cuántica no ha resuelto satisfactoriamente la posición de estos elementos debido a que «La periodicidad en las propiedades químicas de los elementos es un tema complejo y sólo se refleja aproximadamente en las configuraciones electrónicas de los átomos» (Scerri, 1991, 122). Sobre esta base, coincidimos con Scerri (2007, 242) cuando afirma que «[...] la posesión de un determinado número de electrones en la capa externa no es condición necesaria ni suficiente para la pertenencia de un elemento a cualquier grupo particular».

Or, in English:

In this sense, quantum mechanics has not satisfactorily resolved the position of these elements due

that "The periodicity in the chemical properties of the elements is a complex issue and is only approximately reflected in the electronic configurations of atoms" (Scerri, 1991, 122). On this basis, we agree with Scerri (2007, 242) when he says that "[...] the possession of a certain number of electrons in the external layer is not a necessary or sufficient condition for the belonging of an element to any particular group".

This bit is in section 3, which is the section on H and He. In contrast, the longer quote comes from section 2, which outlines the problem itself. Am I missing something?--R8R (talk) 14:51, 30 January 2020 (UTC)

Translated with www.DeepL.com/Translator (free version)"

In section 4 if their paper where they discuss group 3, they say:

"In Section 2 we showed that in problem of the elements of group 3 the arguments made regarding the properties physical and chemical data, as well as the configurations of the elements involved not they are completely convincing both to decide the permanence of La and Ac, or its replacement by Lu and Lr in periods 6 and 7."

They don't explain why triads are important.

On electronegativity they relied on Jensen’s 1982 article in JChemEd, in which he argued that comparisons in periodic trends for Allred-Rochow electronegativity favour Sc-Y-Lu. That is factually correct but incomplete as an argument. The trend in going down Sc-Y-La is instead similar to the trend seen in the group 2 and 1 metals. Further, the choice of electronegativity scale is a little arbitrary. Pauling values, for example, favour Sc-Y-La. Groups 1, 2, 4, and 5 have the period 6 element somewhat more electropositive than the period 5 element; this works with La (1.1) under Y (1.22) but not with Lu (1.27) under Y. In the Mulliken scale, the values for La (1.74) and Lu (1.70) are both less than that of Y (1.81). Sandbh (talk) 07:11, 30 January 2020 (UTC)

A natural kind is a part of the furniture of reality that reflects divisions in the world (“Nature carved at its joints”) that can be considered to exist independently of human classification practices. Examples of natural kinds include electrons, iron, and cats. -- I beg to differ here. "Cats" are a human concept that does depend on humans to function: what's a cat, exactly? If it is spotted and runs fast, is it still a cat? how many mutations should there be for us to say a cat gave birth to what is not one, or vice versa: after all, there was once no cats. Here's a Not-a-Cat Cat, you see where the argument is going. We have a general concept of what a cat is that works in most cases but there are exceptions, and this is a feature of human classifications. (This is also the case with groups and group 3 in particular.)

the chemical behaviour of Group 3 generally resembles that of Groups 1−2 rather than that of Groups 4−11 -- that's indeed the case. Group 3, whether -La-Ac or -Lu-Lr, resembles groups 1 and 2 much more closely than it does resemble groups 4 ~~and 5~~ through 11. This doesn't come as a surprise, however, given that this is not a comparison of the like with the like. A comparison with groups 4 and 5 only would make the difference less staggering and the comparison would be much more even.
- @R8R: I confess I don't understand what you mean here even though I agree with your conclusion. ^_^ If you mean that group 3 is much more like groups 1 and 2 than groups 4 and 5, then your conclusion seems a bit off, because comparing group 3 with groups 4 and 5 should then produce a big differences. So if your conclusion is that group 3 is not that different from groups 4 and 5 (which is something I agree with, having argued it many times below on the grounds of characteristic transition behaviour being weak for Zr/Hf and Nb/Ta), then I think you need to compare Sc/Y/La or Sc/Y/Lu with groups like 6 through 11 in your second sentence. Double sharp (talk) 16:46, 26 January 2020 (UTC)
  - Ah, how embarrassing. Well, serves me right for not re-reading myself. I hope this correction makes it clear enough.--R8R (talk) 18:59, 26 January 2020 (UTC)

R8R is right :) Groups 1 to 3 exhibit a predominately ionic chemistry; groups 4 to 5 are predominantly covalent. That’s a big difference. It then follows that the trends going down group 3 as La follow the trends going down groups 1 to 2 better than the trends going down groups 4 to 5 (which looks better for Lu). Sandbh (talk) 23:03, 26 January 2020 (UTC)
- Nope. He wrote "A comparison with groups 4 and 5 only would make the difference less staggering and the comparison would be much more even" immediately after that. And as I've said below, there is no big difference, because there is no such thing as "predominantly ionic" or "predominantly covalent". It is all a continuum depending on electronegativity difference and what the counter-anion is. Double sharp (talk) 23:38, 26 January 2020 (UTC)
- Let me repeat one of my comments below (so now it appears three times): "Look, there is no such thing as a complete volte-face from ionic to covalent. It depends on what the counter-anion is. We go from ionic to metallic (which you're overlooking completely) across the series NaCl, Na₂O, Na₂S, Na₃P, Na₃As, Na₃Sb, Na₃Bi, Na. And that's in group 1, with an example taken straight from Greenwood & Earnshaw p. 81. Ionic vs. covalent is (1) gradual, from covalent to polar covalent to mildly ionic to strongly ionic, depending on the difference of electronegativity between the two elements; (2) not a complete dichotomy, because you overlook metallic bonding; and (3) not split by elements, but rather by electronegativity differences, which have a lot to do with oxidation state (just compare uranium chemistry as we jack the oxidation state up from +3 to +4 to +5 to +6). So I'm astonished to see you put so much weight on "ionic vs. covalent" as a false dichotomy. (And as I keep saying, the general thing across the periodic table is continuity, and the sharp dichotomies you like to point to have a distinct tendency to not exist.) The whole literature, when it sees fit to split "main group" from "transition", universally uses other criteria like "variable oxidation states", "coloured compounds from d–d transitions", "a wide variety of complexes", "formation of paramagnetic compounds". Ionic vs. covalent has nothing to do with it, and nobody uses that as a criterion in the literature for this divide. Respectfully, I put it to you that Zr, Hf, Nb, and Ta by this standards have weak credentials as transition metals, just as weak as Sc for that matter." Double sharp (talk) 23:41, 26 January 2020 (UTC)

Thank you. I’m a bit hamstrung doing this as on an iPhone. Clearly, according to the literature there is something called typical or predominant or characteristic or majority or 80/20 behaviour. This is such a basic concept of classification science that I’m astonished I have to say so. For example group 18 is characterised by its predominantly noble behaviour.

Clearly according to the literature the chemistry of groups 1 to 3 is mainly ionic, and the chemistry of 4 to 5 is mainly covalent. I’d even cautiously extend this to groups 6 to 10. I have to be cautious as I don’t have access to my library. Just the notion of saying groups 6 to 10 are mainly ionic in their chemistry strikes me as nonsense.

I may not have much more to say here since there is nothing to argue about a reality defying notion that there is no such thing as typical behaviour. Sandbh (talk) 02:42, 27 January 2020 (UTC)

I don't reject typical behaviour. I just reject that your dichotomies exist. As does every basic chemistry text in the world that gives examples of more and more polar covalent bonds running straight into ionicity, e.g. C-C, C-N, C-O, Si-O, Si-F, Al-F, Mg-F, Na-F. Or less and less ionic bonds running straight into metallicity, e.g. Na-F, Na-O, Na-N, Na-P, Na-As, Na-Sb, Na-Bi, Na-Na. All of it depends just on EN differences. And deciding which one is "typical behaviour" will involve drawing a line somewhere, which totally overlooks continuity of the trend. (Where are Be and maybe Mg by your standards?) I put it to you that (1) ionic vs covalent is not a strict dichotomy, (2) is not the key factor defining main group vs transition (otherwise we have a pickle with all those TM salts, and Be and maybe Mg say bye-bye to group 2, not to mention H in group 1), and (3) is clearly untenable because, since it depends on EN, the same element can go both ways depending on oxidation state. Everything I said here has ample support from the literature. Just look at any basic inorganic chemistry textbook. Respectfully, you are creating discontinuities that are not there. So, now that we have drilled down to where this continuity actually comes from (EN), all this argument becomes is "group 3 is more electropositive than group 4". Indeed. So what, given that this is purely and simply one step in a continuous trend? Group 2 is more electropositive than group 3, too. (Maybe not Be and Mg...) And group 4 is more electropositive than group 5, too. Double sharp (talk) 07:47, 27 January 2020 (UTC)

@Double sharp: Oh my. You continually distort or descended into minutiae or go of on irrelevant tangents wrt my argument: 1. Group 3 is a transition metal group showing predominately ionic chemistry. 2. Group 4 is a transition metal group showing predominating covalent behaviour. End of story. From a classification science POV this is a more than adequate divide, per your point 1. I agree with your point 2 and have never adopted this position. Your point 3 is a non-question since I am dealing with groups, not individual elements. My argument is as simple as that. Sandbh (talk) 11:45, 28 January 2020 (UTC)

What on earth is irrelevant about this? You made a statement. I responded to it by criticising its terminology and what it refers to. That is about as relevant as you can get. An irrelevant tangent would be to ignore the challenge set by this statement, which is "predominantly ionic" and "predominantly covalent". Well, I have already explained what the problem is with it. And point (3) works just as well for groups, as usual, because group 2: compare Be/Mg with Ca/Sr/Ba/Ra. It is the same effect: increasing atomic size and decreasing charge corresponds to increasing electronegativity. Both effects will exist whether we are going from Tl³⁺ to Tl⁺ or from Be²⁺ to Mg²⁺. It is you who are introducing artificial differences when the effect is the same, respectfully. Or is anything that doesn't support Sc-Y-La an irrelevant tangent now? It certainly seems so, given that my argument about first-row anomalies is dismissed when I use it for Sc-Y-Lu, but you try to invoke it yourself when attacking He-Be-Mg! Same thing with my argument for condensed-phase configurations: paraded from the rooftops to support Sc-Y-La, but sudden silence when it also argues for Be-Mg-Zn! Double sharp (talk) 12:07, 28 January 2020 (UTC)

re the number of discrepancies: does it matter though? the Argentinian paper mentioned above argues it does not, the Lr anomaly is just that, an anomaly that doesn't have any real consequences, and it mentions a previous paper saying that. That's an important question given that this argument goes in the section titled "The domain of chemistry”.

@R8R: Yes, the number of discrepancies in comparison to the n+l rule does matter. The fewer the discrepancies the more regular the table becomes as a representation of the n + 1 rule. I couldn't find where it said in the Argentinian paper that it doesn't. You can't apply this approach for some of the elements and not the others. I've addressed the consequence question elsewhere in the Lr section of this thread. Sandbh (talk) 22:10, 31 January 2020 (UTC)

Just to be sure I'm getting you right. Why does it exactly matter more than the beauty of the contiguous blocks? What is there precise fundamental ruling behind this if we assume there is none for Aufbau? Especially given that it has ten more exceptions anyway? (I will check the thread myself later, though.)

The paper says this:

Respecto de la reciente confirmación espectroscópica de la configuración electrónica del Lr (103) 7s2 7p1 (Sato et. al. 2015), coincidimos con Jensen (2015) cuando señala que la interpretación más plausible sería que este caso es sólo otro ejemplo de un elemento del bloque d con una configuración electrónica irregular (debida a efectos relativistas, como fue mencionado), pero que químicamente es un análogo del Lu más que comportarse como un elemento del bloque p.

or

Regarding the recent spectroscopic confirmation of the electronic configuration of Lr (103) 7s2 7p1 (Sato et. al. 2015), we agree with Jensen (2015) when he points out that the most plausible would be that this case is just another example of an element of block d with a irregular electronic configuration (due to relativistic effects, as mentioned), but that chemically it's an analogue of the Lu rather than behaving like an element of the p-block.

I am inclined to believe this makes sense. In any case, I am not attacking your paper in order to sink it now; rather, I am pointing at the questions the readers in the IUPAC might have, and I suggest you deal with them before they arise. I realize that I am restating some of the earlier mentioned points but that is in caution that you might have not realized the need to reflect the comments from Double sharp in your paper.--R8R (talk) 22:34, 31 January 2020 (UTC)

@Double sharp: I've added a References section which I think provides sufficient support for my group 3 = typically ionic/group 4 to 12 = typically covalent argument. I've noted your other concerns and will address this once I review all outstanding posts.

The periodic law implies, certius paribus, that since La represents the first recurrence of comparable periodicity after Y it should be the one to go under Y rather than Lu. -- does it though? I tend to think this is a very freeform interpretation of the said law because it does not seem to be concerned with these things. Regardless, I'll allow myself to quote a part of the article that I have not mentioned so far:
Scerri has argued for Lu under Y (and He over Be), since the periodic table can then be arranged, from a philosophical point of view, so that it shows the greatest degree of regularity and symmetry. [...] His argument remains inconclusive as there is no basis to regard regularity or symmetry as fundamental requirements.

For the sake of consistency, the original point would also need to be expanded. For one, I don't think the periodic law implies that, especially given how Sc is not under Al. Even if a case is to be made that Sc should not go under Al while La should go under Y, this is too subtle an argument to say it comes from the vague periodic law.

On this note, I also don't think that the periodic law implies that La should go under Y, or, alternatively, that the periodic law should serve an initial approximation on the basis of which the final decision is to be made. I could expand my thinking on this (though DS did it long before I could), but I presume you realize what I mean here, and it is not covered enough, which will inevitably cause a "yes, but" from some readers. Presumably you want to avoid that and have a strong argument in the first place.

(I note that Sandbh's argument against Sc as eka-Al also seems to force He to go above Be. After all: He is an s-element, Be is an s-element, but Ne is a p-element and hence disqualified, so the next recurrence is Be! But I don't mind this that much, actually. I somewhat think that the ideal periodic table should have helium over beryllium. It emphasises the range of applicability of the "duet" rule, the high anomalousness of the 1s subshell that is like a first-row anomaly on steroids, and how it causes an almost complete lack of incomplete shielding effects that explain for example how Li is "too electropositive" for its position in the periodic table. This way also, the trend for He-Be-Mg nicely complements the trend for H-Li-Na, uniting the two "problem children" of group 1 and 2 among the groups. And He is still predicted to be a full shell, since it's the last element in its row, even if it's separated from the classical noble gases, which now anyway start with the most inert one at Ne. My userpage has a He-Be-Mg + Sc-Y-Lu table. ^_^) Double sharp (talk) 21:12, 26 January 2020 (UTC)

@R8R:@Double sharp: I’ve graduated to an iPad :) It does surprise me that my fairly simple arguments generate such obtuse, tangential or convoluted objections. For example, I see that Double sharp has, after 200k(?) of discussion, accepted that there is such a thing as typical or predominant behaviour. I’ll get to that in another post.

To the best of my knowledge I never claimed that there was no such thing as typical behaviour. I simply claimed that ionic vs. covalent was not the relevant distinction and supported it through examples and the literature. Otherwise, Be and Mg should go over Zn, and H over F. Double sharp (talk) 07:55, 28 January 2020 (UTC)

@Double sharp: I'm of the view that the PT layout is arranged more pragmatically than you give it credit. Only the minimum sufficient change is made, at the time required. The sky will not fall down. Thus, if La goes under Y that is all that will happen. Be and Mg will stay over Ca on regularity grounds including the pattern that the first element of a main group (Be) is apt to constitute a transition to the next (B) main group; the second element (Mg) to the corresponding transition group (Zn); whereas the group character is fully developed for the first time in the third element (Ca).

"Regularity grounds" surely support Sc and Y over Lu, too. So if you want to override it with an argument, you have to make sure your argument would not also override Be and Mg over Ca. That is simple logic. You don't just look for things that confirm your hypothesis, you have to actively put it to the test on cases where you think you already know what the answer should be. Double sharp (talk) 22:58, 31 January 2020 (UTC)

The position of hydrogen in group 1 has been well settled:

Similarities with lithium

Both have a significant covalent chemistry
Lithium, like hydrogen, when bound to highly electronegative atoms such as nitrogen, oxygen, or fluorine, is capable of forming electrostatic bonds with other nearby highly electronegative atoms
Their spectra are similar.

Similarities with the alkali metals

In chemical reactions, hydrogen and the alkali metals usually lose their single valence electrons; all usually have a valence of +1
Both form similar compounds e.g. hydrogen chloride (HCl) and alkali metal chlorides (XCl)
Like hydrogen, most of the alkali metals can form compounds with a charge or oxidation state of –1
Hydrogen can stand in for alkali metals in typical alkali metal structures
Hydrogen is capable of forming alloy-like hydrides, featuring metallic bonding, with some transition metals.

Like an alkali metal and unlike the most of other non-metals, hydrogen forms stable cations in the solution. Droog Andrey (talk) 15:17, 1 February 2020 (UTC)

The anomalous properties of hydrogen can be explained by its unique electron configuration, in that it has no underlying core of electrons. Sandbh (talk) 22:47, 31 January 2020 (UTC)

By this logic, the position of helium in group 2 should also be settled:

Similarities with beryllium

Both have a significant oxygen affinity, and oxygen gets the negative charge when they bond with it
When helium is coaxed into compounds, the predicted ones are analogous to beryllium compounds, and have no neon analogues
Helium bonds are obviously covalent, and beryllium is not a strongly electropositive metal
Their spectra are similar
Both have essentially no electron affinity
Helium can form alloy-like compounds with metals, e.g. FeHe; from helium compounds: "Iron helide (FeHe) was early on claimed to have been found,[89] but the discovery was classified as an alloy.[52]". (added later Double sharp (talk) 14:17, 1 February 2020 (UTC))

And the anomalous properties are perfectly explained just as well by the fact that there is no underlying core and no 1p subshell, the same as for hydrogen. In fact, this is also precisely why He is more reactive than Ne; as soon as the 1s² subshell is even slightly disturbed, reactivity jumps up, just like what happens when H starts losing its electron. Double sharp (talk) 22:58, 31 January 2020 (UTC)

The periodic law seems simple to me and represents the most important aspect of the periodic table. It is a periodic law which implies a recurrence of properties. As noted elsewhere Sc does not go under Al since Sc is at least a predominately d metal whereas Al is a p metal. From a regularity point of view there is no sustainable case for skipping La and Gd in favour of Lu. Every other part of the table observes the regularity of the periodic law, as enhanced by our understanding of the actual electron configuration filling sequence.

Of course I can always tighten this part of the article, so that’s good. Sandbh (talk) 04:44, 28 January 2020 (UTC)

By that logic, He goes over Be, so I know what will follow too: an argument, perhaps even one that has been dismissed when I use it to support Sc-Y-Lu, to override it and force He over Ne anyway. ;) Double sharp (talk) 12:10, 28 January 2020 (UTC)

The second option is awkward, or highly anomalous at best -- I found this particular argument very strange. Why would it matter in the first place? What is the need to have them ordered in a specific bent-line-like order? The general principle would do just fine. I will also recall that this very line of argumentation has already been used by this point, in saying that the elegant appearance of contiguous blocks does not necessarily represent the Nature as there is no point in that. (If it is to be said that now a different argument is being made, then a similar argument should be made here that student will find it more appropriate to have contiguous blocks, though again, I think neither matters.) But more importantly, why would anyone be confused? How are people supposed to take the fact that the platinum group metals are

     Ru Rh Pd
     Os Ir Pt

? Will people realize osmium goes after palladium?

It is not difficult to notice that the elements increase in atomic number by period, and then they do it within each period. So a top element is always lighter than a bottom one regardless of the left-right alignment. The very message you're reading actually also operates on this basis, because the English language has a left-to-right writing, and so a symbol in the line below will undoubtedly follow the symbol in the previous line, regardless of the left-right alignment. So I really can't see why would anyone be confused here or if they somehow (!!) were, why a thirty-second explanation wouldn't satisfy them.

@R8R: Double sharp and I have discussed this at some length. My simple argument is based on regularity across the PT, and that Lu introduces an irregularity. As I wrote, “The REM are recognised by IUPAC in the Red Book, as are the Ln and An. So there are 18 groups with vertically increasing contiguous Z, one series with increasing Z contiguously going around a corner (Sc, Y, and the Ln), and two series with horizontal contiguously increasing Z (Ln and An). These are the key vertical and horizontal trends. The horizontal discontiguous trends along the transition metals are of secondary import.” That is all. Sandbh (talk) 23:22, 26 January 2020 (UTC)
- Since when is "recognised by IUPAC" the be-all and end-all of what is an important chemical series? I bet you will hear "PGM" or "TM" just as often as "REM". Why is your argument prohibitive on one but silent on the others? Double sharp (talk) 23:38, 26 January 2020 (UTC)

@Double sharp: The PGM are arranged in order of increasing Z, as are the TM. Sandbh (talk) 22:53, 31 January 2020 (UTC)

Not by the way you argue about stretching the REM into a straight line, because neither Cu nor Zn is adjacent to Y in the PT. Of course, by the version of "arrangement" used by everybody else reading a book in English, that is reading line by line from left to right, the REM are arranged in order of increasing Z in a Sc-Y-Lu table just as well. Double sharp (talk) 23:04, 31 January 2020 (UTC)

Hasty

- I have read your argument with DS closely enough, and I still think that the particular argument you're presenting is not particularly satisfactory. In a -Lu-Lr table, of course, you would have a vertical Sc-Y-Lu trend. There is, of course, also the horizontal trend if La-Ce-..-Lu, true that. And those are two different trends, and nowhere in the periodic table do we conflate horizontal trends with vertical ones, these are different things. So why is it a problem at all that it's less convenient to shape the two into one when there's no chemical point in doing that in the first place (again, given the argument sits in the section "The domain of chemistry")?
- But also at that comes another point. In the discussion with DS, you mention that there is a philosophical point of doing so. But then again, not only did I not get that from the article, but also then I have to question: why do we ignore the beauty of contiguous blocks as a philosophical argument, instead effectively dismissing as one of the many varieties, "as there is no basis to regard regularity or symmetry as fundamental requirements.14 Scerri acknowledges that we should be aware of arguments based on regularity or symmetry"? Would a similar line of thinking apply for dismissing this unprecedented vertical-horizontal trend? These two questions make me think that there is a visible imbalance in treatment of pro-La-Ac and pro-Lu-Lr arguments, which casts a shadow on the paper as a whole.--R8R (talk) 11:18, 27 January 2020 (UTC)
  - This is also the feeling I get in this thread and in the article. It feels like La-Ac is being accepted from the start as the null hypothesis and that Lu-Lr is not being treated fairly. Indeed, some arguments for La-Ac made here would support things like Al-Sc or Mg-Zn or Tl-Lr or He-Be (the last of which I would actually support!), but seem to mysteriously become inapplicable when I use them as such... Double sharp (talk) 07:57, 28 January 2020 (UTC)

@R8R: @Double sharp: Beauty is a culturally subjective concept as is a preference for symmetry/regularity or asymmetry. That the vertical-horizontal trend is unprecedented does not mean anything remarkable. It's an outcome of the rare earths category, which has been around for many years. Sandbh (talk) 23:06, 30 January 2020 (UTC)

@Sandbh: REM is no less a subjective concept. The simplest proof of that is that it breaks apart chemically similar elements, on the grounds of their natural occurrence, and that despite IUPAC's ruling people cannot agree on what it contains. It excludes Ac, despite its perfect eka-La chemistry. (Presumably on the grounds of its natural occurrence, but then again Pm seems to be a rare earth according to everybody.) And not everybody includes Sc and Y in it (otherwise, why are there so many articles talking about "REY", meaning "rare earths and yttrium"?). Double sharp (talk) 23:41, 30 January 2020 (UTC)

Oh yeah, I am eager to make that point, too. We make up our groupings. We could classify them like that or we could not. The group 12 question, for instance, is far from clear. "Has been around" is a sound argument, if you ask me, but there are also other types of sound arguments that should not be conflated with this one. (Also, to mirror that, the platinum group metals have been around for a long time, too?)

Saying that, however, I am lacking the exact understanding of why anybody would want to have the vertical-horizontal trend. It really seems very artificial to me and it is really the only argument that I can't make any sense of, at all. I sincerely don't see why anyone would want to conflate vertical and horizontal trends. The simple understanding of the periodic trends would argue that Sc-Y-La is the direction in which things like atomic radius should increase and the atomic radius should decrease as you go towards Lu; what kind of trend is that?

I unironically don't see the point of such a construct. I'm not refusing to see it, I can't find it in the first place.--R8R (talk) 19:50, 31 January 2020 (UTC)

@R8R: +1 Double sharp (talk) 12:46, 2 February 2020 (UTC)

@R8R: The elements commonly recognised as metalloids represent a category arising out of vertical-horizontal trends, with two L-shaped around-the- corner bends. Is this a further example in which you can't see why anyone would want to conflate vertical and horizontal trends? The trend of atomic radius increasing towards La and decreasing towards Lu is a very interesting one, illustrating the impact of the Ln contraction. Sandbh (talk) 21:10, 1 February 2020 (UTC)

@Sandbh: I considered this (I did give it some thought despite my initial opposition) and I must say that this is not the same thing. That the metalliods are a category, as you point out, is beyond question. That they form a trend, which you did not point out, is something I have never thought of to this day and having thought of it, don't find of any substance. You specifically mention stretching of the Sc-Y-La-..-Lu line to form a trend; to the best of my knowledge, nobody ever does that to the metalloids. Metalloids, I would rather argue, depend on diagonal relations to keep a common identity, so to speak. This is in substance very different from any possible Sc-Y-La-..-Lu trend, so the comparison does not apply.--R8R (talk) 12:13, 2 February 2020 (UTC)

Also, to add to that, I still don't understand the difference between the dismissed arbitrarily chosen preference for contiguous blocks and the endorsed arbitrarily chosen preference for the stretchable Sc-Y-La-..-Lu line.--R8R (talk) 12:24, 2 February 2020 (UTC)

@R8R: +1 Double sharp (talk) 12:46, 2 February 2020 (UTC)

@R8R: Interim reply (placeholder). Does the narrow range of EN values for the REM not count as a trend? Same would work for the metalloids, I’d have thought. Sandbh (talk) 12:35, 2 February 2020 (UTC)

@Sandbh: No, because a trend should be monotonic (that's why we talk about trendlines), and it should be clear where it starts and stops. Respectfully, the REM do not fulfil this because of the exclusion of Ac. And neither do the metalloids chiefly because every single diagonal or adjacent relationship in the p-block means something and there is no reason to stop at any particular place. (Also, do you know how low the electronegativity of Si is? Sn is actually closer in EN to the other metalloids than Si is. Bi is even within their range!) Double sharp (talk) 12:53, 2 February 2020 (UTC)

@Double sharp:Nonsense. Excuse me if I sound incredulous. I cannot remember all of the trendlines I've ever seen drawn but many are not strictly monotonic. For that matter, who says all trendlines should be montonic? Ac is irrelevant to the REM (but relevant to the Group 3, and to the Ln). The metalloids start at B and finish at Te. If you want to be pedantic, they stop at B since there is nowhere of lower Z for the metalloids to go; they stop in the vicinity of I, Po and At, since none of them are commonly recognised as metalloids. Sn and Bi are irrelevant since none of them are commonly recognised as metalloids. Sandbh (talk) 04:46, 3 February 2020 (UTC)

@Sandbh: If a trend is predicated on one factor controlling it, then you expect it to change somehow proportionally to that factor. If it stops changing proportionally, that suggests that either (1) the trend has entered a range when it is overshadowed by other contrary effects (like atomic radii past Cs down the alkali metals), or (2) we have passed a breakpoint and a new trend has begun, like what happens to a spring past its elastic limit (or, in the periodic table, what happens once we pass a noble gas). That's why I feel that the fact that the Sc-Y-La-...-Lu trend is not monotonic speaks against it as a unified trend. Indeed, there are two separate effects here: atomic radius goes up as we go down the table, but down as we go to the right, and they just happen to overlap here. Same as everywhere else on the table, e.g. B-Al-Ga-In-Tl intersecting Al-Si-P-S-Cl-Ar. It doesn't make sense to me to conflate them.

So we see your methodology: start with the categorisation we see most in the literature and then go and justify it after the fact without critical examination. Never mind, of course, that the trend from Sb to Bi is not too different from that from As to Sb, or anything like that. Literature says As and Sb are metalloids, Bi is a metal, so we cannot question it. Never mind that list of metalloid lists (your own list) adequately demonstrates the lack of agreement about that. Never mind that chemically, the distance from Sb to Bi is actually less than that from As to Sb, given cationic tendencies starting at Sb going down to Bi. We start with the conclusion and justify it. Excuse me if I sound incredulous. Not to mention that it is really strange to see metalloids being argued for as a well-defined category whose limits are placed down and cannot be crossed, by someone who also claims that they are just a specific type of nonmetal. By that logic there should be no problem continuing the trend over to iodine. Tellurium is a nonmetal, so is iodine! Double sharp (talk) 11:47, 3 February 2020 (UTC)

@Double sharp: REM are not a culturally determined concept. It does not matter that it breaks apart chemically similar elements, on the grounds of their natural occurrence. Self-evidently there were enough other similarities to warrant the category name. Crikey! How about breaking apart the coinage metals on account of their heterogenous chemistry? Ac has traditionally been excluded on the grounds of its radioactivity, and location in period 7 (whereas the REM occupy periods 4, 5, and 6). I think some argy bargy about whether or not to include Sc matters does not matter so much; Sc is recognised as a REM by IUPAC and that's a huge achievement by itself. If people want to focus on the REY as a subset of the REM, power to them. That might be the same as focussing on the refractory metals (another wobbly boundary) or the PGM as a subset of the TM. Even the PGM are wobbly; gold is sometimes admitted into the gang of six. Sandbh (talk) 06:51, 31 January 2020 (UTC)

@Sandbh: You say they are not culturally determined, and then invoke tradition to defend the exclusion of Ac; I rest my case. ^_^ Yes, the PGM are wobbly too. Matter of fact, the transition metals are wobbly too. Even the alkaline earth metals are wobbly too! Each group has similarities, yes, that Nature gave us. But grouping them as categories, that we made up. Double sharp (talk) 07:42, 31 January 2020 (UTC)

@Double sharp: Nice catch! That the REM are not culturally determined does not mean I cannot invoke tradition to defend the exclusion of Ac, and I gave another reason. There is some pragmatism applying here, too. Chemistry rides the fine line between quantitative and qualitative and sometimes we have to argue things out in the absence of a categorical argument. And then, like null hypotheses we have to rely on the strength of arguments rather than being able to quantitatively measure them. Categories and classifications form the core of science and we iteratively test and, where required, improve them; that they are "made up" is irrelevant to the scientific process. Sandbh (talk) 06:59, 1 February 2020 (UTC)

@Sandbh: So first we are arguing that they are "not culturally determined", and then retreat and start defending that they are "made up". I prefer to say: the point is not to draw the table so that one category we make up fulfils one method of drawing that does not even work for many others (e.g. TM, PGM). The point is to draw it to be an excellent first-order approximation that is sure about what order it is. As such, I have a very simple procedure for the drawing and block assignment:

Elements go in blocks based on their chemically active subshell of highest angular momentum. (Then they go in groups by how many they are, rather than the exact configuration: see User:Double sharp/Idealised electron configurations.)
When it is not clear what this is (e.g. groups 2 and 12 both vying for a d-block position, La and Lu both vying for an f-block position), use properties to compare which one makes the resulting block more homogeneous.
There is no step 3.

Short, simple, to the point, based on chemistry, founded on the philosophy that categories should be as homogeneous as possible, and totally extendable to every element from hydrogen through oganesson and on to all those undiscovered superheavies in the eighth period. Only with the ninth period, with that [E172] 6g¹ configuration for an s-block-like E173, does it break down. Which is more than can be said for your criteria, which give the "wrong" answer if you apply them elsewhere already within the stable elements everyone knows. Double sharp (talk) 10:08, 1 February 2020 (UTC)

@Double sharp: How does that work for e.g. Nd, which has a condensed phase configuration of 4f³d¹s², and which is not known in the +4 oxidation state? Time to move into the d block? And the second IE of Cs (2234) is less than the second IE of Kr (2350). What happens if Cs can be made to form a +2 cation? Does Cs then become a p element? Sandbh (talk) 03:47, 2 February 2020 (UTC)

@Sandbh: Nd is definitely known in the +4 oxidation state. In fact, an aqueous Nd⁴⁺ cation is known, though it oxidises water, so it exists in a bigger sense than Pr(V). So, not the best example you could have come up with. ^_-☆ Let's take Sm as a less bad example. Well, in the gas phase we have f⁶s², and we form +3 cations, so yes, we diagnose f-block, no problem. The fact that in the condensed phase an f-electron moves to the d-orbital rests my case that the subshell can be used as a chemical reserve and is hence active.
If Cs breaks the 5p subshell it can be a seventh p-element as well, sure. Ca, Sr, Ba, and Ra are already honorary d-elements, and Be and Mg honorary p-elements because of easy 2s2p hybridisation. In general, this criterion only encounters any problem for s-elements since all unoccupied reachable subshells belong to the next n+l level and have angular momentum above 0. But here we just cover it by electron bookkeeping and keeping the other blocks homogeneous. Stricto sensu the Ca group are d-elements, but we draw them as s-elements due to greater similarity. This is not a killing argument because the s-block is usually weird in other ways as well, e.g. lack of double periodicity and trends that affect all other groups. So we may consider this just a specific problem for s-elements, just like all the other specific problems they have. Whence the second criterion.
Nota bene, the unadorned criterion works perfectly for La and Lu. La emerges as clearly f-block and Lu as clearly d-block. ^_^ The second criterion is not even needed for this quarrel, which suggests that the Be-Mg-Zn old quarrel is actually stronger than this Sc-Y-La quarrel. Double sharp (talk) 10:21, 2 February 2020 (UTC)

@Double sharp: Watching the tennis again and the seeming self-destruction of Novak. A quick comment. I’ll think more about this (placeholder) but I’m inclined to keep the differentiating electron criterion since it is quantitatively unambiguous in all cases. On Sm, is the f electron really “chemically” active? It’s only present in the gas phase of an isolated Sm atom in a vacuum, but it’s still an Sm atom. In condensed phase Sm there is no f electron involvement. There is no comparable alteration in chemical identity that I can see, e.g. Sm v Sm2O3. Sandbh (talk) 11:31, 2 February 2020 (UTC)

@Sandbh: What do you mean "no f electron involvement"? The f-electron got promoted and ionised, Sm³⁺ has one less f-electron than Sm. That is pretty much the definition of f-involvement. Na as an isolated gas-phase atom is [Ne]3s¹; in the metal the 3s electron is delocalised; and in ionic compounds it is ionised away. By the standards you impose on Sm, there is no s electron involvement in Na either, which suggests that the standards you impose are irrelevant. The differentiating electron is quantitatively unambiguous but irrelevant precisely because elements in chemical bonds are typically not in their ground-state configurations. Sometimes they are ionised, and sometimes they are in what would be excited states if they were alone, because the chemical bond energy provides the necessary energy to change configuration. I consider them all at the macro level by just asking if the subshell is participating chemically or not. Double sharp (talk) 11:37, 2 February 2020 (UTC)

@Double sharp: I’ll get back to you on that one. In the meantime I’m more convinced that your approach doesn’t work since it does not answer the group 3 question, and a comparison of individual physical, chemical or electronic properties is inconclusive. Whereas differentiating electrons, consistently applied, are. I’ve explained elsewhere that within-block homogeneity or similarity in terms of the minutiae detail doesn’t trump vertical trends in periodicity and overall chemical behaviour at least at the group level. Sandbh (talk) 12:20, 2 February 2020 (UTC)

@Sandbh: It is totally conclusive on Lu below Y. It answers the group 3 question without problem because 4f is not chemically active in Lu but is in La. If we needed confirmation, the physical and chemical properties are also conclusive. Physically, Lu is similar to the d-block metals, and La is totally not. Chemically, Lu is more similar to the d-block metals than La. In this it matches Sc and Y which are physically totally normal d-metals and chemically have incipient transition behaviour, just like Zr/Hf and Nb/Ta. La does not satisfy any of this. Since Sc-Y-Lu looks just as convincing as a trend by itsef as Sc-Y-La, our conclusion is Lu. This is not minutiae detail, this is all trends and overall unskewed physical and chemical behaviour. Differentiating electrons are consistent and consistently irrelevant minutiae because elements in compounds do not usually follow their ground-state gas-phase electron configurations. Double sharp (talk) 12:35, 2 February 2020 (UTC)

The above leaves me thinking the conclusion made is hasty.--R8R (talk) 14:22, 26 January 2020 (UTC)

@R8R: The conclusion is OK such as it is; I think the presentation needs more work, including to address some of the concerns and misperceptions raised in this thread. Sandbh (talk) 22:55, 31 January 2020 (UTC)

Beauty

@Double sharp:@Droog Andrey:@R8R:

Droog Andrey and Double sharp

I am interested also. Droog Andrey (talk) 16:13, 2 January 2020 (UTC)

@Droog Andrey: Righto. Please send me an email address that I can send a dropbox link to. Sandbh (talk) 00:50, 3 January 2020 (UTC)

@Sandbh: Andrey_601 at tut.by Droog Andrey (talk) 10:55, 5 January 2020 (UTC)

I was going to finish my reply yesterday, but I see that Droog Andrey has beaten me to the most important points I was going to raise, so if you don't mind I'll sit down in his section and join the tea ceremony! ^_^ Double sharp (talk) 07:00, 9 January 2020 (UTC)

@Sandbh: Thanks a lot. I've noticed a few statements in "The domain of chemistry" section that are at least doubtful.

Chemical behaviour of Group 3

The chemical behaviour of Group 3 generally resembles that of Groups 1−2 rather than that of Groups 4−11 In fact, chemistry of Sc and Y is equally close to Ca-Sr as to Ti-Zr. Chemistry of La-Ac is indeed closer to Group 2, but that of Lu-Lr is closer to Group 4. And that's the reason to consider Lu-Lr, not La-Ac, as d-elements. Droog Andrey (talk) 11:19, 7 January 2020 (UTC)

Sandbh: @Droog Andrey: I'm trying to stay away from arguments comparing individual elements (given Scerri says that such approach is inconclusive) or even pairs of elements. The chemistry of Sc-Y-La-Ac as a whole is closer to group 2, than is the case for Sc-Y-Lu-Lr.

@Sandbh: OK, Sc-Y-Lu-Lr group is closer to transition elements than Sc-Y-La-Ac, that's why Group 3 should be Sc-Y-Lu-Lr instead of Sc-Y-La-Ac. All is clear. Why should we mess up things inserting Group-2-like elements La-Ac into Group 3 and causing a crutch-like separation of Group 3 from Groups 4-10? Droog Andrey (talk) 19:05, 8 January 2020 (UTC)

@Droog Andrey: [S1] The fit of group 3 as Sc-Y-La-Ac to groups 1-2 is better than the fit of Sc-Y-Lu-Lr to group 4. Either way Group 3 shows chemical behaviour that is manifestly uncharacteristic of the transition metals proper. Group 3 does not show the complex coordination chemistry that is characteristic of transition metals; they do not show multiple oxidation states; and they are more reactive and electropositive than any other transition metals, approaching the s-block metals in both properties. Sc-Y-La-Ac, in a 32-column table, does mess things up but Nature does not care. Sandbh (talk) 05:38, 9 January 2020 (UTC)

@Sandbh: Group 4 organometallic chemistry is mostly cyclopentadienyl derivatives, similar to group 3. Zr and Hf in group 4 are very unhappy to show lower oxidation states, like Sc in group 3. And they are also pretty electropositive: Zr and Hf have Pauling electronegativity similar to Mg and Sc. So we can see similarities on both sides; Zr and Hf are more "pre-transition", while Ti starts to show real transition character. If you put Lu in group 3 the similarities to group 4 become even stronger because Lu is better at forming complexes than La. This is all expected: I guess similarly to delayed collapse, if something happens in one group in the 4th period, it will not happen till a group or two later in the 5th and 6th periods. Not only Zr and Hf in group 4, but also to a lesser extent Nb and Ta in group 5, are also quite strongly "pre-transition" in character with chemistries dominated by the group oxidation state; so where's the sharp difference between "pre-transition" and "transition"? I don't see it in what Nature seems to have provided us. This is just another transition between blocks that often happens at their edges. It is just like how you cannot draw the sharpest line for loss of TM character between group 11 and group 12, because you have Ag where 4d has radial nodes but isn't subject to significant relativistic effects yet. Double sharp (talk) 06:47, 9 January 2020 (UTC)

@Double sharp: The challenge is that effectively everyone regards group 4 as transition metal. This is not the case for group 3, which has a large record of not being regarded as a transition metal group from a chemical perspective. I agree there are no sharp boundaries. That said, faced with a choice of Sc-Y-Lu, which behave substantially like pre-transition metals (PTM) but show vertical trends like groups 4–10; or Sc-Y-La-Ac, which also behave like PTM and show vertical trends matching those of groups 1–2, the weight of arguments, as I see it, rests with Sc-Y-La-Ac. Sandbh (talk) 09:02, 9 January 2020 (UTC)

@Sandbh: Exactly how large is the record of group 3 being regarded as not transition metals? I mean, sure, I was taught that in high school, but it's not even one of the definitions IUPAC allows. I'd bet it's much smaller than the record of group 12 being regarded as not transition metals, which is a lot easier to defend. I'd also add that when I was taught that, the focus was all on the 3d metals and only very basic coordination chemistry. Group 3 as a transition metal group makes a lot more sense once you include organometallic chemistry (mostly because of scandium), but obviously you don't see that much of that in high school. Group 4 and 5 are also mostly pre-transition metals (Ti and V are undoubtedly transition, but Zr-Hf-Rf and Nb-Ta-Db are mostly pre-transition in character), which matches group 3 (Sc is the one with the most transition character). Surely Sc-Y-Lu-Lr is a good match for those, at least as much as Sc-Y-La-Ac is to groups 1 and 2, and so other factors decide it (e.g. that Lu and Lr make a lot more sense viewed as the start of 5d and 6d series than as the end of 4f and 5f series; see my response to [S4]). Double sharp (talk) 09:19, 9 January 2020 (UTC)

@Double sharp: I don’t know how many. My recollection is that effectively every book I’ve read on Group 3 apologises for not treating them as transition metals, chemically speaking. Pardon me if I’m confusing concepts but the coordination chemistry of Sc is *far* less than that of the rest of the 1st row transition metals. We are stuck with Y regardless noting it has a fair degree of ambivalence, as to wether it acts more like a light Ln or a heavy Ln. So my impression is still that the sun represents the main-group-like chemistry of group 3, whether La or Lu. Sandbh (talk) 11:03, 9 January 2020 (UTC)

@Sandbh: I'm talking about organoscandium chemistry. Here you can more easily find lower oxidation states for Sc, and the general behaviour (dominated by cyclopentadienyls) is not so different from Ti. And it's not so difficult to find organolanthanide compounds which have Ln(II). Double sharp (talk) 04:46, 10 January 2020 (UTC)

@Double sharp: AFAIK the situation is still essentially like that described by G&E: "In the main, the chemistry of these elements concerns the formation of a predominantly ionic +3 oxidation state arising from the loss of all 3 valence electrons and giving a well-defined cationic aqueous chemistry. Because of this, although each member of this group is the first member of a transition series, its chemistry is largely atypical of the transition elements. The variable oxidation states and the marked ability to form coordination compounds with a wide variety of ligands are barely hinted at in this group although materials containing the metals in low oxidation states can be prepared (see p. 949) and a limited organometallic (predominantly cyclopentadienyl) chemistry has developed." I don’t disagree with what you said but the chemistry of group 3 is still largely atypical of the transition metal elements and is still more like that of groups 1 and 2. Sandbh (talk) 08:28, 10 January 2020 (UTC)

@Sandbh: But almost all of that paragraph also applies to Zr (and thus to Hf and Rf as well). It mostly forms a rather basic +4 state (for Rf it is basic, no questions asked), where all 4 valence electrons are lost, can form a very hydrolysed Zr⁴⁺ cation in water (typical for states above +3 even for the most electropositive metals like Th⁴⁺ and Pa⁵⁺, so that's not a black mark that it is so hydrolysed), has only "rather sparsely represented" low oxidation states (Greenwood and Earnshaw p. 958), and a mostly cyclopentadienyl-based organometallic chemistry. So the main difference is just that Zr is happier to form complexes (mostly with O-donor ligands); its chemistry when measured by the usual yardstick of "multiple oxidation states differing by units of one" is not all that transition-like. Which is kind of expected; it's still near the start of the d-block, and the transition properties are coming in slowly. But it does mean that Sc and Y don't look so much like they all throw totally towards group 2, but rather like elements "on the way" from group 2 to group 4, with similarities both to Ca/Sr and Ti/Zr as Droog Andrey has mentioned. If our standard of "transition" is so high as to exclude Sc, Y, and Lu from it, then it is probably high enough to exclude Zr, Hf, and even probably Nb and Ta from it, at which point the argument "group 2 vs. group 4" loses force: almost everybody involved is "pre-transition" by this standard with titanium as an outlier! And not even always: Ti⁴⁺, Zr⁴⁺, Hf⁴⁺, and Rf⁴⁺ are hard acids, just like the group 2 and 3 cations! Double sharp (talk) 07:06, 12 January 2020 (UTC)

@Double sharp: For Zr and Hf the trihalides are well established. Cotton et al. [Advanced Inorganic Chemistry, 6th ed.) spend four pages discussing oxidation states of Zr and Hf below III. G & E add, "Even for Ti they [the lower oxidation states] are readily oxidised to +4 but are undoubtedly well defined and, whatever arguments may be advanced against applying the description to Sc, there is no doubt that Ti is a transition metal." To some extent we are fulling back on the old saw that it is in group 4 that we first encounter the classic properties of transition metals. Hence the cut falls between groups 3 and 4. Sandbh (talk) 06:13, 15 January 2020 (UTC)

@Sandbh: By that standard, Sc is a well-established transition metal by virtue of compounds like CsScCl₃. And so are the Ln because of their +2-state organometallic chemistry. Note that G&E are only talking about Ti, not Zr and Hf. If we exclude that by talking about common stable-in-water states in clearly inorganic compounds only, then Zr and Hf go back to being pre-transition. There is no criterion that excludes Sc from being a transition metal without also excluding Zr and Hf. Double sharp (talk) 06:42, 15 January 2020 (UTC)

@Double sharp: The standard I go by is the literature, which I submit is a reasonable one, and effectively 100% of which says that Sc is atypical for a transition metal and that Zr and Hf are transition metals. It is fine to point to the exceptions, which is what makes chemistry so interesting, and there is no case for leveraging these into characteristic considerations. Exceptions are so-named because of their out-of-kilter rather than mundane status. Sandbh (talk) 00:20, 16 January 2020 (UTC)

@Sandbh: IUPAC's definition says nothing about the Sc group possibly being excluded (though it allows the exclusion of the Zn group), so excluding it altogether is probably a minority view. I agree that Sc is not terribly typical, but by the standard G&E are mentioning (and they don't even exclude it!) neither are Zr and Hf (notice that they only say that there is no doubt for Ti). We could spend as much time talking about lower oxidation states of the REM as G&E do for Zr and Hf, as they're now actually known for almost all of them. It doesn't change the fact that Zr and Hf non-organometallic chemistry is predominantly that of the IV state, in which they are quite pre-transition-like. So what? I prefer to say that there is simply a gradual change towards transition metal proper behaviour that arrives later and later in each period, and just point to the split between the s- and d-blocks as a good guide of the region where it appears rather than a strict line which makes the truth look so much simpler than it really is. So: Ba is mostly pre-transition (with a bit of transition character), Hf is mostly transition (with some pre-transition character), and so we ought to pick the one in the middle that falls most closely between them like Sc and Y do for Ca/Ti and Sr/Zr. Lu seems better since its transition character is stronger, whereas for La it is quite weak. Double sharp (talk) 09:21, 16 January 2020 (UTC)

@Double sharp: Oh, I'm not talking excluding the Sc group from the d-block. And yes, the truth is almost more complex than a straight line. I'm being pragmatic. Group 4 is similar to group 3. That said, they are found in several oxidation states and are more likely to form complexes than Group 3. Like Earnshaw and Harrington said, "…this is the first group in which the really characteristic transitional properties of variable oxidation state, colour and paramagnetism are encountered." By any reasonable measure that is good indicator of where to separate the d-block, as has been done in 32-column tables without significant controversy for over at least 50 years. Like Jones said, "Though classification is an essential feature of all branches of science, there are always hard cases at the boundaries. The boundary of a class is rarely sharp…Scientists should not lose sleep over the hard cases. As long as a classification system is beneficial to economy of description, to structuring knowledge and to our understanding, and hard cases constitute a small minority, then keep it. If the system becomes less than useful, then scrap it and replace it with a system based on different shared characteristics." I don't see sufficient merit in changing the status quo. Sandbh (talk) 05:56, 17 January 2020 (UTC)

@Sandbh: The system becomes less than useful if the complexity increases without the increase of explanation power. That's the case of La table: more details, more exceptions, less explanation.

I don't see that. The La table explanations I can remember reading explain that the f-block starts at Ce, rather than La, since that is when the f shell starts filling, akin to B and Sc. Hazel Rossotti's Diverse atoms: Profiles of the chemical elements, (1998) is an excellent example. Sandbh (talk) 04:31, 21 January 2020 (UTC)

The literature simply follows the history. La was discovered before Lu, so it went under Y, but after discovery of Lu the questions began to rise. If Lu had been discovered before La, we would simply have Sc-Y-Lu table and no questions about Group 3 would have appeared at all. Droog Andrey (talk) 13:14, 20 January 2020 (UTC)

@Droog Andrey: There's an analogy with peptic ulcers which were historically attributed to stress, rich food etc. Then it was discovered they were due to bacteria, a development which met huge skepticism. Eventually the bacterium theory replaced the historical view.

La was discovered first, so it went under Y; Lu came later but there wasn't a sufficiently meritorious case made for replacing La under Y. Sandbh (talk) 03:39, 21 January 2020 (UTC)

@Sandbh: Eventually Lu will replace La. That's just a matter of time needed for obsolete understandings to die. Droog Andrey (talk) 13:20, 21 January 2020 (UTC)

@Sandbh: Good luck with that. Some chemists plumbed for Lu in the 1920s, and their efforts faded into obscurity. Jensen had another go in 1982, without success. Scerri has been advocating Lu for quite a few years on regularity grounds. Other notable players in the PT field— Roald Hoffmann, Schwarz, Martyn Poliakoff, Restrepo (on the project), Philip Ball (ditto)—advocate for more than one table, depending on the intended perspective. Lavelle, also in the project, advocates La. IIRC Pekka Pyykkö advocates for a 15-column wide f-block, per unofficial IUPAC. The only other people I know that have advocated for Lu, such as Emsley, did so on the basis of Jensen's article which had several limitations. Ditto Thyssen and Binnemans. Several physicists have had a go over the years, based on generally unbalanced, one-shot, unsuccessful arguments. Sandbh (talk) 02:59, 22 January 2020 (UTC)

I'll look to strengthen my argument by drawing on the following quotes:

"…If scandium, yttrium, lanthanum and actinium are the only rare-earth elements, the series would have revealed the same gradual change in properties as the calcium, strontium, barium and radium series, and hence it would not have been of any special interest." (Hevesy 1929, cited in Trifonov 1970, p. 188).

@Sandbh: But why should Group 3 follow a gradual-change trend which appears exclusively for Groups 1 and 2? Other groups show secondary periodicity like B-Al-Ga-In. Droog Andrey (talk) 19:05, 8 January 2020 (UTC)

@Droog Andrey: As per my above response [S1]. Sandbh (talk) 05:38, 9 January 2020 (UTC)

"For each element…all three outer electrons are easily lost and the chemistry of the elements is confined to the +3 oxidation state. Their monatomic cations are colourless and diamagnetic, and have no catalytic properties. This is the behaviour that would be expected of main-group elements following the alkaline-earth metals." (Greenwood & Harrington 1973, p. 50)

@Sandbh: Not only for main group elements, but also for f-elements and for heavier Group 4 and 5 elements. What's wrong with this? Droog Andrey (talk) 19:05, 8 January 2020 (UTC)

@Droog Andrey: Nothing that I can see. That said, your response does not add anything to my [S1]. Sandbh (talk) 05:38, 9 January 2020 (UTC)

"The trends in properties in the family…are quite regular, and similar to the trends in Groups 1 and 2." (Lee 1996, p. 679)

@Sandbh: But the trends in Sc-Y-Lu-Lr are similar to the trends in Group 4 and onward. Droog Andrey (talk) 19:05, 8 January 2020 (UTC)

@Droog Andrey: See my [S1]. Sandbh (talk) 05:38, 9 January 2020 (UTC)

"…although each member of this group is the first member of a transition series, its chemistry is largely atypical of the transition elements. The variable oxidation states and the marked ability to form coordination compounds…are barely hinted at…although materials containing the metals in low oxidation states can be prepared and a limited organometallic chemistry (predominately cyclopentadienyl) has been developed." (Greenwood & Earnshaw 2002, p. 948). Sandbh (talk) 05:25, 8 January 2020 (UTC)

@Sandbh: Group 10 elements are also atypical, that's really normal for outermost groups in the block, like Groups 13 and 18 in p-block. Droog Andrey (talk) 19:05, 8 January 2020 (UTC)

@Droog Andrey: See my [S1]. Sandbh (talk) 05:38, 9 January 2020 (UTC)

@Double sharp: Further to your edit 06:47, 9 January 2020, re “Group 4 organometallic chemistry is mostly cyclopentadienyl derivatives, similar to group 3.” I found this article re the cyclopentadienyl chemistry of group 2 including d orbital involvement in Ba. Sandbh (talk) 10:33, 11 January 2020 (UTC)

@Sandbh: And that's where you can see that if you focus on organometallic chemistry, the dividing line between "pre-transition" and "transition" looks like it should be earlier than if you focus on other things. So in this case it looks like group 3 is behaving like a d-block group, and heavy group 2 is showing some tendencies in that direction too despite being d⁰: in that case, aren't groups 2 (Ca/Sr/Ba/probably Ra) and 3 both following the clearly transitional group 4, rather than exhibiting typical main-group behaviour?

Note that Greenwood and Earnshaw mention (p. 137) that organometallic chemistry for Ca, Sr, and Ba rather resembles the divalent lanthanides Sm, Eu, and Yb, so this is again a case of f-block being intermediate between s-block and d-block rather than a degenerate bit of the d-block. Be and Mg are more focused on alkyls in their organometallic chemistry (which looks to my inexperienced eyes more like Zn, Cd, and Hg). Double sharp (talk) 06:48, 12 January 2020 (UTC)

@Double sharp: There's nothing here I particularly disagree with. My focus is on the overall or typical behaviour of group 3; your focus (it seems to me) is on the atypical behaviour.

We know from G & E that variable oxidation states and the marked ability to form coordination compounds with a variety of ligands are barely hinted at in group 3 although materials containing the metals in low oxidation sates can be prepared and a limited organometallic chemistry has developed. For Group 4 G & E say the organometallic chemistry has developed rapidly in recent years. For group 10 they say that the organometallic chemistry is rich and varied.

Here's a 2017 PhD thesis which:

treats the Ln as Ce to Lu;
correctly notes the Ln contraction runs from Ce to Lu;
says the Ln are often considered to behave as trivalent versions of the ⁺² cations Ca²⁺, Mg²⁺ of the alkaline earth elements; and
notes that some of the lanthanides have very similarly sized cations to the cations of group 2 or group 3 elements, and that these cations will generally form the same compounds as the lanthanide cation that they substitute.

I think the salient point is that the typical behaviour of the Group 3 metals as per literature consensus is that they behave largely as if they were trivalent group 1 and 2 metals. It is true that the Group 3 metals share some properties with the Group 4 metals but these are the minority rather than representing majority, typical or characteristic behaviour. Another way of looking at this is at the overall chemistry, rather than a subset such as organometallic. For Sm, Eu and Yb we can turn this around and say that their OM chemistry resembles that of Ca, Sr and Ba, as would be as expected.

All of this takes us back to the premise at the top of this section. Sandbh (talk) 22:39, 15 January 2020 (UTC)

"Correctly" only if you want to be pedantic about it, I guess. Lanthanide chemistry is so impacted by differing atomic radii that I consider it frankly unilluminating pedantry to exclude La. What you are doing seems to me like basically taking only the bits of Ln chemistry that are most like main-group behaviour, declaring that subset to be the typical behaviour, and ignoring the growing parts (e.g. organometallic, which is surely not atypical) where things are not the same, whereas I'm looking at everything and saying "OK, group 3 shows similarities to both in various parts of their chemistry, just like every other border group, and so let's not create a graphic trench when there is no total separation". (In fact organometallic chemistry is the main reason why the older definition excluding Sc and Y from the transition metals is falling by the wayside.) Double sharp (talk) 09:25, 16 January 2020 (UTC)

@Double sharp: Our own article on organoscandium chemistry says, "As with the other elements in group 3 – e.g. yttrium, forming organoyttrium compounds – and the lanthanides, the dominant oxidation state for scandium in organometallic compounds is +3 (electron configuration [Ar] 3d¹4s²). The members of this group also have large ionic radii with vacant s,p and d orbitals (88 pm for Sc³⁺ compared to 67 pm for Al³⁺) and as a result they behave as hard Lewis acids and tend to have high coordination numbers of 9 to 12. Sandbh (talk) 06:59, 17 January 2020 (UTC)

Dominant, yes. But not the only one. Organoniobium chemistry has Nb^V as the most common oxidation state, but there is no problem finding lower ones. Again, we expect from the regular shape of the table that a 4f block insertion should occur before the 5d block, just like the 3d block insertion occurs before the 4p block, and so that eka-Y should have some mitigating tendencies towards softness while still being hard due to its size and charge. That points to Lu³⁺ as the less anomalous member (which still has pretty high coordination numbers), unless you want to have Al over Sc again. (Al³⁺ is quite hard due to its noble gas configuration, too!) Double sharp (talk) 17:19, 22 January 2020 (UTC)

@Double sharp: A few things here.

1. You said, “Ln chemistry is so impacted by differing atomic radii that I consider it frankly unilluminating pedantry to exclude La.”

I’ve never excluded La from Ln chemistry.

No, but you exclude it from the Ln contraction trend as the member when n = 0 in the 4fⁿ configuration. It ought to be included in the trend line as just another lanthanide ion, because the contraction is measured by the difference in size between two lanthanides with adjacent values of n, of which n = 0 and n = 1 counts just as well. Double sharp (talk) 12:08, 23 January 2020 (UTC)

@Double sharp: I do and what you are referring to is a different concept. There is no f block f electron caused contraction seen in La. There is in Ce to Lu. Sandbh (talk) 06:15, 24 January 2020 (UTC)

It seems to me that you are making "lanthanide contraction" mean "the difference between a theoretical ionic radius without the results of poor shielding from added 4f electrons and actual ionic radius", rather than just "the contraction observed between Ln³⁺ ions as one proceeds left to right across the series". In which case not only is La not in the first one, but the post-lanthanides Hf through Hg are in it instead, which is clearly not what "lanthanide contraction" means for most people. Double sharp (talk) 17:21, 24 January 2020 (UTC)

P.S. May I also add that the chemical importance of the lanthanide contraction is almost a one-off. Nowhere else in the table do we get a case where fifteen elements in a row all prefer to be in the same oxidation state, so that the contraction of ionic radius is the only significant difference. If you plot Ac through Lr, you get an actinide contraction just as well, but it doesn't matter so much because the early actinides are eager to show higher oxidation states. And we come to that idea, really: the behaviour of the Ln contraction is more or less expected only for the first row of a block with such high azimuthal quantum number that the electrons in the filling shell are stuck very deeply in. This is something we see for 4f, but not even for 3d. We will probably see it for 5g, but that's about it (matter of fact, their chemistry should be more or less like heavier congeners of U, which famously has two major oxidation states of +4 and +6; so if they act like U, Np, and Pu, there should be subtler differences than with the Ln in these early superactinides). As a matter of fact, you can immediately see that Ac through Lr supports Sc-Y-Lu much better than the inconclusive La through Lu: the reason is that the trend at the end of the 5f row is for 5f to sink very deep into the core (something like what happens for the 4d row), and so nobelium becomes a logical end of the trend as we get more and more in favour of the +2 state at the end of the series. Lawrencium, back at the +3 state, appears to be an illogical appendage, and is much more understandable as the beginning of the next series (Lr +3, Rf +4, Db +5, Sg +6 should all mostly dominate). Whereas Ac is totally understandable extrapolating from Th, Pa, and U backwards: it has one less valence electron, and 5f is still above 6d (like for Th), only to cross over at Pa. Double sharp (talk) 23:38, 24 January 2020 (UTC)

@Double sharp:. There is nothing relevant here. I’d only be repeating responses I’ve given several times already. Sandbh (talk) 07:24, 25 January 2020 (UTC)

Yes, there is something relevant here. It's saying that the Ln contraction is by definition an inconclusive argument because it is something that happens over all fifteen lanthanides, not fourteen, and it is caused by a special one-off effect in the periodic table that even the actinides don't follow. It only runs over fourteen if you do some pedantic definition-arguments that usually end up declaring the knock-on effect on Lu/Hf through Hg as part of the Ln contraction as well. Double sharp (talk) 10:32, 25 January 2020 (UTC)

@Double sharp: As you know, the Ln contraction arises as a result of reduced shielding by the f electrons, which are first seen in Ce 3+ and last seen in Lu 3+, as discovered by Goldschmidt. I have nothing further to say about this aspect of the thread since it is incontrovertible. Sandbh (talk) 07:22, 26 January 2020 (UTC)

By those standards, where do the boride and scandide contractions begin? You can't say where, because there's no universal oxidation state. Double sharp (talk) 10:41, 26 January 2020 (UTC)

2. “What you are doing seems to me like basically taking only the bits of Ln chemistry that are most like main-group behaviour, declaring that subset to be the typical behaviour, and ignoring the growing parts (e.g. organometallic, which is surely not atypical)…”

Well yes, that’s what the literature says i.e. that the Ln largely behave as the equivalent of trivalent group 1 and metals. I’ve never said organometallic chemistry is atypical. I’ve only noted, per the literature, that the OMC of group 3 is ionic, like that of groups 1 and 2.

What you are doing—I don’t know why—is focussing on atypical behaviour and assigning it undue significance. Respectfully, that’s not good classification science in my view.

It's not atypical behaviour unless you hold to a standard that makes Zr^III and Hf^III atypical as well. In which case we go back to the starting point: by such a standard, group 4 is mostly main-group too, and therefore there is no reason why group 3 should not follow its trend. Double sharp (talk) 12:08, 23 January 2020 (UTC)

@Double sharp: Zr3 and Hf3 are atypical. +4 is typical and covalent. +3 is typical for group 3 and ionic. That’s the dif. Group 3 does not follow the Group 4 trend in this respect. Sandbh (talk) 06:22, 24 January 2020 (UTC)

Ionic vs. covalent is not totally dependent on charge, but also on size. If we were looking at period 2 and discussing what should happen later, we would take a look at the more covalent-ish Be²⁺ and skip away merrily to Be-Mg-Zn. And it's not even only ionic radius: compare Ge²⁺ vs. Sn²⁺ vs. Pb²⁺, where the first is almost not a thing, the second is close to not being a thing, and the third is well-defined and has some significant ionic behaviour (e.g. PbF₂). Chemically speaking, Zr and Hf are as electropositive as Sc, and Rf should be even more so. By this logic, we may end up excluding group 13 from the p-block, since apart from B at the top it is all more or less ionic while the credentials for group 14 are shaky right up till Pb²⁺ in the "wrong" oxidation state at the bottom. Double sharp (talk) 17:21, 24 January 2020 (UTC)

And I still think you are trying to have it both ways. This argument of yours works only if you consider +3 for Zr and Hf atypical. But in that case group 4 is predominantly main-group in its chemistry, not transition. And given that the difference between main group and transition is not wholly ionicity but about things like variable oxidation states (otherwise, what is Be doing?), that suggests that group 3 can follow the group 4 trend, no problem. The fact that the argument can tip both ways is exactly part of why I think group 3 ought to be compromising: more ionic like group 2, but showing a group-4-like trend. Double sharp (talk) 17:24, 24 January 2020 (UTC)

3. “Again, we expect from the regular shape of the table that a 4f block insertion should occur before the 5d block, just like the 3d block insertion occurs before the 4p block…”

That sounds like a circular argument.

It's not circular. It's saying that the regular shape of the table up to Xe leads us to conjecture that the pattern should hold further, and we can use that as a working hypothesis to be confirmed or disconfirmed by what we find with later elements. And indeed, we find that Lu acts about like how you expect for eka-Y with an f-block insertion beforehand, so there is no strong reason to reject the working hypothesis since Y-La-Lu are here acting completely analogously to Al-Sc-Ga. If Lu was not as good an eka-Y as it is, then we would be more forced to go for Sc-Y-La. But we're not.

Anyway, we can both play the game of "let's start with the format we prefer, and see that it predicts something, and we see it quite well, and the other one can be seen as a perturbation". But looking at the absolutely normal-looking "two rows at a time" pattern in periods 1 through 5, surely the null hypothesis that we are supposed to be testing ought to be that it continues in periods 6 and 7, and it should be the alternative hypothesis that it doesn't that is held to a higher standard? Double sharp (talk) 12:00, 23 January 2020 (UTC)

Other
Noting the overall chemistry of group 3 is like that of groups 1 and 2 I’d expect eka-Y to follow the trend seen in those groups, as is the case with La. I’ve addressed the Al v Sc question before, noting the ionic radius of Al is more like that of Ga than Sc. Sandbh (talk) 08:14, 23 January 2020 (UTC)

And the ionic radius of Y is more like that of Lu than La, so where does that leave us then? Double sharp (talk) 12:00, 23 January 2020 (UTC)

@Double sharp: Y does not necessarily exhibit a chemistry similar to that of Lu (as discussed earlier). With La in group 3 we see an increasing trend in atomic radius, similar to that seen in groups 1 and 2. With Lu in group 3 we see a trend consistent with what is seen in most of the transition metals groups. Noting La has the same core as Sc and Y, whereas Lu does not, La is better placed in group 3 on similarity grounds. This includes the fact that La is the first element with a 5d electron, whereas Lu is the third. There is no plausible reason for skipping La in favour of Lu. Keeping La in group 3 serves to reflect the fact that the 4f subshell does not start filling until Ce. See also Atkins et al. Q&A. Sandbh (talk) 04:25, 9 February 2020 (UTC)

@Sandbh: But that is what it does when it behaves characteristically. On similarity grounds Lu is better placed in group 3 because in every group in the periodic table outside the s-block, the cores change every two elements. The core for Hf is different from that of Ti and Zr; the core for Ga is different from that of B and Al. The "plausible reason for skipping La in favour of Lu" is simply that your focus on ground-state configurations makes your argument groundless because those are simply not the characteristic configurations in chemical environments. When one holistically considers what orbitals are chemically active, one sees that 4f is already an active valence subshell in La (whence cubic complexes among other things), but is clearly core in Lu. The periodic table is based on chemistry, and therefore should be based on valence electrons, not core electrons. Lu and Lr in the f-block are a massive slap in the face to this. (Noble gases are not an exception; from Ar onwards they are chemically active, and anyway the energy gap between 1s resp. 2p and 2s resp. 3s is huge, so that those are still somewhat degenerately valence electrons by virtue of being the highest occupied orbitals. That can't be claimed for Lu and Lr.) Double sharp (talk) 21:57, 9 February 2020 (UTC)

Chemical behaviour of Group 3 (more)

@Double sharp:@Droog Andrew: Here are some more extracts dealing with Sc and Y, taken from Vickery RC 1960, The chemistry of yttrium and scandium, Pergamon Press, New York. A lot of this is new to me.

Sc as a light Ln/role of Ca and La

“When fluoride preparation is to be carried out, Ca is a better “carrier” than the lanthanons...precipitation of Sc as the double salt with potassium sulfate is an excellent method of concentration...Sc thus precipitated as ScK(SO4)2 will be accompanied by any light Ln present. Indeed, if the ratio of light:heavy Ln is previously known to be low, the addition of La to the solution will aid the concentration of Sc by double sulfate precipitation.” (p. 72)

Sc and Y similarity

“In spite of the large difference in Z between Sc and Y, the fact that both are two places removed from the inert configurations of Ar and Kr respectively has much to do with the similarity of their characteristics.” (p. 29)

“…Sc is diamagnetic and its magnetic behaviour presents many analogies to Y and, according to Bommer (1939) also to Pt and Pd." (p. 30)

Y and Ca

"In those instances where Y is found in minerals crystallising early from the magma it is generally present as a replacement of Ca…Because of the closer similarity between the ionic radii of Y and Ca, such replacement by Y, and the heavy Ln, is much more easily accomplished than replacement by the light Ln.

“…a factor in this replacement is the the resemblance of Y to Ca in its co-ordinating power. This suggestion does not however appear completely convincing since the smaller radius of Y will undoubtedly increase the spatial density of a given number of co-ordinating anions, it is now accepted that Y (and the heavy Ln) co-ordinates much more strongly than do the light Ln and these have a coordinating tendency approximately that of Ca.” (pp. 9–10)

“…the precipitation of Y as the alkali double sulfate from an acid solution saturated with NaCl is an effective method of concentration. Calcium will co-precipitate as sulfate...” (p. 36)

Ambiguous Y

“In separating Y from the heavy Ln, advantage is always taken of the phenomenon by which Y sometimes assumes characteristics similar to those of the light Ln, and sometimes follows the heavy Ln in behaviour.” (p. 37)

“In many respects Y resembles Zn...” (p. 38)

Monoxide spectra

“At elevated temperatures, Y gives a stable monoxide, YO, which emits a very bright band spectrum similar to that of LaO and ScO.” (p. 27) [This one is to be treated with caution since it says nothing about LuO]

Afterward
I do know that La shares quite a few similarities with Ca, as do the Ln generally. Sandbh (talk) 07:00, 11 January 2020 (UTC)

@Sandbh: Coordinating power is mostly a function of charge and ionic radius, so Y being similar to Ca seems to be just a diagonal relationship. You want a bigger charge to attract more ligands, except that it makes you smaller, so you have to go down another period. So an early lanthanide will differ from a late one mostly by size: La will be worse at coordination than Y (which is about like Ca), while Lu should be about the same and even a bit better (intermediate between Ca and Sc, which acts more or less like a mini-Lu). Both give a reasonable trend, as usual, except that since this weak coordination power for La and Lu is similar to Hf and Ta as well it strikes me as not enough of a reason for cutting group 3 away from the rest of the d-block. Double sharp (talk) 07:00, 12 January 2020 (UTC)

@Double sharp: It was a quasi-knight's move relationship between La and Ca, not Y and Ca:

The ionic radius of Ca²⁺ is 114 pm; that of La³⁺ is 117 pm (cf. Lu 100).
The basicity of La₂0₃ is almost on par with CaO₂ whereas Lu₂O₃ is the least basic of the Ln oxides.
Freshly prepared La₂O₃ added to water reacts with such vigour that it can be quenched like burnt lime (CaO)—Lu₂O₃ is insoluble in water.
The similarity in sizes means La³⁺ will compete with Ca²⁺ in the human body, and usually win on account of having a higher valence for roughly the same hydrated radius.
The electronegativity of Ca is 1.0; that of La is 1.1 (cf. Lu 1.27).

That swings it for me. Sandbh (talk) 06:39, 15 January 2020 (UTC)

@Sandbh: To me that's a perfect demonstration of why it should be Sc-Y-Lu: Sc and Y are equivocal between group-2-like and group-4-like properties, but as you've demonstrated La is strongly pre-transition-like while Lu is more equivocal, having both pre-transition-like (its lanthanide properties) and transition-like properties (it's the softest lanthanide cation, etc.). Since we are sure that Sc and Y are supposed to be d-block elements, and Lu's behaviour is more like Hf and Ta which are clearly early d-block elements, Lu is the stronger analogue to Sc and Y. This behaviour of La is on the other hand pretty much strongly pre-transition, like most of the early 4f-elements, without the moderating effects that transitionise the late ones due to smaller size. (And the things about La that are not quite pre-transition, e.g. extremely high coordination numbers, are often like the indisputable "direct" f-block elements, e.g. uranium.) Double sharp (talk) 06:50, 15 January 2020 (UTC)

@Double sharp: Sc and Y may be equivocal between group 2-like and group-4 like properties if one focuses on non-characteristic properties. Stepping back and considering their overall properties, including with either La or Lu, I submit that group 3 is more like groups 1 and 2 than group 3, as noted in the literature on several occasions. Sandbh (talk) 00:28, 16 January 2020 (UTC)

@Double sharp: Writing in Comprehensive Inorganic Chemistry, vol. 4, Moeller (1973) makes the follow observations:

"The existence of a common +3 state of oxidation throughout the series does require in most instances that an f electron be removed in its formation. However, the 4f orbitals are sufficiently removed from the valency shell and sufficiently shielded by external shells as to be largely unavailable in other chemical reactions. Herein lies a significant difference from the d-transition species, the atoms and ions of which are characterized by d electrons in their valency shells. There is, therefore, a closer configurational similarity between the lanthanide ions and the Group Ia-IIIa cations than between the lanthanide ions and the d-transition metal ions. The presence of shielded 4f electrons in the lanthanide ions does not materially alter the noble-gas core that they present to incoming chemical groups. The exclusion of lanthanum from the lanthanide group is based solely upon the absence of 4f electrons." (p. 3) [An extract of this passage was included in our IUPAC submission]

"The net result is that in comparison with the d-transition metal ions the lanthanide ions as a whole both form far fewer complexes and yield complexes with significantly different properties. Indeed, there are often better comparisons between the lanthanide complexes and those of the Group IIA cations." (p. 27)

Sandbh (talk) 03:23, 16 January 2020 (UTC)

@Double sharp: I missed this one, which is in vol. 3, by Vickery, on Sc, Y, and La:

"Polymerization of the Y ion has been shown now to account for its apparently nomadic behaviour in earlier classical separation techniques. Evidence is also available for the existence of La hydroxypolymers in solution. There is, indeed, to be seen an interesting sequence through…Group III in this respect. Hydroxyl bridged polymerization has been shown for Al, Sc, Y, and La ions, but does not appear to exist with the series Ce³⁺ —> Lu³⁺. OTOH, Ga, In and Tl do appear to complex in this fashion. On a thermodynamic basis, ionic hydration—or hydroxo complex formation—may depend upon free energy rather than enthalpy and plots of such free energy link the pre-lanthanon triad more closely to Al, on the one hand, and Ga, etc., on the other, than to the lanthanon group of elements.

(p. 344)

Sandbh (talk) 06:59, 16 January 2020 (UTC)

References

I'm listing a few refs here instead of repeatedly looking them up.

Group 3 (Sc, Y, La, and Ac): "As shown in Table 23.8.1, the observed trends in the properties of the group 3 elements are similar to those of groups 1 and 2." (2019)

From chemlibretexts.org (CLT) here

Group 4 (Ti, Zr, Hf): 1. "The +4 oxidation state for titanium gives rise to largely covalent compounds." 2. "…Zr(IV) and Hf(IV) are mainly covalent…"

-- 1. Nicholls D 1974, Complexes and first-row transition elements, MacMillan Press, London, p. 139

-- 2. Talbot DEJ & Talbot JDR 2018, Corrosion science and technology, 3rd ed., CRC Press, p. 336

Group 5 (V, Nb, and Ta): "The chemistry of the two heaviest group 5 metals (Nb and Ta) is dominated by the +5 oxidation state. The chemistry of the lightest element (V) is dominated by lower oxidation states, especially +4."

-- Same CLT source

Group 6 (Cr, Mo, and W): "Due to extensive polarization of the anions, compounds in the +6 oxidation state are highly covalent…For Mo and W, the highest oxidation state (+6) is by far the most important…"

-- Same CLT source

Group 7 (Mn, Tc, Re): "Of the two, technetium more closely resembles rhenium, particularly in its chemical inertness and tendency to form covalent bonds."

-- from our article on technetium

Groups 8−10 (PGM only): "In a number of cases (e.g. P, S, As, Se, the platinum group metals) the oxidation states are formal because the bonding exhibited by these elements is commonly covalent in minerals."

-- Henderson P 1982, Inorganic geochemistry, Pergamon Press, p. 135

Group 11 (Cu, Ag, Au): 1. "It [Ag] tends to bond covalently in most of its compounds." 2. "Gold has common oxidation states of +1 and +3, and as a soft acid usually combine with soft bases in predominately covalent systems…"

-- 1. From our PTM article

-- 2. Porterfield WW 2013, Inorganic chemistry, 2nd ed., Academic Press, p. 528

Group 12 (Zn, Cd, Hg): "All of the [Group 12] metals, but especially mercury, tend to form covalent rather than ionic compounds."

-- From our PTM article

Coverage

These sources cover 24 of the 30 (80%) period 4 to 6 transition metals or 21 of the 27 (77.8%) TMs if Group 12 are left out.

Findings

The group 3 TMs have a predominately ionic chemistry.
For Groups 4 to 11, encompassing twenty-four period 4 to 6 TMs, 18 of these (75%) have typically covalent chemistries.
Group 12 has a predominately covalent chemistry.

Sandbh (talk) 05:04, 30 January 2020 (UTC)

Notice how:

Group 3 is declared to have a trend resembling groups 1 and 2, after it has already been accepted as Sc-Y-La-Ac, which is circular.
As R8R mentioned, it is not fair to compare on one side to groups 1 and 2 (two groups), and on the other side to groups 4 to 12 (nine groups). So let us be fair, and have two on each side. Actually, let me be a bit unbalanced and have three on the "other" side, because it is amazing that I can still do it. So: not only Zr/Hf, but also Nb/Ta and Mo/W have their chemistry dominated by the group oxidation state. In which, of course, transition-metal properties are impossible as there are no d-electrons. This is surely the significant difference here, not "ionic vs. covalent". Most of the main-group elements are not "predominantly ionic" by any stretch of the imagination. Beryllium and magnesium certainly are not for any distribution of anions.
Even if "ionic vs. covalent" were relevant, it would be:
1. ill-defined without a distribution of anions stated; and even if one was stated, it would be:
2. advocating for Be and Mg over Zn.

Double sharp (talk) 13:52, 30 January 2020 (UTC)

Group 3 and the Ln

Showing group 3 split from groups 4 to 12 is consistent with Moeller (1973, p. 3) who observed that: “There is…a closer configurational similarity between the lanthanide ions and the Group Ia–IIIa cations than between the lanthanide ions and the d-transition metal ions. "

Here Moeller (and King after that) say nothing about group 3, but they say that lanthanides are closer to s-block than to d-block. And that's the reason to put f-block immediately after s-block instead of inserting it inside d-block. Droog Andrey (talk) 11:19, 7 January 2020 (UTC)

Sandbh: Moeller refers to the cations of groups Ia, IIa, and IIIa (Sc-Y-La-Ac), so that seems like a good reason to show groups 1 to 3 as being colocated.

@Sandbh: They are colocated in 18-column version of the PT. Droog Andrey (talk) 19:05, 8 January 2020 (UTC)

@Droog Andrey: [S2] I was referring to group 3 as Sc-Y-La-Ac, in the 18-column form. Sandbh (talk) 05:38, 9 January 2020 (UTC)

For King, the context is:

Group 3 shows chemical behaviour that is manifestly uncharacteristic of the transition metals proper. Group 3 does not show the complex coordination chemistry that is characteristic of transition metals; they do not show multiple oxidation states; and they are more reactive and electropositive than any other transition metals, approaching the s-block metals in both properties. In fact, they largely show the behaviour expected of main-group elements following the alkaline-earth metals. This is true for the lanthanide series from La to Lu, as well as in Ac and the late actinides from Cm to Lr (Greenwood & Harrington 1973, p. 50; King 1995, p. 289) Sandbh (talk) 05:25, 8 January 2020 (UTC)

@Sandbh: That behaviour is normal not only for main group elements, see above. Droog Andrey (talk) 19:05, 8 January 2020 (UTC)

@Droog Andrey: See my [S1][S2]. Sandbh (talk) 05:38, 9 January 2020 (UTC)

Basis for blocks

Differentiating electrons are relevant from a chemical perspective since they enable the periodic table to be parsed into four major blocks according to the predominant differentiating electron in each block

In fact, the table is parsed into blocks according to chemically active subshells in atoms. Differences in ground-state configurations have little sense, especially in d- and f-blocks where a lot of low-lying excited states are observed for the vast majority of the elements. Droog Andrey (talk) 11:19, 7 January 2020 (UTC)

Sandbh: There is a supporting citation for what I said here: Stewart PJ 2018a.

@Sandbh: Citation is not an ultimate truth but just another opinion. Droog Andrey (talk) 19:05, 8 January 2020 (UTC)

@Droog Andrey: [S3] Yes, I agree. There's no categorical argument for the resolving the group 3 question, so I have to rely on qualitative and quantitative arguments, supported by citations. Stewart---described by Scerri as a polymath---is a key player in this space, with a formidable reputation (he supports Sc-Y-Lu-Lr). Sandbh (talk) 05:38, 9 January 2020 (UTC)

Your approach won't work for f-block lanthanides, as the f electrons aren't chemically active. It doesn't work that well for group 12 either, where the d electrons aren't comparably chemically active. Even silver has much more main group chemistry than d- chemistry. Sandbh (talk) 05:25, 8 January 2020 (UTC)

@Sandbh: Wow. Just try to calculate some properties of f-elements without explicit f-electrons accounting (e.g. replacing them with an ECP) - the results will be garbage. However, for Lu and Lr such calculations give decentish results, at least better that for Zn-Cd with d-electrons replaced with ECP. Droog Andrey (talk) 19:05, 8 January 2020 (UTC)

@Droog Andrey: [S4] I accept that, and here I feel we are getting into inconclusive micro-argument territory that Scerri finds inconclusive. Stepping back from the dance floor and up into the balcony, the f electrons aren't chemically active. Sandbh (talk) 05:38, 9 January 2020 (UTC)

@Sandbh: Surely they are. Just try to explain coordination numbers around 12. Droog Andrey (talk) 06:59, 9 January 2020 (UTC)

@Sandbh: I don't accept that this is a micro-argument, because a very common theme in lanthanide chemistry is the interplay between 4fⁿ and 4fⁿ⁺¹ configurations. 4f is maybe not directly active in quite the way 6s for example is, obviously, but it is a reserve area where one electron can easily be kicked up (or not) to 5d, most obviously in Eu²⁺ vs. Eu³⁺. On those grounds alone La is already mathematically a better fit than Lu, precisely because if one generalises this to the whole f-block, one quickly realises that this interplay is mathematically impossible for Lu (you need to cram 15 electrons into 4f). For La, it is at least possible, even if we do not see it that much. Now just put in the actinides, which everyone accepts go under the lanthanides; the early ones show lots of f-orbital involvement, and in the late actinides we see this 5fⁿ vs 5fⁿ⁺¹ interplay again. Now, which one looks closer, Ac or Lr? Seems to me that if you put Lr at the end of the f-block you've got a strange caesura between No and it, because +2 has been slowly asserting its dominance from Es to No with one clear reason: 5f is dropping into the core. Then Lr suddenly gets +3 dominating, for a completely different reason: it's no longer fishing out a third electron from 5f. Seems like Ac is a clear winner for this reason, as the trend from it to Th is pretty smooth: in the early actinides, 5f, 6d, and 7s are all happily hybridising, with 6d on top at first and 5f slowly getting more and more involved, and the trend may be continuously extrapolated backward to Ac from the early actinides in a way that it cannot be continuously extrapolated forward to Lr for the late ones. Double sharp (talk) 06:55, 9 January 2020 (UTC)

@Double sharp: @Droog Andrey: Let's not lose sight of what I said in the paper which was about differentiating electrons being used to parse the table into blocks which I recall goes back to the 1920s. I provided a citation about the general principle being supported by Stewart. As far as La and Lu are concerned, in my humble opinion, you're going back to the micro arguments. The consensus in the literature, by a wide margin is that in the very large majority of cases, the f electrons do not take part in ordinary chemistry reactions. There is no point in saying that f orbital participation is a possibility for La but not for Lu. Again, the incidence of this being able to happen for La is like comparing the moon to the sun, and saying therefore that La is a better candidate for the f-block, while simultaneously down playing the much more important global issues of the kind I've tried to set out in the rest of the article. It's these global issues that will swing the argument, not the minutiae of the interplay between 4fⁿ and 4fⁿ⁺¹ configurations. Sandbh (talk) 09:32, 9 January 2020 (UTC)

@Sandbh: If 4f is not involved, then how can the early Ln support such high coordination numbers for their compounds? And how come the Ln all like to be in the +3 state? They are all 4fⁿ6s² in the gas phase; where did that third valence electron come from? And what about the actinides, for which 5f is an obvious major part of chemistry? And what about those late 3d metals that prefer being in the +2 state like Co and Ni: are they somehow less d-elements because of it? Is Mn less of a d-element because its differentiating electron is 4s rather than 3d? And how is the differentiating electron a global issue when the anomalies like Nb vs. Ta or Lu vs. Lr seems to mean absolutely nothing for the chemistry of those elements? For that reason I think differentiating electrons are far more like a micro argument and which subshells are active is actually the global issue. Double sharp (talk) 11:45, 9 January 2020 (UTC)

@Sandbh: You say differentiating electrons are the basis of block structure, I argue that differentiating electrons has no chemical sense for the most of d- and f-elements, and that the overall block structure of PT really comes from the influence of valence subshells symmetry on the chemistry of elements. You start arguing about f-subshell activity, but then retract that plotline. So what? :) Droog Andrey (talk) 12:26, 9 January 2020 (UTC)

@Double sharp:@Droog Andrew: RL obligations mean I won’t necessarily be able to provide a fully considered reply until next week. On the preference by the Ln for trivalency this is because in the condensed form most of them have a 4fⁿds² configuration. The differentiating electron argument is not mine. The argument about the relevance of differentiating electrons to the overall structure of the PT, as a global argument, is supported by e.g. Janet, Stewart, Scerri, Lavelle, and others, and quantum mechanics. F-involvement in the early actinides are not relevant to the article. Actually, that is a good point. The Ln, as far as I know have no comparable f-involvement. It is a sun to moon situation. On high coordination numbers for Ln compounds I remember reading something about that and the possibility of f orbital/electron involvement but there was nothing conclusive that I can remember. Our own article on the Ln says that, “The 4f orbitals penetrate the [Xe] core and are isolated, and thus they do not participate in bonding.” Sandbh (talk) 07:15, 10 January 2020 (UTC)

@Sandbh: What about Ce⁴⁺ compounds? (Yes, they are sort-of mixed-valence according to our cerium article, but that implies at least partial direct 4f involvement in the bonding.) And however you put it, it remains that once you get into the condensed phase one electron that was in 4f in the gas phase has moved to 5d, so there is still some promoting from 4f to 5d going on here. Double sharp (talk) 06:39, 12 January 2020 (UTC)

@Double sharp: Yes, I agree about Ce. Our article should perhaps say, with (very?) few exceptions, the 4f orbitals don’t participate. Mind you I’ve never found a source that clearly addresses this question. Sandbh (talk) 09:00, 12 January 2020 (UTC)

@Sandbh: I recommend this article on the matter. Double sharp (talk) 03:59, 13 January 2020 (UTC)

@Double sharp: I remember reading that odd paper when we were drafting our IUPAC submission. I was never able to find any confirmation of its explanation in the literature. I recall thinking how odd it was basing its arguments on the gas phase and not saying anything about the condensed phase configurations e.g. Greenwood and Earnshaw (2002, pp. 1232, 1234): "…most of the metals are composed of a lattice of Ln^III ions with a 4fⁿ configuration and 3 electrons in the 5d/6s conduction band [i.e. 5d¹6s²]. Metallic Eu and Yb, however, are composed predominately of the larger Ln^II ions with 4fⁿ⁺¹ configurations and only 2 electrons in the conduction band." Sandbh (talk) 22:56, 15 January 2020 (UTC)

@Sandbh: If we go by condensed-phase configurations, Be and Mg are p-metals, and Al goes over Sc because of p-orbital occupancy in the d-metals. Double sharp (talk) 09:31, 16 January 2020 (UTC)

@Double sharp: That's news to me about Be and Mg being p-metals and p-orbital occupancy in the d-metals.

We know that ionic radii strongly influence the chemical properties of the metallic elements.

As our own article on scandium says:

"Sc chemistry is almost completely dominated by the trivalent ion, Sc³⁺. The radii of M³⁺ ions in the table below indicate that the chemical properties of scandium ions have more in common with yttrium ions than with aluminium ions. In part because of this similarity, scandium is often classified as a lanthanide-like element.

Ionic radii (pm)
Al	Sc	Y	La	Lu
53.5	74.5	90.0	103.2	86.1

"

Our ionic radius article gives the following figures

Al 67.5 | Ga 76.0 | In 94

Al 67.5 | Sc 88.5 | Y 104

Sandbh (talk) 00:10, 18 January 2020 (UTC)

@Double sharp: Here are those passages about coordination numbers and suggested f orbital involvement (how does Lu manage 11 coordination?):

"Coordination Numbers 10–12

Sheer congestion or donor atoms around the metal ion and concomitant inter-donor atom repulsions makes these high coordination numbers difficult to attain. They are often associated with multidentate ligands with a small 'bite angle' such as nitrate that take up little space in the coordination sphere, either alone, as in (Ph₄As)₂[Eu(NO₃)₅] or in combination with other ligands, as in Ln(bipy)₂(NO₃)₃, Ln(terpy)(NO₃)₃(H₂O) (Ln = Ce-Ho), and crown ether complexes (Section 4.3.7) such as Ln(12-crown-4)(NO₃)₃ (Ln = Nd-Lu). Other crown ether complexes can have 11 and 12 coordination, e.g. Eu(15-crown-5)(NO₃)₃ (Ln = Nd-Lu) and Ln(18-crown-6)(NO₃)₃ (Ln = La, Nd )."

Cotton S 2006, Lanthanide and actinide chemistry, John Wiley & Sons, Chichester, p. 53

"The one case in which contributions to the bonding from the f orbitals is possible is in complexes of the heavier elements in which the coordination number is high. Use of the s orbital, together with all the p and d orbitals or one valency shell, permits a maximum coordination number of nine in a covalent species. Thus, higher coordination numbers imply either bond orders less than unity or else use of the f orbitals In addition, certain shapes (such as a regular cube) or lower coordination number also demand use or f orbitals on symmetry grounds. These higher coordination numbers have only become clearly established recently, but their occurrence in lanthanide or actinide element complexes suggest the possibility of f orbital participation. Examples include the 10-coordinate complexes mentioned above, LaEDTA(H₂O)₄ and Ce(NO₃)₅^2- or 10-coordinate La₂(CO₃]₃.8H_2O; 11-coordinate Th(NO₃)₄.5H₂O (coordination by four bidentate nitrate groups and three of the water molecules); and the 12-coordinate lanthanum atoms in La₂(SO₄)3.9H₂O-with twelve sulfate O atoms around one type of La atom position."

MacKay KM, MacKay RA &Henderson W 2002, Introduction to modern inorganic chemistry, 6th ed., Nelson Thornes, Cheltenham. p. 256

Periodic law

The periodic law implies, certius paribus, that since La represents the first recurrence of comparable periodicity after Y it should be the one to go under Y rather than Lu. If that had been true, Sc would have gone below Al. Droog Andrey (talk) 11:19, 7 January 2020 (UTC)

Sandbh: This is a very interesting item that I may need to elaborate carefully in the article. For now, I'd say that Sc and Al breaches certius paribus, since Sc is a d element whereas Al is a p element. I know that Mendeleev, in his Principles of chemistry (Ch. XVII, Boron, aluminium, and the analogous metals of the third group) said that the analogues of aluminium were gallium, indium, and thallium. Sandbh (talk) 07:00, 8 January 2020 (UTC)

@Sandbh: As soon as we are accounting d-elementicity, let's note that Lu is much more d-elementish that La, the latter being f-element. Droog Andrey (talk) 19:05, 8 January 2020 (UTC)

@Droog Andrey: [S5] That may be so, peripherally. Unfortunately the macro-effects such as e.g. the binary stoichometry of rare earth compounds, support La under Y. I've seen proposals to place both La and Lu, as d elements, in group 3. Sandbh (talk) 05:38, 9 January 2020 (UTC)

@Sandbh: That's the same for Al-Sc vs. Al-Ga. Droog Andrey (talk) 06:59, 9 January 2020 (UTC)

@Droog Andrey: Not from a binary stoichiometry pov. Al goes over Ga. Sandbh (talk) 09:37, 9 January 2020 (UTC)

@Sandbh: What exactly do you mean by binary stoichiometry? If you mean just binary compounds of each element, e.g. Al₂O₃ vs Sc₂O₃ vs Ga₂O₃, there is no significant difference as everyone is trivalent. If you mean something like which elements substitute for each other preferentially in things like mixed oxides, then like Droog Andrey mentions Al patterns with Sc, not Ga. Double sharp (talk) 11:35, 9 January 2020 (UTC)

@Double sharp: On stoichiometry, see here.

@Sandbh: I've already addressed the methodological problem with using this study exclusively on your talk page, so I'll just quote myself again: "...Restrepo (as I noted before) is concerned about stoichiometry, which implies valence, and thus it is obvious that similarities with elements from different groups like Lu vs. Hf will be ignored. But secondly, the procedure is not to only look at which of La and Lu are more similar to the other lanthanides: obviously this is going to be totally inconclusive because of how similar the lanthanides are to each other. (Note that Sc, Y, and the Ln in Restrepo's article are all in a cyan area of very low difference from each other anyway, so the magnitude of the differences we are talking about is tiny. Double sharp (talk) 10:04, 12 January 2020 (UTC)) We need to ask what we did for the analysis of Zn, Cd, and Hg above (where I was comparing them to transition metals, and noting that the distance between Zn/Cd/Hg and the TMs is less than that between Ca/Sr/Ba and the TMs) Double sharp (talk) 10:04, 12 January 2020 (UTC), i.e.: what are the characteristic properties of the d-block elements, specifically the nine sure 5d elements from hafnium to mercury inclusive, and does La or Lu display more of those properties? In every conclusive case the answer is Lu.

The 5d metals are usually small cations due to the lanthanide contraction; so Lu³⁺ obviously fits better than the La³⁺ as it comes when the lanthanide contraction is at its end. (In fact Lu³⁺ has a similar ionic radius to Au³⁺.)
The early 4f metals often show rather large coordination numbers uncharacteristic of the d-block metals, because the latter are not large enough. (Also because of 4f involvement.) Double sharp (talk) 10:04, 12 January 2020 (UTC) Again, Lu (being the smallest lanthanide) is the closest fit here.
The 5d metals are more covalent than ionic in most of their chemistry, and their oxides and hydroxides mostly acidic or at least amphoteric: as expected from Fajans' rules, Lu more closely approximates this behaviour than La, as Lu(OH)₃ is (barely) amphoteric.
Most of the sure 5d metals are intermediate or soft cations (Hf being the only exception); clearly Lu is closer, as it is the smallest and hence softest lanthanide cation.
The 5d metals are very dense, and the early ones are very hard and often refractory. They are also mostly unreactive in the bulk form. Lutetium, being the hardest, densest, most refractory and least reactive of the lanthanides, is obviously closer to this kind of behaviour than lanthanum, a soft metal which corrodes in the air.

This is more or less what settles it for me: even though sometimes a Sc-Y-La trend looks better, sometimes a Sc-Y-Lu trend looks better, and both La and Lu are full of similarities with the other thirteen lanthanides, it is hands-down obvious that lutetium is a better fit with the other nine 5d metals than lanthanum is. We can for sure put an extra 3 above the La-Ac small column to alert people that the Sc-Y-La trend is also worth looking at, but I submit that the case for Lu under Y is clear-cut because it leads to a more homogeneous d-block. The issue of which elements should be in group 3 should be decided by the prospective group 3 elements and hence can remain unresolved and probably unresolvable, but the issue of which elements should go in the d-block should be decided by looking at everything in the d-block, and that provides an answer. So for me, yes, La and Ac can also be extra group 3 elements just as Lu and Lr are, but the d-block positions below Y in the table must be occupied by Lu and Lr. (Obviously we have to extrapolate a lot to do this analysis for Lr, but the actinide contraction by itself ensures that the points I wrote above for Lu are almost certainly valid for Lr as well when you compare whether actinium or lawrencium acts more like the sure 6d metals from rutherfordium to copernicium inclusive.) Double sharp (talk) 15:25, 11 August 2019 (UTC)" Double sharp (talk) 10:01, 12 January 2020 (UTC)

@Double sharp: The homogeneity (or not) of the d block is interesting. The 3d and 4d rows are about as uniform as we could expect given the more or less steady addition of d electrons. Row 5d post-La disrupts the expected periodic trends going down the d groups due to the interpositioning of the lanthanides. So La is about what we would expect for the metal going under Sc-Y. Whereas Hf onwards buck the trend.

Similarity is one of the key concepts of the periodic table, which was historically addressed by assessing the resemblance of chemical elements through that of their compounds. Mendeleev’s studies were mainly based on compounds, particularly on oxides, hydroxides, hydrides and halides and by studying their similarities he came up with resemblances for the chemical elements. He highlighted the need to rely on compounds and their proportions of combination rather than on properties of chemical elements; this is evident in his statement that “if CO2 and SO2 are two gases which closely resemble each other both in their physical and chemical properties, the reason of this must be looked for not in an analogy of sulphur and carbon, but in that identity of the type of combination, RX4, which both oxides assume.” He adds, “the elements, which are most chemically analogous, are characterized by the fact of their giving compounds of similar form RXn.” Following Mendeleev’s ideas, a key concept to understand similarities of chemical elements is that of valency, which is obtained by stoichiometric decomposition of compounds in chemical analysis.

According to Restrepo’s results, La appears in between two clusters, one of 11 lanthanoids and another of transition metals, namely {Y,Sc}. Lu is part of the clusters of 11 lanthanoids and the smallest cluster containing it is {Ho,Er,Lu}, which shows that Lu is more similar to lanthanoids than to transition metals, while La share similarities with lanthanoids and with transition metals. Therefore La must be the element located at the beginning of the third row of transition metals if chemical resemblances are what it is to be emphasized.

It seems to me that you are emphasising the horizontal fit of Lu with the 5d metals. It seems to me that the vertical fit of La in group 3 is more important, since vertical trends across the PT generally form the basis of periodicity.

The properties of Lu that you listed are what I’d expect for a metal just before Hf. At the same time Lu is universally, in chemical terms, regarded as a lanthanide, there being no widely recognised chemical series encompassing the 5d metals. And the Ln were conceived of as the metals following, but not including La i.e. La retained its 5d status. Let us not forget that Lu usually occurs with the heavy Ln, that it resembles closely erbium and holmium, except that it melts at a slightly higher temperature and is essentially non-magnetic, and that the details of producing, purifying and fabricating it are almost identical with those of holmium. Sandbh (talk) 23:14, 12 January 2020 (UTC)

@Sandbh: But we have to look at those horizontal properties, because the vertical trends for Sc-Y-La and Sc-Y-Lu both look pretty convincing and there is little to choose just from that alone. (Which is why I still think that if you're writing a general inorganic chemistry textbook, you should cover both the -La-Ac and the -Lu-Lr option in the same chapter and create a six-element "group 3", because that sheds light on some things. But then again I also think you should cover Be-Mg both with the Ca group and the Zn group.) Notice that in Restrepo's chart, the REM are all in a region of cyan background, which is a region of very low difference in general. Therefore the differences he is pointing out cannot possibly be very big (as everyone expected, since La and Lu are basically almost always trivalent, just like Sc and Y), so this feels to me like saying "let's just decide it by piling up similarities to Sc/Y on both sides", and my intuition revolts because almost by definition just looking at properties of our candidate group 3 elements alone will be inconclusive (otherwise why has this argument been raging on for so long?). And where are we if we say that actually Sc and Y are pre-transition? Then there's little to choose again; if we take La just because it appears closer to them than Lu in his chart, we're again overlooking just how small the differences are. (And I strongly suspect it might be just some statistical fluctuations in the data at this level, because if anything Lu should better substitute for Sc and Y in everything due to its smaller size.) I prefer to say: if we want to talk about "the element located at the beginning of the third row of transition metals" based on "chemical resemblances", then it's obvious that the second most relevant resemblances are to the rest of the "third row of transition metals" (and that's the desired chemical name for the 5d series) that are being talked about; and we appeal to this second level because the first level is totally inconclusive. And of course, a stoichiometry analysis will never help with that, just as it will never find diagonal relationships like Li-Mg and Be-Al. And it doesn't matter that Lu also acts like an excellent heavy lanthanide, because La also acts like an excellent light lanthanide that usually occurs with Pr and Nd. And it doesn't matter that historically the Ln were considered as the elements following La, because we can always change definitions when something else seems to get closer to the heart of the issue, which is why the transition metals are no longer just Mendeleev's "group VIII". Double sharp (talk) 03:46, 13 January 2020 (UTC)

@Double sharp: I feel you've overlooked the original premise which was the periodic law and what was the case for skipping La in favour of Lu. By itself that is a huge step considering the periodic law forms the basis of the periodic table. The other thing is, as you say, piling up arguments on the basis of a comparison of the properties of La and Lu is inconclusive. That is why I'm relying on global or philosophical arguments. And let us not forget, as mentioned, that it is vertical relationships that are more important in the case of groups, than horizontal trends. I don't accept your premise that the vertical trends are inconclusive. The argument has been going on for so long because nobody has taken a holistic view of the trends going down the groups to either side of Group 3, and the overall chemical behaviour of Group 3, as we did in our IUPAC submission. This includes the multiple quotes from the literature noting the overall behaviour of Group 3, and the Ln, as trivalent versions of Groups 1 and 2. You can argue about the fine details but the overall behaviour is still in favour of La. There are no showstoppers here, only matters of nuance and detail which, at the end of the day, are overshadowed by the broader premise of the period law and the lack of a sufficiently convincing justification for overturning the periodic law, in this instance (IMO). Sandbh (talk) 05:23, 15 January 2020 (UTC)

@Sandbh: Because I don't accept that as a statement of the periodic law. One does not look for the first element that establishes a comparable recurrence of properties, or else Sc goes below Al. One looks for the first one that has a comparable recurrence of properties and matches in valence structure. That allows Ga to go below Al, and also demands that Lu go below Y. Double sharp (talk) 06:38, 15 January 2020 (UTC)

@Double sharp: I agree, we don't place Sc under Al due to the mismatch in configurations, Sc being a d metal and Al being a p metal. The next p metal is Ga so it goes under Al. We place La under Y since it's the next comparable d metal. Lu doesn't go under anything, since it's at the end of the f-block. Sandbh (talk) 00:11, 16 January 2020 (UTC)

@Sandbh: Again: La is not a d metal. It has an empty 4f not so far above, whereas Lu does not. Lu doesn't even have the mathematical possibility of breaching the 4f shell, but La does, and the position of the 4fⁿ⁺¹ excited state can have an effect (as demonstrated in the archives for Ln oxides). Lu is qualitatively different in this case because there's no 4fⁿ⁺¹ state, not even a very high-energy one. Double sharp (talk) 09:34, 16 January 2020 (UTC)

@Sandbh: So Ba is not an s-metal? Sandbh (talk) 05:59, 17 January 2020 (UTC)

@Sandbh: Stricto sensu it is not. Neither are Ca, Sr, and Ra for that matter, so the periodic law is still not broken. (Neither is it from Mg to Ca as there is simply no completely s-metal analogue, so we pick the earliest close one, Ca rather than Zn.) Their placement in the s-block comes from a few reasons:

Be and Mg have some d-metal-like characteristics due to their small size even if they have no d-involvement possibility. (Mg even shows low-valent complexes that are similar to those ones that we see for Ca and group 3.) Therefore the distance is already smaller.
Zn, Cd, and Hg are d-metals too, and the d-block cannot fit 11 columns, so just like for La vs Lu we must extract the triad that is most like the s-metals (which are missing one group). Ca, Sr, and Ba act much like the alkali metals, so they fit better than Zn, Cd, and Hg.
Doing it this way results in a trend that matches group 1, which has to show a straight trend; doing it the other way means that Ca-Sr-Ba is a d-block group that doesn't show an f-block insertion at period 6, which is not the majority trend. (You can't put Yb under Sr for obvious reasons.)
If you make Be-Mg-Zn the other s-block group, it leaves the impression that one s electron goes in first, and then the other one waits for ages, which is a bad first approximation.

If you do the same arguments for La vs Lu you get Lu:

Sc and Y have some f-metal-like characteristics due to similar size (Y masquerades as a rare earth). So the distance is small whether you pick La or Lu.
Even if we accept 4f involvement in Lu, it seems to me that we still must extract out the one that fits better with the d-metals which are missing one group, and that's Lu.
This way leads to a trend matching the other d-block groups; the other way gives an irregularity.
Same thing happens again; it's not really true that one d-electron goes in first and then 14 f-electrons interrupt, due to all the 4fⁿ vs. 4fⁿ⁺¹ interplay.

And that's why, while I'm happy to say that La and Ac are extra group 3 elements in the same way that Zn, Cd, and Hg are extra main-group elements, and prefer a branched group II and a branched group 3 to illuminate what's going on here, I think that the "primary" members shown as vertical columns should be Be-Mg-Ca and Sc-Y-Lu. (Matter of fact, I could get behind a table with H and He duplicated on the top of Li/Be and F/Ne, Be/Mg duplicated above Ca and Zn, and B/Al/Sc/Y duplicated above La with Sc and Y only above Lu as well.) Double sharp (talk) 07:32, 17 January 2020 (UTC)

@Sandbh: How exactly is stoichiometry going to make any difference at all when all the elements involved are quite happily stuck in the +3 state almost all the time? I am confident that if you compare Lu to Y you will also see zero significant difference. As you will if you compare La to Y. Or Gd to Y. Or Ho to Y. (Struck this bit, as I misunderstood what you meant.) The significant difference between La and Lu is the size, with an impact on coordination chemistry, that makes Lu display more transition-like behaviour than La does. And which way does Sc swing? More like a transition metal, a bit like an overly small lanthanide. And which way does Y swing? It pretends to be a late lanthanide, which is what Lu also is. So if we speak of similarity to d-elements, it seems that the ways Lu displays this are anything but peripheral, but dominate its chemistry. Double sharp (talk) 06:55, 9 January 2020 (UTC)

@Double sharp: I guess Sandbh means that in mixed oxides La has more affinity to Y than Lu. But the same situation is for Sc, which has more affinity to Al than Ga, but it not placed below Al. Droog Andrey (talk) 07:12, 9 January 2020 (UTC)

@Droog Andrey: OK, thanks for the explanation. I've struck the first three sentences in my reply, since it's not relevant to what he means. Double sharp (talk) 07:15, 9 January 2020 (UTC)

@Droog Andrey: @Double sharp:. Can I get rid of Y first, and then see what's left.

I was under the impression that the chemistry of Y was similar to Lu, given their comparable sizes and that Y and Lu occur in the so called yttrium group.

It turns out that things are not so straightforward. Y can behave like a cerium earth (e.g. Pr, Nd, Sm) or a yttrium earth (e.g. Dy, Tm, Lu).

Here are some extracts from the literature.

[1] Bünzli J & McGill I 2000, "Rare-earth elements" in B Elvers (ed.) 2011, Ullmann’s Encyclopaedia of Industrial Chemistry, 7th ed.

In separating the rare earths via ion exchange, the behaviour of yttrium varies with the chelating agent over a range from Pr to Dy (p. 19).

Along similar lines:

"The separation of yttrium oxide [from europium oxide] exploits the fact that yttrium is unique among the rare earth elements in that its position in the series of elements with respect to separation operations is not constant...The last cycle extracts Tm, Yb, and Lu by means of tricaprylmethylammonium thiocyanate. Here, yttrium behaves like a cerium earth element." (p. 26)

[2] Jowsey J, Rowland RE & Marshall JH 1958, "The comparative deposition of yttrium, cerium, and thallium in bone tissue of dogs", in Argonne National Laboratory, Radiological Physics Division Semiannual Report, July to December 1957, Illinois, pp. 63--75

"Yttrium behaves chemically and metabolically in a way similar to cerium and thulium and may be classified with these two elements in the lanthanon rare-earth series." (p. 64)

[3] Marsh JK 1947, "The relation of yttrium to the lanthanons: A study of molecular volumes", Journal of the Chemical Society, pp. 1084--1086

"...yttrium and holmium ions are approximately of the same size, but sometimes yttrium shows behaviour indicating a resemblance to neodymium and samarium, which elements have larger ions than holmium. Certain sparingly soluble and basic salts incline to show yttrium associating with elements larger than holmium." (p. 1084)

[4] Gupta CK & Krishnamurthy N 2005, Extractive metallurgy of rare earths, CRC Press, Boca Raton, p. 165

"Yttrium...exhibits interesting behaviour in fractional precipitation and is amenable to purification by a combination of hydroxide and double sulfate precipitation. In [the latter]…yttrium behaves like holmium, and in [the former]…like neodymium."

[5] Finally, there is Restrepo's article (details following) showing Y is more similar to La, at least from a binary stoichiometric perspective:

See: Restrepo G 2017, "Building classes of similar chemical elements from binary compounds and and their stoichiometries", in MA Benvenuto and T Williamson (eds), Elements old and new: Discoveries, developments, challenges, and environmental implications, American Chemical Society, Washington, DC, pp. 95–110 (101).

I was surprised to learn that in the case of Y, there is still more to the question than the simple observation that Sc, Y and Lu occur in the so-called yttrium group.

In my view, we're again straying from the premise which is that there is no plausible explanation for skipping La, which represents the first comparable example of periodicity (including in terms of the overall chemical behaviour of group 3 being closer to groups 1 and 2) in favour of Lu. Sandbh (talk) 09:51, 9 January 2020 (UTC)

Because by that logic Sc goes under Al. The chemical behaviour of Al is pre-transitionised because it lacks the d-subshell over the noble gas core that Ga, In, and Tl have, so the same logic applies. Double sharp (talk) 11:35, 9 January 2020 (UTC)

Good point. The valence electrons are more important than the underlying core, however. Sandbh (talk) 04:21, 10 January 2020 (UTC)

So in that case we have our answer for La vs. Lu already: the chemical behaviour of La is pre-transitionised for the same reason, but we cannot put it under Y because the relevant valence shells don't match. La has low-lying empty f-orbitals; Y and Lu do not. Same as why Th doesn't go under Hf, but Rf does. Note that I say "valence shells" because the minutiae of Madelung exceptions are not important if they don't affect the chemistry, so Lr can go under Lu without any qualms. Groups 1 and 2 are a consistent exception even when relativistic effects are not at issue; delayed collapses for things like Ac are a normal thing for high atomic number and are easier to see as a second-order correction. Double sharp (talk) 04:33, 10 January 2020 (UTC)

@Double sharp: La goes under Y since the low-lying empty f-orbitals do not play a predominant role. Same as Sr under Ca even though the empty d orbitals of Sr play a bit-part role in its chemistry. Thorium goes in the f-block since it has an f electron available for chemistry. Sandbh (talk) 22:12, 10 January 2020 (UTC)

@Sandbh: The influence of 4f is tiny for Lu, even tinier than 3d for Zn, so even though 4f plays a relatively minor role for La it can be better accepted as a peripheral f-block element than Lu can (you have to pick one). In fact 4f influence in Lu is more or less at the same level of a core subshell. If you do the comparison for Ca vs. Zn, Droog Andrey has implied back in 2018 that he suspects Ca would show less 3d influence than Zn, so the argument works for that too (see Wikipedia talk:WikiProject Elements/Archive 33#Part 4). Double sharp (talk) 06:34, 12 January 2020 (UTC)

@Double sharp: I don't disagree. I do think that in a chemical table, where Ln³⁺ has the configuration [Xe] and Yb and Lu have the configurations [Xe]4^f13 and [Xe]4f¹⁴, that this carries much more weight than the tiny influence of 4f in the gaseous state of an isolated La or Lu atom. Sandbh (talk) 22:46, 15 January 2020 (UTC)

@Sandbh: It seems to carry about zero weight when you consider that that 4f shell in Lu never gets breached for anything and never contributes anything significant to the bonding. At least the filled 3d shell in Zn does the second. Lu doesn't even have a 4f gas-phase differentiating electron (which is the criterion you've mentioned before), doesn't even have 4f as a valence shell, and insisting on ions is simply not generalisable across the table to look at equal-charged ions of elements from different columns. At least La has some low-lying 4f shell that we can say is weakened a bit in effect (but not that much, notice the high coordination numbers) just by the typical delayed collapse that happens as Z increases. Same as Ac and Th at the start of 5f, same as Lr at the start of 6d, same as E121 probably will be at the start of 5g. Double sharp (talk) 09:35, 16 January 2020 (UTC)

@Double sharp: That is why Scerri disdains arguments based on individual physical, chemical and electronic properties. They go back and forth. We talked about the possible influence of the f electrons in Lu, in our IUPAC paper. Ratto, Coqblin and d'Agliano (1969, pp. 498, 509) suggested that its lack of superconductivity might be attributable to a small 4f character. A few other authors have referred to some of the properties of Lu being influenced by the presence of its filled 4f shell: Langley 1981; Tibbetts and Harmon 1982; Clavaguéra, Dognon and Pyykkö 2006; Xu et al. 2013; Ji et al. 2015. The most surprising of these is likely to have been Clavaguéra and colleagues, who reported a pronounced 4f hybridisation in LuF3 on the basis of three different relativistic calculations. Their findings were questioned by Roos et al. (2008) and Ramakrishnan, Matveev and Rösch (2009).

I never ran all these references down, but there it is.

I think arguing about 4f character in La v Lu, compared to the other more major attempted arguments in the paper, is inconclusive and peripheral. Sandbh (talk) 06:10, 17 January 2020 (UTC)

They may go a bit back and forth, but without them you have nothing. If you ignore physical, chemical, and electronic properties, then just where did our periodic table come from? Might we not be just as fine arranging the elements alphabetically, as some wag suggested to John Newlands? Anyway, Droog Andrey is the computational chemist here, and he's mentioned that some calculations may overestimate 4f. (From Archive 34: "it seems for me that MP2 is not a good choice for correlation test. I'll try to use CASSCF if I have some spare CPU days.") Now, I'm sure I don't understand why this is the case (maybe he can explain the differences, or maybe it is too complicated), but there you go. To me, it is conclusive to say that the fact that Lu would have to ideally switch between "4f¹⁴5d¹" and "4f¹⁵" [the second one is nonsense] as an f-block element if it followed the mutability of configurations of the other 4f elements is a argument that Lu is not an f-block element. Double sharp (talk) 17:09, 22 January 2020 (UTC)

@Double sharp: That is why I’ve attempted to go more global/philisophical. I’ve talked elsewhere about the purported impact of Lu’s filled 4f shell on its reactivity, unlike Sc, Y and La. And the historical chemical perspective post. Sandbh (talk) 08:32, 23 January 2020 (UTC)

By that standard, we have to consider the impact of Rf's filled 5f shell on its reactivity (i.e. post-actinide contraction effects), and arrive at the conclusion that since Th has an empty 5f shell it should be the heavier congener of Hf. Which is exactly the traditional placement of it, and even after Seaborg's actinide concept won the day, there was some grumbling that U and Nd are almost strangers to each other chemically. So, from a historical chemical perspective, postulating a thoride series (which was, in fact, historically postulated before) would be just as justified as postulating Sc-Y-La. Is there a study that has not been subsequently disputed about 4f involvement in Lu that isn't just post-lanthanide contraction effects, anyway? As mentioned, Droog Andrey gives a plausible reason why some calculations may overestimate its importance. Double sharp (talk) 17:12, 24 January 2020 (UTC)

Greenwood & Earnshaw on Al, group 3, and Ti

@Double sharp: The first passage speaks to the better fit of Al over Ga; the second passage notes the mainly ionic chemistry of group 3 [consistent with groups 1 to 2] and the largely atypical behaviour of the group 3 transition metals; and third passage says that while Sc's status as a TM is arguable, there is no doubt that Ti is a TM.

1. "For instance, the mps and bps along with the enthalpies associated with these transitions, all show discontinuous increases in passing from Al to Sc rather than Ga, indicating the d electron has a more cohesive effect than the p electron." (p. 947)

2. "In the main, the chemistry of these elements concerns the formation of a predominantly ionic +3 oxidation state…although each member of this group is the first member of a transition series, its chemistry is largely atypical of the transition elements." (p. 948)

3. "The most important oxidation state in the chemistry of these elements is the group oxidation state of +4. This is too high to be ionic…whatever arguments may be advanced against applying the description to Sc, there is no doubt that Ti is a transition metal."

Sandbh (talk) 01:04, 19 January 2020 (UTC)

Notice that Zr and Hf are not mentioned, because by the standards that make Sc arguable, so are they. Double sharp (talk) 17:14, 22 January 2020 (UTC)

Helium over beryllium

P.S. By this version of the periodic law (which I agree with R8R is not the whole of what it is about), it seems to me that He has to go over Be: He is an s-element, Ne is a p-element, and comes after Be. So beryllium is the only possible next applicable recurrence of properties, as bad as it is in some respects, as Ne got disqualified by the same argument that you used to disqualify Sc as eka-Al. That one doesn't bother me, since I half-suspect now that the table really should have He over Be to respect the first-row anomaly principle. But perhaps it bothers you!~~ ^_-☆ ミ／ミ／ Double sharp (talk) 21:15, 26 January 2020 (UTC)

@Double sharp:He over Be won’t work since Ne is no longer then anomalous. Sandbh (talk) 22:16, 26 January 2020 (UTC)

Neon is still anomalous: it replicates perfectly the usual themes of the first-row anomaly of the 2p elements. Ne has a totally full n = 2 shell. Ar does not have a totally full n = 3 shell, since there are 3d orbitals. That's why Ne is the most electronegative element in its period, but Ar is effectively less electronegative than Cl (see Droog Andrey's scale). Indeed, the small radius of the 2p orbital means that the 2p elements are anomalously highly electronegative, and Ne conforms perfectly to this pattern, being even more electronegative than O and F(!). The huge electronegativity drop between the 2p and 3p elements is replicated perfectly between Ne and Ar (Droog Andrey's scale: 4.50 vs. 2.94; Allen scale: 4.787 vs. 3.242). The overly high electron density of Ne is also a consequence of 2s and 2p being so close in energy to each other, which is why it has such a hard time forming compounds: Ar does not have this problem, and can form a few. This is exactly like lone-pair repulsion in F₂. Again, see Kaupp's paper on radial nodes.

P.S. Since you seem to be accepting the first-row anomaly principle in order to try to demolish He over Be: note that accepting that principle means that the actinides run the show for the La vs. Lu question, in which case the balance is even more skewed towards Lu/Lr, as Lr is very weird for a late actinide, but Ac is similar to the early actinides like Th. Double sharp (talk) 23:13, 26 January 2020 (UTC)

This strikes me as another example of an obtuse argument, never mind the main headline. You can only justify Ne as anomalous on the basis of an EN scale that nobody else has heard of. Meanwhile Ne is the least reactive of the elements, as opposed to He. That’s the headline anomaly. If it helps there was this article suggesting the halogens have the highest EN, the noble gases having values on par with the chalcogens. The author concluded that the chemistry of the noble gases is for a large part determined by their extreme hardness, equivalent to a high resistance to change in its electronic population coupled to their high electronegativity. Sandbh (talk) 06:50, 28 January 2020 (UTC)

Funny, I also gave the Allen scale. So much for "nobody else has heard of". And it also puts He and Ne as the most electronegative of the elements, even if it disagrees with Droog Andrey w.r.t. Ar. Ne being the least reactive element supports Ne as the first element in group 18 rather than He, so that's "another fruit in my bin" as Droog Andrey would say. It is not a front-line anomaly as you would like it to be because that is simply not how the 2p anomalies work. First-row anomaly is not a free-for-all that lets you put any element in the first row and declare it an anomaly, you know: they are strictly defined by what we see in the elements that we are sure are in the first row because of the effects of primogenic repulsion. Anything that cannot be attributed to that is not a first-row anomaly. It is either another kind of anomaly (e.g. inert pair effect) or it is just putting an element in the wrong place. The first-row anomaly effects for 2p make N, O, F by far the most extreme and electronegative elements in their columns, so the same should be true for Ne, and guess what, it is only if you let Ne head group 18. ^_^ Meanwhile, I hear nothing refuting my statement that Ne's difficulty in forming compounds comes from lone-pair repulsion just like for F. So, half of my reply is unrefuted, the other half is still valid because Allen's scale agrees completely with Droog Andrey's w.r.t. He and Ne, and some of your reply supports my argument anyway.

And your article still makes Ne significantly more electronegative than O, which is different from any other period! ^_^ And it states several times that He is always an outlier in these trends, but you can see in a very different way to how O and F are, which is more similar to Ne (He is just not on the trendline at all, while Ne-Ar goes in the right direction, just "too much", as O-S and F-Cl do)!! And uniformly, the biggest change in the normal direction is always from Ne to Ar, just like between O and S and between F and Cl in their columns!!! So, thank you for showing me an article that supports He over Be and group 18 starting with Ne like nothing else I've ever seen before!!!!

But I do find it amusing that you are now fighting my argument on my terms with first-row anomaly considerations. I wonder why this is suddenly not valid for Sc-Y-Lu? I wonder why the periodicity and differentiating electron argument is suddenly not valid when it looks like it has started to support He-Be-Mg? So are you sure you are being objective, or did you start with whatever you wanted to show, search for things to justify it, and neglect to look at what happens in the rest of the table? ^_^ Double sharp (talk) 12:16, 28 January 2020 (UTC)

@Double sharp: I addressed much of this in the General comments section. I haven't intrinsically relied on EN scales in my draft. There is no strict definition of the first row anomaly. Primogenic repulsion can play a part but that is not all there is to the story. Sandbh (talk) 23:04, 31 January 2020 (UTC)

That's precisely why it's useful: it's not strictly defined by one property, but is characterised by a multitude of them showing up. We're not trying to pick out properties willy-nilly. We're trying to see what properties can be theoretically attributed to primogenic repulsion. Given how much it impacts the 2p, 3d, and 4f elements (I trust I do not have to scour the literature to prove what Kaupp already did), surely we should reflect it for the 1s elements. And you still haven't addressed that your version of the periodic law points unambiguously to He over Be. Is that what you want? Many of your arguments, if applied to groups 2, would either support He in group 2 or Be and Mg over Zn, which I have demonstrated several times. (Immediate neighbours support Be-Mg-Zn because Be and Mg are weak metals, more similar to Zn than to Ca; this weakening does not appear with Li-Na-K. They also don't oppose H-He, because H stands in relation to Li much as He stands in relation to Be. Differentiating electrons are inconclusive for Be-Mg-Zn, and roundly support He over Be to put it in the right block. Your version of the periodic law supports He over Be, not to mention that in the way it is phrased in your article it supports Al over Sc as well. And the rare-earths argument just does not make any sense to me, given that we all know how to read text from left to right within each line.) Is that what you want? If not, then I claim it at least casts doubt on the usefulness of an argument about group 3, if it gives the "wrong" answer elsewhere. Double sharp (talk) 23:10, 31 January 2020 (UTC)

@Droog Andrey: What's your opinion on He over Be, actually? (Just curious.) Double sharp (talk) 13:57, 28 January 2020 (UTC)

@Double sharp: I'd place He over Ne and (He) over Be, and at the same time H over Li and (H) over F. Droog Andrey (talk) 18:46, 29 January 2020 (UTC)

@Droog Andrey: Yeah, I can agree with that. Everyone knows they are s-elements sometimes drawn apart anyway, so the s>>p>d>f first-row distinctiveness is retained anyway. ^_^ Double sharp (talk) 18:57, 29 January 2020 (UTC)

@Double sharp: You know, I was hunting (computationally) for He-bonded structures in 2011, and discovered HeNiCH4 (C2v symmetry) with He-Ni bond of 1.6Å. The bond was quite strong (around 30 kJ/mol), but unfortunately Ni-CH4 complex appeared to be metastable against H-Ni-CH3. At that time I studied a lot of VdW-bonded complexes of noble gases, and figured out that, indeed, Ne is much more inert than He, with He quite resembling Be in bond nature. It is pleasure for me that Grochala made the same conclusions. Droog Andrey (talk) 19:44, 30 January 2020 (UTC)

@Droog Andrey: Wow, that's cool! So maybe it really should be He over Be and (He) over Ne after all. ^_-☆ I guess I should link to Grochala's PCCP paper on (HeO)(LiF)₂ and the supplementary information (the latter is where he considers the implications for the periodic table). It seems that He follows Be in showing more affinity to O than to F. I cannot resist quoting his section S14:

Having studied (HeO)(LiF)₂ we have scrutinized its heavier noble gas analogues. However, neither (NeO)(LiF)₂ nor (NeO)(NaF)₂ could be detected as minima on the singlet PES. This stability difference is interesting since electronegativity and many other chemical properties of elements change quite monotonically when one goes down any of the Groups 13–18. For example, O is more electronegative than S, F than Cl, Ne than Ar, etc. Hence, He should be more electronegative and as such less prone to chemical bonding than Ne. The atypical behaviour of He vs. Ne (i.e. reversal of stability for their theorized chemical connections) which obviously contrasts with the trend for the 1st ionization potentials of these elements (He > Ne), has been noticed before. Various explanations were provided from electrostatic arguments to increased Pauli repulsion from the filled 2p orbital on Ne. We think that a relatively large reactivity of He with respect to Ne may be understood simply in terms of substantial charge density which appears at a small He center when its 1s² shell is even partially depopulated. The incr[e]ased charge density obviously leads to stronger electrostatic and dispersive interactions with ligands.

This no doubt recalls hydrogen; helium then joins it as an example of what happens when you literally have no shielding at all from the nucleus, as only happens in the 1s row. ^_^ He then argues for He over Be, by virtue of the isoelectronic 1s²-2s² analogy (of course Be-O is more ionic in character than He-O), and by the properties that you mentioned (where Ne is much more inert than He, whose bonds resemble those of Be). Personally, I found this very convincing myself. It's amazing that He seems to be less electronegative than O here(!!). Previously I thought He over Be was silly, but now I see it has actually significant chemical and physical sense. (I changed my userpage periodic table to support it back in August last year. ^_^) Double sharp (talk) 20:08, 30 January 2020 (UTC)

Rare earth series

The rare earth series (Sc, Y and the lanthanides La–Lu) appear listed in order of their atomic numbers in a 32-column periodic table with Group 3 as Sc-Y-La-Ac. If Group 3 is shown as Sc-Y-Lu-Lr, the minority of the rare earths appear in order of their atomic number whereas the majority appear in a backwards order. [...] The second option is awkward, or highly anomalous at best, since the horizontal, vertical, and diagonal trends that characterise the periodic table are based on an increasing sequence of atomic numbers. In both variants the atomic number increase from left to right and from upside down, there's no any backwards order. All the trends remain. Droog Andrey (talk) 11:19, 7 January 2020 (UTC)

Sandbh: What I meant to convey was that IUPAC defines the rare earths as Sc, Y and the lanthanides…

Sc21
Y39
La57 Ce58 Pr59 Nd60 Pm61 Sm62 Eu63 Gd64 Tb65 Dy66 Ho67 Er68 Tm69 Yb70 Lu71

…rather than the lanthanides and Sc, Y:

                                                                      Sc21
                                                                      Y39
La57 Ce58 Pr59 Nd60 Pm61 Sm62 Eu63 Gd64 Tb65 Dy66 Ho67 Er68 Tm69 Yb70 Lu71

The first option can be "bent", in ascending numerical order, to read Sc 21 to Lu 71.

@Sandbh: But that has nothing to do in "The domain of chemistry" section. That's about design and personal taste. Droog Andrey (talk) 19:05, 8 January 2020 (UTC)

@Droog Andrey: [S6] I supported what I said here with my citation to Scerri: "The horizontal, vertical, and diagonal trends that characterise the periodic table are based on an increasing sequence of atomic numbers." Sandbh (talk) 05:38, 9 January 2020 (UTC)

@Sandbh: Well, which particular trends are broken, in your opinion? Droog Andrey (talk) 06:59, 9 January 2020 (UTC)

It's not possible to bend option 2 in ascending numerical order. Sandbh (talk) 05:25, 8 January 2020 (UTC)

@Sandbh: But you can just read each one, left to right in each row, and one line at a time from top to bottom, the order you read anything. Where is the difference? Only the design. Double sharp (talk) 06:55, 9 January 2020 (UTC)

@Droog Andrey: @Double sharp: Well, the majority of graphs I can recall plotting various properties of the the rare earths, as is the case with all other groups, list the elements concerned in order of Z. Increasing Z = the foundation of the periodic system. I'm aiming for cognitive congruence here not dissonance. Sandbh (talk) 09:11, 9 January 2020 (UTC)

@Sandbh: But once you read it left to right within each row, and row by row (which is the normal reading order), it is in order of increasing Z regardless of whether you show it as Sc-Y-La or Sc-Y-Lu. Double sharp (talk) 09:22, 9 January 2020 (UTC)

@Double sharp: Yes, I follow that. The cognitive dissonance arises when IUPAC says the rare earths are Sc, Y, La to Lu. In an La table you can see that Sc-Y-La overlaps with La to Lu. In an Lu table the rare earths appear to be…well, I don't know what they are. You can't get to Sc, Y, La to Lu, without going backwards at some point. Sandbh (talk) 10:02, 9 January 2020 (UTC)

@Sandbh: They still form a continuous series defined by continuous sets of rows and columns that can be read left to right in each row. Double sharp (talk) 11:28, 9 January 2020 (UTC)

@Sandbh: I usually say that rare earths are IIIB from Sc to Lu and 4f from La to Yb. Droog Andrey (talk) 12:32, 9 January 2020 (UTC)

@Droog Andrey: @Double sharp: It’s clear I need a major relook at this part of the article. Perhaps my argument should be that the REM in a ScYLu table appear odd since they represent the only set of elements in which the second component (i.e. the Ln namely La-Lu) starts with a lower Z (57) than the end of the first component i.e. the ScYLu triad as a subset of Group 3 (71). I’ve probably just repeated my earlier observation that the REM in option 2 (ScYLu) can’t be straightened out into a continuous line. They can in your head; they can’t in the conventional 2D PT since the horizontal, vertical, and diagonal trends that characterise it are based on an increasing sequence of atomic numbers. That works for the REM in an La table but not in an Lu table. Sandbh (talk) 04:10, 10 January 2020 (UTC)

@Sandbh: Post-transition metals look about like that too if you consider group 12 as a post-transition group, with them starting in group 13 in period 3, but in group 12 for the later periods. What does it matter? And why is it important to straighten out sets of elements into a continuous line, when the PT is 2D, and both the horizontal and vertical neighbours are significant? Double sharp (talk) 04:38, 10 January 2020 (UTC)

@Double sharp:That’s a good observation about the PTM. I think I know what I meant to say all along. The 18 groups, the Ln, and An appear in order of increasing Z. This also applies to the RE in an La table, but not in an Lu table. I haven’t said anything different here but it is expressed more clearly. Sandbh (talk) 21:57, 10 January 2020 (UTC)

@Sandbh: OK, I think I finally understand what you are saying: if you force the above arrangements topologically into a straight line by forgetting about everything but which cell is next to which cell, then indeed Sc-Y-La produces a sequence in atomic number order and Sc-Y-Lu doesn't. However, I question the strength of this argument: to me it seems completely inconsequential. They always appear in the order of increasing Z if you just read every row from left to right, just like anything else on the periodic table, and in just the way you read everything else including this text, which does not involve bending anything into a straight-line arrangement at all. Even on a Sc-Y-Lu 18-column table you are going to have some asterisks before Lu telling you to go down and read the insertion of La through Yb first. Isn't this bending all pretty artificial anyway? Where does this argument end up for a completely 2D arrangement like the transition metals, where you can't flatten it into a 1D straight line at all? But of course, no one has any trouble reading the TM's in order of increasing Z even if Cu and Zn are not adjacent to Y in any way. Double sharp (talk) 13:38, 12 January 2020 (UTC)

@Double sharp: It think it’s a philosophical argument based on the foundational nature of the horizontal and vertical relationships seen in the 18 groups, Ln, An, and REM, all of which feature contiguous increasing Z. There’s nothing artificial about that. It goes deeper than L to R reading. Sandbh (talk) 04:01, 13 January 2020 (UTC)

@Sandbh: But important classifications such as transition metals, nonmetals, etc. don't feature contiguous increasing Z, whereas every single one of them does if you just read from left to right (inherited from the periodic table's layout). And bending a line of elements into a straight line, when it isn't actually straight in the PT, already requires artificially pulling it away from a more chemically sensible 2D arrangement. Double sharp (talk) 04:05, 13 January 2020 (UTC)

@Double sharp: I think we're talking about different concepts. One is about IUPAC periodic groups and series; the other is about metallicity regions in the table as we do with our own Wikipedia table. It's a bugger I have to keep going on about this but I get hammered about the importance of vertical groups and horizontal series in increasing order of Z all the time. This is not about L-R reading order, its a philosophical argument about the "regularity" of trends in groups and series. In this philosophical context an Lu table is less regular than an La table. Sandbh (talk) 04:25, 15 January 2020 (UTC)

@Sandbh: REM is not a group. It doesn't stretch to period 7, and even if it did, group 3 shouldn't contain 32 elements. So comparisons to other classes of chemically similar elements like transition metals or platinum group metals is absolutely relevant, and then the lack of Z order is no big deal since the PGM cannot even be flattened out into 1D without breaking any neighbours. (Not that it ever was in the first place IMHO, since "unfolding" the group into 1D breaks the arrangement of the periodic table in the first place that we are supposed to be justifying.) So I continue to be totally unconvinced by this philosophical argument since it's totally irrelevant to almost any other series of a similar type to REM. Double sharp (talk) 05:16, 15 January 2020 (UTC)

@Double sharp: The REM are recognised by IUPAC in the Red Book, as are the Ln and An. So there are 18 groups with vertically increasing contiguous Z, one series with increasing Z contiguously going around a corner (Sc, Y, and the Ln), and two series with horizontal contiguously increasing Z (Ln and An). These are the key vertical and horizontal trends. The horizontal discontiguous trends along the transition metals are of secondary import. Sandbh (talk) 23:08, 15 January 2020 (UTC)

@Sandbh: So then why are we mixing the vertical trend across the group 3 column with the horizontal trend across the Ln? They can overlap at Lu, but they're different lines. Where is the chemical sense in the trend Sc-Y-La-Ce-Pr-...-.Yb-Lu, rather than subsets of it? Double sharp (talk) 09:37, 16 January 2020 (UTC)

@Double sharp: The mixing of the vertical and the horizontal occurs with either option. Discussions of the rare earths list them in order of Z. The trends can then be discussed as Sc-->La-->Lu, rather than the "cumbersome" Sc-->Lu and La-->Lu. I did recently see a graph of the ionic radii of Sc-->La-->Lu, with Ce to Lu shown as not having a contraction, compared to them having the contraction. Sandbh (talk) 00:24, 18 January 2020 (UTC)

@Sandbh: Sc-->La is a useful trend, but so is Sc-->Lu, so in any case you will want to show both to give an idea of what is happening in group 3. And once you do that you are going to have separate overlapping horizontal and vertical trends anyway, so why not do that instead of pouncing on the fact that one glues in "the right order"?, even if a trend starting Sc-Y-La-Ce-Pr doesn't really make any sense when you graph it? Double sharp (talk) 10:03, 19 January 2020 (UTC)

@Double sharp: My clumsy wording may not have helped. By Sc-->La-->Lu, I mean Sc²¹-->Y³⁹-->La⁵⁷ and then La⁵⁷-->Ce⁵⁸-->Lu⁷¹. On the other hand, Sc²¹-->Y³⁹-->Lu⁷¹, followed by La⁵⁷-->Lu⁷¹ is cumbersome, irregular, and backwards even. The Sc-Y-La-Ce-Pr trend makes sense if you graph it and include a Ce-->Pr--> etc line showing the trend without the Ln contraction. Sandbh (talk) 06:53, 20 January 2020 (UTC)

So what if it is backwards? They are two separate trends, you don't need to glue them together. You can show B-->Al-->Ga as a trend along with (Ca)-->Sc-->Ti-->…-->Zn-->Ga to show the d-block contraction as well as the group 13 trend, but that doesn't mean that B-->Al-->Ga is somehow creating a backwards trend and B-->Al-->Sc would be better. Double sharp (talk) 17:08, 22 January 2020 (UTC)

@Double sharp: It’s cognitively dissonant with the relevance of increasing Z seen everywhere in the PT. Sandbh (talk) 08:36, 23 January 2020 (UTC)

Well, so is B-->Al-->Ga combined with a d-block contraction trend (comparing Sc with what Ga ends up as, as they differ more or less by 3d¹⁰). Is that an argument for B-->Al-->Sc? I doubt it. We have two trends, each with increasing Z, that happen to intersect: Sc-->Y-->Lu and La-->Ce-->…-->Yb-->Lu. Increasing Z is respected within each trend. Only when you glue them together is there any problem, but it is artificial since there was never any reason to do it in the first place. If you interpolate and extrapolate within a trend like Sc-->Y-->Lu-->Lr, or even Sc-->Y-->La-->Ac, you get actually relevant results. Where is the sense of Sc-->Y-->La-->Ce-->…-->Lu, again? And where do the poor actinides end up, with Ac so close to La in chemistry, and Lr so close to Lu (never mind the odd p-electron that seems to mean nothing chemically)? Double sharp (talk) 11:52, 23 January 2020 (UTC)

@Double sharp: No it isn’t, given they are all p elements. I’ve already explained the sense of the rare earths in terms of increasing Z, and showing what would happen if there was no contraction. I have no particular interest in opening up the 5f can of worms more than I already have, noting they less or more fall into line under the 4f series. Sandbh (talk) 06:08, 24 January 2020 (UTC)

A trend that continues from Sc, Y, La and then to Ce does not make any sense, mathematical, chemical, or otherwise. If you extrapolate downwards given such a trend the only sensible thing to put there is Ac. That's why I stand by the statement that you are forcing two separate trends together, cutting off the 7th period artificially (yes, totally artificially, or else why does the periodic table go past Rn?), and arguing about how the gluing comes out. When in actuality the gluing does not make sense in the first place. So for B-Al-Ga you have to appeal to blocks instead to get the conclusion you want; well, in that case, Lu is far more like a d-element than La is, and we're back to Sc-Y-Lu. Double sharp (talk) 17:07, 24 January 2020 (UTC)

References

Hevesy G 1929, Redkie zemeli s tochki zreniya stroeniya atoma, (Rare earths from the point of view of structure of atom), NKhTI, Lenningrad, cited in Trifonov 1970
Greenwood NN & Earnshaw A 2002, Chemistry of the elements, 2nd ed., Butterworth-Heinemann, Oxford
Greenwood NN & Harrington TJ 1973, The chemistry of the transition elements, Clarendon Press, Oxford
Lee JD 1996, Concise inorganic chemistry, 5th ed., Blackwell Science, Oxford
Stewart 2018a, “Tetrahedral and spherical representations of the periodic system”, Foundations of chemistry, vol. 20, pp. 111–120
Trifonov DN 1970, Rare-earth elements and their position in the periodic system, translated from the 1966 Russian edition, Academy of Sciences of the USSR Institute of the History of Natural Sciences and Technology, Moscow, published for the Atomic Energy Commission and the National Science Foundation, Washington, by the Indian National Scientific Documentation Centre

@Sandbh: An overall impression is that the article provides enough opinions from literature, but lacks analysis of chemistry. Droog Andrey (talk) 12:38, 9 January 2020 (UTC)

@Droog Anthony: Thank you. That’s probably ok since the article is premised on the supposition that the question can’t be resolved on the basis of a comparison of individual physical, chemical or electric properties. Sandbh (talk) 07:27, 10 January 2020 (UTC)

@Sandbh: Why do you repeatedly distort my nickname? Droog Andrey (talk) 09:51, 15 January 2020 (UTC)

@Droog Andrey: That's my fault, sorry. I subconsciously had the Doug Anthony All Stars on my mind. Sandbh (talk) 23:33, 15 January 2020 (UTC)

Horizontal triads

@Double sharp: Can I revisit this, last discussed in Archive 40.

It's the recurring sequence of maximum oxidation numbers of +2, +3, and +4. This happens for the following sets of horizontal triads (P = period):

P +2 +3 +4
==========
2 Be B  C
----------
3 Mg Al Si
----------
4 Ca Sc Ti
4 Zn Ga Ge
----------
5 Sr Y  Zr
5 Cd In Sn
----------
6 Ba La Ce
6 Hg Tl Pb 
----------
7 Ra Ac Th

Whereas Sc, Y, La, and Ac are the middle elements of such horizontal triads, Lu and Lr are not:

Yb (+3) Lu (+3) Hf (+4)
No (+3) Lr (+3) Rf (+4)

This seems to be another example of where an La table is more regular than an Lu table.

Last time you responded by focussing on what happens in the rest of that table. That's not relevant since I'm only interested in the implications for group 3. Sandbh (talk) 06:42, 17 January 2020 (UTC)

That is completely relevant in my opinion, because you can't expect a criterion that doesn't work for most of the table to be a relevant rather than an overly localised one. Besides, where are we going to be with Cn (+4) Nh (+3) Fl (+2), like I said? Double sharp (talk) 10:01, 19 January 2020 (UTC)

@Double sharp: I'm only noting that an Lu table is less regular than an La table, wrt these oxidation state triads. What happens to Cn (+4) Nh (+3) Fl (+2) makes no difference. What's happening in the rest of the table is irrelevant to this particular pattern encompassing group 3. Sandbh (talk) 07:07, 20 January 2020 (UTC)

@Sandbh: That's the whole point. How is this an important criterion for regularity when it cannot extend to the whole table? If we want a philosophical justification IMHO it must make sense for the PT as a whole rather than just be an ad hoc situation for part of one group. Double sharp (talk) 14:44, 20 January 2020 (UTC)

@Double sharp: It can be applied to the whole PT, just like the n + l rule can be applied to the whole table. In both cases it makes no difference to the overall result. Sandbh (talk) 08:40, 23 January 2020 (UTC)

So how does group 16 look under such a criterion, when the maximum oxidation state of O breaks the pattern from S downwards? This is why for periodicity it makes more sense not to look at maximum oxidation states but at all significant ones. Clearly Mendeleev must have done this too, since he put O in group VI and F in group VII. And then there is no problematic difference in regularity, because Yb and No have a significant +2 state as well. Double sharp (talk) 11:50, 23 January 2020 (UTC)

@Double sharp: I don’t know and I don’t care. The outcome would be the same for an Lu table or an La table. Sandbh (talk) 05:58, 24 January 2020 (UTC)

So, as it stands, it doesn't make sense as a criterion. If we correct it to consider all significant oxidation states, it becomes more sensible. But then it is inconclusive between Sc-Y-La and Sc-Y-Lu, correctly highlighting the small difference involved. Double sharp (talk) 17:01, 24 January 2020 (UTC)

@Double sharp: It doesn’t need correcting. It is a criterion based on maximum oxidation state, which is fine by itself. Like I have repeatedly said, extending the criterion to the rest of the table makes no difference. The 234 pattern is only present in an La table. End of story. Sandbh (talk) 11:58, 25 January 2020 (UTC)

I can make an infinite number of criteria, applicable only to one group, that will conclusively point to any possible next element for it and declare everything else to create an irregularity. And in the absence of evidence why each of these criteria should be upgraded to the status of a law of the periodic table, which means seeing if they actually apply in any significant other part of the periodic table it wasn't invented for, their relevances will all be equal: that is, equal to zero. That's why I insist that a criterion must meet that minimal standard. Respectfully, a criterion like this one, which considers N to be an irregularity because it breaks the recurring sequence of 456 oxidation states, does not meet it. IMHO it also fails the test of looking only at relevancies. Suppose Hg did happen to show a +4 state after all: does that in any way weaken Tl as a group 13 element for breaking this pattern? Double sharp (talk) 12:33, 25 January 2020 (UTC)

Coordination complexes of the lanthanides: a case study

Consider the complexes Ln(2,2′-bipyridine-1,1′-dioxide)₄](ClO₄)₃, studied in this 2002 article.

As the lanthanide ion Ln³⁺ gets smaller, we of course have a difference in geometry due to steric hindrance. But it is revealing what exactly these differences are, because it reveals something that appears quite significant when it comes to 4f involvement.

The shapes of the La and Ce complexes are almost perfect cubic. Although this demands only 8-coordination, symmetry grounds force us to posit 4f involvement because of this shape – including for La!

Once we get to Pr and Nd, some symmetry is lost, and we arrive at a slightly distorted snub disphenoid. At Eu we have lost enough symmetry that there are now two crystallographically different types of Eu³⁺ ions, and this structure appears to hold at Ho as well. But at Lu³⁺ we have distorted the cube, it appears mostly continuously, all the way to a slightly distorted square antiprism, which (since it is a known geometry for Xe) clearly requires no invocation of f-involvement.

I find this pretty revealing. Since 4f energy is highest for La and Ce, and should go down gradually while it sinks into the core, I suspect the change in shape may be related to the lowering 4f contribution, though I regret that I am not well-versed enough in f-block chemistry to say that for sure. ^_^ Double sharp (talk) 17:28, 22 January 2020 (UTC)

@Double sharp: Yes, I’ve seen speculation about 4f orbital involvement by La on symmetry grounds but nothing more. That article says naught about this. If there is something to it then it strikes me as being similar to d orbital involvement in the incipient transition metals Ca, Sr and Ba. Sandbh (talk) 09:06, 23 January 2020 (UTC)

So we have exactly the same situation in the f-block as we have in the d-block: Ca through Zn all have some d-involvement, and so do La through Lu. But the reason why we put Zn, Cd, and Hg in the d-block, and not Ca, Sr, and Ba, is simply that:

The d-block cannot fit eleven columns, so we must decide which one is more anomalous for the d-block, and clearly it's Ca-Sr-Ba:
Putting Ca-Sr-Ba as an s-block group gives the right idea that the s² shell is the covering one for the most part:
And the energy level of the d subshell increases down group 12 relatively speaking (to the point that at Cn it is expected to become chemically active), so it is clearly not yet a core subshell.

If we apply these principles to the f-block question, (1) and (3) clearly favour La as an f-block element. (2) also gives the right idea for the gas phase that it is 4f-5d that are the chemically relevant occupied subshells in ions and 6s is mostly ionised away and empty. If we put Lu as an f-block element, then we're sort of implying that 5d6s² always gets ionised away, which is weird when you consider configurations like La²⁺ [Xe]5d¹ in compounds. You never see 6s occupied in a Ln²⁺ or Ln³⁺ or Ln⁴⁺ ion, but you might see 5d and you will almost always see 4f, suggesting that the difference is between 6s and the others. Double sharp (talk) 11:49, 23 January 2020 (UTC)

Lanthanide contraction

I’ve talked about this before in another context.

Goldschmidt's Ln contraction, which is caused by poor shielding from the f-electrons, starts at Ce³⁺ [Xe]4f¹ and finishes in Lu, since Yb³⁺ is [Xe]4f¹³, and Lu³⁺ is [Xe]4f¹⁴. Same thing happens with the actinides.

In an La table the cause of contraction naturally spans the f block as Ce to Lu. Form and cause are harmonised. In an Lu table the cause of contraction does not start until the second element of the f block; the cause of the contraction then finishes after the end of the f-block, in the d-block (1st element, period 6). Form and cause are disaggregated.

That is to say, in an La table the cause is congruent with its associated boundaries whereas in an Lu table the cause is misaligned with these boundaries.

OTOH, in an Lu table the number of f electrons in each individual Ln in the gas phase mostly matches its position in the f-block. Then again, in an La table the number of f electrons in the trivalent ions perfectly matches their f block position number.

In the above light I’d conclude that the La table is a better chemical table, in the context of the Ln contraction. Sandbh (talk) 05:27, 12 January 2020 (UTC)

That's not all there is to it, actually:

The contraction readily extrapolates backward to the case of La³⁺ at [Xe]4f⁰, which is (as everyone expected) bigger than Ce³⁺. Such contractions are common enough throughout the entire table. Just look at Y³⁺ through Ag³⁺, for example, or look at the atomic radii of neutral Li through Ne. They are just more significant in the Ln than anywhere else because they are all usually in the same oxidation state and the noise that usually wipes these contractions out into irrelevance disappears. But then it becomes important to include La as part of the effect.

This is not directly relevant to my argument. La is not a part of the Ln contraction per se, since the filling of the f orbital has not yet started. Of course, the knock-on effects are felt from Hf onwards, but this is easily distinguished in that the number of f electrons in the applicable ion peaks at Lu. Sandbh (talk) 10:24, 12 January 2020 (UTC)

@Sandbh: Yes it is because part of the point of the lanthanide contraction is that each Ln is smaller than its predecessor because it has one more poorly shielding f electron that doesn't offset very well the effect of one more proton in the nucleus. And then La vs Ce is relevant because 0 + 1 = 1. Double sharp (talk) 05:20, 15 January 2020 (UTC)

Another effect of the Ln contraction is that the 5d series that comes after it is made much more similar to the 4d series than you would otherwise expect, because it almost exactly cancels out the expected increase in atomic radius. In a Lu table, the whole 5d series from Lu to Hg is uniformly affected. In a La table, La is the odd man out from Hf to Hg. The 5d series then becomes less homogeneous because obviously Lu is more similar to the 5d transition metals than La (look at just about any properties: coordination chemistry, melting and boiling points, hardness...)

Double sharp (talk) 06:21, 12 January 2020 (UTC)

@Double sharp: This is another good example of focussing on minutiae while ignoring predominating characteristics. IUPAC submission Double sharp (IDS) would’ve demolished this one.

In the absence of IDS I’ll step up to the plate.

Rather than dwelling upon minutiae let’s look at general characteristics.

Metallurgically speaking we know that Lu resembles closely erbium and holmium, except that it melts at a slightly higher temperature and is essentially non-magnetic, while the details of producing, purifying and fabricating it are almost identical with those applicable to holmium.

Restrepo separately found that Lu ended up in a cluster with Er and Ho and that Lu is more similar to lanthanoids than to transition metals, while La share similarities with lanthanoids and with transition metals.

Like DIM, Restrepo based his work compounds and their proportions of combination.

Case closed! Demolition complete! Send in the clean up crew :) Sandbh (talk) 23:41, 25 January 2020 (UTC)

As I keep saying: Restrepo is only considering resemblances between stoichiometrically identical compounds. Such an argument will never find any similarities between elements from different groups, even when they are relevant. (And indeed, my case for Sc-Y-La was more sophisticated, based on delayed collapses and condensed-phase configurations, until Droog Andrey kindly explained back in Archive 33 what the problem with them was.) I'm also not terribly thrilled about separating "IDS" from "current DS" as if we are separate people. Current DS just knows more chemistry and had his actually not-so-bad Sc-Y-La arguments very kindly critiqued and explained by Droog Andrey in archive 33. His logical style is the same; it's just that now he's combating bad Sc-Y-La arguments instead of bad Sc-Y-Lu arguments. There are a lot of bad Sc-Y-Lu arguments in the submission that I am quite happy to stand by my 2016 criticism of. There are also some where I think our initial criticism was true but not the full story. But there are also some, like this one, where I think we missed the point of the original argument.

Again, surely no one is disputing that Lu closely resembles the late lanthanides. Equally well, La closely resembles the early lanthanides. No one is arguing that Lu is not a lanthanide. No one is arguing that La is not a lanthanide. I am arguing that among La and Lu, Lu has more transition metal properties. Not only is this just obvious from looking at all properties, and certainly not minutiae (unless just about all properties are minutiae, since it affects melting points, hardness, etc.), our submission even mentions a paper that does exactly this: https://link.springer.com/article/10.1007%2Fs11837-014-1247-x. We critiqued it by saying that the authors go too far by saying that Lu is a transition metal, and I agree with that: it's also a lanthanide, not only a transition metal, and clearly it is more similar to the other lanthanides than the transition metals. But come on, so is La. Double sharp (talk) 00:00, 26 January 2020 (UTC)

Here is a short summary of my logic, since I think you may have misunderstood it:

La and Lu are obviously very normal lanthanides, and no one is disputing that.
However, we want to give one of them the 5d¹ position.
Therefore we must find which one is closer to the metals Hf through Hg in the 5d² through 5d¹⁰ positions. Notice that nothing in this denies that both La and Lu are close to the early and late f-block lanthanides respectively. Those are obviously their closest kin chemically. We just want to make the d-block as homogeneous as possible.
And obviously, in spite of Restrepo (whose argument I have demolished several times identically already), the answer is Lu. Just compare melting points. Or boiling points. Or coordination power. Or density. Or hardness. Or just about anything else. If these are "minutiae", we have nothing at all to draw a periodic table based on, and we can all pack up and go home.

Double sharp (talk) 00:03, 26 January 2020 (UTC)

@Double sharp: Nice. Thanks for that.

As well as Restrepo’s peer-reviewed article, here’s another paper showing La is not close to the Ln but instead falls into a cluster with 1 and 2 metals. [Of course the story is more involved than that but the broad contours are there]. So much for La as a normal Ln. See how Lu falls into the same cluster as the Ln. And what about, as I’ve noted elsewhere, the metallurgy etc of Lu showing it closely resembles that of Ho and Er? Your line of reasoning doesn’t hold up. Sandbh (talk) 10:40, 26 January 2020 (UTC)

While I am a bit sceptical about anything separating La from Ce, Pr, and Nd, which are so similar that lanthanum-gobbling bacteria don't even notice which of them they got, notice how the cluster La falls into is with group 1 and 2 metals. In other words, not transition metals. So it is clearly even farther away from being like Hf through Hg, which we are trying to mimic for the first 5d position.
Once again, the whole point is not "which one is more like a normal lanthanide". The whole point is "which one is closer to the metals Hf through Hg" (my point 3 previously). I put it to you that this supports that the answer is not La. And just plot all those properties, you'll see the answer is almost 100% skewed towards Lu (see my point 4).
(If comparing to nine elements at once is confusing: here is an even bigger simplification. Compare the pairs La-Hf and Lu-Hf. Everyone can see that the second pair has more in common.)
And just to hammer the point home: do the same thing for Ac vs Lr. Not only will you find that Lr is by far closer to Rf through Cn, you will find that lawrencium is in fact extremely weird for a late actinide by preferring trivalency! Actinium, in going for the maximum oxidation state it can muster, fits pretty well with thorium through uranium, at least.
And if any further proof were needed, the 6f series is expected to side with the 5f series, not the 4f series. Seaborg seems to have been completely right when he predicted prophetically that if we could have a very extended table with numerous "f" series, like we could with "d" series, "p" series, and "s" series, we would find that the actinides are more representative of typical f-elements than the lanthanides. The first row is always anomalous.
For that reason, the following principle should hold for La vs. Lu arguments: the actinides overrule the lanthanides. Just like normal p-behaviour is 3p onwards, normal s-behaviour is 2s onwards, and normal d-behaviour is 4d onwards: normal f-behaviour should be taken as 5f (since we currently do not have the 6f elements to examine). So: if looking at the lanthanides is inconclusive, but looking at the actinides is conclusive, we follow the actinides by the principle of looking at more representative examples of each category (here, f-elements). This is not slavish devotion to the Madelung rule; we know the first-row anomaly in each block really well, and it is well-known that the cause is the absence of radial nodes (see Kaupp's paper). And deriving their presence or absence is almost pure mathematics: solve the Schrodinger equation. (See this Chemistry Stack Exchange answer.)
In this case, of course, this principle is only needed for confirmation. The 5d homogeneity argument favours Lu quite clearly; the 6d homogeneity argument if anything favours Lr even more clearly. Therefore, Sc-Y-Lu-Lr is the recommended version by them. Double sharp (talk) 10:44, 26 January 2020 (UTC)

@Double sharp: This is a good example of ignoring the broad contours and delving into details (noise) and struggling to draw attention away from the findings of the article since it does not support your view.

Note that Lu falls into the Ce-Yb etc cluster, rather than the transition metals.

In the article, La is as much a TM as is Lu. La has the same colour as Au an Hg; ditto Lu for Os Ir.

Colour wise, La would fit better under Y and Lu (and Lr) would fit more naturally at the end of the f-block.

The authors did not recommend Sc-Y-Lu-Lr; they just happened to use the WebElements table.

As per my recent post, the issue is not block homogeneity or similarity in terms of details but chemical behaviour and periodic trends. Sandbh (talk) 02:28, 2 February 2020 (UTC)

@Sandbh: If you have any sense of chemistry left, and not just parroting classification papers, you should realise that a resemblance from La to the weak metals Au and Hg is simply laughable. Which sums up what I have to say about this. I don't ignore it because it is inconvenient. But because what you say about it suggests that it is chemical nonsense. Double sharp (talk) 10:30, 2 February 2020 (UTC)

In an Lu table, Lu to Hg are not uniformly affected since the effect peaks at Lu and diminishes thereafter. In an La table, La is not the odd man per se, but rather Hf onwards are odd due to the impact of the intervening Ln contraction. I do agree La is more similar to Ba. Lu is quite a good heavy Ln based at least on its occurrence, method of preparation, mechanical properties, reactivity IIRC), and the stoichometry of its binary compounds. Sandbh (talk) 10:24, 12 January 2020 (UTC)

@Sandbh: That's bad use of language on my part, sorry: I mean that all ten of Lu through Hg are affected, whereas if you make your d-block La + Hf through Hg only nine are. Still, it makes a more sensible trend if the effect peaks at the first one and then goes down monotonically, as we get with the Lu table, than if we start with no effect, and then have a huge jump for the second element before going back down monotonically (and yet not to zero again), as we get with the La table.

As for Hf onwards being odd, allow me to quote Restrepo back at you ^_^: 'Although the Zr-Hf similarity is well documented in the literature, it is striking to find that it is considered an exception, “due to an anomalous cancellation of relativistic effects,” of the differences between 5th- and 6th-row elements of the same group (30, 31). In the current study we found that out of the 17 possible pairs of 5th- and 6th-row elements belonging to a group, there are other five pairs sharing similarities: {Nb,Ta}, {Mo,W}, {Tc,Re}, {Ru,Os} and {Rh,Ir}.' But if most of the 5d elements are showing it, it's hardly exceptional behaviour! Indeed it's more exceptional if it doesn't happen! The Ln contraction is less visible for groups 10 through 12 but still can be seen in atomic radii; in that case, truly everyone in the 5d stretch is showing it, except for La if we insist on shoving it in; doesn't that make it more obviously out of place? Here we have an entire paragraph in italics, so to speak, and what is unusual is the roman type (just like how we indeed use roman type to emphasise something in an all-italics passage).

Yes, Lu makes a good heavy Ln. La also makes a good light Ln, and nobody here is saying that La or Lu is not a lanthanide. They obviously both are, and that is completely irrelevant for the group 3 question because it is so inconclusive. What we are trying to do instead is to determine which one is the d-block lanthanide, as we know that there is one. And to do that we compare each of La and Lu with the elements that we know are supposed to be 5d metals, not the lanthanides. So: which distance is closer, La to Hf-Hg, or Lu to Hf-Hg? It's really obvious that the answer is Lu, Restrepo not withstanding. When he opines that his work favours La under Y on the grounds of greater resemblance to transition metals, he seems to have overlooked that once you are considering only stoichiometry, you can never notice similarities between elements with different valences (which is why all the famous diagonal relationships fail to show up on his chart), and so you cannot usefully compare the pairs {La vs. Hf-Hg} and {Lu vs. Hf-Hg} using that methodology. So of course the only transition metals that he gets as similar to La are Sc and Y (no surprise at all, as they are also REMs), and judging from the cyan colour all those REMs have in the background the distances are all negligible for Lu too (as everyone could have guessed from atomic radii and reading Greenwood and Earnshaw). Double sharp (talk) 13:34, 12 January 2020 (UTC)

@Double sharp: I think you are too focussed on the 18-column table, in which there is some abstraction of detail caused by the footnoting of the Ln/An. In a 32-column table the Ln contraction is smoothly and precisely seen in the interposing f-block, between group 3 and group 4 i.e. from Ce to Lu. The knock-on consequences are then felt starting from Hf, which is a visually more accurate presentation, rather than mushing the end of the contraction and the start of its consequences in the 5th row of the d-block.

I agree with Restrepo and am not familiar with Zr/Hf being viewed as an "isolated" anomaly.

He compared La and and Lu to the rest of the Ln largely on the basis of the trivalency of all the elements involved. There was no valence mismatch for La and Lu since all the elements involved were rare earths. As noted in the Periodic law section, the vertical trends are more important than the horizontal trends. There is no overwhelming case for overturning the periodic law, which says that La goes below Y, and is consistent with the behaviour of group 3 as trivalent group 1 to 2 equivalents. Sandbh (talk) 05:50, 15 January 2020 (UTC)

@Sandbh: In a 32-column table the Ln contraction is going to cut across blocks anyway, because the effect is that each Ln is smaller than its predecessor because it adds an f-electron (including Ce smaller than La). So you'll have one d-block lanthanide and fourteen f-block lanthanides anyway, and it smears across both. So the relevant thing, as I have been saying for the last few days, to find which one the d-block lanthanide is to find with lanthanide is most d-block-like. Lu clearly qualifies. And as I mentioned above, the periodic law does not say "look for the next analogue" (or else Sc goes below Al), but "look for the next analogue with the same valence structure". For Y this is Lu, not La, because for La we have an empty 4f that has some relevance, but for Lu we don't have that possibility as 4f is stuck in the core. Double sharp (talk) 06:48, 15 January 2020 (UTC)

@Double sharp: Yes, I agree about the 32-column table. It goes groups 1-2 as part of the s-block; group 3 as d-block; the f-block as Ce to Lu, and then group 4 onwards. Chemically, the Ln contraction per se starts in the f-block with Ce³⁺ as [Xe]4^f1 and finishes in the f-block with Lu³⁺ as [Xe]4f¹⁴. There is no smearing of the contraction across blocks. Let's recall that historically the Ln were the elements like La, and thus did not include La. We can however see why Ce to Lu are like the Ln, and understand the laziness of including La as an Ln. The structure going down group 3 is consistently [NG] d¹s². The structure of the 6d row, starting with Hf, is perturbed by the intrusion of the 4f shell, so group 4 for example vertically goes [NG] d¹s²; [NG] d¹s²; [NG] 4f¹⁴d¹s².

@Sandbh: The more we speak "chemically", the more it becomes silly pedantry to exclude La from all effects about atomic size that are so important for the lanthanides. Where is the difference between, say, La^III chemistry and Pr^III chemistry? (Ignoring redox.) And since when is the introduction of a 4f shell a perturbation? By that logic, it looks like every other row in the periodic table is perturbed, e.g. Ga-Kr add a d shell over Al-Ar, Tl-Rn add an f shell over In-Xe. This is not a perturbation, this is a common thing that comes straight out of the two-rows-at-a-time shape of the periodic table. It would be a real perturbation to insist that group 3, alone among the groups that start a new row in a p-, d-, or f-block, never show this. Double sharp (talk) 09:40, 16 January 2020 (UTC)

@Double sharp: It isn't pedantry IMO. It's about clarity, cognitive congruence, and accuracy as to cause and effect. The s and p blocks are fairly harmonious. The d-block and the f-block mess up the sp tea party, with their anomalous configurations, and this gets worse the further down the table we go. God knows what sort of mess the g-block, should we ever get there, will make. An Lu table obscures the perturbation by starting the f block at La. It's about showing the table as it really is rather than how we'd like it to be (I don't think that applies to you, but it certainly applies to LST aficionados, where the push for Lu in group 3 is coming from). Sandbh (talk) 06:24, 17 January 2020 (UTC)

@Double sharp: On the d and f block as perturbations see here.

@Sandbh: To me it is rather the anomalous configurations that are the perturbations. I mean, look at group 5: niobium is d⁴s¹, tantalum is d³s². Does it make much difference to their chemistry? Honestly no, they are so similar. Lutetium is ds², lawrencium is s²p. So what? Can't we just mentally call it just the group with five s and d valence electrons (mostly d in compounds), never mind where they are? The important thing is just:

In the same column, the number of valence electrons is supposed to stay constant.
In the same column, the types of valence electrons is supposed to stay constant whenever it is possible. (You can think of helium as a degenerate case with no valence electrons, if you don't want to move it to go on top of beryllium.) What this means is that the available subshells for hybridisation should not change when you can help it: in the d-block they should be dsp, in the f-block they should be fdsp, in the g-block they should be gfdsp. There is a minor difficulty that arises for group 2 (which has some incipient transition behaviour), but you cannot help that.
The cores change regularly down each column. They go to the next noble gas configuration, plus filling the subshells that have been inserted in later rows. So we expect the core in the 3p elements to be [Ar], but in the 4p ones to be [Kr]4d¹⁰. In other words: OK, inserting the d- and f- (later g-) blocks are a perturbation, but a completely regular and predictable perturbation, so let's show that.

Once you put it that way the anomalous configurations don't really mean anything. Which makes sense, because they certainly don't seem to mean anything for chemistry! Why do we have to show the second-order perturbation of delayed collapse in the periodic table, then, when it certainly doesn't seem to lessen the big divide between La and every other 5d element? We're not suggesting to move Lr into the p-block, so why must La move into the d-block for the same reason? (And if you show the perturbations in the early g-block you'll never end up drawing anything at all, judging by the predictions where 8p, 7d, 6f, and 5g start filling at E121, E122, E123, and E125 respectively.) Double sharp (talk) 09:58, 19 January 2020 (UTC)

Relevance of anomalous ground-state configurations

@Double sharp: Anomalous configurations can make a difference to chemistry.

Take Group 11, for example, and their schizoid transition metal/main group chemistry that arises due to their anomalous configurations.

A rather doubtful statement in my opinion, since Rg should have a 6d⁹7s² ground state and yet be a good heavier homologue of Au. Ag has a d⁹s² state at 3.7495 eV (NIST tables) again, and for Cu and Au they are even lower down. All well within chemical bond energy range. Double sharp (talk) 16:28, 3 February 2020 (UTC)

@Double sharp: Rg = fog. Cu, Ag, Au should have the configurations 3d⁹. In fact they are all 3d¹⁰ 4^s1, with Ag having an s differenting electron, rather than a d differenting electron. The result is that +1 is the most stable and common oxidation state for Ag in which it acts predominately like a main-group metal. This is a text book example of the chemical significance of a d/e. In Cu the d/e is a d electron. This has a significant impact on the electron configuration of and chemistry of Cu, since the preceding element Ni, is 3d⁸4s². The addition of a d electron to Ni results in 3d⁹4s². Energetically, it's more efficient to have a 3d¹⁰ sub-shell, so one of the two s electrons is shifted so that in the end the configuration of Cu is 3d¹⁰4s¹. So, rather than Cu being 3d⁹, and having only transition metal chemistry, it can also show main-group chemistry with the loss of its lone s electron. Here's another example of where a d/e has a significant impact on the chemistry of an element over and above what the n+1 rule tells us. Sandbh (talk) 04:17, 11 February 2020 (UTC)

@Sandbh: I don't see how Rg is fog here. Yes, it's severely unstable, but it is an element like any other that we put in the periodic table on the grounds of its predicted chemical properties. Nuclear properties are irrelevant for element placement in the PT. The fact that the chemistry of Rg should be close to that of Au, despite the configuration difference, suggests that the whole thing is rather weak here. The DE for Mn and Tc are s-electrons, whereas for Re and Bh they are d-electrons, but I do not see how Re and Bh are less main-group-like than Mn and Tc. Indeed it's more or less the opposite way round.

The differing behaviours of group 11 metals are simply explained from the relative energy differences between (n-1)d and ns (the chemically active valence subshells) at the end of the d-block. In Cu the gap is not so big, we see +1 and +2 states frequently. In Ag it is bigger, in Au it is smaller again because of relativistic destabilisation of 5d. That's what controls the ionisation energies and hence common oxidation states, not the differentiating electrons. Double sharp (talk) 12:14, 11 February 2020 (UTC)

@Double sharp: Well, my focus is not on the explanation of the differing behaviours of group 11 metals. My focus is at a higher, d/e anomaly level bearing in mind you were looking for examples of where the d/e make a difference. It's like the n+l rule, which is admired for its regularity, just by itself. Never mind the underlying explanation. Sandbh (talk) 23:07, 11 February 2020 (UTC)

@Sandbh: This is an astonishing statement. We need to look for the underlying explanation because that will lead us to the most basic possible basis for the PT. Only then will our focus be as high as the situation warrants. In every example you give of the DE's supposedly making a difference, I've demonstrated that the DE are not the cause of that difference. Either because the difference appears when the DE anomaly isn't present, or because the DE anomaly predicts a difference where there is not one. (In group 7 it even predicts exactly the opposite of reality.) Instead, in every case the cause is the energy levels of, you guessed it, chemically active valence subshells. That by all rights ought to be decisive. Just like Mendeleev's use of atomic weight has long been overthrown by atomic number. Double sharp (talk) 23:17, 11 February 2020 (UTC)

@Double sharp: I agree with Scerri who believes there is great merit in taking as philosophical, and as abstract as possible, an approach to the periodic table. It's not necessary to drill down. In group 11, for example, their dualistic behaviour is a byproduct of their anomalous configurations or d/e's i.e. d¹⁰s¹ as opposed to their expected configurations of d⁹.

@Sandbh: I've already debunked that reason. Where is the dualistic behaviour of Au? Why are there magically no repercussions on Mn/Tc having the s differentiating electron instead of the d one of Re/Bh? I say there is great merit in a philosophical and abstract approach if and only if it is also a relevant approach. Double sharp (talk) 23:54, 11 February 2020 (UTC)

@Double sharp: Eh? What kind of chemistry do you think +1 compounds of Au show?

@Sandbh: OK, I did not say what I meant to say, sorry. :) What I'm trying to get at is that Au has +3 as the dominant state, so it's not exactly an even split like Cu, or dominant main-group-like chemistry like Ag. For Au it's the main-group state that is uncharacteristic, and you cannot predict this from DE's. I don't disagree that Au(I) has main-group character but so does any TM oxidation state that reaches d⁰ or d¹⁰. The group 3 to 7 elements in their group oxidation states are basically like main-group elements since they reach d⁰, but where are the DE's to prove it? And Rg(I) is predicted to be a good heavy homologue of Au(I), forming the homologous cyanide complex; so it should be "main-group-like". Except, a free Rg⁺ ion is 6d⁸7s² (p. 1672). (Chemical environments should make it 6d¹⁰ due to 6d destabilisation, another case where we have to look at chemical environments rather than ground-state free gaseous atoms.)

You can't claim P is the big cause of Q if we very often have P and not-Q together, or not-P and yet Q. The important thing here is just: has the number of valence electrons dropped below 10 yet, or not? (Since in compounds the TM's are usually dⁿ.) That is important because you need a partially filled d-subshell to show TM properties (of course, DE's are completely silent about the later start of that in each period, whereas chemically active valence subshells explains it with aplomb.) And that happens even if group 11 was d⁹s², as we see in the case of Rg. Double sharp (talk) 07:50, 12 February 2020 (UTC)

@Double sharp: No matter. It's good to have an educated squabble.

Now then, here's example of you attempting to undermine one of my arguments, on the basis of an erroneous assumption. In this case you seek to do so by downplaying the significance of the +1 OS of Au. Never mind that our article on gold says, "The oxidation state of gold in its compounds ranges from −1 to +5, but Au(I) and Au(III) dominate its chemistry." It's the s d/e that enables this dualistic nature.

Steele 1966, The chemistry of the metallic elements, p. 67:

"The overlap in properties between the b-subgroup metals and the transition metals is shown in the properties of copper, silver, and gold. In their monovalent compounds they are typical b-subgroup elements. The d-electrons can, however, be used in bond formation to give compounds of the elements in the divalent and trivalent states. In these compounds the d-subshell is incomplete and their chemistry is typical of transition metal compounds."

Sandbh (talk) 01:03, 13 February 2020 (UTC)

Straight from Post-transition metal: "The chemistry of gold is dominated by its +3 valence state". And your last quote exactly supports my point. The reason for this change between B-subgroupness and transition-metal-ness in group 11 is not because of DE's. What matters is if the d-shell is incomplete or not. Just like what matter for the early transition metals is where the d-shell is occupied or not. Double sharp (talk) 19:31, 13 February 2020 (UTC)

The absence of an f electron in La means that its trivalent compounds don’t have any magnetic moment, unlike Ce to Yb. The accelerated completion of the 4f shell, over thirteen elements, results in Lu compounds having 0 magnetic moment.

That has nothing to do with La's configuration. Even if La was [Xe]4f¹6s² in the ground state, the 4f electron would be ionised away in La³⁺ anyway. Double sharp (talk) 16:24, 3 February 2020 (UTC)

@Double sharp: You're right, my response was poorly worded. Who knows what else I may have been trying to do at the time. I will say that the absence of an f electron in La means that its divalent compounds don’t have any magnetic moment, unlike Ce to Tm. Sandbh (talk) 04:17, 11 February 2020 (UTC)

Cerium(IV) compounds are finely balanced. The energy of the 4f electron is nearly the same as that of the outer 5d and 6s electrons that are delocalized in the metallic state, and only a small amount of energy is required to change the relative occupancy of these electronic levels. The 4f electron in cerocene, Ce(C₈H₈)₂, is poised ambiguously between being localized and delocalized and this compound is considered intermediate-valent.

So the important thing is the energy levels of the subshells, not the 4f¹5d¹6s² configuration that happens to be barely the ground state, with 4f¹5d²6s¹ 0.2937 eV above, and 4f²6s² 0.5905 eV above, according to NIST. You said it yourself, only a small amount of energy is required to change the relative occupancy of these electronic levels, and chemical bonds are enough to provide that. Lanthanum has a 4f¹6s² state at 1.8842 eV, which is well within the normal range of chemical bond energies (1 to 10 eV). The ground state for f- and d-block elements is often quite close to many excited states, that all contribute. (Why do you think the transition metals in group 3 through 10 are mostly dⁿs⁰ in compounds?) Double sharp (talk) 16:24, 3 February 2020 (UTC)

@Double sharp: Ce is peculiar since we expect its d/e (per n+l) to be a second f electron, to give it f²6s² and probably a stable +4 oxidation state, analogous to Th (I don't know what the condensed configuration of Ce would be, in this case). Instead, due to the delayed start of filling of the 4f sub-shell, the f d/e in Ce is only its first 4f electron, resulting in a configuration of 4f¹5d¹6s², and a stable +3 oxidation state, and a +4 oxidation state. Sandbh (talk) 04:17, 11 February 2020 (UTC)

@Sandbh: By that logic, consider Pa. Due to the delayed start of filling in 5f, two 5f electrons appear for the first time here, giving [Rn]5f²6d¹7s². Your analysis of Ce would lead you to predict a stable +3 state for Pa, but Pa(III) is an absolutely unstable rarity. The stable oxidation state is +5 (the "group" one), with marginally important +4, which is not at all what you would predict. So it seems that ground-state configuration analysis is not being consistently helpful here. Double sharp (talk) 12:07, 11 February 2020 (UTC)

Gd has an f⁷d¹s² configuration rather than the expected f⁸s² configuration, and this has major implications for its role as the central metal of the Ln, rather than Eu.

That's just because Gd³⁺ is f⁷. Which it would be even if the neutral configuration was f⁸s². Double sharp (talk) 16:28, 3 February 2020 (UTC)

@Double sharp: If Gd really was f⁸s² then perhaps it would also have +2 oxidation state of comparable stability to +2 Eu and Yb. Sandbh (talk) 04:17, 11 February 2020 (UTC)

@Sandbh: And this one is a perfect example of why DE's are mostly chemically irrelevant: the majority of the Ln are fⁿs² (Ln = Pr, Nd, Pm, Sm, Eu, Tb, Dy, Ho, Er, Tm, Yb), but their predominant oxidation state is +3 instead of +2. (Note that Tb has a well-defined +4 state.) The important thing controlling stability of +2 and +4 states is how close the result is to a stable half-full f⁷ or f¹⁴ configuration. The DE never makes any difference here. Sm, Eu, Tm, and Yb form well-defined +2 states that are not too uncommon because Eu²⁺ and Yb²⁺ land right on the half- and fully-filled marks, and Sm²⁺ and Tm²⁺ are close and get horseshoes-and-kisses benefits. Tb, which is [Xe]4f⁹6s², prefers to form a +3 and sometimes +4 state: +2 is a rarity (though well-defined), but combustion of Tb in O₂ produces a mixed Tb(III,IV) oxide. The DE clearly doesn't have anything to do with the existence of Tb⁴⁺, that's because doing so lets it reach 4f⁷. As it would even if Tb happened to be 4f⁸5d¹6s² or 4f⁷5d²6s² in the ground state instead. Double sharp (talk) 12:02, 11 February 2020 (UTC)

Among the light actinides the difference in energy between the 6^d and 5^f orbitals is very small and results in competing 5fⁿ7s² and 5f^n-17s²6d¹ configurations in molecular bonding, contributing to some of the complex chemistry of these actinides.

Yet more proof of the approach of looking at chemically active subshells rather than individual configurations, like I do! ^_^ Double sharp (talk) 16:28, 3 February 2020 (UTC)

@Double sharp: No need for that. We can just be amazed at the similarities between the light An and the early 5d metals, caused by the anomalous configurations under consideration. Sandbh (talk) 04:17, 11 February 2020 (UTC)

@Sandbh: It has nothing to do with the anomalous configurations, which do not match from Ta/Pa onwards. From Pa onwards, the differentiating electrons are f-electrons, and yet the similarities Ta/Pa and W/U still go on fairly strongly. Meanwhile the transition to a "uranide"-like situation happens for {U, Np, Pu}, even though the change from fⁿds² to fⁿ⁺¹s² only happens at Pu. I don't see any way you can predict this from the DE's, which are changing totally orthogonally to the chemistry here. Double sharp (talk) 14:10, 11 February 2020 (UTC)

@Double sharp: I was referring to the anomalous retention of a 6d electron, up to Np. Sandbh (talk) 23:10, 11 February 2020 (UTC)

@Sandbh: Which I refuted in the third sentence. The little problem is that resemblances to the "right" 5d metal stop at uranium, because Np and Pu prefer +6 in which they imitate uranium, rather than going on to +7 and +8. And strong resemblances to 5d chemistry stop at plutonium (Am is unhappy to be oxidised far). And if you want any resemblance at all, it goes to curium with its +6 state, at which we have included Pu and Am which have no anomalous d-electron. In every case the break does not coincide with that of the anomalous DE's "up to Np". Double sharp (talk) 23:24, 11 February 2020 (UTC)

Lr has to go into the d-block as there is no other place it can practically go.

So what happened to being interested in Nature as She was, rather than how we can most easily draw Her? ^_^ Double sharp (talk) 16:28, 3 February 2020 (UTC)

@Double sharp: Pragmatism. Just like what happens in an Lu table, with a p metal in the 5d row. That said, I don't even have to worry about the anomalous configurations per se. I can just compare the n+l rule, with the La table and the Lu table, and note that the Lu table has one more anomalous configuration. Sandbh (talk) 04:17, 11 February 2020 (UTC)

@Sandbh: Lr is not a p-metal, by my and Jensen's criteria. It has a chemically active valence 6d subshell, that's what counts. And it has three valence electrons that can occupy 6d, 7s, and 7p but not 5f; that's why it's in group 3. We consider the exact DE and ground-state configurations to be irrelevant and only consider chemically active subshells and how many electrons are in them. The second point means that even group 2 is not an exception, because the Zn group have twelve valence electrons in d+s+p, but the Ca group have two, just like Be and Mg. (For sanity's sake, given prominent sp hybridisation in things like Be, it seems reasonable to consider the s and p outer shells together as part of a normal valence octet Actually, I am not even sure it has any exceptions once you go down to this second step until the really strong superheavies (Mc, Lv, Ts, and Og may be a bit problematic with premature 8s involvement thanks to the lower-than-usual 7p_3/2-8s gap, but 7p is still the highest angular-momentum subshell).

You can see how this works in practice at User:Double sharp/Idealised electron configurations: the fuzzy approach works pretty much perfectly in period 7 and even holds the fort in period 8. Double sharp (talk) 14:13, 11 February 2020 (UTC)

If we set aside the anomalies and look at (as I’ve done before) the configurations of ions in precipitation chemistry and the solid-state chemistry of salts—since such ions don’t have anomalous configurations—this is what we get:

s-block
Cations have an s⁰ configuration

p-bock
Cations are s⁰ (or s²)

d-block
Cations are group number less charge, which gives a range of d⁰ to d¹⁰

f-block
With La starting, cations are f⁰ to f¹³ With Ce starting, are f⁰ to f¹⁴.

→ The f-block starting with La introduces a new irregularity, at the global level.

→ Another irregularity arises wrt to the boride, scandide, and lanthanide contractions. Each contraction starts with the first appearance of a p, d or f electron at the start of the applicable block. This regularity is not observed in an Lu table. Sandbh (talk) 03:05, 21 January 2020 (UTC)

The important thing is the energy levels; anomalous-looking configurations are just a symptom of many shells being close together, e.g. 4d/5s in early 4d metals, 4f/5d/6s in Ce, 5f/6d/7s in the early actinides. It does not much matter which anomalous configuration it happens to be. The characteristic configuration for a d-block element in compounds is dⁿs⁰, so here it is indeed group 11 and 12 that are the weird ones. But it's not because they all happen to be d¹⁰s¹ in the ground state so much as that they cannot possibly stuff eleven electrons into the d-subshell, so this is something like Lu being unable to be f¹⁵. Ag is predominantly main-group, Cu is pretty balanced, and Au is strongly transition, but that is a function of the differing 3d/4s, 4d/5s, and 5d/6s gaps because of radial nodes (3d) and relativistic effects (5d). Secondly: for La³⁺, whatever anomalous electron there had been has been ionised anyway as expected, so there is no difference between it and Al³⁺ or Sc³⁺. Thirdly, no one is claiming that Eu is the central metal of the Ln, because no one is disputing that Lu is a lanthanide chemically. (I just think it is the d-block lanthanide.) And fourthly, you're forgetting Yb²⁺ (f¹⁴), so there is no difference with the f-block either way. And you are going to get that irregularity anyway from the actinide contraction as Th lacks that 5f electron in the ground state, which is why I prefer to start looking when the subshells get active even if they are unoccupied. So we can include La through Lu as well as include Ca through Zn for such contractions. Double sharp (talk) 13:55, 21 January 2020 (UTC)

@Double sharp: Too hard. D/e's are so much easier. Sandbh (talk) 04:17, 11 February 2020 (UTC)

@Sandbh: I'll take what is relevant over what is easy any time, thank you very much. The easiest possible way to arrange the periodic table is to just list the elements in alphabetical order, but that will get us precisely nowhere. Double sharp (talk) 14:15, 11 February 2020 (UTC)

@Double sharp: With the f block as Ce to Lu, the range is 0 to 14. With La to Yb the range is 0 to 14, as you say, my oversight. I would not count La as an f-block metal, since the 4f subshell has not started filling yet. So the second option is not comparing like with like. Sandbh (talk) 09:53, 23 January 2020 (UTC)

So Th is not an f-block metal either, by that logic. Both La and Th have low-lying f-orbitals that seem to have chemical consequences (cubic La complexes, extremely high coordination numbers for Th), unlike the completely core-like f-orbitals of Lu that just act like the d-orbitals of Ga, but unfortunately neither of them happens to have an f-electron in the ground state. I prefer to say that this is just a simple consequence of high atomic number causing delayed collapse. That takes care of what happens at La, Ac, Lr, and E121 all in exactly the same way, without having to bang our heads against the wall at the craziness that is expected to start brewing once we synthesise three more elements. Double sharp (talk) 11:38, 23 January 2020 (UTC)

@Double sharp: Th is an f-block metal by way of Ce starting the f-block. The sky won't fall down. Sandbh (talk) 04:17, 11 February 2020 (UTC)

@Sandbh: So you're still assuming symmetry to force a block to begin in a vertical column, even if your first criterion of DE's says it doesn't. So why is this symmetry inviolable when you seem to consider it fine to violate the symmetry of rectangular blocks? Double sharp (talk) 14:15, 11 February 2020 (UTC)

@Double sharp: I'm assuming regularity rather than symmetry. Our IUPAC criterion says a block starts upon the first appearance of the applicable electron. The f block starts with Ce, that is all. That Th does not have an f electron is not relevant in this context. Sandbh (talk) 23:18, 11 February 2020 (UTC)

@Sandbh: Different word, same idea. The symmetry of the LSPT is just as much a "regularity"/"symmetry" as your criterion (I have since rejected it) as yours is, because the whole point of symmetry is that you get some information for free due to the invariance. To his credit, Prof Poliakoff (who you quote a lot re Nature and drawing Her) realised that this was also an issue, and pointed it out, to quote you:

“

At the end of the video the professor entertains the amusing possibility that the "break" in periods 6 and 7 could occur in different positions i.e. that La might go under Y and Lr under La! He says this would be a real mess for the people that draw periodic tables but that,

"What we are interested in is what nature is like not how easy it is to draw it."

To which I say, "Bravo Prof Poliakoff!"

”

And yet now you reject that possibility on regularity/symmetry grounds! If you wanted to be consistent about this and exclude La because of its lack of an f-electron as a ground-state gas-phase atom, you need to start the 5f block at Pa. Otherwise you are invoking symmetry in one case and disallowing it in another. ;) Double sharp (talk) 23:22, 11 February 2020 (UTC)

@Double sharp: Per our IUPAC submission, a block starts on the first appearance of the applicable electron. Subsequent rows fall into place as an outcome of the aufbau process. That is all. Regularity is not the same as symmetry. Sandbh (talk) 23:43, 11 February 2020 (UTC)

@Sandbh: Yes it is. A regular form is more symmetric than an irregular form. Double sharp (talk) 23:55, 11 February 2020 (UTC)

@Double sharp: That's not what I said. The bifurcation of the lungs in humans is quite regular, but not symmetric. To accomodate the heart, the left lung has 45% of the total lung volume, whereas the right side has 55%. Ditto, that humans have two hands is a regular pattern but only 11% or so are left handed. The aufbau sequence is not symmetric but it does show regularity in continually (evenutally) returning back to the n+l rule, after each anomaly. Regularity and symmetry are closely related, but not identical. Sandbh (talk) 03:03, 12 February 2020 (UTC)

PS: A square is regular and symmetrical. A rectangle is irregular and symmetrical. Sandbh (talk) 03:10, 12 February 2020 (UTC)

Anyone can see that that is because a rectangle has less symmetry than a square (e.g. it lacks the 90-degree rotation or reflection in a diagonal). But you turn symmetry into "all or nothing". Double sharp (talk) 07:58, 12 February 2020 (UTC)

Organometallic chemistry

@Double sharp: We know compounds of Ti generally are mainly covalent in nature since its most stable oxidation state is +4. Ditto Zr and Hf. As we wrote in our IUPAC submission:

"Sc-Y-La-Ac further shows simple trends of increasing basicity and in this respect are much more like their leftward neighbours Ca-Sr-Ba than their rightward neighbours Ti-Zr-Hf. The +4 state is too high to be ionic in group 4, even for Th and what little we know of Rf. While KCl, CaCl₂, and ScCl₃ are ionic compounds, the group 4 tetrahalides (Cl, Br, I) are volatile covalent liquids or solids. While one can obtain aquated La³⁺ (or Lu³⁺), hydrolysis proceeds so far for Hf that HfO²⁺ is obtained instead. Lanthanum in particular is such a hard base that it is taken up by the body as if it were calcium."

…I have this picture in my mind of you trying to beat up your IUPAC-submission-pro-La self… :)

'Nothing more refreshing than a change of opinions, or as a friend of mine says: "I take back everything I said and claim the opposite."' – Tim Krabbé. ^_^ Double sharp (talk) 12:53, 23 January 2020 (UTC)

@Double sharp: Do you realise that your arguments in the IUPAC submission were much stronger and more direct than the arguments you’ve raised in this thread? Sandbh (talk) 07:46, 25 January 2020 (UTC)

Here are three quotes from the IUPAC submission that I actually still agree with:

"In advancing their positions, we think these authors fail to demonstrate why similarity in properties (aside from valency) necessarily connotes group membership. In some other parts of the periodic table, most germanely in groups 1 and 2, we see a continuation of trends upon descending a group (such as increasing atomic radius, basicity and electropositivity), rather than a convergence of such properties. Either pattern could apply to the eka-yttrium position. That is to say, if group 3 were treated as early main group elements we would expect more of a linear trend going down the group. On the other hand, if group 3 was treated as a transition metal group, it would be reasonable to expect more of a convergence properties on going from period 5 to period 6, as a result of the lanthanide contraction."

"We think it plausible that the low-lying 4f levels in La may influence some of its properties. It is also conceivable that the filled 4f shell of Lu may influence some its properties but, if so, the scope of this influence is likely to be smaller and more obscure. Overall, we think the presence of any 4f influence, as a relatively low-order phenomenon, would only be a "tipping point" argument. That is to say, if the merits of -La-Ac and -Lu-Lr are otherwise similar in terms of which one is placed under Y a case could then be made for -Lu-Lr."

"Furthermore, the historical record does not necessarily flag ongoing relevance. As noted, many old tables from this time period also place Be and Mg in group 12 with Zn, Cd, and Hg, a practice which has since been deprecated." That argument was used against the historical theme of promoting Lu under Y, but it works just as well against the huge historical record of La under Y.

The important thing is that I've come round to the position that the merits of La and Lu under Y are actually pretty similar, all things considered. Therefore the "tipping point" argument works, because it is essentially "let's keep the status quo/null hypothesis" for Lu, which fits the pattern of the first 5 rows better. You seem to be taking La as your null hypothesis instead, when it seems to me that it should be an alternative hypothesis that the pattern breaks. That's why we both find the arguments for the other one not strong enough and keep on sticking to our respective sides now.

You see, the reason why all those "tipping point" arguments were rejected was "let's look at group 2". But now I think Droog Andrey had a point in Wikipedia talk:WikiProject Elements/Archive 33#Part 2: the s-block is in some sense fundamentally different from the other blocks. Look down any other column of the periodic table and you get double periodicity out of the n+l rule. B and Al are just s²p; Ga and In add d¹⁰; Tl and Nh add f¹⁴ on top of that. Ti and Zr are just d²s²; Hf and Rf add f¹⁴ on top of it. So why should group 3 follow the s-block's singular pattern when it is a clearly a d-block group? If we allow this border to stand, we can start raising uncomfortable questions like Ti-Zr-Ce-Th (all are d²s² but Ce, which could work as an anomaly like Lr with a subshell getting active "too early"), and B-Al-Sc (which even has many sound chemical arguments for placing Al above Sc like Rayner-Canham's table does!). And it doesn't really work as well as we thought to say that group 3 mostly follows group 1 and 2 in its chemistry, because the heavier members of groups 4 and 5 also do that.

And if you look at where the d-block ends, it becomes clear that our argument doesn't really work: the energy of the d-electrons rises from Zn going downwards, but the energy of the f-electrons falls from Lu going downwards. So the only problem is delayed collapses, but that is totally normal as elements get heavier, and as the elements are ionised the problem mostly corrects itself. But once you have refuted delayed collapses, kinship ties supposedly stronger to the left than to the right (when it turns out to be equal), and condensed-phase configurations, what is left to support Sc-Y-La with its strange s-block trend outside the s-block? So that's my current argument: H₀ is Sc-Y-Lu, and there is not enough force from Sc-Y-La arguments to reject it. Maybe this is unsatisfying, since failing to reject the null hypothesis is hardly an interesting story. Maybe it feels like an argument from despair that Nature is too complicated and plumping for the simplest option. But in the long run, it seems to me scientifically more honest to admit that there is not enough basis for a revolution, and that we erred as a whole in creating one in the first place back when La was first put under Y.

@Droog Andrey: Do you have the results of your test from Wikipedia talk:WikiProject Elements/Archive 38#4f involvement from La through Lu that you suggested (bond angle in LnF₂⁺)?

@Double sharp: I've computed about a half of these cations, and the results appeared to be quite dependent on the level of theory. Unfortunately, available CPU power doesn't allow me to use as high level of theory as CASPT2. Droog Andrey (talk) 11:19, 27 January 2020 (UTC)

I honestly don't plan on responding much more over the next few days in this much detail. Firstly, I have some important stuff IRL to do, and secondly, it seems we are going in circles. My whole case for Sc-Y-Lu is more or less set out in this post, modulo the experimental results on 4f involvement in the Ln that haven't been posted at the moment, so you can more or less just read this, and refer back to the other posts for ancillary arguments like Lu creating a more homogeneous d-block.

P.S. I love how a thread about group 3 and classification was enough to get this talk page all the way up from 11K to 200K without any articles being affected. So, everything is normal again! ^_^ Double sharp (talk) 10:47, 25 January 2020 (UTC)

@Double sharp:

“And it doesn't really work as well as we thought to say that group 3 mostly follows group 1 and 2 in its chemistry, because the heavier members of groups 4 and 5 also do that.”

Speaking calmly, this is the line that beggars belief. Effectively the entire chemistry world recognises that group 3 mostly follows groups 1 and 2 in their ionic chemistry, whereas groups 4 and 5 are predominately covalent. Yes the s block is fundamentally different from the other blocks, it being the only one whose electrons are nearly always involved in chemistry, but for Pd. That said, its chemistry is predominately ionic, as is the case for the rare earths. That’s another fact recognised by the entire chemistry world. The double periodicity you are referring to derives from the n + l rule which is only an approximation, has no first principles basis, and starts cracking in the d and f blocks (albeit persisting in any event). As I said elsewhere, on the basis of the most common stable oxidation state in each row of the d-block, the d block does not exhibit double periodicity. The n + l rule is a nice idealisation that does not strictly apply in the real world in ambient conditions. Droog Andrey’s 3rd IP argument doesn’t stand up compared to the most common most stable oxidation state, per DIM, in each row of the d block. I admit that one stumped me for a while but now that I know so much more about the misleading n + l rule, as well as thinking about the relevance of the 3rd IPs v the most common most stable oxidation state, I can see that the 3IP argument doesn’t hold up. Never mind about your RL; take your time and respond when you can. I intend to rule a line under this thread at the end of January, unless R8R has any more thoughts. Sandbh (talk) 09:02, 26 January 2020 (UTC)

Let me repeat one of my comments below: "Look, there is no such thing as a complete volte-face from ionic to covalent. It depends on what the counter-anion is. We go from ionic to metallic (which you're overlooking completely) across the series NaCl, Na₂O, Na₂S, Na₃P, Na₃As, Na₃Sb, Na₃Bi, Na. And that's in group 1, with an example taken straight from Greenwood & Earnshaw p. 81. Ionic vs. covalent is (1) gradual, from covalent to polar covalent to mildly ionic to strongly ionic, depending on the difference of electronegativity between the two elements; (2) not a complete dichotomy, because you overlook metallic bonding; and (3) not split by elements, but rather by electronegativity differences, which have a lot to do with oxidation state (just compare uranium chemistry as we jack the oxidation state up from +3 to +4 to +5 to +6). So I'm astonished to see you put so much weight on "ionic vs. covalent" as a false dichotomy. (And as I keep saying, the general thing across the periodic table is continuity, and the sharp dichotomies you like to point to have a distinct tendency to not exist.) The whole literature, when it sees fit to split "main group" from "transition", universally uses other criteria like "variable oxidation states", "coloured compounds from d–d transitions", "a wide variety of complexes", "formation of paramagnetic compounds". Ionic vs. covalent has nothing to do with it, and nobody uses that as a criterion in the literature for this divide. Respectfully, I put it to you that Zr, Hf, Nb, and Ta by this standards have weak credentials as transition metals, just as weak as Sc for that matter."

By those standards, the typical high school trend of first ionisation energies across main-group elements must also be thrown out the window. And double periodicity must also be thrown out the window as well in the p-block, because as we go down the table the most common oxidation state keeps changing. (For oxygen it is −2, for sulfur +4 and +6, for selenium, tellurium, and polonium +4, for livermorium probably +2.) E pur si muove: it is still absolutely relevant, as anybody can see just plotting trends down every p-block group. Which seems to be a good sign that your standards are excluding a lot of things that are relevant to the question. Indeed, it seems to me that they are excluding so much that we are left with nothing to stand on. What is the point of a philosophical argument if it ignores the properties that Mendeleev was looking at in the first place? Double sharp (talk) 16:51, 26 January 2020 (UTC)

Whereas compounds of the rare earths are mainly ionic.

Drilling down into organometallic chemistry, nothing changes.

You wrote:

"Group 4 organometallic chemistry is mostly cyclopentadienyl derivatives, similar to group 3. Zr and Hf in group 4 are very unhappy to show lower oxidation states, like Sc in group 3."

Now, the cyclopentadienyl derivatives of group 3 are ionic in nature, consistent with the largely ionic chemistry of groups 1 and 2. Same goes for the cyclopentadienyl actinide (III) derivatives.

OTOH the derivatives of group 4 are more covalent in nature as is the case for cyclopentadienyl actinide (IV) derivatives.

The organometallic distinction between main groups 1 to 3 (noting groups 1 and 2 are main group, and group 3 is transition), and group 4 is thus clear.

On the above basis, I submit that the organometallic argument supports La in group 3. Sandbh (talk) 23:36, 17 January 2020 (UTC)

This is just another example of the difference between +3 and +4 states: the former can be supported as water-soluble real cations, the latter are too highly charged for it to happen even for such electropositive metals as Th⁴⁺ and U⁴⁺. Similarly, the former are more ionic than the latter, by Fajans' rules. Then I have to ask, how ionic are organometallic derivatives of Ti, Zr, Hf in states lower than +4? (At least for Ti, +3 is a characteristic state, after all.) Because if the same shift happens when you oxidise uranium (for example) from +3 (more ionic) to +4 (less ionic), then it seems to me to be a difference between oxidation states, not between group 3 and group 4 per se. Double sharp (talk) 09:48, 19 January 2020 (UTC)

Ionic vs. covalent 1

@Double sharp: I agree, and it's a key difference rather than just another example. I say this because the organometallic chemistry (OMC) of states lower than +4 is not a relevant consideration since the OMC of the Group 4 elements is mainly that of the elements in their +4, covalent states. +3 is not a characteristic state of Ti; +4 is. Similarly, the OM chemistry of the Group 3 elements is mainly that in their +3 ionic oxidation state. So there is a pretty clear distinction between the two Groups, at the general chemistry level, including OMC. Sandbh (talk) 06:38, 20 January 2020 (UTC)

@Sandbh: You cannot have it both ways. If the characteristic state of Ti, and especially Zr and Hf, is +4, and we discount +3, then my point about them acting mostly like main group elements stands, and there is no significant caesura between groups 2, 3, and 4. If on the other hand we consider group 4 to be transition-metal-like on the grounds of +3 as a significant lower oxidation state for Zr and Hf, then by that logic Sc qualifies by its +2 state, and there is again no significant caesura between group 3 and 4. Double sharp (talk) 14:39, 20 January 2020 (UTC)

@Double sharp: Groups 1, 2 and 3 have a predominately ionic chemistry. Group 4 has a predominately covalent chemistry. Trends going down group 3 are like those of groups 1 and 2. Trends going down group 4 are like those going down groups 5 to 10, or so. The group 5 elements are similar in many ways to group 4, expect for being less electropositive. Those are key differences between Groups 1 to 3, and 4 to 5+. Sandbh (talk) 03:51, 21 January 2020 (UTC)

@Sandbh: That is, again, just a matter of characteristic oxidation state. Compare Sn²⁺ and Pb²⁺ vs. Sn⁴⁺ and Pb⁴⁺ (the same element, even). (Note that Mendeleev in his first table put Pb as a heavier homologue of Ba, because of the +2 state.) Also compare the chemistry of Fe (mostly ionic Fe²⁺ and Fe³⁺) with that of Ru and Os in the same group (which prefer higher states, with covalent compounds like the famous OsO₄). As we can see: the 3d metals from Cr onwards (which prefer lower oxidation states like +3 and later +2) are not too dissimilar from main-group elements in this respect. And trends going down group 3 are only like those in group 1 and 2 if you've decided on Sc-Y-La already Double sharp (talk) 13:45, 21 January 2020 (UTC)

@Double sharp: I see the trends going down group 3 (as La) resemble those going down groups 1 and 2. Indeed, we know that Laing said a reasonable case could be made for La below Y on the basis of comparing the pairs Ca-Sc and Sr-Y with Ba-La.

By that logic one could compare Be-B and Mg-Al with Ca-Sc, and arrive at Sc as the heavier congener of Al, because the reason why La matches here is because it doesn't have the later block insertion that characterises Ca-Ga and Ba-Lu. Double sharp (talk) 16:11, 22 January 2020 (UTC)

@Double sharp: Your analogy is a non-starter since the differentiating electrons aren’t the same: p for Al (as with Ga); d for Sc. Sandbh (talk) 10:48, 23 January 2020 (UTC)

In the condensed phase, they are the same. So if that is a supporting argument for Sc-Y-La, it also works for B-Al-Sc. Double sharp (talk) 12:54, 23 January 2020 (UTC)

@Double sharp: Could you support this with a reference? I find it hard to believe that Al and Sc have the same condensed phase config. Sandbh (talk) 06:24, 25 January 2020 (UTC)

Scandium metal has significant p-character at the Fermi surface (14.8%). There is also a large p-character in ScS and YS (in contrast to ScO where it appears the electron is mostly s). At the very least, this shows the condensed phase configuration as rather inconclusive, as for Sc there is both some d- and some p-occupancy and so there's nothing in principle based on this argument standing in the way of B-Al-Sc. (At least, nothing more than what seems to still allow Be and Mg into the s-block with an sp configuration in the condensed phase.) Double sharp (talk) 10:27, 25 January 2020 (UTC)

This is not the case for Lu, where the trends tend to resemble those of groups 4 to 10. That is a statement that has nothing to do with whether or not I've decided on Sc-Y-La already.

We already know that a reasonable case case can be made for distinguishing groups 1 to 3 from 4+ on the basis of iconicity v covalency. The next decision is La or Y, which is rather easily decided on the basis of vertical trends.

And what about most of the 3d transition row? The characteristic oxidation states are Sc^III, Ti^IV, V^IV, Cr^III, Mn^II, Fe^II and Fe^III, Co^II, Ni^II, and Cu^II. The majority of these prefer a +2 or a +3 state, and they're pretty electropositive, too. Same kind of thing happens in the 4d transition row from Ru onwards, so that already covers some of "groups 4 to 10". So no, I don't buy that this is a group 1 to 3 vs. group 4+ distinction. It's rather a low oxidation state vs. high oxidation state distinction, which is underscored by the fact that the same element can behave differently depending on oxidation state (consider Pb^II vs. Pb^IV). It only looks like a distinction purely because the elements in group 3 and 4 like to be in their group oxidation state, but if you circled all the electropositive low-oxidation state metals that act more or less like what you think electropositive metals should act like from school, you'd have to cover most of the 3d row already.

As well: one of the main reasons why the "main group vs. transition" bar is rarely set between groups 3 and 4 is because of the lower oxidation states of the group 4 elements. (Which especially for Zr and Hf are at about the same level as Sc^II, but never mind that.) But then you can't have it both ways. If you are considering +3 oxidation states as characteristic for group 4 as well as +4, then they should be more ionic in that state, and there is no caesura between groups 3 and 4. And if you are considering only +4 oxidation states as characteristic, then group 4 does not show characteristic transition metal properties and there is again no caesura between groups 3 and 4. Neither was there between groups 2 and 3, for that matter. So why not let it be intermediate, and show the simple cations but the transition-group trend as a bridge between both, an argument that I'm sure Droog Andrey used before? Double sharp (talk) 17:05, 22 January 2020 (UTC)

@Double sharp: We know Sc chemistry, and the rest of transition metal Group 3 is predominately ionic. We know the chemistry of the transition metals in groups 4 to 12 is predominately not per e.g. what happens to their electronegativity values. Sandbh (talk) 11:14, 23 January 2020 (UTC)

For something like Cu²⁺ you not only have all those covalent complexes, but you also have well-defined famous salts like CuSO₄ and CuBr₂, so clearly at least for Cr through Zn we have a significant amount of ionic chemistry as well. Same as for Sc³⁺, which I'm sure is more covalent in complexes and more ionic in salts. Double sharp (talk) 11:49, 23 January 2020 (UTC)

@Double sharp: There’s a difference between predominant behaviour and significant behaviour. With an electronegativity of 1.9 there’s no way, IMO, that the general chemistry of Cu could be regarded as being predominately ionic. Sandbh (talk) 05:53, 24 January 2020 (UTC)

It has a significant ionic component, that exists in many famous salts, so again we just see a continuum as we pass from left to right of ionicity giving way to covalency, with the vast majority in the middle being able to go both ways. Anyway: notice that you need lower electronegativity to be ionic with a larger charge (think of things like Sn²⁺, which is about the limit of a dipositive cation), so we should weight that appropriately or else the early actinides are also "predominantly covalent" despite being such active metals. Pa⁵⁺ has absolutely no chance to be a simple cation, but so what, given its electronegativity of 1.5? But: if Pa gets in as a main-group element under something like R. Bruce King's definition, then shouldn't the pseudohomologues Nb and Ta get in too? Double sharp (talk) 23:27, 24 January 2020 (UTC)

Consider what would have happened if the trends going down group 3 as Lu resembled those of groups 1 and 2 more than the case for La. The question would've been resolved about 100 years ago. Sandbh (talk) 02:12, 22 January 2020 (UTC)

@Double sharp: Pls see my earlier response re the difference between significant and predominant. Pls also see my response re the predominately ionic behaviour of group 3 and the predominately covalent nature of groups 4 and 5. There is no continuum here. Group 3 are transition metals that behave mainly like main group metals. The An are not relevant here. Sandbh (talk) 07:09, 25 January 2020 (UTC)

And my response is also going to be "please read my previous responses". See, the whole point is just the oxidation state difference, and the border will be different depending on where in the periodic table you are looking. The further you go down the periodic table, the later the shift towards covalency happens. In period 2, Be is the first to show it significantly; in period 3, Al; in periods 4 through 6, Ti/Zr/Hf; in period 7, probably Db (since Rf⁴⁺ ought to be basic given its size). The fact that the break happens to coincide here is more or less coincidental. And we again have to look at what the anion is: TiCl₄ is molecular, but ZrCl₄ and HfCl₄ are polymeric. TiF₄ is polymeric, but ZrF₄ and HfF₄ have an honest-to-goodness ionic structure. So we see, once again, that the relative proportion of ionic to covalent chemistry for each of these elements is not suddenly changing from 100% to 0% when we cross the group 3 to group 4 line; there is instead a continuum, as everywhere else on the periodic table. Only if you arbitrarily declare some threshold as "predominant" does this continuity degenerate into a change from positive to negative, but how Nature really is is much more subtle than that. Double sharp (talk) 10:24, 25 January 2020 (UTC)

Ionic vs. covalent 2

@Double sharp: With respect, this is another example of your inability to engage with arguments at the most general characteristic level. Because you can’t do this you put up a barrage of minutiae which does nothing to hide the elephants in the room. I cite the literature which says 3 = predominately ionic; 4 and 5 = predominately covalent. Because you can’t refute this you resort to sideshow arguments and ignore the main game. Always with respect, DIM would never have produced his table if he had taken your approach of ignoring the inconvenient broad contours and dwelling on the micro cracks. Sandbh (talk) 00:10, 26 January 2020 (UTC)

Respectfully, all you do is cite the literature, and not ask why something happens to be, or why it should be relevant. Once you do that it becomes clear that it's not about group 3, but purely a matter of oxidation state. And you yourself already showed it using the actinides. Compare uranium(III) with uranium(IV), the same element even, with 3 predominantly ionic and 4 predominantly covalent. Or just look at Pb^II vs. Pb^IV with their vastly different electronegativity values to see how much oxidation state affects these things. I simply take the approach of ignoring the micro crack that makes group 3 the coincidental borderline for periods 4 through 6, when it is earlier in previous periods and later in the next period, and just draw the broad contour of simple, rectangular blocks.

Group 3 are chemically more main-group and physically more transition, so it is obvious that it should be intermediate, and it comes as no surprise to me that the transition into transition chemistry happens slowly over a few elements. (Which is what all the literature says, noting the reluctance of Zr/Hf and Nb/Ta to enter lower oxidation states, and their main-group like behaviour, but respectfully you seem at the moment to be only interested in whatever can be teased out of the literature if it can be seen as supporting Sc-Y-La.) My principle is simply that of continuity, not catastrophism. Mendeleev, basing his table on trends, would probably have agreed. I agree that, from the perspective of supporting Lu, the mostly ionic main-group-like chemistry of group 3 is a bit inconvenient. But their transition-like physical properties and their incipient transition behaviour, just like Zr/Hf and Nb/Ta, is decisive. Double sharp (talk) 00:18, 26 January 2020 (UTC)

@Double sharp: I cite the literature, and I use it to make new arguments along the lines of what we put together in our IUPAC submission. Never forget that I started off as an Lu supporter until Scerri (also an Lu supporter) started me off on the critical thinking path and later the philosophical/global path.

I’ve addressed the metallurgy of group 3 elsewhere as well as Restrepo’s analysis of Lu being closer to a lanthanide than a transition metal and La being in between. And I’ve written elsewhere about the universally recognised ionic-covalent difference between groups 3 and 4. That’s a done deal. That’s one of the bigger aspects of chemistry—the difference between ionic and covalent—so how you could call that a bit inconvenient is beyond me. Sandbh (talk) 09:22, 26 January 2020 (UTC)

I've flipped between La and Lu before too, and I distinctly recall that at every stage of flipping I thought I had the answer. This is exactly why I think there is not enough evidence to overthrow Lu as the null hypothesis. So, for the 9001st time:

Restrepo's argument has been refuted by me 9001 times on your talk page and here by now, so I'm not going to repeat it. For goodness' sake, take almost any physical or chemical property, and plot the values for La, Lu, and Hf through Hg. The value for Lu will be closer to the values for Hf through Hg so many times that, respectfully, the fact that you keep denying it beggars belief.

@Double sharp: Yes I understand what you are saying. You simply aren’t comparing like with like. There are 14 elements between La and Hf and you pretend they are not there. It’s like the basketball match in which a gorilla walks across the court and none of the audience sees it. Your logic here beggars belief, as the two us like to say to one another :) Do you understated what I’m saying here. It has nil to do the homogeneity of the 5d metals. You may as well compare Sc to Ga and ignore the intervening 9 elements. Sandbh (talk) 11:33, 28 January 2020 (UTC)

I understand what you are saying here. I just think your logic is completely backwards. You talk about comparing Sc to Ga; fine, let's try that. Suppose Sandbh Prime comes and talks to us about how B-Al-Sc is the right and completely logical periodic table choice because Al shows pre-transition character that is manifestly uncharacteristic of group 13, and B acts as an honorary metal atom. Well, the trend B-Al-Sc-Y-La is no worse than the trend Be-Mg-Ca-Sr-Ba. Sc-Y-La have d-occupancy, it is true, but we can rationalise it away like we do for the pre-d character of Ca-Sr-Ba. Now let's take B-Al-Sc as an axiom and grasp at straws to defend it. Now we can say that it has nil to do with the homogeneity of the 4p elements. It's now not relevant that Ga in every way acts more like a 4p element than Sc does, because you are ignoring the d-block insertion that has happened between them over nine intervening elements, you see. Where is the difference in logic? Not only that, I can argue that the cleft in the p-block is completely right because of the big difference between +3 and +4 aqueous cations in water: the former exist in group 13, the latter don't exist in group 14 (even Th⁴⁺ is strongly hydrolysed). Same logic as your "ionic vs. covalent" one; this one is actually even better because it's actually more well-defined, whereas "ionic vs. covalent" raises the question "with respect to what distribution of counter-anions?".

So here is my challenge for you. Pretend that you are, in fact, a supporter of H-F-Cl, He-Be-Mg, Be-Mg-Zn, B-Al-Sc, Tl-Lr, or any number of other strange choices. (Well, He-Be-Mg is not so strange, for me, but never mind that.) And try to make arguments that defend them. And I mean seriously defend them, like you are doing for Sc-Y-La. (Maybe I can do that better because I remember supporting both Sc-Y-La and Sc-Y-Lu at various points.) I bet you that your arguments for Sc-Y-La are always going to support one of those other decisions that you have decided in advance not to support. In which case they are not arguments, just rationalisations after the big decision.

It seems to me, respectfully, that you have started with Sc-Y-La as an axiom and just search for arguments to support it. Once you find anything that can be interpreted that way, it's OK. But once you find something against it, it's not OK. And once I take your Sc-Y-La arguments and note that they also support something else you don't like, such as He-Be-Mg or B-Al-Sc, suddenly they are inadmissible and the goalposts move. Indeed, an argument like "first-row anomaly" that I use to defend Sc-Y-Lu is somehow not applicable there, but you then use it yourself to attempt to demolish He-Be-Mg. (Not very successfully, I might add, given that Ne-Ar displays the same differences as F-Cl for the most part.) All I can say is: this is not science. I don't regret reopening the question back in 2016 by considering Sc-Y-La arguments. I remember R8R was impressed that some of the Sc-Y-La arguments were good, as well as some of the Sc-Y-Lu arguments. But if the result is that Sc-Y-La has for you become an axiom not to be questioned, then yes, I do regret reopening it with you, if it means that you cannot open your mind again. Double sharp (talk) 12:00, 28 January 2020 (UTC)

@Double sharp: Yes, I started with a view that an La table was a "better" form. I did that in light of Scerri's opinion that the question of the composition of Group 3 can't be resolved on the basis of physical (including spectroscopic), chemical, and electronic properties and trends. So, like Scerri, I turned to philosophical arguments. The only such arguments Scerri has presented for Lu are triads and regularity. The triad argument is circular; the regularity argument eats itself. I've addressed both of these points in my article (not well enough for regularity). It turns out there are stronger IMO philosophical arguments for La.

If something is put up against one of my arguments I look at what's been put up and respond with my views. I don't move the goal posts as far as I can recall. I do try to explain why such an argument is not relevant or inconsequential to the main question. I haven't encountered any arguments, so far, that have made me think I've missed something substantial. I've addressed the first-row argument elsewhere including your unfounded premise that it's nature is exclusively attributed to primogenic repulsion.

My overall impression is that your arguments delve into fine details. Meanwhile the 18-wheeler big rig carries on its way. It's like having a lever big enough to lift the world, while you argue about how a lever a few thousandths of an inch longer, shorter or wider would produced a fundamentally different outcome. Sandbh (talk) 02:24, 1 February 2020 (UTC)

Ionic vs. covalent is, firstly, not a catastrophic change. It is a gradual one. As your electronegativity difference increases, the bond gets more and more polar and eventually ionic in character. That is why there is a difference between AlF₃ and the heavier aluminium trihalides, for example. Secondly, it is not even a complete breakdown, as you are forgetting metallic bonding: consider the difference in the alkali metal pnictides as the pnictogen varies from Bi up to N. So I hope I have made it more or less clear that while the difference is fundamental, it is continuous, it is not two-way, and it does not force elements to always stay on one side of the street. Just look at lead(II) vs. lead(IV). Double sharp (talk) 10:15, 26 January 2020 (UTC)

@Double sharp: You have recognised the concept of “typical or predominating behaviour” and that’s a good start. Now, do you recognise that the group 3 metals have a predominately ionic chemistry whereas group 4 metals have a predominately covalent chemistry? No obtuse content focussing on anything other than predominant chemical behaviour will be allowed. Sandbh (talk) 11:33, 28 January 2020 (UTC)

I suspect just about anything that is not a "yes" will be considered "obtuse", so I don't know why I am trying, but: no. There is no such thing as "predominantely ionic chemistry". Not even Na shows such a thing. Just compare bonds from Na to every other element on the periodic table. It will depend on electronegativity differences, most will still not be high enough, and you will get metallic bonding. OK, you say, we should not weight all the elements equally. OK, I think we can all agree that the element forming the most compounds that we know of is carbon, so let's compare electronegativities to that. Do you see where this is going? The electronegativity difference is just not big enough to form a totally ionic bond unless you are literally one of Li-Fr or Ca-Ra. The electronegativity difference between Sc and C is only 1.19, and you'll get a polar covalent bond in organoscandium chemistry. (Hurray, now the gap is between heavy group 2 and group 3. You will notice that although that supports Sc-Y-Lu, I am consistent and refrain from using it as an argument because I think it is not a good one. Even if I happen to like its conclusion for other reasons. Respectfully, I don't see that from you at the moment.)

So saying an element's chemistry is "predominantly ionic" or "predominantly covalent" immediately raises the question "with respect to what distribution of "counter-anions?". If you focus on fluorides, you will get a different answer than if you focus on chlorides, and you will get a different answer than if you focus on oxides, nitrides, carbides, hydrides, etc. Again, it is probably going to be called "obtuse", but I insist: we can only say one element generally shows more ionic character in its bonds than another. Since we are focusing on metals, that just means it is more electropositive. Big deal. Of course anything further to the left of the table shows greater electropositivity. Respectfully, that's 1st-year school chemistry, and even there everybody knows that the trend is continuous, all the way from Cs at the lower left corner to Ne at the upper right corner, through schizophrenic metalloids like Ge or Sb in the middle. Just as it is on the large scale, so it is on the small scale between each individual group and the next. Between each individual element and the next. Between each individual isotope and the next, even (look at inductive effects for bonds to protium, deuterium, and tritium). There is no sudden gap between "predominantly yes" and "predominantly no". Just a continuum. Just like metals to nonmetals. Just like main group to transition and back. Just like class A to class B. Just like hard to soft. Just like every other criterion you can think of. Everything is continuous here. There is no such thing as a sudden break between "predominantly X" and "predominantly not X" anywhere on the periodic table for any single criterion X. Only a transition. If you want to talk about "predominant" behaviour, you have to do it on some complex of criteria, e.g. "predominant main-group behaviour", "predominant transition behaviour", "predominant f-block behaviour", "predominant metallic behaviour", "predominant noble-gas behaviour", etc. etc. etc. When you say one of those, I agree completely. When you argue that group 3 is predominantly main-group in its chemistry, and group 4 starts to show more serious transition properties, I agree with you. That is a much better argument, even if it fails because of the staggering of the entrance of transition properties in each period, with 4d and 5d metals being more sluggish than 3d metals to start it. But not arguing on ionic vs. covalent. Not by a single property alone. Every one of those will just give a continuum across all 118 (soon to be more) elements! Only a complex of them can possibly swing together and make something decisive!

Everything just depends on the electronegativity difference. So insofar as "predominantly ionic" makes any sense it just means "low electronegativity, so that the average difference is higher". In which case, as I've said before, this is just a matter of oxidation state. U(III) is more ionic, U(IV) is more covalent. (I only accept comparatives here, there is no dominance.) Tl(I) is so ionic Mendeleev put it as eka-Cs, Tl(III) is mostly covalent. Pb(II) was put by Mendeleev as eka-Ba, Pb(IV) is mostly covalent. ZrF₄ is more ionic than ZrCl₄ and TiF₄ which are more ionic than TiCl₄. Not the slightest problem here. NaF is more ionic than Na₂O is more ionic than Na₃N is more ionic than Na₃P is more ionic than Na₃As is more ionic than Na₃Sb is more ionic than Na₃Bi. Everything is continuous here. You cannot even talk about "predominant ionicity" for elements because it varies with their oxidation state and your chosen distribution of what they are bonded to. You cannot even think about it for groups, where the variance is even worse. For a concrete example: just look at group 2 starting at Be. Or group 1, starting at H. Or group 13!

So, instead of arguing from supposed philosophical arguments that are either hopelessly bound to human terminology and groupings (e.g. REM, for which people cannot agree on whether Sc is included anyway, despite IUPAC), or hopelessly out of touch with the rich complexity of chemistry by seeking to reduce it to one dimension, I say: look at the pattern. Look at the trends. Look at the chemistry, that we are trying to reflect. Make a table that reflects that chemically active subshells, and the number of electrons in them, are the key Fate determining an element's destiny. That brings you to the Madelung n+l rule as the simplest way to display all that information. And wonderfully, it works really well, produces homogeneous groupings that are easy to learn and understand for a beginner, easy to use as a predictive tool for an expert, and conceals a wealth of amazing ideas behind the surface. And when we need to graduate to focusing on some 2nd-order effect, you will have a rock-solid 1st-order base to start from. Forget about displaying all those 2nd-order effects at once and reducing them to one simple chart. Go for a realistic goal, and do it the best you possibly can, and never forget where you came from: the principles of periodicity in chemical and physical properties. Not some sort of bean-counting of exceptions that forget if the exceptions to the strict pattern had relevance, not putting any one isolated effect on a pedestal and ignoring how it interacts with all the others that come together to create chemical and physical properties, and certainly not forgetting humility before Nature and confusing man-made categories with natural kinds. Just an approximate pattern with astonishing predictive power as a prism to give at least an image of the richness of reality. And never forgetting that reality is so much richer than you can possibly draw. And for that reason, Sc-Y-Lu will do well exactly because it discourages a false sense of precision and understanding about the group 3 divide. End of story. Double sharp (talk) 12:00, 28 January 2020 (UTC)

@Double sharp: There is not much point continuing this particular mini-discussion if you believe there is no such thing as "predominantely ionic chemistry", in the face of what the literature says (as per the General comments section of the thread). Your observation, "never forgetting that reality is so much richer than you can possibly draw" is overly dramatic; the La table provides a nice representation of the richness involved, and has done so for many years. The "false sense of precision" you refer to is a null argument since it can be applied to either form of table. Sandbh (talk) 23:33, 31 January 2020 (UTC)

There's only a continuum going from more ionic to more covalent. If all "predominately ionic" means is "pretty low EN", as I've just unpacked it, then yes, sure, except that Zr and Hf have a lower EN than Sc and we are back to there being no significant divide yet again. And if we add to it "pretty low oxidation state", we start to see why this is a biased indicator, because the divide then appears from something that is pretty orthogonal to group assignment and block characterisation. Unless we want thallium and lead to fall out of their groups. When the literature actually explains what "predominantly ionic" actually means if anything (i.e. low EN), like I quoted Wulfsberg below, it runs into two problems counteracting the narrative of "groups 1, 2, 3, and the f-block": (0) hydrogen [easily swept under the rug], (1) beryllium [not so easy], and (2) zirconium and hafnium [that have EN values lower than scandium]. And limiting by oxidation state results in contradictions like (1) Th, Pa, and U, highly active metals whose characteristic oxidation states are too high to be ionic, but act very pre-transition anyway, and (2) thallium, which shows up as "too ionic" just because its favoured oxidation state is +1.

It's not "overly dramatic". It's a true statement of facts. Everything you draw will be some sort of distortion. I bet R8R will agree about that; IIRC he's said it himself a few times. ^_^ A Lu table is evidently a first-order approximation (it becomes even more evidently one if it becomes perfectly symmetric with He over Be). A La table, in trying to show a second-order phenomenon as well, sets up expectations it cannot possibly fulfill as you can't reflect absolutely everything at that order! Double sharp (talk) 00:26, 1 February 2020 (UTC)

@Double sharp: Nope, that's not what I said. I didn't refer to a continuum of more ionic to covalent. I talked about group 3 having a predominately ionic chemistry whereas group 4 has a predominately covalent chemistry. Once again you change my context and add irrelevant details. Sandbh (talk) 02:57, 2 February 2020 (UTC)

@Sandbh: I'm well aware that you did not. But you should have, because a continuum is what really happens. ^_^ And these are not irrelevant details: they expose the problem with saying "predominantly ionic" or "predominantly covalent", and point to the factors that control it: atomic size and charge, just like Fajans' rules told us. Once you look at it that way, you realise that this break is inconsequential because Th and U look "predominantly covalent" too. And yet, how active they are, and how s-like their chemistry is. Double sharp (talk) 09:47, 2 February 2020 (UTC)

On other important breakpoints in electropositivity, showing that "ionic vs. covalent" insofar as it means anything is assuredly not the only one, we have this contribution: from Greenwood and Earnshaw, p. 347: "The metals which form silicate and aluminosilicate minerals are the more electropositive metals, i.e. those in Groups 1, 2, and the 3d transition series (except Co), together with Y, La and the lanthanoids [excuse the pedantic exclusion of La as a lanthanide], Zr, Hf, [notice something?] Th, U, and to a much lesser extent the post-transition elements Sn^II, Pb^II, and Bi^III." As I wrote in Archive 27: "This accords pretty well with what I've always been thinking, with a few exceptions. The exclusion of the rest of the actinides must be due to their short half-lives, as this is a geochemical context; the need to specify the oxidation states for Sn, Pb, and Bi is quite reasonable given what I've been saying about the increase of metallicity as the oxidation state lowers. The exclusion of Tl (Ga and In are too happy in the +3 state) may be due to the fact that it is quite widely distributed and tends not to occur in quantity; given that Co is almost invariably associated with Ni, I also understand its exclusion from the club as being for geochemical reasons." Double sharp (talk) 18:37, 10 February 2020 (UTC)

Monocations of Sc, Y, La and Lu

My reference is this article: "Periodic trends in chemical reactivity: Reactions of Sc⁺, Y⁺, La⁺ and Lu⁺ with H₂, D₂, and HD".

I saw this it when were doing our IUPAC sub but never looked too closely. Looking again, I see there is quite a bit of support for La in group 3.

The primary electron configurations of the +1 ions are curious:

Sc⁺ 4s3d
Y⁺  3d² 5s4d
La⁺ 5d²
Lu⁺ 6s²

@Sandbh: Ground state of Y⁺ is 5s². Since Ac⁺ and Lr⁺ are both 7s², we see that Lu⁺(6s²) fits much better than La⁺(5d²). Droog Andrey (talk) 15:01, 20 January 2020 (UTC)

@Droog Andrey: My mistake. 5s² for Y is non-representative, at 11%. 5s4d is 80.7%. Y is more like Sc. Sandbh (talk) 04:19, 21 January 2020 (UTC)

In that case it is still in favour of Lu for giving a more homogeneous trend (two one way, two the other way, rather than two one way, and each of the other two another way). Well, you can explain the La trend by noting that relativistic effects are not significant at La but must be taken into account for Lu (a bit), Ac, and Lr, but why go for the split d-block when you don't have to? Double sharp (talk) 08:14, 21 January 2020 (UTC)

@Double sharp: No. La acts even more like a d element with its d2 configuration; Lu acts more like an end-of-block element. Sandbh (talk) 11:33, 23 January 2020 (UTC)

@Sandbh: Y⁺ is 5s². Droog Andrey (talk) 13:43, 21 January 2020 (UTC)

Well, then Droog Andrey's initial comment stands completely. ^_^ Double sharp (talk) 16:08, 22 January 2020 (UTC)

@Droog Andrey: @Double sharp: The NIST ref is not relevant here. Under the experimental conditions set out in the article (which applied to Sc, Y, La and Lu) the predominant configuration of Y, by a > 7 to 1 margin, was 5s4d. Sandbh (talk) 11:33, 23 January 2020 (UTC)

Extracts:

1. "The apparent thresholds and shapes of the cross sections in the threshold region are very similar for Sc, Y, and La. For Lu, the onset of reactivity is slower than for the other ions (Figure 2)." (pp. 3154—3155)

2. "For M = Sc, Y, and La, formation of MH⁺ is favored over formation of MD⁺ by factors of approximately 2.0, 1.4, and 1.2, respectively. The behavior of Lu is quite different from the other three systems." (p. 3156)

3. "For several other systems, we were able to observe the reaction of a single state and this simplified the thermochemical analysis. For the Sc⁺, Y⁺, and La⁺ systems, several states are always present and presumed reacting. In the absence of experimental information to the contrary, we assume all states are present with populations given by Table I and that they have equal reactivity. This is our standard procedure for cases such as these. In the case of Lu⁺, it is assumed that the only state that reacts is the ground state, since the only significantly populated excited state is expected to react inefficiently, as discussed below. (p. 3156)

4. "The Lu⁺(SI) system is rather different from the other three systems in several respects." (p. 3158)

5. "The diabatic reactivity rules developed previously for the first-row transition-metal elements do not hold for the group 3 elements. This is consistent with the existence of surface crossings that are avoided, leading to adiabatic reactivity. Sc⁺, Y⁺, and La⁺ are seen to react primarily via insertion, while Lu⁺ reacts via an impulsive mechanism at threshold and via a direct reaction at higher energies. (p. 3158)

6. "Sc⁺, Y⁺, and Lu⁺ show adiabatic behavior, with crossings from potential energy surfaces derived from s² and sd configurations to more reactive surfaces derived from d² configurations (Sc and Y) or sd configurations (Lu). For La⁺, diabatic reaction along a d² surface explains the bulk of the reactivity." (p. 3158)

The last extract is interesting. While Sc, Y and La interact with dihydrogen via an insertion mechanism, and Lu impulsively at threshold energy and in a direct manner at higher energies, how they get there is different depending on the electron configurations involved, including at higher energies. So Sc, Y and Lu get there adiabatically and La gets there diabatically. The electron configurations at higher energies are:

And I wonder why this particular case, where Sc and Y show behaviour like Lu, and La is different, is being given nary a mention? Double sharp (talk) 00:36, 26 January 2020 (UTC)

Sc⁺ ³D 4s3d   88.6%
    ¹D 4s3d    6.0
    ³F 3d²     5.4
   ≥¹D 3d²    <0.1

Y⁺
    ¹S 5s²    11.6
    ³D 5s4d   80.7
    ¹D 5s4d    6.7
    ³F 4d²     1.0
   ≥³P 4d²    <0.1

La⁺
    ³F 5d²    69.3
    ¹D 6s5d   12.6
    ³D 6s5d   16.4
    ³P 5d²     1.2
    ³P 6s²    <0.6

Lu⁺
    ¹S 6s²    99.7
    ³D 6s5d    0.3
   ≥¹D 6sSd  <0.01

Sandbh (talk) 05:51, 19 January 2020 (UTC)

How is the +1 oxidation state significant for any of these elements? And electron configurations at higher energies cut both ways: if you look at La³⁺, the first excited state is 5p⁵4f¹: the 5d configuration is 1.6 eV higher in energy. Double sharp (talk) 09:49, 19 January 2020 (UTC)

In the same way that the first IE of the elements is a key indicator of periodic trends. Sandbh (talk) 06:59, 20 January 2020 (UTC)

And what about the third one, which (1) often corresponds to an actually existent oxidation state for these elements, and (2) consistently for everybody means that the outer s-electrons have been ionised anyway already and results in comparing a more analogous situation for everybody? To quote Droog Andrey's plot again:

Double sharp (talk) 14:41, 20 January 2020 (UTC)

@Double sharp: Preliminary comments. The graph doesn't appear to compare like-with-like at least in the case of the Ln. In La, Ce and Gd atoms, a d electron is ionized; in Pr to Yb (excl. Gd) an f electron is ionized; and in Lu a d electron is being ionized. In the case of the An, at least for Ac and Cm a d electron is being ionized, whereas for Lr a p electron is ionized? Sandbh (talk) 07:03, 21 January 2020 (UTC)

By this standard, first ionisation potential would be irrelevant because the first electron to go varies across the table (certainly Pd is not giving up an s-electron). So this 3rd IP trend is no worse and maybe even better for f- and d-block elements, to ionise away the outer s-shell most of the time. Anyway: for La and Gd, a d electron is ionised, but for every other f-block lanthanide it is an f electron. For Lu it is an s electron. Ac gives up an s electron, Th and Pa give up a d electron; but for every other f-block actinide it is an f electron. And Lr gives up an s electron and is here completely homologous to Lu. The point of this graph is that the position of Eu and Yb in most representative lanthanide trends, not Gd and Lu, is analogous to that of Mn and Zn in a 3d trend, which suggests that the real end of the block is Yb. Double sharp (talk) 08:09, 21 January 2020 (UTC)

@Double sharp: I’m still looking at this. It seems (a scary word for me) that the pattern moves to the left or right depending on whether the IE is for +2, +3, or +4. For example, the +2 peak in the 3d metals is Cr; +3 is Mn; and +4 is Fe. Curiously, for the Ln, +2 peaks at Gd, +3 at Eu, and +4 at Gd! And the +4 IE for Lu is nothing that special, compared to Yb, which is weird. Sandbh (talk) 10:01, 21 January 2020 (UTC)

So what? Look at 2nd ionisation energies from He onwards and you will see the big gap occurring between group 1 and group 2, not group 18 and group 1. But we look at the most relevant one in each case. For main group elements, 1st IE is the most reasonable; but for transition elements, since the difference is in the inner shells, 3rd IE is the most reasonable because that ionises away the covering s-shell. Double sharp (talk) 13:39, 21 January 2020 (UTC)

I see the 3rd IE pattern doesn’t work for the p- block elements. Sandbh (talk) 11:02, 21 January 2020 (UTC)

Because those do not have a covering s-shell like the d- and f-block metals do. 3rd IE is the most relevant for groups with this outer covering s-shell, and thus to the whole transition region. So it's relevant for a wide swath of the periodic table, and not just a single group. Looking at 3rd IP smooths out the irregularities caused by differing configurations for transition elements as of the most stable oxidation states. For the 3d metals this is +2, with a peak in the IE trend line at Cr (group 6). For the 4d metals it's +4 peaking at Ru (group 8), and for the 5d metals it's +4 peaking at Os (group 8). So the TM trend lines have no particular relevance.

The third IE trend line along the f-block can be shown as…

La to Eu            |Gd to Yb            |
--------------------------------------------
La Ce Pr Nd Pm Sm Eu|Gd Tb Dy Ho Er Ym Yb|Lu
  U  U  U  U  U  U  D  U  U  U  U  U  U  D
                    |                    |

In this case each half of the f-block has a UD finish.

or as:

  |Ce to Gd            |Tb to Lu            |
-----------------------------------------------
La|Ce Pr Nd Pm Sm Eu Gd|Tb Dy Ho Er Ym Yb Lu|Hf
  U  U  U  U  U  U  D  U  U  U  U  U  U  D  U
  |                    |                    |

In this case each half of the f-block has a DU finish.

It makes no intrinsic difference. Sandbh (talk) 01:08, 22 January 2020 (UTC)

@Sandbh:It makes a huge difference. Droog Andrey (talk) 15:05, 22 January 2020 (UTC)

@Droog Andrey: Well, I did say “intrinsically” for a reason. Sandbh (talk) 04:48, 23 January 2020 (UTC)

@Sandbh: And we all know that reason: your devotion to La table :) Droog Andrey (talk) 11:51, 23 January 2020 (UTC)

+1 Double sharp (talk) 19:57, 8 February 2020 (UTC)

Just graph 1st IEs in B through Ne. Or 3rd IEs in Sc through Zn. In every first row of a block, you get the UD finish. As you obviously must because getting the D means that you have started the second half of the block, as the new electron is ideally paired with another one and the repulsion means ionisation energy should decrease! The fact that you see this going from Eu to Gd, but not from Gd to Tb, speaks volumes about how this effect is important and that it is really Gd which is anomalous (should be f⁸ but happens to be f⁷d). A La table creates an irregularity that is absent from a Lu table. (As everyone expected, since a La table looks irregular in the first place.) Double sharp (talk) 15:51, 22 January 2020 (UTC)

@Double sharp: I agree. The irregularity arises because of the delayed start of filling of the 4f subshell. Sandbh (talk) 04:58, 23 January 2020 (UTC)

Here’s a related article, “Periodic trends in chemical reactivity: Reactions of Sc+, Y+, La+, and Lu+ with methane and ethane".

The conclusion is interesting re the influence of the closed 4f shell on the reactivity of Lu.

"In most respects the data for the different metals are quite similar, although Lu+ has distinct low-energy behaviour.”

"Overall, the reactivities of the group 3 metal ions with methane and ethane are quite similar. Further, the thermal chemistry of the metal hydride ions, metal dihydride ions, metal methyl ions, and metal methylidene ions for Sc+, Y+, and La+ are all comparable. Lu+ differs somewhat in both respects. The difference between La+ (which has no 4f electrons) and Lu+ (which has a filled 4f shell) must be a result of the differing 4f orbital occupancy. However, there is no indication of direct participation of the 4f orbitals. Rather the effect of the 4f orbitals is probably an indirect one. Namely, the occupation of these orbitals raises the energy of the 5d shell such that the two valence electrons in the ground state of Lu+ both occupy the 6s orbital. In La+, the energy of the 5d and 6s orbitals is much closer, leading to open shell electron configurations. The closed-shell stability of the Lu⁺(^lS,6s²) ground state probably accounts for its distinct reactivity compared with Sc+, Y+,and La+."

Sandbh (talk) 08:28, 22 January 2020 (UTC)

So the fact that 4f is added going down from Y to Lu has an effect. That's exactly like how the fact that 3d is added going down from Al to Ga has an effect, so it's more evidence for Sc-Y-Lu for the regularity of the table pattern. It brings Lu closer to the rest of the 5d elements and follows the regular pattern that in every even period, we add a new block, and that the contraction that results impacts the properties of the following elements. The scandide contraction impacts Ga through Kr (all six elements in the next 4p row) just like the lanthanide one should impact Lu through Hg (all ten elements in the next 5d row). Double sharp (talk) 16:08, 22 January 2020 (UTC)

@Double sharp: No, what regularities there are arise out of considering periodicity in the properties of the elements, not the other way around. The Ln contraction is still going in Lu; that’s not the same as what happens in the 4p row. Sandbh (talk) 11:41, 23 January 2020 (UTC)

No, we have a uniform contraction across the whole period, as we know from high school chemistry. Just look at the table at atomic radius. All that we are doing is singling out bits of it that correspond to the filling of various periods. You will get a contraction whether you look at Y³⁺ through Ag³⁺ or Y²⁺ through Ag²⁺. And either way, it will extend to limit cases like Sr, Cd, or In depending on what exactly you are plotting. So why can't we say that Lu is not only the end of a Ln contraction (which is significant mostly because the Ln are in the same oxidation state almost all the time), it is also the start of a 5d contraction? We could say the same about Zn as well, since Zn²⁺ vs. Mg²⁺ shows similar behaviour to Ga³⁺ vs. Al³⁺. Double sharp (talk) 12:18, 23 January 2020 (UTC)

@Double sharp: It’s not uniform. It varies according to the electron type. Lu 3+ [wrong; meant to say La 3+ Sandbh (talk) 07:10, 26 January 2020 (UTC)] doesn’t start the 5d contraction; it has no d electrons. Sandbh (talk) 04:51, 25 January 2020 (UTC)

By that logic, neither do Sc³⁺ and Y³⁺. And by that logic, the d-block in period 6 runs from Hf to Tl. Which is exactly why I think saying "oh, there is this separate contraction, and it has to start when the appropriate cation has 1 electron of the appropriate block and not 0" is a bit silly. Where, other than the 4f row, is there an "appropriate cation"? Double sharp (talk) 10:11, 25 January 2020 (UTC)

P.S. Your correction doesn't matter. Neither La³⁺ nor Lu³⁺ have a d-electron. So in any case, by this logic, a d-contraction must start in group 4 and end in group 13. Which is clearly silly. ^_^ Double sharp (talk) 14:23, 30 January 2020 (UTC)

@Double sharp: Let’s exercise some common sense here. I’ve only seen the scandide contraction referred to in the sense of its impact on, for example, group 13 onwards and, for example, what happens to the pattern of ionic radii going down group 13. Yes, the Ln contraction is unique. Welcome to one of Nature’s subtleties. Sandbh (talk) 07:10, 26 January 2020 (UTC)

Yes! And again, that is because only in the 4f series is there a constant cationic charge that lets you see it. See Greenwood and Earnshaw's chapter on the Ln (see, I can refer to the literature too, just as well). This is so unique that even the 5f series does not display it, which speaks volumes against considering it as something that should affect the entire f-block. And the 6f series should be even further from this kind of behaviour. In every other case (broadening it to the whole periodic table, not just f series), the important thing is the knock-on effect after the shell has completed, because there is no constant cationic charge across a contraction like Ca through Zn. In a case when the new shell has no radial nodes, this creates secondary periodicity because we are just starting to have a new incomplete shielding effect. Switching out La for Lu destroys this pattern. And for what reason? Only to satisfy the completely one-off occurrence where the +3 state is a good comparison for everybody in the lanthanides. It doesn't even hold for the actinides, when Lr is extremely weird for a late actinide, but Ac is more normal as an early actinide. So are we going to show a Sc-Y-La-Lr table with the break in a different place for each, or are we going to apply some common sense about the pattern and recognise that it's the 4f series that is singular and shouldn't dictate things? We know very well that the first subshell of a given angular momentum is anomalous, going s >> p > d > f. Why are we letting the anomalous 4f, rather than the normal 5f, set the tone for how we draw the f-series? We can't even argue that 5f is outside the sphere of the average chemist, since thorium and uranium are almost normal elements. Double sharp (talk) 10:22, 26 January 2020 (UTC)

@Double sharp: Eh? The Ln and An have in common the +3 oxidation state. A consistent contraction (absent Th 3+) can be discerned across the +3 An ions. See this article. Note the comments about the unusual behaviour of La and Ac, once again separating them from the rest of the Ln and An. I know what will follow :) an obtuse argument that attempts to leverage this nice article to supporting Lu! Sandbh (talk) 07:38, 28 January 2020 (UTC)

Right in one, except that the argument will not be obtuse. Firstly, +3 is manifestly not a characteristic oxidation state for Th, Pa, U, and Np. U³⁺ even reduces water, so if +3 is characteristic for it, we're back to admitting +3 for Zr and Hf. Secondly, this is not in any way "unusual behaviour". It is simply an effect of the Ln and An contractions: La and Ac are the largest Ln and An cations respectively, which totally explains all this behaviour. We could equally well single out Lu and Lr as the smallest for the same reason. Double sharp (talk) 11:36, 28 January 2020 (UTC)

@Double sharp: This is a good example of setting aside my context ("Ln and An have in common the +3 oxidation state") and substituting your own "+3 is manifestly not a characteristic oxidation state for Th, Pa, U, and Np" noting I never said that, and then going down your own path about +3 for Zr and Hf. I am able to say "Ln and An have in common the +3 oxidation state", and that there is an Ln contraction which parallels the An contraction. The fact that the +3 oxidation state is not the most stable for Th to Pu, and No, doesn't invalidate my argument. The fact of the existence of +3 for Zr and Hf doesn't invalidate my literature supported argument that the chemistry of group 3 is predominately ionic, whereas that of group 4 is predominately covalent. Sandbh (talk) 06:08, 1 February 2020 (UTC)

@Sandbh: By your standard, I can equally well claim a +3 contraction from Sc through Cu, Y through Ag, and Lu through Au. (Every one of those elements has a +3 state. Whether or not it is happy to be in it is another story). Then I can equally conclude that group 3 does not belong in the d-block because the contractions have not started yet. Or even better, I can claim a +1 contraction. (Yes, all of them have it but Lu so far, and I have no doubt that that's just because no one has bothered to try it!) Then the d-block evidently starts in group 2 instead! All I am saying is: be consistent. If you say that weird oxidation states are invalid in one argument, then I'm not seeing why this is so different that they suddenly become valid. Meanwhile, as I've already explained, "predominantly ionic" if it means anything just means "low EN and low oxidation state", which are two properties that matter more for the chemistry. In that case we get into serious difficulties, with: (1) Zr and Hf having lower EN than Sc (so if +3 matters, suddenly they also become "quite ionic"); (2) Tl looking more ionic than its EN should allow just because it prefers to be in the +1 state; (3) Th, Pa, and U being strongly active metals whose preferred states are too high to be ionic. You can't really resolve (3) without also letting (1) swing the way you don't want, because protactinium also prefers high oxidation states and has EN 1.5 on the Pauling scale: this is far too high to be ionic, but somehow Pa is an active metal anyway patterning with the pre-transition ones. Did I mention that Pa prefers +5, which is one step higher than +4 for Zr and Hf, which also have EN less than 1.4? Meanwhile, my criterion (look at chemically active subshells if conclusive, if inconclusive look at properties to homogenise a block) works perfectly from element 1 to element 172, even. Double sharp (talk) 10:15, 1 February 2020 (UTC)

@Double sharp: Unfortunately you’re taking my context and applying it to a different, obtuse context. The scandide contraction describes the effect of having full 3d orbitals on the period 4 p elements. That’s all. I’ve never seen it applied to the 3d ions per se. It doesn’t apply to the whole of the d-block first row, since it would start at Ti3+ and finish at Cu3+ since Sc 3+ has no d electron and there is no Zn 3+. The comparison with the Ln and An contractions isn’t there.

Just read what Greenwood and Earnshaw has to say about the Ln contraction in their chapter on the Ln. It agrees with what I have been saying: there are 1001 contractions in the whole periodic table, and the Ln one is special only because everyone is in the +3 oxidation state most of the time. They even give the 4d example of Y³⁺ (nota bene, with no 4d electrons!) through Ag³⁺. The moment the constant +3 oxidation state is not maintained, the Ln behave differently, like in any other contraction. Notice how the An contraction is much more rarely referred to than the Ln one, for precisely this reason. Double sharp (talk) 11:26, 1 February 2020 (UTC)

On predominately ionic v predominately covalent you’re again drifting off the broad contours and descending into details that are irrelevant at the broad contour level. Sandbh (talk) 10:53, 1 February 2020 (UTC)

Nope. The details determine the broad contour. In particular, Be and Mg are neither "highly electropositive" nor "predominantly ionic". And Th, Pa, and U are "highly electropositive" but not "predominantly ionic". And Tl is "predominantly ionic" but not "highly electropositive". I think that says it all about which one is the relevant criterion. Wulfsberg had the right idea by focusing on EN, even if his breakdown is not quite right: really, by his EN < 1.4 criterion, the highly electropositive ones ought to be: Li through Fr; Ca through Ra (peripheral Mg); Ln and An (Pa is too high only because of its high oxidation state); Sc through Lr; Zr through Rf. Double sharp (talk) 11:26, 1 February 2020 (UTC)

@Double sharp: The broad contours are generally determined by an 80/20 approach. The 80 = the big picture; the 20 = the noise. For example, oxygen generally has an oxidation number of -2 in the combined state. Group 3 has a mainly ionic chemistry; groups 4 to 12 have a mainly covalent chemistry. If all you know about the weather is that there are four seasons then you know about 80% of what there is to know, as another example. Sandbh (talk) 03:08, 2 February 2020 (UTC)

@Sandbh: As I have already demonstrated by reference to Tl and Th, this is not the most relevant criterion at the large scale. You would, in fact, do much better just looking at EN like Wulfsberg does to get a broad contour. Double sharp (talk) 09:49, 2 February 2020 (UTC)

A historical chemical perspective on group 3

@Double sharp: @Droog Andrey: As noted by Jensen, early spectroscopic work on the Ln seemed to indicate that the ground states of their atoms had, with few exceptions, an electronic configuration of the form:

f = 1 to 14, d1 s2

So La was d1 s2 and Yb was thought to be f 13 d1 s2 and Lu f 14 d1 s2.

It was subsequently determined that most of the Ln were:

f = 1 to 14, s2

Only Ce, Gd, and Lu also had a d electron. And it turned out that Yb was f14 s2 i.e. the f shell was completed over the course of 13 rather than 14 elements, a little bit like the d shell being filled over the course of 8 or 9 rather than 10 elements.

The interesting thing about the new configurations is that nothing changed for La and Lu in terms of their configurations and their chemistry.

So they stayed where they were, La under Y, and Lu at the end of the Ln.

A few tables of the 1920s and 30s showed Lu under Y for reasons of regularity (Janet) or because Lu occurred in the “yttrium” group (along with Sc and Y) rather than the “cerium” group (which included La).

But this never took off.

That Sc, Y and Lu occurred in the so called yttrium group, and that La occurred in the "cerium" group did not imply anything particularly significant; it is simply a reflection of the increasing basicity of these elements as atomic radius increases. Taking the alkaline earth metals as another example, Mg (less basic) belongs in the "soluble group" and Ca, Sr and Ba (more basic) occur in the "ammonium carbonate group". Moving Lu under Y because they occur in the same chemical separation group failed to consider separation group patterns elsewhere in the periodic table.

Further, the separation group behaviour of Y can be ambiguous, and Sc, Y, and La appear to show complexation behaviour different to that of Lu, per the quotes by Vickery (1960, 1973) earlier in our discussion.

In this context, the old chemists who kept La under Y were on the mark, chemically speaking.

It’s ironic that the condensed phase configurations of most of the Ln is indeed f1-14, d1 s2 and that, in this context, the 4f shell is not completed until Lu. Sandbh (talk) 04:24, 23 January 2020 (UTC)

Chemically speaking, there are probably about as many cases when Y is more like La as cases when Y is more like Lu. Again, that is expected, because of the small differences involved. So neither is "mistaken" in that sense. It is like comparing Al to Sc and Ga. Or comparing Mg to Ca and Zn.
Inertia could hold for Sc-Y-La because it is not obviously wrong. It gives an OK trend, even if it is weird that it acts like groups 1 and 2, which have absolutely no double periodicity because of the way the Madelung rule works (even the other main groups don't follow that). And La is not obviously a wrong congener for Y. Now that we understand this better, and actually know all the elements involved up to the seventh period, the star of Sc-Y-Lu has been rising due to significant adoption (e.g. WebElements).
Condensed phase configurations suggest that Be and Mg are p-block elements, which just about says it all about why I think this is not a good argument.

So now that we know all the elements involved, and we know the general Madelung pattern, it seems to me that Sc-Y-Lu is the simpler case (that nothing fancy is going on) and should be our null hypothesis. Since the evidence that brings Sc-Y-La over Sc-Y-Lu is pretty small, all things considered (despite the amount of verbiage we alone have written about it ^_^), I put it that there is not enough evidence to reject H₀. Double sharp (talk) 12:14, 23 January 2020 (UTC)

@Double sharp: I try to stay away from comparisons of individual elements like Y v La or Lu but I do get sucked in now and then. It occurs to me that Al goes over Ga since both are p elements. Mg goes over Ca since the fit is better in terms of electron configurations. This principle can be extended to La and Lu.

And I try to stay away from anything other than chemistry, because after thinking about it for this long I am almost certain that you will not find a philosophical argument that actually stands up to all the counterexamples the elements seem willing to provide us and actually reflects the richness of what we are trying to depict. Again: without the chemical properties that Mendeleev observed, what is the basis of periodicity?
@Double sharp: The elements do provide many counter examples at their level. When you step up into the balcony and observe the dance floor, you’ll see the general patterns and that the La form provides greater regularity/fewer irregularities. DIMs focuses was on the binary compounds rather than the individual elements so much. Sandbh (talk) 06:48, 26 January 2020 (UTC)
Lu fits better under Y in terms of electronic configurations because we are in an even period outside the s-block, and we expect a new shell type to be added. Same as Zr to Hf, Nb to Ta, all the way to Xe to Rn. And Al to Ga, too. Double sharp (talk) 00:20, 25 January 2020 (UTC)
@Double sharp: No, we don’t necessarily expect a shell type to be added because we know the n + l rule is an approximation only, and it has no first principles basis. Sandbh (talk) 06:48, 26 January 2020 (UTC)
@Sandbh: Yes we do because it works perfectly well from H to Xe. The null hypothesis is clearly that nothing special happens, and it is the alternative hypothesis that something new and different happens that demands proof. Proof which I still don't see. Double sharp (talk) 10:34, 26 January 2020 (UTC)

There’s nothing particularly weird about group 3 acting more like groups 1 and 2.

Indeed, since groups 4 and 5 also act more like groups 1 and 2 very often, so the argument does not amount to that much in hindsight. Double sharp (talk) 00:20, 25 January 2020 (UTC)

@Double sharp: That’s complete nonsense. I’m astonished to think you could post such rubbish. For the seven thousandth time, as per the literature, groups 1 to 3 have a predominately ionic chemistry. Groups 4 and 5 have a predominately covalent chemistry. End of story. The end. Period. Sandbh (talk) 06:48, 26 January 2020 (UTC)

Look, there is no such thing as a complete volte-face from ionic to covalent. It depends on what the counter-anion is. We go from ionic to metallic (which you're overlooking completely) across the series NaCl, Na₂O, Na₂S, Na₃P, Na₃As, Na₃Sb, Na₃Bi, Na. And that's in group 1, with an example taken straight from Greenwood & Earnshaw p. 81. Ionic vs. covalent is (1) gradual, from covalent to polar covalent to mildly ionic to strongly ionic, depending on the difference of electronegativity between the two elements; (2) not a complete dichotomy, because you overlook metallic bonding; and (3) not split by elements, but rather by electronegativity differences, which have a lot to do with oxidation state (just compare uranium chemistry as we jack the oxidation state up from +3 to +4 to +5 to +6). So I'm astonished to see you put so much weight on "ionic vs. covalent" as a false dichotomy. (And as I keep saying, the general thing across the periodic table is continuity, and the sharp dichotomies you like to point to have a distinct tendency to not exist.) The whole literature, when it sees fit to split "main group" from "transition", universally uses other criteria like "variable oxidation states", "coloured compounds from d–d transitions", "a wide variety of complexes", "formation of paramagnetic compounds". Ionic vs. covalent has nothing to do with it, and nobody uses that as a criterion in the literature for this divide. Respectfully, I put it to you that Zr, Hf, Nb, and Ta by this standards have weak credentials as transition metals, just as weak as Sc for that matter. Double sharp (talk) 10:32, 26 January 2020 (UTC)

Jensen did spark some interest in the Lu form but nothing substantial came of it. Webelements adopted it on the basis of his arguments, which were not balanced, as per our IUPAC submission.

On balance, I would tend to say now that he did not give the full story and that it is more complicated than his arguments would suggest. (As it is for his treatment of group 12, where in particular I think he's being far too extremist about it being totally not a transition group; it is even wrong for Cn.) However, in this case I think his conclusion is more or less sound, even if not always his arguments. There is just not enough reason to go for Sc-Y-La because both the La and Lu forms exhibit good trends, and the Lu form shows a balance between the s- and d-blocks for this peripheral group 3. Double sharp (talk) 00:20, 25 January 2020 (UTC)

AFAIK the chemistry of Be and Mg is that of hybridised sp elements, not that this makes any difference.

The n + l “rule” is not that helpful since an Lu table has 13 n + l irregularities while the La form has only 12. For sure, if the 4f subshell started filling at La there’d be no issue.

We have to remember that the forces that interact to produce the actual sequence of electron configurations do so consistently and regularly. The fact that we interpret the end result as featuring “anomalies” is a result of focussing too much on the regularity of the n + l rule, which is only an approximation.

The whole point is that the n+l rule is approximately right on what subshells are going to be filled. It is even completely right on what subshells will turn out to be chemically active. And I stand by calling them anomalies, when stuff like Nb d⁴s¹ vs. Ta d³s² and Lu ds² vs. Lr s²p means about nothing for their chemistry, which follows more or less ideal configurations of d⁵ and d³ respectively for compounds. Double sharp (talk) 00:20, 25 January 2020 (UTC)

Like Eric Scerri wrote in the 2nd edition (2020) of his periodic table book:

"Too many proponents of alternative periodic tables seem to argue about the regularity in their representation and forget that they may be talking about the representation and not the chemical world itself." (p. 387)

"...we should beware of arguments based on symmetry and regularity." (p. 401)

Sure, but there's nothing wrong with them when the chemistry is itself inconclusive. In that case the symmetric form is preferable because breaking the symmetry when both options are finely balanced makes it look like the situation is more conclusive than it really is, just because the symmetric form is by definition a null hypothesis: "things shall go on as they always did". Double sharp (talk) 00:20, 25 January 2020 (UTC)

Of the Lu tables out there the LST or ADOMAH can be regarded as representing, at least in some sense, the situation pre-symmetry breaking as per the n + l rule. Those tables are representations of this theoretical and beautiful tetrahedral symmetry. The n + l rule provides the underlying basis or spine of the periodic system. Despite the blemishes, periodicity continually returns back to the n + l rule. That is worth showing, as a table towards the physics end of Scerri’s continuum of periodic tables. At the other end is Rayner-Canham’s unruly inorganic chemist’s table. In the middle somewhere is the conventional La form. Sandbh (talk) 00:06, 25 January 2020 (UTC)

@Sandbh: n+l rule was derived from 1st principles by Klechkovsky in 1951. Droog Andrey (talk) 11:14, 27 January 2020 (UTC)

@Droog Andrey: Klechkovsky‘s article is disputed. According to Scerri the rule has still not been so derived. The Löwdin challenge for a first principles derivation still stands.

@Sandbh: And yet the n+l rule works absolutely perfectly, except for the Ca group, if you take it at the broad level of "what subshells are chemically active". (Which makes sense, as I have repeatedly noted that counting exceptions is silly if you realise that Nb d⁴s¹ and Ta d³s² are so similar.) So even if a 1st-principles derivation for the n+l rule happens to not yet exist, its power and accuracy suggests that seeking to derive it is a worthwhile goal with significant likelihood of success, and that it makes a good basis for the PT. Double sharp (talk) 19:39, 1 February 2020 (UTC)

And I wonder how this "historical chemical perspective" would look for Be-Mg-Zn? If we argue that Be-Mg-Zn is "obsolete", then how do we know that it is Sc-Y-Lu rather than Sc-Y-La that will eventually turn out to be "obsolete"? I rather think the Sc-Y-La option is more likely to go that way. If Sc-Y-Lu were to become the default, and generations grew up learning it, no one would be suggesting Sc-Y-La as a symmetry break when it is self-evident that the trends are inconclusive. (This is indebted to one of R8R's arguments from one of the previous times this was discussed.) But if Sc-Y-La continued to be the default, there would probably continue to be a sizable unhappy minority advocating Sc-Y-Lu, just like there is now. And indeed, the minority has been arguing for long enough that Sc-Y-Lu has, if not become dominant, at least become a widespread alternative. That strongly suggests that Sc-Y-La is just chugging along as a fossil of the time with no f-block. Double sharp (talk) 19:43, 1 February 2020 (UTC)

A historical perspective, cont.

@Double sharp:

I think I know why the La form remains popular.

Historically, the Ln were known to be chemically very similar.

Originally, the 4f sub-shell was thought to be complete only at Lu.

So, with the popularity of electronic periodic tables, La was placed under Y since La did not have an f electron, and the Ln ran from Ce to Lu.

It was later recognised that the 4f shell was prematurely completed at Yb, and that Lu was in fact 4f¹⁴5d¹.

Nothing happened however, since the chemistry of Lu, as a lanthanide, remained 100% unchanged.

So La remained under Y in recognition of the delayed start to the filling of the 4f subshells, and the unchanged chemistry of Lu.

The resulting separation of the d-block in the 32-column form never became an issue in light of the overwhelming popularity of the 18-column form.

PS: Library day looks like it will be Monday. Sandbh (talk) 10:34, 5 February 2020 (UTC)

@Sandbh: I bet it is simply inertia combined with not being too obviously wrong, since the lanthanides are so similar anyway. But while chemically speaking in isolation both Sc-Y-La and Sc-Y-Lu make sense as trends (and I would still advocate considering both elements in a comparative chemistry review for group 3), La in group 3 flies in the face of the logic of the periodic table, since La is an f-block element with its low-lying f-orbitals. (Yes, for the same reason, I side with Henry Bent on He over Be.) Double sharp (talk) 20:29, 5 February 2020 (UTC)

@Double sharp: Was it really inertia? Let's recall that differentiating electrons sorted out the placement of La. And when it was realised that the f series in fact finished at Yb rather than Lu, this had zero impact on the chemistry involved. The presence of low-lying f orbitals are not on the radar in this fundamental context. OTOH, the fourteen f electrons in Lu³⁺ and the impact of their poor shielding on the size of the Lu cation, are on the radar. That's not just my opinion; it's the consensus in the literature.

More history. It occurred to me that there is another aspect to this.

The recent interest in symmetrical forms such as ADOMAH, can be traced back to Janet's Left Step Table (1928). His table was neither a chemical table nor an electronic table, since he choose it for its symmetry. In fact he corrected some of what he thought were incorrect electron configurations to make it fit with the n + 1 rule. He was wrong since what he took to be erroneous electron configurations were in fact correct. So the n + l rule was wrong too.

In contrast to Janet's approach it was known from as early as 1929 that "…If Sc, Y, La and Ac are the only rare-earth elements, the series would have revealed the same gradual change in properties as the Ca, Sr, Ba and Ra series, and hence it would not have been of any special interest." (from our IUPAC submission).

Now, in Jensen's seminal 1986 paper, "Classification, symmetry and the periodic table", he wrote that if the classes in a periodic table appear in symmetry related positions, rather than being imposed beforehand, then both phenomena would suggest the resulting classification is really a natural one (pp. 496-497).

In other words, the interest in symmetrical forms and the n + 1 approximation is mis-founded since this starts with symmetry first, rather than arranging the elements DIM fashion according to the periodic law. This resulted in a non-symmetric table, which eventually evolved into the non-symmetric 18-column La form.

Jensen's words are echoed by C. A. Coulson, theoretical chemist and professor of mathematics, who concluded his Faraday lecture on symmetry with the words:

"Man's sense of shape—his feeling for form—the fact that he exists in three dimensions—these must have conditioned his mind to thinking of structure, and sometimes encouraged him to dream dreams about it. I recall that it was Kekule himself who said: "Let us learn to dream, gentlemen, and then we shall learn the truth." Yet we must not carry this policy too far. Symmetry is important, but it is not everything. To quote Michael Faraday writing of his childhood: “Do not suppose that I was a very deep thinker and was marked as a precocious person. I was a lively imaginative person, and could believe in the Arabian Nights as easily as in the Encyclopedia. But facts were important to me, and saved me.” It is when symmetry interprets facts that it serves its purpose: and then it delights us because it links our study of chemistry with another world of the human spirit—the world of order, pattern, beauty, satisfaction. But facts come first. Symmetry encompasses much—but not quite all!
Coulson CA 1968, "Symmetry”, Chemistry in Britain, vol. 4, pp. 113–120.

The takeaway from Coulson is that "facts come first" per DIM, and later the real aufbau sequence, which together resulted in the La form.

How do you see this? I can see a very strong additional argument coming out of it. Sandbh (talk) 23:25, 5 February 2020 (UTC)

Philosophical considerations

@Droog Andrew:@Double sharp:@YBG: In drafting the article I tried to take a more philosophical slant. By this I mean considering the foundational concepts, theories, and methods associated with the PT, and the interrelations between them rather than the properties of individual elements. Well, that sounds good anyway. For now, until I replace the above placeholders and address the other outstanding remarks it appears to me that:

the global considerations are interrelated;
in an La table they reinforce one another; and
in an Lu table each consideration is breached.

Sandbh (talk) 04:27, 13 January 2020 (UTC)

The problem is that I'm not convinced that your considerations are indeed foundational. Differentiating electrons are only conclusive about group 3 because of Lr's p-electron, which is both (1) a weird side effect of relativity and (2) completely irrelevant chemically; and valence shells have a whole lot more to do with the chemical considerations that underpin the PT and make a better philosophical basis in my opinion. But that would support Lu-Lr again. Group 3 doesn't unequivocally side one side or the other; it's just a manifestation of the philosophical principle that trends should be continuous, which also supports Lu-Lr (look at the d-block trend). And your last argument seems predicated on distorting the PT arrangement and looking at the patterns you get from doing it, and given that the whole point of the PT is its arrangement I don't see how that could be a philosophical basis for the PT. For me, the PT is based on chemistry, thus valence shells, thus how best to reflect it in a 2D grid and show trends. Each builds on the previous and the last three all point to Lu-Lr.

We have to bear in mind that the PT is not a document engraved in stone that says "this is what the elements are like according to what Nature has given us". It instead says "here is a very useful guideline to how Nature is like, distilled into some generalisations for us humans". Knowing how humans are, the d-block break that Sc-Y-La gives creates a sense of false precision: if we just draw rectangles as for Sc-Y-Lu, we can more easily accept "remember, ye intrepid ones, that this is just an approximation", but breaking something apart as obviously as Sc-Y-La makes it seem like there is some huge qualitative difference between group 3 and the rest of the d-block and makes it look like the PT is reflecting higher-order phenomena than it really is. If there were such a thing, I would most certainly support Sc-Y-La, but I'm not seeing it. I am sure that aliens from the planet Skyron somewhere in the Andromeda Galaxy (I always enjoyed Monty Python's Science Fiction Sketch, where this name is from) will have different psychologies and therefore automatically infer different things when they see different arrangements of elements. They too will see some trends and similarities in the elements and organise it in some way, and who knows how they will do it to connote the right idea? I know not. All I can say is it might not be ours. Let's draw the PT then, conscious that it is not what Nature gave us, but a way to let us understand and organise somehow what She did. And it will be all the more useful to us once we understand what it is for. Double sharp (talk) 04:38, 13 January 2020 (UTC)

@Double sharp:

Well, the good thing is I don't appear to have made any clangers. After that it comes down to opinions.

Main arguments:
1. considerations of Group 3’s neighbours (ionic v covalent chemistry);
2. predominant differentiating electrons across the four blocks of the periodic table;
3. the periodic law (chemistry); and
4. the nature of the rare earths (add including their ionic chemistry).

Ancillary supporting arguments:
5. the predominance of the La form in the literature; and
6. the fact that an Lu table results in more irregularities among all four main considerations across the table, as well as in the regularity of term symbols, and that placing lanthanum (La) and actinium (Ac) in the f-block would be only case where a pair of elements that belong in the same column are placed such that they have no outer electrons in common with that block.

New argument pending:
7. Horizontal triads (chemistry)

Analysis:
1. Per the literature, overall this supports the La form. The secondary considerations you've noted aren't sufficient, IMO, to tip the balance the other way.
2. I don't focus on individual elements, so I don't in that sense care about Lr. As to the foundational nature of d/e's I can go back to Bohr, and others, and at least cite Stewart and Scerri along the way.
3. I've addressed all your objections about this.
4. Ditto.

You're 100% on the mark with the PT not being engraved in stone. That's why I've questioned why IUPAC needs to make a decision about Group 3, when each option can serve its purpose.

There's no false sense of precision about the d-block break. We know that Hamilton (1965; over 50 years ago), shows a periodic table extract (groups 1 to 11, plus footnoted Ln and An, showing Ce, Pr…Lu; and Th, Pa…Lw) with a split d block (the gap is between groups 3 and 4) and says that—without any fuss—this is "the periodic table as it is usually presented".

Indeed it is usually presented that way when done in 32-column form.

None of the split d block tables I've seen recently in text books have raised any fuss on behalf of the authors concerned.

Sir Martyn Poliakoff shows a spit-d block table at the start of his you tube video on the IE of Lr. Again no fuss. [Caveat: the authors of the Lr article did not speculate as to any implications for Group 3, not officially anyway]

The Inorganic Chemistry Division of the ACS, until recently, used a split-d block logo, until I pointed this out to Eric, and he wrote to them about it, possibly in the context of his IUPAC project. See here for a picture. Sandbh (talk) 00:54, 18 January 2020 (UTC)

It's certainly not often (if ever) remarked on, but often when the split d-block is shown, it is shown with a Madelung rule that does not reflect it and instead predicts Sc-Y-Lu. The inconsistency is swept under the rug, but it is still there, and the student who actually reads carefully will likely wonder about it. (I know I did.) Double sharp (talk) 12:19, 23 January 2020 (UTC)

P.S. Re term symbols and "a pair out of place":

In a Lu table, every block ends with a column of nothing but ¹S₀, as we expect since all subshells are supposed to be completely full. A La table violates this.
The fact that extending the periodic table to the 8th-period predictions results in even more elements out of place at the beginning of the putative g-block (unless you want to begin it at E125 and create a chasm inside a chasm) suggests that this has got everything to do with delayed collapses, and can be safely treated as a second-order perturbation to the pattern. And notice that it does not seem to affect when the subshell sinks into the core at all, only when it begins filling up with actual electrons (at a point where it can already be used for hybridisation): Lu, Lr, and E157 have an f-subshell drowned deeper and deeper into the core, something like the d-subshell down group 13 (ignoring Nh; I allow considering E157 as relativistic effects almost exactly cancel out for E157 through E172). Double sharp (talk) 12:23, 23 January 2020 (UTC)

@Double sharp: Yes, I second your observation about the needless confusion surrounding the MR.

On term symbols you are right but for Pd, which also has that kind of symbol. The other thing about term symbols is that two elements can have the same term symbol but differing electron configurations. There is at least one other example (I can’t look it up right now). So I don’t assign too much weight to term symbols. That said, an La table has one less term symbol irregularity than an Lu table which I think is a more important consideration, along with the other irregularities, as discussed, that the Lu table brings. It’s like we want to depict Nature as we think it should be rather than how it really is. That goes for the g block, too. I don’t regard the delayed collapses as second order perturbations, since the pattern is an approximation albeit a very persistent one. Sandbh (talk) 05:49, 25 January 2020 (UTC)

That's the trouble. If you insist on delayed collapses as something first-order that must be represented at all costs, then the sky falls down on our heads once period 8 finally gets started, with a brief foretaste already happening with the asteroid at Lr. If you pragmatically say that it's a second-order phenomenon that is totally normal for heavy elements, pointing to La, incipient Lu (with a surprisingly low 6p level), Ac, Lr, and E121, then you can continue with periodicity with no problem at all. You cannot depict Nature as how She really is, it is far too complex for that. Everything you draw will be a distortion. Everything you draw will be distorted based on some subjectively chosen criteria. And everything you draw will be subject to how humans, with their cognitive predispositions, are likely to see it. So why not just give a first-order approximation that works really, really well? Double sharp (talk) 10:58, 25 January 2020 (UTC)

@Double sharp: The delayed collapse is easy to draw. I recall seeing a 1946 table showing the general approach. It’s no big deal. The sky will not fall down. Let us draw nature as it is not how we think it should look like. Sandbh (talk) 09:34, 26 January 2020 (UTC)

A pretty slogan, apart from the fact that any drawing will bring us away from "nature as it is". Just look at the electron configuration table in extended periodic table and let's see how any drawing can possibly reflect what happens in a few elements' time when 8p collapses at E121, 7d at E122, 6f at E123, and finally 5g at E125, while the superactinide series goes on for so long that 8s and 8p fall into the core and get replaced as valence electrons by 9s and 9p instead to create normal-looking 4d-like transition metals from E157 to E166. Or even just see how any drawing can possibly accommodate Lr with its 7p electron caused by delayed collapses. Double sharp (talk) 10:18, 26 January 2020 (UTC)

@Double sharp: Eh? We make our drawings and seek to iteratively improve them in order to make better and better representations of Nature as we understand it. A pretty slogan? As Proff Poliakoff said "what we're interested in is what nature is like not how easy it is to draw it." Sandbh (talk) 21:25, 1 February 2020 (UTC)

@Sandbh: It's exactly a pretty slogan because Nature is too complicated to draw everything. Think Rayner-Canham's periodic table times a hundred. Double sharp (talk) 00:49, 2 February 2020 (UTC)

@Double sharp: It's the level of abstraction that's the issue. It's funny that I attempt to argue philosophically and you attempt to argue in detail. Sandbh (talk) 01:50, 2 February 2020 (UTC)

@Sandbh: No, I argue both from chemistry and philosophy. I even use some philosophical arguments like homogeneity that you yourself used before, but funnily enough they seem to become invalid when I use them to support a Lu table. ^_-☆ Double sharp (talk) 09:51, 2 February 2020 (UTC)

Fitting Lu to Hf through Hg

Since saying the same thing over and over again seems not to work, I guess I have to do the tables. In every single case I just hurriedly looked at and typed up, the fit for Lu at least is about equal to, and often outperforms, that for La. (Kulsha-Kolevich EN = EN from User:Droog Andrey and his colleague's table, which fixes the problem of Pauling assigning many transition metals overly high values because of strong homoatomic multiple bonds e.g. Mo, W).

property	La	Lu	Hf	Ta	W	Re	Os	Ir	Pt	Au	Hg
m.p. (K)	1193	1925	2506	3290	3695	3459	3306	2719	2041.4	1337.33	234.43
b.p. (K)	3737	3675	4876	5731	5828	5869	5285	4701	4098	3129	629.88
specific heat capacity (J/(g*K))	.195	.154	.144	.14	.132	.137	.13	.131	.133	.129	.14
EN (Pauling)	1.1	1.27	1.3	1.5	2.36	1.9	2.2	2.2	2.28	2.54	2.0
EN (Kulsha-Kolevich)	1.11	1.31	1.38	1.46	1.54	1.55	1.67	1.75	1.84	1.93	1.81
Density	6.145	9.84	13.31	16.654	19.25	21.02	22.61	22.56	21.46	19.282	13.5336
Young's modulus	36.6	68.6	78	186	411	463	???	528	168	78	???
Bulk modulus	27.9	47.6	110	200	310	370	462	320	230	180	25
Resistivity (nΩm, close to r.t.)	615	582	331	131	52.8	193	81	47.1	105	22.14	960
Brinell hardness (MPa)	350-400	893-1300	1450-2100	441-3430	2000-4000	1320-2500	3920-4000	1670	310-500	188-245	???
Heat of fusion (kJ/mol)	6.20	22	27.2	36.57	52.31	60.43	57.85	41.12	22.17	12.55	2.29

And I'm even restricting myself mostly to physical properties, and already the difference is so big. With chemistry it is the same, as Lu is softer than La as a cation and coordinates better, making it a closer match for Hf through Hg. If you did it using predictions for period 7, it would (looking at the meagre data we have) probably be even bigger.

P.S. Any references to lanthanides like Ho and Er are irrelevant here. The goal is not to compete which of La and Lu is more like a lanthanide. They both obviously are. The goal is to see which of them better fits the first position of the 5d row. To do that, the right elements to compare with are Hf through Hg, which form the rest of the 5d row. Double sharp (talk) 17:14, 26 January 2020 (UTC)

My first response is to observe that this is not a question of which 5d metal best fits the position of first 5d metal. We have to remember that the first appearance of the 5d electron is followed by 14 4f electrons. So it is disingenuous to compare La with metals that occur at least 15 atomic numbers later. Sandbh (talk) 22:39, 26 January 2020 (UTC)

Do you want a homogeneous d-block or not? Let me quote you from Archive 38: "a set of items is presumably more representative of its label the more the individual items in it match the label." Well, the label of d-block chemistry is given by what we see of the behaviour of the totally sure d-block elements. So of course we should be comparing with those elements to decide which element to shunt off to the d-block. If you don't want a homogeneous d-block, or homogeneous categories, then what are we doing drawing a table? Double sharp (talk) 23:36, 26 January 2020 (UTC)

P.S. The first appearance of the 7p electron at Lr is followed by ten 6d electrons; the "premature" (of course it is nothing of the sort) filling at Cn is indeed exactly like that at Yb. So by this argument we could argue that it's just as disingenuous to compare Lr with Fl through Og, even though it's obvious that Nh is a much better fit. But would you advocate Lr under Tl? Double sharp (talk) 23:55, 26 January 2020 (UTC)

@Double sharp: The homogeneity of the d block, or otherwise, is not my call—it’s Nature’s call. Nature chooses to delay the filling of the 4f sub-shell. That’s all I’m trying to show. Effectively ignoring this and saying we compare La with the 5d metals from Hf onwards ignores the elephant in the room. Lr under Tl is a non-starter as I believe I’ve addressed elsewhere. Sandbh (talk) 07:08, 28 January 2020 (UTC)

Nature also sees fit to delay the start of the 5f shell to Pa, the start of the 6d shell to Rf, and the start of the 5g shell to E125, so claiming that "Lr under Tl is a non-starter" at the very least casts some aspersions about the very similar case of La and Ac. Again, if you look away from the dance floor of individual weird configurations, this is all just the heavy-element delayed collapse pattern, none of which prevents 4f and 5f from having some sort of rôle at La and Ac anyway. It's certainly bigger than the essentially non-f character of Lu and especially Lr. Double sharp (talk) 07:52, 28 January 2020 (UTC)

@Double sharp: I looked at the figures for La and Lu and compared then to the average values for Hf to Hg, and Ce to Yb, and with Ba.

Lu has more Ln character than 5d character.
La has more Ln character than Ba character.

Neither Lu nor La fit particularly well under Y, on the basis of the eleven properties under consideration. Sandbh (talk) 05:57, 1 February 2020 (UTC)

Of course they do, that's not the point. I can guarantee you that yttrium will show more lanthanide character than 5s or 4d character as well just because of its size and charge. The point is that Lu clearly has more d character than La. Allied with Gschneider's pointful arguments, which we even agreed with in the old submission by noting that La clearly has more f character than Lu, the block assignment is immediately clear just by the principle of categorisation that similar items belong together, which is about as philosophical as you can get for such a thing. No minutiae here. For Ac and Lr, it would be even more conclusive if not for the fact that most things now become predictions. Double sharp (talk) 09:57, 1 February 2020 (UTC)

@Double sharp: Hmm. I feel you are leaving the broad contours and descending into details; and confusing similarity with periodic trends.

Block identity works on the following basis:

predominant differentiating electron;
s is characterised, except in H, by highly electropositive metals; and by the fact that its outer electrons do not withdraw completely into the core until the next subshell of s elements is added; instead it contributes to bonding in the subsequent p, d and f blocks;
p by a range of very distinctive metals and non-metals, many of them essential to life; and by the fact that, when its orbitals are all filled, the six electrons with the two s electrons form an almost impregnable octet in the noble gases;
d by metals with multiple oxidation states; and by the fact that, as its orbitals fill up, they withdraw increasingly into the core until withdrawal is complete in Zn, Cd, Hg;
f by metals so similar that their separation is problematic; and by the fact that withdrawal into the core starts immediately, leaving only one (or two) electrons to combine with s electrons in bonding.

The periodic table is more than similar items belonging together. It is more importantly a demonstration of vertical periodic trends (acknowledging the arguable exception of He, on pragmatic "screaming physical" grounds, among others).

Per our IUPAC submission, La fits better under Y on periodic trend grounds, and chemical behaviour grounds. This is not the case for Lu.

Arguments to do with f character (in the absence of any f electrons) and d character, in the absence of characteristic d properties in La and Lu (multiple oxidation states etc), can only every be regarded as tipping point arguments.

Like we said in our submission, "While Lu may be somewhat more of an outlier than La, the shortfall is insignificant in comparison to broader trends." Sandbh (talk) 00:48, 2 February 2020 (UTC)

No, block identity works on the following basis:

What is the chemically active subshell of the highest angular momentum?

That's it. Done. One criterion, very simple. As broad contour as you can ask for, not focusing on details like trying to "characterise" the blocks. Droog Andrey has already well demolished in Archive 33 the bases for our old IUPAC submission arguments: group 3 is not overwhelmingly skewed towards group 2 in similarity, the delayed collapse is totally normal throughout the periodic table, Lu has no significant 4f character, and condensed-phase configurations are irrelevant because they support B-Al-Sc and Be and Mg as p-block elements. In the absence of those strong arguments to lead the charge, Sc-Y-La in my view has no more leg to stand on. Double sharp (talk) 00:52, 2 February 2020 (UTC)

@Double sharp: Is it though? I've asked a question about Nd elsewhere in this thread dealing with your one criterion. According to the literature, group 3 is skewed towards group 2 in similarity; the delayed collapse is most prominent in the Ln and trying to conflate it with the rest of the blocks is disingenuous; and suggesting condensed-phase configurations are irrelevant because they support B-Al-Sc and Be and Mg as p-block elements, is a one puff argument that conveniently ignores all the other arguments pointing to how silly this is. You throw out a lot of distractions or minutiae that have no impact on the broad contours, including block homogeneity, never mind broad chemical patterns and periodic vertical trends. Sandbh (talk) 03:59, 2 February 2020 (UTC)

@Sandbh: On Nd, see above.
Nope. Sc and Y in group 3 have the physical properties of normal transition metals. And may I add that under "similarity", Be and Mg are more like p-block than s-block elements, and therefore Be-Mg-Zn is the recommended trend to produce something more like B-Al-Ga.
Nope. The delayed collapse is most prominent in heavy elements in general, not only the f-block. That's why we see it in Lr and E121 as well. Once period 8 comes along every block but the s-block seems to be delayed!
Well it seems to me that the only good case for Sc-Y-La came from weak 4f involvement (refuted) and condensed-phase configurations. But now we have a simple philosophical syllogism:
1. Condensed phase configurations lead to Be and Mg in the p-block.
2. Be and Mg in the p-block is silly.
3. An argument that argues for something silly is suspect and not a strong one for anything else, by reductio ad absurdum.
4. Condensed phase configurations are a suspect argument.
Block homogeneity supports a Lu table. The f-block is about the same either way, but the d-block suffers a big loss of homogeneity when you force La into it. Respectfully, differences between La and the other lanthanides are minutiae.
Broad chemical patterns entirely support a Lu table as it matches the trend of every other transition group. Same for periodic vertical trends. Since Sc and Y are physically perfect d-block metals, and chemically are not far removed from Zr, Nb, Hf, and Ta, the argument of similarity to group 2 dies a natural death. Double sharp (talk) 10:02, 2 February 2020 (UTC)

Lawrencium, with another glance at helium over beryllium

Let's examine what the criteria Sandbh seems to be using for group 3 have to say about the placement of Lr.

Lr shows the configuration [Rn]5f¹⁴7s²7p¹, so by those criteria it ends up as a p-element since the 6d orbital has undergone a delayed collapse like for Ac. Therefore we have two possible recurrences after Tl, being Lr and Nh, and unless I've misunderstood it Sandbh's interpretation of the periodic law demands that we take Lr as the first one.
The 234 argument is inconclusive, since neither No nor Cn has maximum oxidation state +2. Therefore, nothing stands in the way of Tl-Lr.
By how Sandbh seems to be interpreting contractions, Lr cannot be considered to be the start of the 6d contraction as it does not have a 6d electron. In fact, it does not even satisfy IUPAC's definition of a transition metal as Lr and Lr³⁺ both lack 6d electrons. OTOH, some predictions for Nh suggest 6d involvement in its chemistry for higher oxidation states. So the 6d contraction must start at Rf and end at Nh!
Putting Lr into the p-block gets rid of one thorny differentiating electron anomaly. It unfortunately creates one for Nh wherever else we put it, so this is balanced: nihil obstat again.
Inconveniently, Lr does not add the 6d¹⁰ core that eka-Tl should following double periodicity literally everywhere else in the table, but we can insist that that just shows that the n+l rule must be discarded – for an isolated anomaly, that is paralleled very well at the start of most blocks in the heavy elements, see Ac and E121, but never mind that(!!).
Inconveniently, Lr does not behave much like Fl through Og, but we can simply insist that one 7p electron fills followed by ten 6d ones with a "premature" closure at Cn and declare it irrelevant, as the situation looks kind of like that going from La to Lu(!!!). We can even draw analogies between Cn-Nh-Fl and Pd-Ag-Cd due to the characteristic oxidation states, with a "prematurely closed shell" occurring at Cn and Pd, and a full shell at Nh and Ag that can be breached, but only with great difficulty.
We can simply insist that we are delimiting the differences in the d-block and make comparisons not to Fl through Og, but the other 6d transition metals, and then we find that Nh actually behaves reasonably similarly to the late 6d transition metals like Rg and Cn, but that Lr does not behave very "transition-y", and therefore that it is actually Lr and not Nh that must be excluded from the d-block(!!!!). And the means of discovery of Nh (bombarding Pb/Bi rather than actinides) is similar to how the late 6d metals were discovered, but not how Lr was discovered, by bombardment of actinides which is more like the means of discovery of Fl through Og(!!!!!).
So the only difficulty that what appear to be Sandbh's current criteria cannot so easily sweep aside is that Lr is a lot more electropositive than Nh (which in the current criteria would be distorted into "ionicity"). But we can invoke Mendeleev, who originally put Tl as a heavier congener of the alkali metals because of its higher electropositivity in the +1 state, which is the more stable one! And therefore Lr as a "trivalent pre-transition metal" could be argued to fit better with this new and improved group 13 element thallium than Nh, for which the +1 state is amphoteric and the behaviour is more similar to Ag and At!

So, it looks like the case for Tl-Lr is holding up reasonably well under these criteria! Only one problem: how on earth do you draw it?

And if the biggest difference between accepting Sc-Y-La-Ac but not Tl-Lr is "but we can't draw the latter", then we have to abandon the line about drawing Nature as She really is. Double sharp (talk) 12:05, 27 January 2020 (UTC)

Easy. Just put Hf-Tl over Th-Lr, but stretch out Hf-Tl so that Tl and Lr are together. Do something like the atomic flower structure. And then fold the table up in such a way that Lu and Lr are still on top of each other as well as Tl and Lr, and also put Lu under Y and also not under Y because Group 3, combined with all of the problems hydrogen has... it's nature's perfect periodic table! ― Дрейгорич / Dreigorich Talk 00:01, 28 January 2020 (UTC)

If it helps, Lr is likely to have a d rather than p electron in the condensed phase. Lr 3+ will be f14, analogous to Lu. Sandbh (talk) 05:22, 28 January 2020 (UTC)

So condensed-phase configurations are OK when they give the result we want (Lr under Lu), but not when they don't (Al over Sc due to partial p-occupancy in Sc, Be and Mg as p-block elements)? Double sharp (talk) 07:48, 28 January 2020 (UTC)

@Double sharp: Sc is predominately (> 85% in this case, noting I haven’t read the article yet) a d metal That’s all that matters. Just as La goes under Y, and Ac goes under La, we’d expect Lr to go under Lu. For sure Lr has a p electron, which looks odd until we consider its condensed phase configuration, which is expected to have a d electron, and we see that Lr 3+ will be f14, analogously to Lu. Sandbh (talk) 10:58, 28 January 2020 (UTC)

In that case He goes over Be, since He is 100% an s-element, and Be is more of an s-element than Ne. And Be and Mg go over Zn, because all three are sp in the condensed phase (see the old chat at our old group 3 submission), which makes it inconclusive with Ca (noting that Ca has some pre-d character), and then the "similarity argument" argues for Be-Mg-Zn because Be and Mg have chemistry that is not very characteristic of Ca through Ra and more like Zn and Cd. Double sharp (talk) 11:29, 28 January 2020 (UTC)

@Double sharp: No. I don't change the goal posts. I observe the ones that are already there, as required, that you overlook. The periodic table layout is more pragmatic than saying He goes over Be since He is 100% an s-element. It's also 100% a noble gas. Be and Mg don't go over Zn for the reason that group 2 is a better choice given the commonality of underlying cores, among other things. Sandbh (talk) 06:28, 1 February 2020 (UTC)

@Sandbh: OTOH helium also 100% doesn't fit in the noble gas trend. Just plot properties, like in the article you linked for me. And I don't mean "doesn't fit" in the sense of O, F, and Ne with the first-row anomaly, I mean literally "He is not even trending in the right direction". And, nota bene, when helium is coaxed into compounds, the theoretically modelled ones are homologous to beryllium and certainly not neon. Which is why I prefer to say: let us stick to something that totally affects chemistry, i.e. chemically active subshells. If it produces He over Be, well, there are good reasons for that, so I don't complain.

As for Be and Mg over Zn: if we argue "commonality of underlying cores", then we cannot have B and Al over Ga (because Ga has the extra 3d¹⁰), and we cannot have Ti and Zr over Ce and Th (because Hf and Rf have the extra f¹⁴; Th even has the right configuration to not look like an anomaly here). If you want to specify where "commonality of underlying cores" is desirable and where it is not, you basically end up reinventing the Madelung rule to tell you when the underlying core should change, presumably messing with it at La in order to get the result you want. But if we argue "commonality of chemistry", like how you like to argue about group 3 being more like groups 1 and 2 than 4 and 5 (which is in itself not quite true anyway), then Be and Mg go straight over Zn! That's why I think your arguments are weak. The moment you try to apply them as a basis for most of the table, suddenly they all start fighting against each other. Mine doesn't: it just steers pragmatically all the way to the undiscovered element 172. And an attack of sanity should make it work for element 173, as well! Double sharp (talk) 10:22, 1 February 2020 (UTC)

@Double sharp: Ah, well, I was watching the tennis when I typed that. By 100% noble gas I meant it is effectively recognised 100% as a noble gas, nothing more detailed than that. We have B and Al (p elements) over Ga (also a p) because over Sc (a d element)is worse. See also the new section about what Main Groups are. Ti and Zr don't go over Ce and Th in a within same group congener sense, so there's nothing to that observation. I argue commonality of ionic v covalent chemistry, that is all. This is not the same as Be and Mg going over Zn. As I said, see the new section about what Main Groups are. The Be and Mg over Zn argument was lost a long time ago. Remy (1956) says the AEM illustrate the rule that the first element (Be) is apt to constitute a transition to the next Main Group, the second element (Mg) to the Sub-group belonging to the same family, whereas the group character is full developed for the first time in the third element (Ca). That's another pattern that works quite well with the Main groups as they are. I posted about this rule earlier. Sandbh (talk) 11:20, 1 February 2020 (UTC)

Hydrogen is effectively recognised 100% as not an alkali metal, yet it goes at the top of group 1 anyway, so there is more to it than that. "Ti and Zr don't go over Ce and Th in a within same group congener sense, so there's nothing to that observation." – says who? How do you know they're not in the same group? You must have some criteria, or you can take anything as your starting point and defend it after the fact. "Commonality of ionic v covalent chemistry" supports Be and Mg going over Zn because Be and Mg are only slightly electropositive, not highly, which is similar to the Zn group but not the Ca group. A viewpoint being "lost a long time ago" simply suggests that any argument that leads to it is suspect, no matter what else it happens to say. P.S. Remy's rule only really applies much for groups II and III, far from a majority. In what sense is Na a transition to the Cu group, or Si a transition to the Ti group? The character of Si vs. Ge is very similar, as is Na vs. K. Double sharp (talk) 11:35, 1 February 2020 (UTC)

@Дрейгорич: Put helium over beryllium as well as over neon and you have a follower. ^_^ Maybe add a bifurcating group 2 and trifurcating group 3 for that matter! Double sharp (talk) 13:55, 28 January 2020 (UTC)

Why wouldn't I? I was proposing we go all in and wrap the transition metals around the main group elements, in the original Mendeleevian style. ― Дрейгорич / Dreigorich Talk 14:07, 28 January 2020 (UTC)

@Дрейгорич: Perfect! So all the A and B groups make their triumphant reappareance! H and He shall also appear in two spaces, as shall Cu-Ag-Au, Be-Mg, B-Al, and Sc-Y! For good measure, let's toss in all the other secondary-periodicity things from Rayner-Canham's table! What a sight it would be to behold, and how singularly unhelpful for the students taking their first chemistry class! ;) (But a remarkable sight anyway!)

Seriously, this is more or less why I advocate He-Be-Mg with Sc-Y-Lu. There are so many second-order deviations from the ideal n+l arrangement and these are just two of them, so we might as well be consistent and just draw none of them, not just pick and choose only the ones we can draw in a tabular arrangement. Double sharp (talk) 15:06, 28 January 2020 (UTC)

@Double sharp: Ahahahahahaha, yep. This is why there will never be the ideal periodic table, and all attempts must be a compromise, like map projections. There is no ideal map projection. No matter how we slice and dice it to present it to students, there will always be oversimplifications. Different projections may work for different tasks, but as for the one we've got right now, it seems to do its job well at explaining the basic properties of elements, maybe with the exception of a nonmetal being on the "wrong" side of the line (hydrogen). ― Дрейгорич / Dreigorich Talk 15:11, 28 January 2020 (UTC)

@Дрейгорич: Let helium join it; then it won't be alone on the wrong side. ;) Now we can nicely separate the s- and p-blocks, let each one have its characteristic (1s vs. 2p) anomaly, let the Lewis doublet stand apart from the octet, and the trends will be nice and consistent! I recommend particularly the articles of Grochala and of Furtado, De Proft, and Geerlings (the latter does not explicitly call for He over Be, but you can see all the plots showing He simply out of place from the noble gas trend in many basic properties such as electronegativity, hardness and IP; this is distinct from Ne, which shows the right qualitative trend but a quantitative anomaly with a big 2p-3p gap just like what heads groups 13 through 17). Double sharp (talk) 18:41, 28 January 2020 (UTC)

@Double sharp: Nah, helium's physical properties scream "noble gas". How could it join the solid alkaline earths? Sure, it's an s element, but an anomaly from the main group of s elements (along with hydrogen). Maybe in some ways helium is better above the nobles (especially in its normal chemical bonding behavior and physical properties), but in others it fits better above the alkalines (periodic trends, though some trends like boiling point are clearly better suited for He above Ne). As for H, I'm torn (there's so much going on that H deserves its own unique group in the eyes of a beginning chemist), and I'm indifferent on what's below Y. The rest of the table is pretty much settled in my opinion, but then again, stuff.

What if beginning chemistry students are taught the standard 18-column table with a few anomalies, and then they get introduced to the twisty loopy place every element below every other element monstrosity I proposed above in advanced chemistry to try and show that this is how it really is, with branching chemical paths? Now the advanced students hate the beginning students for not initially seeing the whole scheme of things and having misconceptions about the periodic table, and the beginning students hate the advanced students for having an overcomplicated periodic table to fit every minor detail in. Win-win. ― Дрейгорич / Dreigorich Talk 23:55, 28 January 2020 (UTC)

@Дрейгорич: I heartily agree that the average lack of chemistry of He is more like Ne than like Be. :) However, there is one little wrinkle: it's predicted to be possible to coax He into compounds, and theoretical modelling has identified some possibilities (see Grochala's article). Not only do these not have Ne analogues (even predicted; Lewars' Modeling Marvels has a chapter on He compounds that notes that Ne seems to be surprisingly barren), but the bonding in them shows He as a lighter congener of Be, with a strong affinity to oxygen and a He-O bond where oxygen seems to be the more electronegative of the two. ;) So maybe the basic first table should float H and put He in group 18, but after a while when you're ready they should magically float off to groups 1 and 2. ;) (I recommend using He as your balloon when doing this floating, not H. ^_^)

I also agree that H-Li and He-Be are much harder to defend physically than chemically. However: every main group seems to start with a nonmetal, that shielding effects then metallise when you go down the table. But only with H-Li and He-Be; otherwise Be is already a metal, and the s-anomaly for Be is not of the same order as for H. Double sharp (talk) 08:09, 29 January 2020 (UTC)

this is going on for far too long Lawrencium. Back to lawrencium. It's pretty settled that Lu goes above Lr (Tl above Lr would probably be silly, right?), but the question is what's below Y. It doesn't help that La and Ac have a d electron (Th has two and no f electrons!) and the early lanthanides and actinides resemble group 4, 5, etc. which is a solid case for La/Ac. However pure Aufbau suggests Lu/Lr is better, and Lr has an anomalous electron configuration no matter where we place it. And Lr might not be the least of our worries once relativistic effects kick in and might disorganize Nh-Og. Maybe Lr is a warning that the order of the earlier atomic numbers is ending, and to be cautious in how to proceed. Maybe Lr will end up like H, and belong in multiple places, maybe one of them below Tl. For now we don't know. And I'm talking WP:OR without backing anything up, so feel free to dismiss me. ― Дрейгорич / Dreigorich Talk 08:24, 29 January 2020 (UTC)

@Дрейгорич: The early actinides do have some resemblance to transition metals; Ac to Pu have resemblance to Lu to Os. And if you squint you may consider Am and Cm, though especially for the latter this is no longer characteristic. (Nota bene, this is OK as it is a complex of properties, not just one.) For the Ln, not really, apart maybe for Ce a little, but they are anomalous as 4f has no radial nodes; 5f is more like typical f-block behaviour. The fact that the f-block is mostly intermediate between the s- and d-blocks looking holistically at all properties suggests to put it between them (i.e. Lu under Y) and not sandwiched only by the d-block (i.e. La under Y). Lr has an anomalous configuration that seems to mean nothing chemically, so I advocate considering the slow start of 5f in Ac-Th-Pa as the same effect as the slow start of 6d in Lr-Rf-Db and the slow start of 5g in E121+ and not drawing any of them explicitly. Periodicity works almost perfectly up to Rg, probably. It's Cn through Og which are really weird: if Au through At are "super-B" or "C" metals, then Rg is too, and Cn through Og are "super-duper-B" or even "D" metals. Ts and Og are probably actually similar to Ga and Sn respectively, with Cn kind of like Rn and Nh kind of like At, so everything has gone a bit bonkers here. But since the Aufbau principle should be totally valid with no exceptions from Rf through E120(!!), I think it's clear that it's folly to argue about Ac from exceptions, when Lr has an exception with no effect, but Cn through Og have no exceptions but huge effects! Double sharp (talk) 11:34, 29 January 2020 (UTC)

@Double sharp: Fun convo. Learned something new about the superheavies. Best to treat Lr as regular, and not make any assumptions past Rg. It will be very interesting to see where Cn-Og end up in the periodic table in ten, twenty, thirty, fifty years. Will they still be in order like we have now or will it have been better to disorgnanize them to better match their chemical properties? (Rg-X-Ts-Og-Mc-Lv-Nh-Cn/Fl? Jeez that looks weird.) If so, will chemistry teachers just cut the periodic table off at Rg? Will Cn-Og or whatever the last element is at the time be added as asterisks? Who knows. Also, if Wikipedia is still around, when will that conversation happen? ― Дрейгорич / Dreigorich Talk 00:45, 30 January 2020 (UTC)

@Дрейгорич: If the island of stability does not permit long-enough half-lives for Cn through Og, no one will care, I expect. If it does, then I suspect people will just continue to draw them below Hg through Rn for lack of anything better that doesn't look crazy. The fundamental problem is that you have two strong (6d and 7p_1/2) shell closures in a row followed by a weak one (7p_3/2), and this is a situation which has no good precedents. (The p-subshell splitting is not so strong for Pb. Po, At, and Rn have some problems getting to high oxidation states, but this is a well-known effect of radioactivity, and it seems likely that just like for Pb, Po^VI for instance would be stabilised in organopolonium compounds.) So I suppose that we will have to rationalise it as a super "inert pair effect", that for Mc through Og becomes an "inert quartet effect". Indeed, in period 8 this is expected to be so big that the groups are quite literally staggered by four. A simple Aufbau extrapolation would give E163 and E168 as the p-block elements of the 8th period. But it is expected that E167 to E172 should, because of a super inert quartet effect (on 8s+8p_1/2 rather than 7s+7p_1/2 this time), become almost perfect members of groups 13 through 18, completely analogous to indium through xenon, even though their atomic numbers are four out! This situation in which E157 through E172 are expected to have a miraculous cancellation of relativistic effects and mimic Y through Xe is really weird. (How I wish we could get there soon! But probably not. T_T) Double sharp (talk) 14:33, 30 January 2020 (UTC)

@Double sharp: Re: "The fact that the f-block is mostly intermediate between the s- and d-blocks looking holistically at all properties suggests to put it between them (i.e. Lu under Y) and not sandwiched only by the d-block (i.e. La under Y)."

The sandwich is only seen in the 32-column form, which is a distraction compared to the 18-column form. Getting rid of the sandwich risks being seen as a false sense of precision or idealisation. Sandbh (talk) 06:41, 1 February 2020 (UTC)

No, even in an 18-column table you have asterisks interrupting the d-block. The periodic table is already an idealisation and everyone who looks deeply at the elements knows it. I claim that a La table, in singling out only one among many second-order anomalies to draw, muddies the waters about how precise it is supposed to be. Double sharp (talk) 09:53, 1 February 2020 (UTC)

@Дрейгорич: When you said earlier, "the early lanthanides and actinides resemble group 4, 5, etc. which is a solid case for La/Ac" is that something you had formed a personal view about? Sandbh (talk) 07:00, 31 January 2020 (UTC)

@Sandbh: Oxidation states. +4 for Ce, +5 for Pr, etc. though this may be a weak argument, given that most lanthanides have a +3 oxidation state or are primarily a +3 oxidation state. Surely Mendeleev would have approved based on typical oxidation states. Too bad of the four elements in controversy, only lanthanum was known. If more were known and the list of lanthanides were more complete, what would Mendeleev have done? ― Дрейгорич / Dreigorich Talk 07:21, 31 January 2020 (UTC)

@Дрейгорич: In fact, we know very well what he would have done, since his last table dates from 1906, the year Lu was discovered. (And also the year before his death.) The 6th period as we have it now stands as Cs, Ba, La, Ce, and then many blanks because the rare earths obviously don't fit the transition-metal pattern – and then Yb in group III (a reasonable mistake), a blank in group IV (later Hf, following his original 1869 prediction), Ta, W, and so on. So, the "redundancy" that Sandbh seems to dislike of La and Ac aligning under Lu and Lr in fact goes back to Mendeleev himself. ^_^

P.S. +5 for Pr is, as I said, just plain silly. We can talk about it again when it is found in something other than matrix isolation. Double sharp (talk) 11:49, 31 January 2020 (UTC)

@Double sharp: Start talking; it's been found in the gas phase. Sandbh (talk) 02:43, 2 February 2020 (UTC)

@Sandbh: Poor choice of words, sorry. I mean "when it is found in something resembling a normal chemical environment". But OK, I'll accept Pr(V), since otherwise He compounds become dodgy (I have referred to them; of course a stronger argument for He atop Be is atomic property trends), and I want to avoid a double standard. (I already dislike seeing it used to accept Pr^V and Th^III as conclusive and bar Ti^III and Zr^III, so I will accept them all for now, plus predicted Ar^II and maybe even He^II.) I still don't see how it supports a La table, since the same argument I gave holds whether or not we accept it. Double sharp (talk) 10:04, 2 February 2020 (UTC)

Transition character of early f-block elements

@Дрейгорич: @Double sharp: I'd forgotten about the early Ln and An resembling group 4, 5, etc. "which is a solid case for La/Ac", as Дрейгорич said. The resemblances are Ce +4 and Th +4 to Group 4; Pr +5 and Pa +5 to Group 5; and U +6 to Group 6. Here's an La table with the relevant electron configurations:

In the above table I can see that La and Ac are d elements. The f block starts at Ce, with the first appearance of an f electron. Th is anomalous but we know the condensed form has about ½ of an f electron; this impacts its crystalline structure; and there is an f electron in Th³⁺. The intrinsic Ln contraction (Ce³⁺ to Lu³⁺) is wholly contained within the f-block.

Here's an Lu table:

1 2 3 4 5 6 -----+----+-------+-----------+-----------+--------- 6 Cs | Ba | Lu d1 | Hf d2s2 | Ta d3s2 | W d4s2 -----+----+-------+-----------+-----------+--------- 7 | Lr p1 | Rf d2s2 | +-------+-----------+ +-------+-----------+-----------+ 6 | La d1 | Ce f1d1s2 | Pr f3s2 | --> Yb -----+----+-------+-----------+-----------+--------- 7 Fr | Ra | Ac d1 | Th d2s2 | Pa f2d1s2 | U f3d1s2 --> No -----+----+-------+-----------+-----------+---------

In the above table Lu is regarded as a d block metal, as is Lr. Lawrencium is anomalous but is likely to have a d electron in its condensed phase. It is notable that the low ionisation energy of Lr has been attributed the presence of this p electron. La and Ac, which line up under Lu and Lr, are regarded as starting the f-block but neither have f electrons. Why La and Ac aren't regarded as d metals isn't apparent. The intrinsic Ln contraction starts at the second metal in the f-block (Ce), and finishes in the first Ln in the d-block (Lu).

I can't quite put my finger on it but there is something peculiar or redundant about lining up the first Ln (La) under the last one (Lu). We already know +3 is the most common and stable state across the Ln. It reminds me of a snake eating its own tail. Sandbh (talk) 04:34, 30 January 2020 (UTC)

@Sandbh: Very interesting table, although still having two versions doesn't necessarily solve La/Lu but instead just rewords the problem, trying to offer a compromise by putting both in group 3 while still leaving the spot between Ba and Hf ambiguous. I personally think of the lanthanides like a 14- or 15-element long string below Y that can be taken out of its spot, stretched out and presented if needed. They all sit in one spot for me, in a line. Preparing my brain. Lanthanum lies hidden (pun intended) in its spot below Y, cerium falls out of that spot a bit, trying to get below zirconium but failing, praseodymium follows, and the line loops out of the main table doing its own lanthanide thing for some time before it curls back in with thulium and ytterbium going to head back into the spot below Y, and at the end lutetium sits below Y. It's like a long string that is tied with Ba at one end and Hf on the other, and the entire thing falls out of its designated spot. Both lanthanum and lutetium however claim sole ownership of the "ambassador" of that spot on the periodic table, and in the end no one can agree. The actinides follow the same thing but exactly mirror the lanthanides so there's no disagreement on who's related to who (Ce-Th, Pr-Pa, Nd-U... Yb-No). ― Дрейгорич / Dreigorich Talk 05:38, 30 January 2020 (UTC)

@Sandbh: On the contrary, this line-up is exactly why a Lu table is superior on counting extra homologies. In a Lu table, not only are Lu and Lr in group 3, but La and Ac are also aligned in the footnote below group 3, which is more or less right: La and Ac are useful "extra group 3 members" for comparative chemistry. In a La table, La and Ac are in group 3 of course, but if you want to keep the homologies of Th through Pu, then Lu and Lr appear under the totally irrelevant group 17. And just plot properties along the Ln correlated with the number of f-electrons. Of course you will get a snake eating its own tail as the effect grows on the first half as the f-electrons go in, and shrinks on the second half as they get paired. Nothing new here.

We have beaten the horse about 4f and 5f for La and Ac to death: suffice it to say that they have more such involvement than Lu and Lr. (Do you know the 5f energy in Lr? Consider for a moment how Fm, Md, and No increasingly prefer not to dig into that reserve...) And as for your "intrinsic" Ln contraction (I see that now there is an adjective), you cannot even apply it to the An where there isn't a unifying standard oxidation state, so there's no a priori reason why we should reject an f-block beginning at La and Ac. Otherwise I could equally well say that the d-block cannot begin at group 3 because Sc³⁺ has no d-electrons.

Also, you referring to Th³⁺ (not even known in aqueous solution!) and Pr⁵⁺ (known in exactly one matrix-isolation compound!!), while calling me out for references to supposedly uncharacteristic Zr³⁺ and Ti³⁺(!!!, which should be more on the ionic side) is a double standard if I ever saw one! Double sharp (talk) 08:13, 30 January 2020 (UTC)

@Double sharp: Interesting. I don’t count La and Ac being lined up under Lu Lr as an extra homology due to its redundancy. I also have concerns about the block membership confusion issue; and the associated issue of an intrinsic Ln contraction over two blocks (f, d) rather than one (f).

I recall plots of Ln properties are inconclusive.

In the particular An contraction context I raised, your comment is not relevant. The contraction can be seen in the An as per the Nature article. Like I said, the Ln and An have the +3 oxidation state in common.

The d block can begin at Sc since it has a d electron and this at least impacts its physical properties (per the G & E Group 3 commentary).

My context for referring to Th 3+ and Pr 5+ was not the same as the context for our discussion on Zr 3+ and Ti 3+. Funny :), I recall you tipped me as to the existence of Th 3+ in our IUPAC submission! I was tipped off to Pr 5+ by our list of oxidation states of the elements template. Interestingly, one of the articles on Pr 5+ notes long-standing speculation as to its existence. Sandbh (talk) 11:08, 30 January 2020 (UTC)

@Sandbh: There is no "block membership confusion issue". A Sc-Y-Lu table makes the scientific statement that Lu is more of a d-block element and La is more of an f-block element, between the two. I hope we agree that 4f in Lu, and even more so 5f in Lr, is more or less a core subshell, so there's nothing wrong with that; high coordination numbers can anyway be explained away with bond orders less than unity. (If you needed proof of that, for Lr, just look at the 5f energies going from Es to No, so much so that No has +2 as the preferred oxidation state). OTOH, you cannot "explain away" cubic complexes for La so easily. On symmetry grounds you really need f-orbital involvement from that. I seem to recall Gschneider has been an advocate for 4f character of La, that we did not wholly refute in our submission! To quote it: "These effects largely encompassed thermodynamic properties, and the stability constants of rare earth EDTA complexes. While we found evidence for the former effects to be plausible..." (my new emphasis). I absolutely agree with the conclusion we made: "We think it plausible that the low-lying 4f levels in La may influence some of its properties. It is also conceivable that the filled 4f shell of Lu may influence some its properties but, if so, the scope of this influence is likely to be smaller and more obscure." In other words: Lu has significantly less 4f involvement than La, so if it comes down to that, it is La that must stand as the f-block lanthanide. That is why the f-block may begin at La even without a 4f electron there. Otherwise, the d-block cannot begin at Lr.

(P.S. If you want a block membership confusion issue, try drawing He above Ne. ^_^ You cannot argue that He is anything other than an s-block element, so the difference is whether you draw it there or not. And the placement of He over Ne at least has something more than the Pr⁵⁺-level of support: the atomic properties of He very often just do not fit in the noble-gas trend, creating an anomaly on top of a perfectly orthodox first-row anomaly from Ne to Ar.)

Again, you are misunderstanding what I am saying. I am not comparing the Sc-Y-La to the Sc-Y-Lu trend. I am noting the trend across the lanthanide series. In every case where 4f electrons matter and the lanthanides are in the +3 state, the trend will follow the number of 4f electrons from a minimum at La to a maximum somewhere in the middle to a minimum at Lu again. (Of course, the trends go all over the place once the maxim of "constant +3 oxidation state" is violated.) So of course it is like a little circle running in place and the supposed redundancy is not only justified, it also reflects perfectly what we see by giving equal visual weight to the equally plausible trends of Sc-Y-La and Sc-Y-Lu a priori. That is why, while advocating Sc-Y-Lu as a default, I advocate that La and Ac should be included in a comparative chemistry discussion of group 3. But I also think that Al should be included too. ^_^

"The Ln and An have the +3 oxidation state it common": funny, the most common actinides for anybody are thorium and uranium. And for thorium the most common state is +4, and for uranium they are +4 and +6. In fact, throughout most of the first half of the actinide series, +4 might be a better "constant state" to take as the baseline. In the second half +2 gains in importance. So where is this +3 that is had in common? It seems to be about as consequential as the observation that most of the 3d metals have +2 and/or +3 as the significant state. Is that relevant at all for the 4d and 5d ones? The contraction is only significantly visible if everybody involved is in the same oxidation state. And once you force that, it is not special to the lanthanides, it is visible literally everywhere in the periodic table by first-year school chemistry. But then you cannot point to a special oxidation state to force where the contraction "should" begin. What is there to choose between Sr²⁺ through Pd²⁺ as your contraction and Y³⁺ through Ag³⁺ as your contraction? In terms of choosing common oxidation states they are equally bad, just like +4 vs. +3 vs. +2 for the actinide contraction.

I don't disagree that Th^III is of some relevance, sure. It certainly shows 5f involvement in Th, as does its crystal structure. However, it seems to me that Ti^III and Zr^III are even more relevant. You cannot deny the relevance of those two when you argue about group 4's "ionic vs. covalent" behaviour (once you define what that is supposed to mean), and yet accept the relevance of Th^III when arguing about the slow start of 5f activity, when the former are actually more common oxidation states! Ti³⁺ is stable in water, Zr³⁺ reduces water, but Th³⁺ has not even been confirmed in water at all! Even your article refrains from drawing a tripositive thorium ion when showing the An³⁺ contraction (for which, at least from Th to Pu, we are comparing elements that are unhappy to be in the +3 state, a far cry from what we do when invoking the Ln³⁺ contraction!)

As for Pr^V: you have got to be kidding me. There must be thousands of things that have a long-standing speculation of existence that are nearly totally irrelevant. Hg^IV, for instance. Respectfully, I put it to you that an oxidation state only seen in one Pr compound, that is only stable in matrix isolation, is not at all a demonstration that Pr has crypto-group 5 properties when in every single possible way it will not follow the chemistry of V, Nb, and Ta. Double sharp (talk) 14:17, 30 January 2020 (UTC)

P.S. If the f-elements have some s-character and some d-character, surely this is evidence that the f-block should be drawn between the s- and d-blocks, and not sandwiched inside the d-block, no? Double sharp (talk) 14:26, 30 January 2020 (UTC)

Yes, and perhaps this is why Lu at least theoretically has a better shot of being below Y than La. Maybe the answer to group 3 should be "how does the d block fit between the s/f (depending on if extended periodic table or not) and p blocks, and by analogy, how should this indicate the f block? ― Дрейгорич / Dreigorich Talk 16:33, 30 January 2020 (UTC)

@Дрейгорич: Well, the early d-block groups (3, heavy 4, heavy 5, heavy 6) have similarities to the s-block and f-block (consider Th/Pa/U vs. Hf/Ta/W), and the late ones (12, somewhat 11) have similarities to the p-block, so it works just as well. The groups on the edge of each block have some similarities to the adjacent block: again, this is totally normal in the periodic table, and is just another expression of how it is continuity, not discontinuity, that rules the day. As for the extended table: the 5g series seems to be something like a hexavalent 4f series, which would indicate similarities most of all to the s- and f-blocks (s- in the early groups; later, more similarities to uranium, and the border between 5g and 6f should not be all that clear). That seems to suggest to me that pseudohomology should work more or less all the way up to eka-Pu as E126 (using it in a loose sense; the element below Pu would of course be E148 instead), actually. Maybe at a second order you could see similarities to the d-block through uranium as well. Double sharp (talk) 19:18, 30 January 2020 (UTC)

@Double sharp: Righto.

The block membership confusion issue I was referring to is that in group 3 of the Lu table, Lu is regarded as a d block metal, as is lawrencium. La and Ac, which line up under Lu and Lr, are regarded as starting the f-block but neither have f electrons. Rather, they have d electrons. Why La and Ac aren't regarded as d metals isn't apparent.

It's perfectly apparent from the arrangement that we are claiming them as f metals with the "wrong" electron configuration. Just like thorium. Double sharp (talk) 12:08, 31 January 2020 (UTC)

There is no confusion about He. It's an s-block element placed over a p-block element on stronger resemblance grounds.

And it's the only element that is unarguably in one block and placed visually with elements of the wrong block. Double sharp (talk) 12:11, 31 January 2020 (UTC)

I like Gschneider. As a tipping point argument.

Well, since you yourself claim that the trends of Sc-Y-La and Sc-Y-Lu are inconclusive (thus we are at a tipping point), and you agree that 4f involvement being stronger in La than in Lu works as a tipping point argument, it seems that Lu is immediately recommended. ^_^ Double sharp (talk) 12:11, 31 January 2020 (UTC)

The d-block does not start at Lr; it starts at Sc.

The 6d row starts at Lr by most normal criteria, but not by yours, because it lacks a 6d electron. (Not that it seems to make it very much different from Lu.) So if you want to use the first element as a guideline, we run into delayed collapses everywhere, and the blocks stagger by periods. If that actually corresponded with a natural break in the chemistry of the elements that would be one thing, but it obviously doesn't because Lr is a strong homologue of Lu. Double sharp (talk) 12:08, 31 January 2020 (UTC)

I agree with you about trends across the Ln. These are inconclusive.

The whole point here is that they are inconclusive, which is precisely why it is useful and not "redundancy" to have La and Ac align in the footnote under Lu and Lr, just like Th, Pa, and U align under Hf, Ta, and W. Double sharp (talk) 12:08, 31 January 2020 (UTC)

On the An contraction it seems to me that you overlook my context or roll my argument into different contexts, which I didn't raise. My specific context was that +3 is a state shared by all La and An (Wiberg, p. 1645). Further, in this state, they show an Ln contraction (Ce to Lu) and an An contraction (Th to Lr). Both contractions start with f1 and finish at f14. On contractions generally, the Ln is the most notable. The scandide and boride contractions are of less significance.

If our standards are for a shared +3 state, never mind Th and Pa which are so unhappy in it (from compounds of thorium: "On 1997, reports of amber Th³⁺ (aq) being generated from thorium tetrachloride and ammonia were published: the ion was supposedly stable for about an hour before it was oxidised by water. However, the reaction was shown the next year to be thermodynamically impossible and the more likely explanation for the signals was azido-chloro complexes of thorium(IV)."), and U which oxidises water in it, then we can equally well say produce shared states across the 3d row. Well, apart from the early elements, +2 is common and stable for everybody, no? So I claim the actinide contraction is equally relevant as the scandide one: not very. The relevance of the Ln contraction is once again, an outlier among all contractions purely because of the common +3 state, which, I reiterate, is something you cannot claim for the An. Double sharp (talk) 12:08, 31 January 2020 (UTC)

You wrote:

" I don't disagree that Th^III is of some relevance, sure. It certainly shows 5f involvement in Th, as does its crystal structure. However, it seems to me that Ti^III and Zr^III are even more relevant. You cannot deny the relevance of those two when you argue about group 4's "ionic vs. covalent" behaviour (once you define what that is supposed to mean), and yet accept the relevance of Th^III when arguing about the slow start of 5f activity, when the former are actually more common oxidation states! Ti³⁺ is stable in water, Zr³⁺ reduces water, but Th³⁺ has not even been confirmed in water at all! Even your article refrains from drawing a tripositive thorium ion when showing the An³⁺ contraction (for which, at least from Th to Pu, we are comparing elements that are unhappy to be in the +3 state, a far cry from what we do when invoking the Ln³⁺ contraction!)"

This is an example of mixed contexts.

The Th(III) context was the established f involvement in Th, and the An contraction. That was all. [For unstable Th 3+, Wiberg, p. 1719, says it has a deep blue colour in aqueous solution. See also this article for a reference to crystallographically-characterized Th(III) complexes.] This context does not having anything to do with the stand-alone argument that (a) the chemistry of group 3 is predominately ionic whereas that of group 4 is predominately covalent, nor does it (b) have anything to do with a comparison to the status of Ti 3+ and Zr 3+. The fact of the existence of Ti 3+ and Zr 3+ does not usurp my argument that the chemistry of group 4, as per the literature, is predominately covalent.

On Pr(V) it seems to me that you overlooked my context and rolled my argument into a different context, that I didn't raise. The only context is the existence of Pr(V) and its alignment under group 5. The first article on Pr(V) says, "We report the formation of the lanthanide oxide species PrO₄ and PrO₂⁺ complexes in the gas phase and in a solid noble‐gas matrix…thus demonstrating that the pentavalent state is viable for lanthanide elements in a suitable coordination environment." The second article notes that, "it has been postulated since the early 1900s that praseodymium, with five valence electrons and the lowest fifth ionization energy, could be oxidizable beyond the +IV oxidation state."

As for the significance of gas phase Pr(V) I can only note the amazement and publicity associated with the isolation of Ir(IX), which was also in the gas phase.

If the possibility of NG compounds had been assigned the insignificance you assign to Pr(V) I surmise we'd still be calling the NG inert gases, and there would be no NG chemistry.

Oh come on. There is such a big difference between a standard reagent in organic chemistry (XeF₂) and compounds that are not even known as solid salts (IrO⁺
₄ and PrO⁺
₂). You can bottle krypton and xenon compounds, and you can't do this with Ir(IX) and Pr(V). If Pr(V) is alone to justify Pr as a pseudo-d element (which is about as far from "characteristic behaviour" as you can get), then we can look at the group 4 elements in the +2 oxidation state, even. I bet they will be very much more ionic in that state purely from Fajans' rules. Why is "characteristic behaviour" suddenly important for "ionicity", but not at all important for "resemblances to other blocks", for which we may apparently point to any number of one-hit extreme-condition wonders? If you really force the conditions, potassium is a d-block element with a 3d¹ configuration. Are we going to call it relevant like you do for Pr(V), or irrelevant like you do for Ti(III) (which is strangely enough a major oxidation state, despite your dismissal)? I stand by the characterisation of a double standard here. Double sharp (talk) 12:01, 31 January 2020 (UTC)

On the position of the f block, it is the f nature of the f block that is important, as is the case for the s, d, and p nature of the blocks of the same name. So the f-block fits between the s and d blocks. Sandbh (talk) 06:33, 31 January 2020 (UTC)

And it's only there with Lu in group 3. With La in group 3 it's sandwiched between two d-block groups. Double sharp (talk) 12:11, 31 January 2020 (UTC)

@Double sharp: I don't know what I meant to say there. What you said was, "If the f-elements have some s-character and some d-character, surely this is evidence that the f-block should be drawn between the s- and d-blocks, and not sandwiched inside the d-block, no?" My response should've been, no, all of the elements (but for Pd) show some involvement of s electrons, so the question is meaningless. Sandbh (talk) 00:56, 2 February 2020 (UTC)

@Sandbh: Poor choice of words, sorry: s-character means typical characteristics of s-block elements here. Double sharp (talk) 10:06, 2 February 2020 (UTC)

Null hypothesis

@Double sharp: What do you mean by this? Sandbh (talk) 22:56, 30 January 2020 (UTC)

@Sandbh: From the lede of null hypothesis: "In inferential statistics, the null hypothesis is a general statement or default position that there is nothing significantly different happening, like there is no association among groups or variables, or that there is no relationship between two measured phenomena." It is what you start with, and the burden of proof is to marshal evidence to show it cannot hold. If the evidence is not strong enough, we cannot reject the null hypothesis. Since the blocks fall out so well from H to Xe, the null hypothesis should surely be that the n+l pattern keeps going without change in the 6th and 7th periods. Since the Sc-Y-La vs. Sc-Y-Lu trends are inconclusive, and Lu leads to a more homogeneous d-block and better fits the concept of blocks in the first place (4f involvement is significantly stronger in La than in Lu), the strength to overturn the Sc-Y-Lu null hypothesis is just not there. Double sharp (talk) 23:37, 30 January 2020 (UTC)

@Double sharp: If I understand the first part of your edit right, the null hypothesis (H₀) is that there are no relationships among the elements.

Like DIM, evidence is then gathered in attempt to show that H₀ does not hold.

I don't understand what you mean when you say, "the null hypothesis should surely be that the n+l pattern keeps going…". You seem to be saying that H₀ is something (i.e. the n+l pattern) whereas, per our H₀ article, "the null hypothesis is a general statement or default position that there is nothing significantly different happening."

I'll pause there and await your response. Sandbh (talk) 02:29, 31 January 2020 (UTC)

@Sandbh: Note the phrase "there is nothing significantly different happening". In other words, we have a clearly defined n+l law that is valid for H through Xe, and the hypothesis we are trying to nullify (the null hypothesis) is that nothing significantly different happens. Previously, indeed, we started with a null hypothesis that there was no correlation between the elements, and H through Xe was enough evidence to refute that and go to the alternate hypothesis that the n+l rule holds. So now past Xe we have a new one that says "well, if it holds so far, it should keep going, right"? Your alternate hypothesis is then that Sc-Y-La is significantly better than Sc-Y-Lu, and it clearly doesn't reach that level of difference. Double sharp (talk) 12:19, 31 January 2020 (UTC)

@Double sharp: OK. The n + l rule is not valid for H through Xe, given the anomalies. And what did you mean by the "two rows at a time hypothesis" up to row 5? Sandbh (talk) 01:59, 2 February 2020 (UTC)

@Sandbh: You focus on the minutiae of anomalies, I focus on the big picture of chemically active subshells noting that mostly the elements are in excited states when chemically bonded, and yet you accuse me of focusing on details instead of your broad-contour philosophy? ^_-☆ "Two rows at a time" just means the shape of the table as it is from H to Xe. Double sharp (talk) 10:10, 2 February 2020 (UTC)

@Double sharp: Why is the Lu table the null hypotheses rather than the La table which is the most common form by a wide margin? Presumably Jensen started with the La table as H_o. Since when did the Lu table become H_o? Sandbh (talk) 04:43, 2 February 2020 (UTC)

@Sandbh: For the same reason the 8-column table is not the null hypothesis? You don't choose your null hypothesis by tradition. You choose it by a simple assessment of what assumes nothing new is going on. If you want to do an experiment on average size of red dragons vs blue dragons, your null hypothesis is that there is no difference. Not even if the received wisdom of the bravest knights in the kingdom reports one. That received wisdom is what you are here to test. Double sharp (talk) 10:10, 2 February 2020 (UTC)

@Double sharp: I so far think the null hypothesis approach is a waste of time. But I will plough on. In the case of red v blue dragons, the null hypothesis is that there is no difference. How does this translate into La table v Lu table? You seem to have started with the Lu table, which is not analogous to a null hypothesis that there is no difference. Or are you saying there is no difference and that symmetry therefore prevails? Yes, I'm confused. Our article on null hypothesis is no clearer. Sandbh (talk) 04:30, 3 February 2020 (UTC)

@Sandbh: The whole point is that a Lu table is saying "there is no difference between elements before and after period 5, the n+l rule still works when examining chemically active subshells". (I have already refuted differentiating electrons too many times to count by now. That if anything is a "waste of time" given its chemical irrelevance.) And that's true. The evidence for a La table (mostly just inconclusive trends, now that everything stronger has been refuted by reduction ad absurdum) is not enough to topple it. Double sharp (talk) 11:50, 3 February 2020 (UTC)

General comments

1. Double sharp, you do not accept predominately ionic v predominately covalent as a relevant distinction. That’s OK. Broad categories such as these are good enough for classification science, as is the concept of predominant or typical behaviour such as acid-base, or metal-nonmetal, in chemistry.

@Sandbh: There is an essential difference between your broad categories: metal-nonmetal is based on a complex of categories together, which I accepted, while acid-base and ionic-covalent are categories that are continuous and are ill-defined without some sort of comparison. Now I have in mind aliens from some hellish planet from our perspective, praising hydrogen fluoride as their water of life, and regarding as self-evident the basic properties of what we call nitric and sulfuric acids. Double sharp (talk) 07:56, 31 January 2020 (UTC)

2. My reference to cats as an example of a natural kind attracted some criticism. There is nothing to argue about. I took this from the literature and will add the source.

Being from the literature does not give you a free pass for a bad argument, you know. ^_^ Double sharp (talk) 07:56, 31 January 2020 (UTC)

3. The composition of Group 2 (Be to Ra) and Group 12 (Zn to Cn) is effectively universally established and, as I see it, there is no need to revisit this.

Precisely, which is why you should look at it for fairness. If you have a new decisive criterion that strenuously pleads for a La table, but applying it to group 2 makes it plead for Be and Mg over Zn, surely this weakens its relevance if you think you know the latter should not happen. It's just like proof by contradiction.

What rule did I use to come up with these four sequences of three numbers each: 1-2-3, 2-4-6, 4-7-10, 8-15-22? Was it "the three numbers are natural numbers in arithmetic progression"? Not a bad guess. But if you keep asking me if such sequences fit the bill, and I keep answering yes, you have no information that you did not have already. You must try to prove yourself wrong. I bet you never would have guessed it, BTW: my rule was "pick any three complex numbers in order of non-decreasing modulus". But of course, would you have thought to test your criterion on something as crazy-looking as i, 4 + i, 17 + 2πi? And do you see why even that would not be enough to figure it out? (I forgot where I heard of this example, unfortunately, but it is a good one.) Double sharp (talk) 07:56, 31 January 2020 (UTC)

4. The "rule" of first row distinctiveness was first extended to 3d and 4f by Jensen AFAIK. Primogenic repulsion has a role to play but does not explain everything. H in Group 1 and He in Group 18 provides the strongest example of distinctiveness across the 1s row (H, He), and the 2s2p row (Li to Ne).

It explains so much in 3d and 4f that denying it is pretty silly, just read Kaupp's paper. He over Ne is not a very distinctive element in the "correct" way that H and the 2p elements are. He over Be stands in the same relation as H over Li. Double sharp (talk) 07:56, 31 January 2020 (UTC)

@Double sharp: When did I say I denied it? Sandbh (talk) 02:39, 2 February 2020 (UTC)

@Sandbh: Poor choice of words, sorry: I mean that you seem to be trying to downplay its relevance, judging from the scare quotes you put around the word "rule". It is not only primogenic repulsion, OK (since 2s shows a sort of "anomaly" that is similar to 2p as well), but that is obviously the most important factor. Double sharp (talk) 16:14, 3 February 2020 (UTC)

5. The differentiating electron criterion drew a lot of interest mainly along the line of the d/e in the d- and f-blocks making no difference to chemistry. I gave examples of where they made a difference. Will the p differentiating electron in Lr make a difference to the chemistry of Lr? This is a complicated question since it looks like condensed Lr will have a d electron. With a p electron, the ionisation energy of Lr is very low. Chemically, our own Lr article includes the following:

Lr behaving more like Cm, Fm, and No and much less that of Ru
Lr compounds should be similar to those of the other trivalent An
LrH₂, is predicted to be bent, and the 6d orbital of Lr is not expected to play a role in the bonding, unlike that of LaH₂
Molecular LrH₂ and LrH are expected to resemble the corresponding Tl species (Tl having a 6s²6p¹ valence configuration in the gas phase, like Lr's 7s²7p¹) more than the corresponding Ln species
Lr may behave similarly to the alkali metals Na and K in some ways
Metallic Lr will behave similarly to Cm
If Lr has a p electron this is not expected to affect its chemistry in simple compounds.

Yuichiro Nagame , who was a member of the project team that measured the first ionisation energy of Lr, wrote that its place as an f-block actinide, a d-block transition metal or a p element, is yet to be unambiguously settled.

Since the only stable oxidation state is expected to be +3, I consistently don't really care about how the very simplest +1 and +2 compounds look. In that case Lr looks perfectly like a trivalent actinide and a heavier congener of Lu, in which the chemistry is not affected. Not only that, but the trend at the end of the actinide series supports divalency, with Lr as a weird addition (because it is not using a 5f reserve anymore), so the chemistry of Lr perfectly supports a 5f row from Ac to No. Double sharp (talk) 10:26, 1 February 2020 (UTC)

6. There were some perceptions that my article was unbalanced or biased towards La. That is fair enough and I need to consider how to address this in the final draft.

Sandbh (talk) 02:15, 31 January 2020 (UTC)

Default to lutetium and redraw all of the periodic tables?

Reading, er, glancing at this entire conversation (at least 50 thousand words and 100 pages of text so far), maybe we don't have enough evidence to overthrow the Aufbau Sc/Y/Lu/Lr arrangement. I don't know why Wikipedia was changed to Sc/Y/La/Ac other than "tradition" (I was much younger when that conversation took place). The conversations here are interesting, and I've learned quite a bit from it. Maybe it's time to redraw all of the periodic tables on Wikipedia? After all of this talk, aren't we overdue for a conclusion? ― Дрейгорич / Dreigorich Talk

While I'm rather receptive to the argument, I find it important to point a few things:

first, there is no known overreaching reason as for why Aufbau even is in the first place, which would make foundation of such a move on that basis alone rather wobbly;
second, the argument generally goes that group 3 is more like group 2 and 1 than 4 and 5, which makes it reasonable to have a group 3 that would retain trends that match those of groups 2 and 1 rather than 4 and 5.

As for me, I am not particularly impressed by these arguments, but I won't dismiss them, either. Different people have different opinions, and this question, in the end of the day, boils down to what opinion you have. The periodic table is first and foremost a great tool for describing the existing chemical elements but its predictive power is also impressive but not quite as much so, because further research into the periodic table extensions change not only the table but also on which principle the periodic table is based (Mendeleev arranged the elements by their atomic mass, later it was shown that it was the atomic number that mattered; Seaborg fantasized of a 218-element table that continue the current block trends, later calculations put the very notion of blocks at some point under question), and there is no exact agreement on what a periodic trend is (everybody thinks of more or less the same in general, but different people have different views of that). Sandbh used the notion of the periodic trends in this discussion in a way I would not, but while I disagree, I don't want to dismiss his opinion. Given the nature of a debate, I don't think a conclusion is in sight, and it would be great to have an external arbiter of sorts, and that's where the IUPAC taskforce come in. I'm sure that somebody will want to revisit the issue if they rule something different than what we have now, but right now doesn't seem like the time for such a change.--R8R (talk) 18:28, 31 January 2020 (UTC)

The discussion that led to this was at Template_talk:Periodic_table. You can read it to see the novelty of me fighting on the Sc-Y-La-Ac side. ^_^ (I have learnt several more things since then, in Archive 33, that make the arguments that I thought were decisive then look weaker, and that's why I shifted.) IMHO, as long as IUPAC has not come to a decision, Sc-Y-La-Ac should stay on WP. I do not think it is the ideal form myself anymore, but it is the most common form in the literature, and that's what counts for WP. We can and do, of course, discuss the issue where it is relevant. Once IUPAC makes a decision (which I hope will be Sc-Y-Lu-Lr), we should follow it IMHO, whatever it ends up being. (Now, if we can just convince them to start a task force about helium... ^_^)

We started discussing this here because Sandbh wrote an article about it externally, anyway; it didn't really have anything to do with WP. But I do love having a good argument about group 3! ^_^ Double sharp (talk) 19:54, 31 January 2020 (UTC)

P.S. The desired endpoint is to gain insight even if the conclusion is not yet in sight. ;) (With apologies to Richard Hamming.) Double sharp (talk) 11:41, 1 February 2020 (UTC)

P.S. My ideal periodic table at the moment would look something like my userpage. The positions of group 3 and helium have fluctuated a number of times in the past as my views changed. And I absolutely don't rule out changing it again. ^_^ But FWIW, this is how it would look, without those highlights that reflect my WIPs:

(Still not totally decided on whether "alkaline earth metal" should include Be and Mg. Or whether "transition metal" should include group 12. Copernicium makes the exclusion a bit iffy, but since it does follow the weirdness of 7p more than the orthodoxy of 6d, you could still support this arrangement.) Double sharp (talk) 21:37, 31 January 2020 (UTC)

@Double sharp: Be and Mg are not alkaline, so they should not be included into alkaline earths. Droog Andrey (talk) 17:54, 2 February 2020 (UTC)

@Droog Andrey: Well, that's good, since in this table I didn't. ^_^ Double sharp (talk) 18:41, 2 February 2020 (UTC)

P.S. Wulfsberg (see Principles of Descriptive Inorganic Chemistry, pp. 154ff.) breaks "very electropositive metals" as EN < 1.4, "electropositive metals" as 1.4 < EN < 1.9, and "electronegative metals" as EN > 1.9. This is, at least, a better form of "ionic vs. covalent". Though I note that despite him calling the first group groups 1-3 + f-block, Zr and Hf (as usual) satisfy that criterion as well, and in fact Be does not. But a very rough guide would be s+f vs. 3d+4p+5p vs. 4d+5d+6d+6p+7p, noting to put Be and Mg, Al, groups 3, 4 (minus Ti), and 12 with the neighbouring blocks here. Double sharp (talk) 21:52, 31 January 2020 (UTC)

Interesting. My own periodic table would not be divided like that, but go strictly by groups. Hydrogen would float above all of the others in its own color. The alkali and alkaline earth metals form groups 1 and 2 (no H or He), the transition elements (for me synonymous with "d block elements") and the inner transition elements (lanthanides and actinides), with Lu under Y. Lu and Lr are considered to be both inner and outer transition metals, so the categorizations could be merged (non-main group element?). After that would be the icosagens, the tetragens, the pnictogens, the chalcogens, the halogens, and the noble gases (with He). Nh-Og are not out of order. I don't know how you'd draw a periodic table like that, though. But that would be my categorization. ― Дрейгорич / Dreigorich Talk 00:13, 1 February 2020 (UTC)

Main groups, Be, Mg, and Al

@Double sharp: Here’s a further observation on why Be and Mg are in Group 2 and Al is in Group 13.

”The chemical behaviour of the elements of the Main Groups…is determined principally by [their] position with respect to the inert gases…Elements…with atomic numbers which are 1 to 2 units larger, or 5 to 1 units smaller than the atomic number of an inert gas are assigned to the Main Groups.”

Remy H 1956, Treatise on inorganic chemistry, vol 1, Elsevier, Amsterdam, p. 5

Sandbh (talk) 10:16, 1 February 2020 (UTC)

The last sentence is excellent for a treatise. OTOH, if you misread it as an argument for the position rather than as a way to remember it, it is hilariously circular because the atomic numbers he gives just define the placement we want. Why not 3 units larger or 6 units smaller, for example? That would include groups 3 and 12, and the latter is mostly main-group. Then the placement of Be, B, Mg, and Al suddenly ambiguous. And if we are playing the game of "look at history and the old treatises", crack open most of them from before WWII, and you will see Be and Mg discussed with the Zn group rather than the Ca group, as Jensen has noted. Double sharp (talk) 10:28, 1 February 2020 (UTC)

@Double sharp: The world has moved on from the days of Be and Mg over Zn. Remy adds: "Defining the main groups as has been done above, the same division of the elements is obtained as can be reached on grounds of [electronic] atomic structure." Precisely. Let's also laugh at the circularity of the n + l rule as well because it has no first principle basis and is based on empirical observations, inaccurate as the rule itself is. Sandbh (talk) 11:47, 1 February 2020 (UTC)

@Sandbh: By that logic I may start by axiomatically defining group 3 as Sc-Y-Lu-Lr. Which is the same division as obtained from electronic structure, due to the core-like f-orbitals of Lu and Lr. The n+l rule is simply a quick way to summarise how chemical relevance of orbitals really goes all the way from H through Og; even delayed collapses do not target chemical relevance (e.g. 4f for La) and never affect the entry into the core (e.g. 5f ends relevance at No still, and 6d at Cn still). As a statement of chemical relevance of orbitals, it is 100% accurate with only the Ca group as mild exceptions (which have to be, since all chemically accessible orbitals have azimuthal quantum number above 0). So I think we can look forward to the day when the world moves on from Sc and Y over La, too. As Droog Andrey has said, it is just a remnant of days when the f-block was unknown, and it is just a matter of time before the final flicker of that obsolete idea dies just like Be and Mg over Zn. Both obsolete Be-Mg-Zn and Sc-Y-La have some sense, but neither had the justification to overthrow electronic structure. Double sharp (talk) 12:18, 1 February 2020 (UTC)

@Double sharp: Nope. The division obtained from electronic structure points to Sc-Y-La-Ac, since the 4f shell does not start filling until Ce. The n + l rule, in this context, is nonsense since it doesn't reflect the situation on the ground. For that matter, when Janet proposed his LSPT in 1928 on the basis of the same value of n + l in each row, he thought that the measured electron configurations of the anomalous elements must have been wrong, so he "corrected" them to obtain a perfect LSPT. Yet another example of drawing the table like we expect it to be rather than how it really is. Sandbh (talk) 01:44, 2 February 2020 (UTC)

@Sandbh: You focus on the minutiae of exact ground-state configurations. I focus on the big picture of chemically active subshells. Chemically bonded elements are not exclusively in the ground state and unionised (mostly they are not), so your criterion is mostly irrelevant anyway for everybody but the noble gases. I acknowledge that in the ground state La has the "wrong" configuration. I don't care because 4f is clearly chemically active and within reach. For Lu it is not. Same for anomalies like Cr, Cu, Nb, Mo, etc. I'm astonished that you argue for the big picture and simultaneously keep talking about this minute thing. Double sharp (talk) 09:39, 2 February 2020 (UTC)

@Double sharp: Well, differentiating electrons only form the foundations of the periodic table so I’m not sure what planet you’re standing on, so to speak. Sandbh (talk) 11:57, 2 February 2020 (UTC)

@Sandbh: I reject that given their general chemical irrelevance. I propose instead Jensen's criteria, that are pretty much the same as the ones I have stated.

Assignment to a major block based on the kinds of available valence electrons (i.e., s, p, d, f, etc.). [In other words, chemically active subshell of highest angular momentum.]
Assignment of the elements within each block to groups based on the total number of available valence electrons. [In other words, Nb vs Ta does not matter.]
Verification of the validity of the resulting block and group assignments through the establishment of consistent patterns in overall block, group, and period property trends. [Which they do, as in a Lu table group 3 follows the rest of the d-block, which is made more homogeneous.]
Verification that the elements are arranged in order of increasing atomic number as required by the periodic law. [Which is why we allow some flexibility in period 8.]

Double sharp (talk) 12:25, 2 February 2020 (UTC)

P.S. This also explains why I believe helium should go in group 2. By its available valence electrons, helium must be an s-block element: there is no room for dispute. And it has to go in the s² column, thus stuck with Be, Mg, and the alkaline earths. Then helium stands in relation to beryllium in much the same way hydrogen stands in relation to lithium. The trend looks like a typical first-row anomaly for both, so nothing forbids it, and elements remain in order of increasing atomic number. Of course we can talk about it with the noble gases anyway, but putting it above Ne as if it were a p-block element flies in the face of the importance of blocks as a fundamental criterion. It would be the only element clearly in one block placed among elements of another. We understand and agree with all the ways 1s is utterly anomalous for the s-block, and indeed for almost the whole table; but the periodic law should apply to everybody, and these should be second-order corrections to it, even if by far the largest of all of them. Double sharp (talk) 17:24, 2 February 2020 (UTC)

Yet another paper

2019, argues for 15-element f-rows because of inconclusiveness. They find Lu and Lr with core-like f-orbitals following 18-electron rule in the compounds they studied (sticking La/Lu/Ac/Lr into Zintl ion clusters Sn²⁻
₁₂ and Pb²⁻
₁₂). La and Ac are also 18-electron here. So we're back to "weak 4f for La vs core 4f for Lu". Since I consider 15-element f-rows unacceptable, we are still in the same situation, which I argue supports Lu. Double sharp (talk) 10:51, 1 February 2020 (UTC)

@Droog Andrey: What do you think of the authors' methodology? Double sharp (talk) 10:52, 1 February 2020 (UTC)

@Double sharp: They found some clear similarities between La-Ac and Lu-Lr, but that is surely not enough to put them both into the f-block. Droog Andrey (talk) 17:58, 2 February 2020 (UTC)

@Droog Andrey: I agree. ^_^ That La-Ac and Lu-Lr would have similarities is pretty much a given due to their electron configurations, but the f-block ought to have only fourteen columns. Double sharp (talk) 19:04, 2 February 2020 (UTC)

Symmetry in chemistry

I've picked up some sense that others feel that symmetry is special, and that we should not break it without a strong reason. In fact there is nothing intrinsically special about symmetry.

What follows is an anonymous and erudite blogger’s account of a public lecture given on Sep 18th, 2015, in conjunction with an exhibition called Periodic Tales: Art of the Elements, which took place at the Compton Verney Art Gallery (Warwickshire, UK) from 3rd October to 11th December, 2015.

I found it to be rather extraordinary.

The public lecture was given at the Inorganic Chemistry Laboratory (Department of Chemistry) of the University of Oxford (one of the first events of the 2015 Alumni Weekend of the University).

Relevant extracts are:

"Later on, the panel of speakers took questions from the audience. The first question addressed allotropes and how they have (or not) changed our conception of the elements. This prompts us to remind Mendeleev’s philosophical stance, underpinned by the distinction between simple substances (graphite and diamond) and elements (carbon)."

"The second question touched on the equivalence symmetry-beauty, a truly broad topic. Georgiana Hedesan pointed out that symmetry was at the heart of the alchemical thought, from the figures used (squares, circles) to the fact that, supposedly, the four elements came in identical amounts. Peter Battle remarked that, although we tend to see symmetry as neat, too much symmetry might hurt (and – I add – sometimes unexpected properties of materials indeed arise from the suppression of long-range regularities and symmetry, the so-called “defects”). All of this makes me think of Italo Calvino’s reflection on literature in his essay Exactitude in his Six Memos for the Next Millennium, in which, discussing 20th-century literature, he pitted the party of the crystal against that of the flame: “Crystal and flame: two forms of perfect beauty that we cannot tear our eyes away from, two modes of growth in time, of expenditure of the matter surrounding them, two moral symbols, two absolutes, two categories for classifying facts and ideas, styles and feelings…”

"Again on the issue of symmetry and beauty, we should remember that symmetry in chemistry is a deeply mathematical concept, based as it is on group theory. Hence, we can recall what the philosopher of chemistry Joachim Schummer wrote in his sweeping paper on the aesthetics of molecules: “apart from early Pythagorean views on beauty in nature, it is difficult to find any source in the whole history of western theory of art that considers mathematical symmetry the essence of beauty. Instead, we have severe criticism of that idea as well as aesthetic theories based either on the alternative concepts of proportion and harmony or on the interplay of symmetry and asymmetry in a broad sense”[8]. Schummer’s remark is at odds with what is generally perceived as a natural relationship between between beauty and harmony of proportions, as in Palladian villas or Leonardo da Vinci’s man. As a final comment on symmetry, progress in the periodic classification of the elements took off when scientists stopped trying to force all elements in neatly symmetrical groups and periods (see for example Gmelin’s V-shaped periodic system, almost perfectly symmetrical), allowing for the existence of separate subgroups."

8. J. Schummer, Aesthetics of Chemical Products, HYLE, 2003, 73-104

I like the contrast between alchemy and chemistry, and between crystal and flame, and the parallels between the two. Sandbh (talk) 04:59, 2 February 2020 (UTC)

@Sandbh: However: symmetry works perfectly from H to Xe, considering the big picture of chemically active subshells and block homogeneity, not the dance floor of differentiating electrons, so widely squashed by the dancing shoes of excited states in chemistry. Therefore, since it works for Cs through Og as well, there is zero reason to reject it. We can talk again when period 8 happens and continuing the symmetry really breaks down. Then I advocate breaking it in the nicest possible way. Because symmetry, which is by definition a reduction of pluralities (because some bits are enough to tell you everything), must be correlated with Occam's razor. Double sharp (talk) 10:37, 2 February 2020 (UTC)

@Double sharp: Well, no, it doesn't work for Cs to Og, as I've pointed out elsewhere, given the ambiguity of La and Lu at the step 1 level. When Occam's razor was formulated, nobody knew about symmetry breaking. Here are a few quotes to this end:

From a recent New Scientist article:
"…symmetries matter, largely because we like to see them broken sometimes: the laws, particles and forces of physics all have their roots in symmetry-breaking. They create what David Gross of the Kavli Institute for Theoretical Physics at the University of California, Santa Barbara, calls the “texture of the world”. These considerations have led Florian Goertz at the Max Planck Institute for Particle and Astroparticle Physics in Heidelberg to propose the existence of a new particle that is single-handedly capable of cleaning up five of the stickiest problems in physics. “Complete symmetry is boring,” says Goertz. “If symmetry is slightly broken, interesting things can happen."

"While the laws of Nature, “are simple, symmetrical, and elegant, the real world isn’t. It’s messy and complicated…The reason is clear. We do not observe the laws of Nature: we observe their outcomes. Since these laws find their most efficient representation as mathematical equations, we might say that we see only the solutions of those equations not the equations themselves. This is the secret which reconciles the complexity observed in Nature with the advertised simplicity of her laws. Outcomes are much more complicated than laws; solutions much more subtle than equations. For, although a law of Nature might possess a certain symmetry, this does not mean that all the outcomes of the law need manifest that same symmetry.” Barrow JD 2008, New theories of everything, Oxford University Press, Oxford, pp. 136–140

"Nature always takes the path of "simplest sufficient complexity"; matter is complex only because it cannot be made any simpler and still come into existence through symmetry-breaking." from here.

Sandbh (talk) 03:47, 3 February 2020 (UTC)

Nope. La has 4f character, Lu doesn't. Symmetry works perfectly applied to chemically relevant subshells rather than chemically irrelevant differentiating electrons. You would do better to argue about group 2. We have a little problem there, and then all the symmetry breaking we want in period 8 when relativity cannot be ignored. (Though even then it breaks in the nicest possible way.) Double sharp (talk) 12:20, 3 February 2020 (UTC)

Greenwood & Earnshaw (2ED)

@Double sharp: I was reading G & E and was surprised to see them discussing the same things as me.

On group 3 they say:

they display the gradation in properties that might be expected for elements immediately following the strongly electropositive AEM and preceding the TM proper. (p. 946)
- Exactly, they're intermediate and there is no big divide like a Sc-Y-La table suggests there is. Nota bene, Be and Mg are not "strongly electropositive". Double sharp (talk) 11:30, 2 February 2020 (UTC)

@Double sharp: The important part here is, "preceding the TM proper".

@Sandbh: So what else is new? The group 3 elements are physically normal transition metals. Only chemically are they not "TM proper", but since the literature widely focuses TM proper on characteristic properties like variable oxidation states, Zr, Hf, Nb, and Ta are also not "TM proper". As usual we have intermediacy and continuity. Double sharp (talk) 23:27, 2 February 2020 (UTC)

@Double sharp: I think you let things like intermediacy and continuity get in the way. Biological taxonomies would never exist but for focussing on the broad contours rather than obsessing about intermediacy and continuity and never making hard-nosed decisions about differences in classes. Classification science usually involves less than sharp boundaries. I choose to be pragmatic about these things. There’s no need to lose sleep about the hard cases. If the boundaries become less than useful then fine, change them. G & E’s “transition metal proper” works well enough. So does E and H’s. As do all the authors who effectively apologise for calling group 3 transition metals. This never happens to group 4. Well, apart from your own view. A case of Double sharp v the world. Sandbh (talk) 00:11, 3 February 2020 (UTC)

@Sandbh: I simply note that many authors who talk about excluding the Sc group unwittingly give criteria that would also exclude Zr, Hf, Nb, and Ta. And I quote their chemistry and even what those authors say about it to justify that. Apparently, you are allowed to scour the literature and criticise it when you see a Lu argument, but I'm not allowed to for this. Double sharp (talk) 07:50, 3 February 2020 (UTC)

@Double sharp: I agree. I'd attribute this to shorthand, and to the fact that transition metal status seems to be attributed to ions containing partly filled d shells. Group 3 doesn't have this, not at a level of mainstream chemistry significance. Group 4 easily does so, with Ti 3+ 2+ etc. If you feel you're not allowed to criticise this because I criticise you for doing it, you're giving away power to me. Your power is your own to use as you see fit unless you let yourself fall into auto-routine mode. Don't give away your power subconsciously. Sandbh (talk) 10:09, 3 February 2020 (UTC)

@Sandbh: Amazing, so M³⁺ and M²⁺ (M = Ti, Zr, Hf) according to you are totally relevant for finding ions with partially filled d-shells, but totally irrelevant for finding ionic character in group 4. (I argued heavy group 4 and group 5, so if you're saying "group 4 easily does so" based on one element, it contradicts you saying the covalent Be and Mg don't matter for group 2.) Sorry, but I find myself incredulous. I'm not giving away power to you subconsciously. I'm just saying what I see here: you appear to allow yourself to use properties in favour of La that you don't allow me to use in favour of Lu. Respectfully, that seems like a double standard. Double sharp (talk) 12:10, 3 February 2020 (UTC)

@Double sharp: It doesn't seem amazing to me. I'd say it was pragmatic. C & W 6ed, say, "The main transition group or d block includes the elements that have partially filled d shells only. Thus…Sc…is the lightest member…Ti-Cu all have partly filled 3d shells either in the ground state of the free atom (all expect Cu) or in one or more of their chemically important ions (all except Sc)." (p. 634) So they are saying lower oxidation states in Sc are not chemically important, compared to the situation for Ti. There's no contradiction. They allocate two paragraphs to lower oxidation states of Sc; nine pages to Ti(IV) and 2.5 pages to Ti(III). Sandbh (talk) 01:19, 4 February 2020 (UTC)

@Sandbh: That was published in 1999. Today we know so much better that divalent complexes are known for all stable lanthanides (2013 paper). All three lower oxidation states of Sc are known in organoscandium compounds: 0, +1, +2 (2004 paper). And CsScCl₃ (and the analogues with Br and I, as well as Rb analogues for the halogens Cl and Br) was already known in 1980. The borderline between group 3 as not-really-transition and group 4 as "transition proper" has long since stopped working, now that +2 as an oxidation state in group 3 is pretty much as well-characterised as lower oxidation states for Zr, Nb, Hf, and Ta. Double sharp (talk) 19:40, 4 February 2020 (UTC)

the chemistry in the main concerns the formation of a predominately ionic +3 oxidation state. (p. 948)
- So just like Zr, Nb, Hf, and Ta, whose chemistry mostly concerns the formation of the group oxidation state. Page 979: "by contrast most of the chemistries of niobium and tantalum are confined to the group oxidation state +5." Double sharp (talk) 11:30, 2 February 2020 (UTC)

@Double sharp: I left out 'ionic' [now inserted]. So, no, not like Zr, Nb, Hf, and Ta. Sandbh (talk) 22:07, 2 February 2020 (UTC)

@Sandbh: Which we shouldn't read too much into as a foundation for the periodic table, because Be and Mg have a +2 oxidation state that is if anything more covalent. So focusing on ionic vs. covalent, rather than being pragmatic and recognising that oxidation state and atomic size matters as Fajans did, leads to Be and Mg over Zn. And, of course, the fact that Mg is rather covalent suggests that Sc, with a higher charge and a higher electronegativity, should have significant covalence as well. The difference that the literature agrees is fundamental between main-group and transition is variable oxidation states, but then group 3 is just like Zr, Nb, Hf, and Ta. Double sharp (talk) 22:22, 2 February 2020 (UTC)

@Double sharp: Eh? One of the early—foundational—things taught in chemistry is the contrast between ionic and covalent.

Mg, as far as I know, has a mainly ionic chemistry. The EN of Mg to Ra ranges from 1.31 to 0.89. Be is more covalent than ionic, for sure. That said, 5 of the 6 AEM are ionic so yes, they are predominately ionic/strongly electropositive. Your comparison of Mg and Sc a hilarious and baseless distraction. Your fundamental difference is right, and group 4 is the first time this difference is encountered, as per Earnshaw and Harrington. Sandbh (talk) 23:34, 2 February 2020 (UTC)

@Sandbh: Nope, one of the foundational things taught is the EN difference controlling the continuum between ionic and covalent bonding. Everyone knows at that level that there is a difference between nonpolar covalent (e.g. C-C), polar covalent (e.g. C-F), weakly ionic (e.g. Be-F), and strongly ionic (e.g. Na-F). It's not a catastrophic change.

Scandium is more electronegative than magnesium and forms a higher charge, so if anything it should be more covalent. Organomagnesium compounds are mostly covalent (quite polar, sure). Earnshaw and Harrington are just wrong here, since any dismissal of lower oxidation states for group 3 runs into the same problem that Zr, Hf, Nb, and Ta are also very unhappy to be in anything other than the group oxidation state. Double sharp (talk) 23:40, 2 February 2020 (UTC)

@Double sharp: Yes, my mistake. I found this among my documents (source unknown) "The ionic radius for the +2 cation of magnesium is fairly small (0.65 Å). As a consequence the charge density (z/r) is high, which results in a high polarizing power of the Mg2+ ion. Thus, magnesium tends to form polar covalent bonds rather than ionic complexes." That does not make any difference to the predominating ionic behaviour of group 2.

Re continuums, I'm not interested. I'm only interested in predominating behaviour. That is, is the locus of the chemistry more towards the ionic end or the covalent end of the continuum? There is no issue with E & H. Their conclusion is the same as G & E and C & W and everyone else who comments about the atypical behaviour of group 3. No one says this of group 4. I don't know of any genuine lower oxidation state compounds of Sc. Wiberg says there are only a few lower valency cluster halides known in which the formal oxidation states are less than +3. They go on and say in this respect the Sc group metals are not typical transition elements because one would expect them to form the +2 oxidation state by the loss of the two s electrons.

Lower oxidation states for Zr and Hf, while rare, are well established. Sandbh (talk) 04:12, 3 February 2020 (UTC)

CsScCl₃. Plus lots of recently discovered Ln(II) complexes that surely have Sc and Y analogues. Double sharp (talk) 07:50, 3 February 2020 (UTC)

On group 4 the most important oxidation state in the chemistry of these elements is +4, which they say is too high to be ionic. Lower oxidation states are rather sparsely represented for Zr and Hf. Whatever arguments may be advanced against describing to Sc, there is no doubt Ti is a “transition metal”. (p. 958)

Which is precisely why I focus on Zr and Hf. By standards of "main group vs. transition" that exclude Sc, the status of Zr/Hf and Nb/Ta suddenly becomes iffy. Indeed, +4 is too high to be ionic, but let's not read too much into it, because otherwise Th and U are incongruous: active metals with predominant states too high to be ionic. Double sharp (talk) 11:30, 2 February 2020 (UTC)

@Double sharp: Ah, well, I observe the overwhelming majority consensus in the literature per the esteemed G & E. More noise about Th and U, I see. Sandbh (talk) 23:45, 2 February 2020 (UTC)

@Sandbh: It's not noise. It's a simple refutation of the relevance of "ionic vs. covalent" distinction. Everyone knows Th and U are active metals, they just have too high oxidation states to be ionic. Everyone knows Tl is a weak post-transition metal, but it has a very low oxidation state and is ionic anyway. Fajans got it right: this is a continuous trend based on oxidation state and ionic radius. That is the broad contour, not the accident of how it ends up looking in the periods. (Of course, we have amphoteric scandium, which then suggests some covalency like for magnesium, which is less electronegative and has a lower charge. ^_^)

The overwhelming majority consensus in the literature has apparently forgotten the vast preference of Zr, Hf, Nb, and Ta for their group oxidation state. Except that I doubt it is the overwhelming majority consensus, since IUPAC has two definitions of a transition metal, and neither actually allows the exclusion of group 3. Funnily enough, my statements about the heavy group 4 and 5 elements are supported by the literature, like Greenwood and Earnshaw. Notice their conspicuous silence on Zr and Hf when defending Ti as a transition metal. As well as their frank admission that Nb and Ta have chemistries mostly confined to the +5 state. Double sharp (talk) 23:57, 2 February 2020 (UTC)

@Double sharp: Zr and Hf are irrelevant to my premise: group 3 = predominately ionic main group-like chemistry; group 4 = predominately covalent main group-like chemistry, as backed up by G & E (not that I need them, as this point is common in the literature). Not forgetting that group 4 is the first group (per Earnshaw and Harrington) in which the really characteristic transitional properties of variable oxidation state, colour and paramagnetism are encountered. Th and U are irrelevant at the broad contour level: On active metals we can say that "They are mostly strongly electropositive, with a few of the light actinides (U to Am) being only moderately electropositive." Sandbh (talk) 22:27, 2 February 2020 (UTC)

@Sandbh: Only because of oxidation state. Which is why Th and U are totally relevant for broad contours because they reveal the real broad contour trend. It's called Fajans' rules: ionic character increases as magnitude of charge goes down, as cations grow, and as anions shrink. The break is later in each period. Be²⁺ is very covalent, Mg²⁺ has tendencies, and from Ca²⁺ onwards we have strongly ionic cations. Al³⁺ is very covalent, Sc³⁺ has tendencies (it is an amphoteric cation), and only from Y³⁺ onwards is it really more ionic. With group 4 we have to wait for Rf⁴⁺ before we get something like ionicity, judging from the basicity of that cation. Lumping it together as "group 3 predominantly ionic vs. group 4 predominantly covalent" obscures what is going on. It also fails to do justice to Sc, judging by its amphoterism and diagonal relationship with Mg.

Also, in spite of Earnshaw and Harrington, these "really characteristic transitional properties" are about as weak for Zr, Hf, Nb, and Ta as they are for group 3. Double sharp (talk) 23:27, 2 February 2020 (UTC)

@Double sharp: You're clutching at straws again. The details of what is going on aren't relevant to the broad contours. That's not to say they aren't interesting. I'm not concerned with where the break is in each period, at the broad contour level. I'm only concerned with where the break is at the predominating behaviour within groups level. The weak amphoterism of Sc is irrelevant at this level. So is it's diagonal relationship with Mg. Failing to do justice to Sc. Eh? That would be why Cotton and Wilkison (6 ed) say, "Since the properties of Y are extremely similar to, and those of Sc mainly like, those of the Ln proper, and quite different from those of the regular d-block elements, we treat them also in Chapter 19 [The Group 3 elements and Ln]. I know, of course, C & W must be wrong too. Sandbh (talk) 03:16, 3 February 2020 (UTC)

See, they say Sc is only "mainly like" the Ln. And they're right, because its atomic radius makes it intermediate between the Ln and the later 3d metals starting at Ti. And guess which Ln it is most like, due to its small size? Lu. Double sharp (talk) 07:50, 3 February 2020 (UTC)

On the An they say, “it is clear an ‘actinide contraction’ exists, especially for the +3 state, which is closely similar to the ‘lanthanide contraction”. (p. 1264).

And what do they say about the Ln contraction? Exactly what I said about Y³⁺ through Ag³⁺. These contractions are only relevant when the state is always the same, which is not the case for the An. The An contraction is most relevant (1) in the +3 state, i.e. mostly for the second half of the series only and (2) for the transactinides. Looks rather like the 3d contraction with +2 a dominant state only from Mn onwards, and its effect on Ga through Kr. The moment the Ln change oxidation state, suddenly properties stop varying consistently with the contraction. I am very sure I remember them making that point in their chapter about the lanthanides. ^_^ Double sharp (talk) 11:30, 2 February 2020 (UTC)

@Double sharp: The headline is what they say about the status of the An contraction, contrary to your own view. It was relevant enough for them; it's relevant enough for me. The rest of what you said is not relevant to the broad contours.

@Sandbh: Nothing they said contradicts my view. The An contraction exists, I never disputed it. For the +3 state it is closely similar to the Ln contraction, I never disputed that either. The only trouble is that the An are mostly unhappy to be in the +3 state, and I would be astonished if they did not support that. So broad contours say that every other contraction but the Ln is weakened by lack of constant oxidation state, and therefore we should treat that as an exception. Double sharp (talk) 23:27, 2 February 2020 (UTC)

@Double sharp: Who said you disputed its existence? I didn’t. You never said the +3 state is closely similar to the Ln contraction. So why do you need to say you never disputed this? You sought to downplay the relevance of the An contraction. And yet two of our favourite authors, in a calm and non-plussed manner, refer to it and its similarity to the Ln contraction. And there you go again still seeking to downplay its significance, on the basis of irrelevant grounds. The relevance is that the Ln contraction spans the 4f row as does an analogous 5f contraction. This does not work in an Lu table. That’s all. Sandbh (talk) 00:32, 3 February 2020 (UTC)

By your standard it doesn't work for the 5f row either because Th. Oh, but excited states are apparently decisive for Th but cannot be considered for La and Ac. Never mind that chemically bound atoms are usually found in what would be excited states were they alone. You need to start actually looking at what the literature does not say as well as what it says. And maybe read it somewhat critically to note when something said does not make sense or self-contradicts. You're certainly good enough at it whenever someone in the literature supports Lu for not-so-good reasons. Except that then irrelevancies are paraded pretending to be philosophical concerns like the 234 argument, with no evidence in the literature why that is important. Sandbh vs the world, maybe? Double sharp (talk) 07:50, 3 February 2020 (UTC)

I know you like G & E. I do too. Sandbh (talk) 11:04, 2 February 2020 (UTC)

To reduction ad absurdum "predominantly ionic vs. predominantly covalent" further: let's look at anions. Is F predominantly ionic or covalent? Don't be silly, it depends on what it's bonded to. A metal fluoride is probably ionic, a nonmetal fluoride is probably covalent. A higher fluoride is probably covalent, a lower fluoride is probably ionic. (E.g. PtF₆ is pretty covalent.) The same is true for the metals. Is Cs predominantly ionic or metallic? It equally well depends on what we're bonding to. Double sharp (talk) 11:58, 3 February 2020 (UTC)

@Double sharp: I've made an exception for this one since it's so close to the intermission lounge:

"Fluorine, the smallest and most electronegative of the halogens, frequently forms predominately ionic compounds." (Bailar JC 1984, Chemistry, p. 829)

Since I'm in the main arena here, I'll add, yes, this is a case of Double sharp v the World, as you put it. Sandbh (talk) 06:31, 6 February 2020 (UTC)

@Sandbh: You said that first, not me. And since the world is well aware of fluoride volatility, and how oxidation state matters here, your statement is highly dubious. Not to mention that here the important oxidation state difference is not the 3 vs. 4 you like to talk about, but 4 vs. 5. ^_^ Double sharp (talk) 12:08, 6 February 2020 (UTC)

Intermission

@Double sharp:@R8R:@Droog Andrey:

At this point I'd like to spend a day in a library assimilating all that we have written, rather than continuing the thread by replying to each and every post. If I have anymore questions I'll post them. I'll post a little mini-summary of where I think things are up to, shortly. Sandbh (talk) 05:21, 3 February 2020 (UTC)

Mini-summary

@Double sharp:@R8R:@Droog Andrey:

Here it is, my pre-library day perspective. All mistakes, omissions, and oversights are my own.

Chemical behaviour

I’m satisfied that the argument about the overall chemical behaviour of group 3 being more like that of groups 1 and 2 than 4 to 12 holds up well enough. Double sharp argues there is a continuum of chemical behaviour and that, effectively, you can’t slice the continuum non-arbitrarily. I think there is a well enough defined hiccough in the continuum between the behaviour of group 3 as predominantly main group ionic metals v the behaviour of groups 4 and 5 as predominantly covalent metals, main group for group 4; TM for group 5. That explains why, in the literature, group 3 metals are frequently referred to as atypical transition metals, whereas this is never the case for groups 4 and 5.

But the literature (or rather the small subset of it that doesn't like group 3 to be transition) has overlooked that Zr, Hf, Nb, and Ta have equally weak credentials as transition metals proper, being stuck mostly in their group oxidation state. (They have lower oxidation states, but at the same order of those for Sc: well-characterised, but uncommon.) Meanwhile, "ionic" vs "covalent" has not stopped depending on what is the other member of the bond. Is fluorine predominantly ionic or covalent? That's a silly question, because it depends on the EN difference (i.e. what it's bonded to and in what oxidation state that other element is). Sodium? Of course, NaF is strongly ionic. Uranium? Er, harder to say: UF₃ is certainly ionic, judging from its high melting point, but UF₄ is starting to be iffy despite also having a high melting point (it reacts with water in a way that covalent halides like BeCl₂ does and MgCl₂ slightly does). UF₅ is polymeric, and UF₆ is molecular. Carbon? Of course, polar covalent. Another fluorine atom? Of course, nonpolar covalent. Double sharp (talk) 12:03, 3 February 2020 (UTC)

@Double sharp: I think there is an order of magnitude difference between lower oxidation Sc and Ti³⁺. Yes, the dependence of ionic v covalent depends of the other member of the bond. That said, the literature is quite clear that group 3 is predominately ionic whereas group 4 is predominately covalent; it isn't necessary to examine every possible other member of the bond to conclude this is so. Sandbh (talk) 00:21, 5 February 2020 (UTC)

@Sandbh: Yes, it is because of that word "predominately". Just because the literature says something does not mean you can accept it without question, especially when it is something this nonsensical, just look at fluorine. Sure, there is some difference between lower oxidation states of Sc and Ti. That is just because transition properties proper flower later in each period. Sc is not so different from Zr and Hf, here. Double sharp (talk) 17:05, 5 February 2020 (UTC)

@Double sharp: Our own entry on fluorine says, "Fluorine's high electron affinity results in a preference for ionic bonding; when it forms covalent bonds, these are polar, and almost always single." Sandbh (talk) 06:21, 6 February 2020 (UTC)

Homogeneity

Double sharp also argues that Lu is more homogenous with the individual physical and chemical properties of the rest of the d-block elements than is the case for La. Since Lu is more like an Ln than a TM and since this is also the case for La, acknowledging that Lu is more TM-like than La, I argue that periodic vertical trends, and overall group behaviour is more important than homogeneity with the individual physical and chemical properties of the rest of the d-block, given this block already spans a heterogenous range of such properties.

Overall group behaviour is more similar with Lu in group 3, and you yourself claim that periodic vertical trends between Sc-Y-La and Sc-Y-Lu are inconclusive. Double sharp (talk) 12:03, 3 February 2020 (UTC)

@Double sharp: I agree periodic vertical trends between Sc-Y-La and Sc-Y-Lu are inconclusive, as per the six graphs. That's why I say, "Since the chemical behaviour of Group 3 generally resembles that of Groups 1−2 rather than that of Groups 4−11 it follows that Group 3 is better placed next to Groups 1−2, with the result that elements of like chemistry are more closely grouped together." And the only way to properly show that is La under Y, with a split d block in the 32-column form. Sandbh (talk) 06:51, 4 February 2020 (UTC)

@Sandbh: The problem is, they don't. Zr, Nb, Hf, Ta are also basically pre-transition. And Sc should not even be fully ionic, judging by applying Fajans' rules to compare it with Mg. Double sharp (talk) 07:54, 4 February 2020 (UTC)

@Double sharp: Group 3 is mostly pre-transition ionic (per groups 1 and 2); groups 4 and 5 are mostly pre-transition covalent. Sc atoms don't care what you think they should be :) Remy (1956, p. 32): "Sc and its homologues have only a very slight tendency to form covalent compounds…". Sandbh (talk) 00:01, 5 February 2020 (UTC)

@Sandbh: Then they're wrong, just look at organoscandium compounds with that small EN difference. I see we finally agree that by the usual standards of main group vs. transition that authors who exclude group 3 as transition use, group 4 and 5 are mostly pre-transition. Now, does it make any sense to call an element mostly ionic or covalent? I've already answered why it is in fact a silly notion: just look at fluorine. Fluorides are more ionic or more covalent depending on how electropositive the counter-cation is and what oxidation state it is in. Same for the metals, just look at the counter-anion. So all this is is "look at EN and oxidation state", in which case Sc must definitely have as much covalent character as Mg. That's not me thinking, that's simply Fajans' rules: calculate charge over radius for Sc³⁺, it is more than for Mg²⁺. Double sharp (talk) 00:08, 5 February 2020 (UTC)

@Double sharp: Per G&E: "In the main, the chemistry of these elements concerns the formation of a predominantly ionic +3 oxidation state arising from the loss of all 3 valence electrons and giving a well-defined cationic aqueous chemistry. Because of this, although each member of this group is the first member of a transition series, its chemistry is largely atypical of the transition elements. The variable oxidation states and the marked ability to form coordination compounds with a wide variety of ligands are barely hinted at in this group although materials containing the metals in low oxidation states can be prepared (see p. 949) and a limited organometallic (predominantly cyclopentadienyl) chemistry has developed."

Yes, per the literature, it is useful to call an element mostly ionic or covalent; the group 1, 2 and 3 metals, for example, as well the Ln, are mostly ionic. "For chemists…the most important feature of an element is its pattern of chemical behaviour, in particular, its tendency toward covalent bond formation (or its preference for cation formation)" (Rayner-Canham Overton 2010, p. 29). Sandbh (talk) 00:43, 5 February 2020 (UTC)

@Sandbh: The literature saying this has evidently never taken a moment to think about what they are saying. Exercise: based purely on the chemistry of these four elements, decide whether their chemistries are predominantly ionic or covalent.

Fluorine;
Caesium;
Uranium;
Thallium.
[optional] Carbon.

You are allowed to refer to the literature to see what the chemistry is like, but not just quote what they say about "predominantly ionic". You have to use the chemistry to decide for yourself if such a characterisation is warranted for any of these four elements. (Hint: it is not, as it varies too much on what the elements are bonded to, in what oxidation state they are in, and in what oxidation state the other element they are bonded to is in.) Double sharp (talk) 17:03, 5 February 2020 (UTC)h

@Double sharp: Here you are. I've indicated the most common oxidation state/s and whether the element in that state is predominately ionic or covalent. For added interest I added some commentary from the literature after each entry.

F (−1) ionic

"Fluorine's high electron affinity results in a preference for ionic bonding; when it forms covalent bonds, these are polar, and almost always single."

Cs (+1) ionic

"Cesium is the most electropositive and most alkaline element, and thus, more easily than all other elements, it loses its single valence electron and forms ionic bonds with nearly all the inorganic and organic anions"

U = (+6) covalent

"Because of the actinide contraction, uranium's chemistry is quite similar to that of molybdenum."

"The uranyl oxygen bonds are covalent in nature."

Tl (+1) ionic

As previously quoted

C = (±4) covalent

"In most organometallic compounds, the metal-carbon bond has predominantly covalent character…"

"Carbon chemistry is overwhelmingly covalent…"

Sandbh (talk) 06:19, 6 February 2020 (UTC)

Differentiating electrons

I’m satisfied that block membership as a global property, in which the focus is on predominant differentiating electrons, provides a purely quantitative way of distinguishing between an La table and an Lu table. Double sharp has proposed an alternative which is not fully quantitative. Double sharp also argues that anomalous differentiating electrons don’t make a difference to the actual chemistry of the elements. I’ve given examples of where they do make a difference. Double sharp argues that the anomalous presence of a p electron in Lr won’t make any difference to its chemistry. I’ve said that we can’t pick and choose as to which differentiating electrons do or do not count, since block membership is a global property based on predominant differentiating electrons. I have further noted that we don’t yet know enough about the chemistry of Lr.

Nope. Predominant differentiating electrons are predicated on ground states that the elements, in compounds, simply are not in. It is also predicated on "add a proton and an electron, that's our next element", which never happens chemically. Whereas examining chemically active subshells, like Jensen and I do, is something global that deeply controls chemistry. Double sharp (talk) 12:05, 3 February 2020 (UTC)

@Double sharp: I rest my case on the periodic table as the organising icon of chemistry, and the role of differentiating electrons (per Bohr) in determining its structure and shaping periodic trends. Sandbh (talk) 22:12, 4 February 2020 (UTC)

@Sandbh: So all we have to go on is "tradition". And sometimes you advocate looking at condensed-phase configurations for this, and sometimes gas-phase. I rest my case on the simple fact that in chemically bonded environments, atoms don't show their ground-state gas-phase configurations for the most part, and therefore considering differentiating electrons alone is folly. Whereas chemically active subshells are actually based on chemistry and not an irrelevant idealisation like isolated gas-phase atoms, which is in favour of them since the periodic table is the organising icon of chemistry. Differentiating electrons don't shape periodic trends, not in the d- and f-blocks with so many excited states so close to each other. Double sharp (talk) 00:06, 5 February 2020 (UTC)

@Double sharp: What we go on is the periodic table which represents an accumulation of scientific thought. I start with gas-phase and if need to, then consider condensed-phase configurations, and other relevant factors. I don't do this arbitrarily. Differenting electrons give order and shape to the periodic table, per the idealised n + l approximation, and Jensen's sorting hierarchy. From them we are able to discern the s, p, d, and f blocks, and the periodic trends occurring in each of them. Sandbh (talk) 01:46, 5 February 2020 (UTC)

@Sandbh: So you start with something irrelevant to most chemical environments, and then go on only if needed(!) to something that only reflects one particular chemical environment with no other elements around! The wonder is how much of the ideal n+l rule, that works perfectly for chemically active subshells considered holistically (rather than one or two special cases), still manages to survive this transformation with its huge kernel. It must surely be fundamental with how hardy it is under such trying conditions! Double sharp (talk) 17:09, 5 February 2020 (UTC)

@Double sharp: If you're confident the n + l rule works "perfectly" for "chemically active sub-shells" considered holistically you should be writing this up for a journal. Differentiating electrons are plain as day; chemically active sub-shells will be quite another thing, and convincing the chemistry community that such things are chemically significant for e.g. La while they are not for e.g. the heavy alkaline earths will be a challenge. What does "active" mean, anyway?Sandbh (talk) 05:37, 6 February 2020 (UTC)

@Sandbh: I don't need to write it up, as anything I write about this is going to be a rehash of Jensen. (Which is good, because I am not that free. ^_^) There is nothing new at all about it that requires the chemistry community to be convinced, because it already uses such considerations. From the thorium article: "A thorium atom has 90 electrons, of which four are valence electrons. Three atomic orbitals are theoretically available for the valence electrons to occupy: 5f, 6d, and 7s." (With a citation, that includes 7p as well, even!) And it's so well-known that the TM's are not dⁿs² but dⁿ⁺² in complexes that G & E's tables in their chapters on those groups even explicitly write out those electronic configurations (like we have at iron and silver). "Active" simply means that it may be occupied by the valence electrons in chemical environments, which includes all low-excitation-energy configurations.

I also recommend to some extent Schwarz's article, even if he's not quite right once we reach very heavy elements. He goes beyond me in stating an order of energy levels for chemically active subshells, which I don't; but, as usual, the exception is the s-block. But I think it is better not to do that. The first trouble is that you never see a non-delayed f-block collapse because by the time it starts we are already at medium-to-high Z; you see a mildly delayed one and then a significant delayed one. (Nota bene, if you insist on delaying the start of the f-block, then it extends to Lu and Lr, maybe Rf if you are consistent, where the f-electrons are totally inactive. And I can much better stomach having the pre-f character of La in the f-block than the non-f character of Lu.) And then by the time of the 5d elements it is no longer completely true that 5d lies below 6s, and it's even more wrong for the 6d elements. So I prefer to say that the n+l rule gives chemically active subshells, though their energy level order may change. And for almost all the elements it does it perfectly.

And this brings me to my last point. The perfection is marred by the Ca group, indeed. It is also marred by Cs, which is starting to show some honorary d-character too; it is also probably marred by Mc through Og with that small 7p-8s gap. But note:

Even counting all of these, I have just nine anomalies. That's less than any differentiating electron scheme can come up with.
Chemically active subshells even in defeat retain relevance. OK, the Ca group mars the perfection, and they actually show it in some honorary transition-metal character. That's why I say, OK, calcium and company are strictly speaking d-elements, but we call them s-elements because of greater commonalities at broad strokes level with the alkali metals. Now, does anyone seriously think that Nb d⁴s¹ vs Ta d³s² actually changes anything in their chemistries? In a real chemical environment both are d⁵⁻ⁿ in oxidation state n anyway.
This seems to imply that Be-Mg-Zn is actually a harder case than Sc-Y-La. Which is borne out by Be and Mg siding Zn in most occasions rather than Ca, so by homogeneity of group trends it's a shoo-in. Note that the only reason why Be-Mg-Zn gives one more anomaly in differentiating electrons is because Rg has for once in group 11 produced a d⁹s² configuration, so counting anomalies once again means silliness like deciding for Sc-Y-La purely based on that 7p electron in Lr (which I can fight just by quoting Jensen), since we are here apparently deciding for Be-Mg-Ca purely based on that configuration of Rg over a hundred elements away from Be(!). Whereas considering periodic trends here at least focuses on something actually relevant to the elements involved, and it goes entirely on Be-Mg-Ca so that the s-block is harmonised (as the d-block is a bit inconclusive, though physically speaking the Zn group is a much better fit). Similarly, it goes entirely on Sc-Y-Lu so that the d-block is harmonised (as the f-block is a bit inconclusive). Double sharp (talk) 12:06, 6 February 2020 (UTC)

P.S. I missed your examples where differentiating electrons supposedly made a difference. So now I have posted some refutations. ^_^ Double sharp (talk) 16:29, 3 February 2020 (UTC)

Homogeneity hypocrisy

Double sharp regards my position on the homogeneity of differentiating electrons and the chemical behaviour of groups 1-3 as being inconsistent because I have criticised him for his arguments to do with best fit homogeneity for the element under Y in terms of individual physical and chemical properties of the rest of the d-block. I regard differentiating electrons as a more fundamental property, that shapes the periodic table. I regard the overall chemical behaviour of groups as being more important than the panoply of individual chemical and physical properties of elements within a block. Of course, individual blocks show their own characteristics but group 3 does not show typical d-block behaviour. Nor does group 12, for that matter.

Overall chemical behaviour of group 3 is more homogeneous with Lu in it. Y is like a late lanthanide (which Lu is), and Sc is intermediate between late lanthanides and early 3d metals (closer to Lu than La due to atomic size). Double sharp (talk) 12:05, 3 February 2020 (UTC)

@Double sharp: Homogeneity, absent of any consideration of periodic trends, does not imply group kinship.

From our IUPAC submission:

A comparison of ionic data by Atkins et al. (2006, p. 34) concludes that Sc-Y-La is preferred over Sc-Y-Lu. Their comparison is expressed as a problem and answer, in the context that ionic radii generally increase down a group (pp. 89–90):

Problem 1.14
At various times the following two sequences have been proposed for the elements to be included in Group 3: (a) Sc, Y, La, Ac; (b) Sc, Y, Lu, Lr. Because ionic radii strongly influence the chemical properties of the metallic elements, it might be thought that ionic radii could be employed as one criterion for the periodic arrangement of the elements. Use this criterion to describe which of the sequences is preferred.
Answer The common ionic state for the group 3 elements is +3, so the electron configurations for the elements in each sequence are:
Sequence (a) Sc³⁺: [Ar] Y³⁺: [Kr] La³⁺: [Xe] Ac³⁺: [Rn]
Sequence (b) Sc³⁺: [Ar] Y³⁺: [Kr] Lu³⁺: [Xe]4f¹⁴ Lr³⁺: [Rn]5f¹⁴
The electron configurations in sequence (a) are all rare gas configurations so the ionic radii should increase slowly as the principal quantum number, n, increases. In sequence (b), Lu³⁺ and Lr³⁺ also have filled f subshells. Since f electrons shield the nuclear charge so poorly, Z* is expected to be much larger for Lu³⁺ and Lr³⁺, thereby reducing the ionic radius. Thus, sequence (a) is preferred based on ionic radii. The measured ionic radii bear this conclusion out. For six coordinate radii, the values found are 0.885 Å for Sc³⁺, 1.040 Å for Y³⁺, 1.172 Å for La³⁺, and 1.001 Å for Lu³+.

Sandbh (talk) 22:05, 4 February 2020 (UTC)

@Sandbh: This logic alone suggests B and Al over Sc. In sequence B³⁺, Al³⁺, Sc³⁺ etc., everyone has a rare gas configuration. In sequence B³⁺, Al³⁺, Ga³⁺ etc., we get a d-block contraction and hence a reduction of ionic radius. Therefore B-Al-Sc is preferred based on ionic radii. Ionic radii do not generally increase down a group because of contractions. Therefore, Atkins et al.'s argument is flawed because it presupposes that the group 1 and 2 s-block trend should work for everybody. Sc, Y, and Lu are d-elements, and should follow the trend set by all the other d-block groups. Which they do, and Sc-Y-La doesn't. Case closed. Double sharp (talk) 23:59, 4 February 2020 (UTC)

@Double sharp: Al is a p block element, which is the more important consideration, per the literature.

@Sandbh: And I've already conclusively demonstrated that La is an f-block element just like Ac and Th, so this argument is, indeed, needless. But I carry on because it confirms what we already knew. Double sharp (talk) 16:41, 5 February 2020 (UTC)

As per Atkins et al. (pp. 89–90): "The general trends for ionic radii are the same as for atomic radii. Thus: ionic radii increase down a group (The Ln contraction restricts the increase between the 4d- and 5- series metal ions)."

@Sandbh: That's exactly why the increase should be "restricted" here. It always happens just after a new block is inserted. Look at 1s-2s (pure) vs. 2s-3s (restricted); 2p-3p (pure) vs. 3p-4p (restricted); 3d-4d (pure) vs. 4d-5d (restricted); 4f-5f (pure) vs. 5f-6f (surely restricted by that enormous superactinide contraction that's looming). Regularity of the general trend demands double periodicity that is not fulfilled by Sc-Y-La, only by Sc-Y-Lu. Double sharp (talk) 16:41, 5 February 2020 (UTC)

From our article on ionic radius: "The ionic radius is not a fixed property of a given ion, but varies with coordination number, spin state and other parameters. Nevertheless, ionic radius values are sufficiently transferable to allow periodic trends to be recognized. As with other types of atomic radius, ionic radii increase on descending a group.

I looked at the crystalline ionic radii in our ionic radius article. The general rule works for 14 of 17 groups (not counting group 3). Sandbh (talk) 02:46, 5 February 2020 (UTC)

@Sandbh: You neglect the generality of the result of contractions, just like from 3p to 4p and from 4d to 5d. And as usual you fixate purely on reducing a number to its sign (does it increase or not), forgetting the important thing: the magnitude of the increase is, as usual, dampened significantly by a contraction. Double sharp (talk) 16:58, 5 February 2020 (UTC)

s-block:

H⁺-Li⁺	He²⁺-Be²⁺
90	59
Li⁺-Na⁺	Be²⁺-Mg²⁺
26	27

p-block:

B³⁺-Al³⁺	C⁴⁺-Si⁴⁺	N⁵⁺-P⁵⁺	O²⁻-S²⁻	F⁻-Cl⁻
26.5	24	25	44	48
Al³⁺-Ga³⁺	Si⁴⁺-Ge⁴⁺	P⁵⁺-As⁵⁺	S²⁻-Se²⁻	Cl⁻-Br⁻
8.5	13	8	14	15

d-block (just the first half, to avoid arguments about choosing oxidation states; low-spin values chosen):

Sc³⁺-Y³⁺	Ti⁴⁺-Zr⁴⁺	V⁵⁺-Nb⁵⁺	Cr⁶⁺-Mo⁶⁺	Mn⁷⁺-Tc⁷⁺
15.5	11.5	10	15	10
Y³⁺-Lu³⁺	Zr⁴⁺-Hf⁴⁺	Nb⁵⁺-Ta⁵⁺	Mo⁶⁺-W⁶⁺	Tc⁷⁺-Re⁷⁺	Ru⁸⁺-Os⁸⁺
−3.9	−1	0	1	−3	3

The same drop is encountered and the s >> p > d (> f) motif is faithfully reproduced. That is, unless you insist on La under Y and creating a one-time-only exception to the wider periodicity. It's just that for 3d-4d, the increase was already so small that for 4d-5d the increase hovers around zero. With the variation between high- and low-spin complexes for the 3d metals being over 10 pm in some cases, let's not pretend that the sign differences are some important cleft given to us by Nature herself. Double sharp (talk) 16:58, 5 February 2020 (UTC)

@Double sharp: I'm relaxed and comfortable (since we're in the intermission lounge) with my original post that mapped the broad contours of the situation. The same can be said for Atkins et al.; Jensen 1982 in his trigger paper; and Scerri and Parsons 2018. Wulfsberg (2000) has a nice Lu periodic table of crystal ionic radii for 6 CN for multiple oxidation states. Ionic radii increase going down 14 of 18 groups.

When we prepared our IUPAC submission referencing Atkins, I remember checking what they said about the general pattern of ionic radii going down groups, and I found they were right. Otherwise I would've taken it out. Same thing happened when I rechecked it this time. Sandbh (talk) 05:24, 6 February 2020 (UTC)

@Sandbh: As you can see, the differences from the 4d row to the 5d row are minuscule and hovering around zero. As I noted already, the difference in ionic radius for the same 3d metal, in the same oxidation state, between high-spin and low-spin complexes, can vary by around 10 pm. This suggests a similar sort of variation for the 4d and 5d metals in such chemical environments. Therefore I put it to you that your analysis is seriously flawed because the possible changes in ionic radius for a single element are larger than the difference between increasing and decreasing for the 4d-5d comparison! Nothing significant can be drawn there for a difference between whether the radii increase or decrease here. All we know is that the increase from 4d to 5d is mostly cancelled out, which supports the trend where after the first row, increase drops. Lu in group 3 confirms this trend, La in group 3 spits in its face. Double sharp (talk) 12:35, 6 February 2020 (UTC)

@Double sharp: I'll continue to rely on the literature, which notes the general trends involved, based on comparable data, in comparable conditions, and same oxidations state; and same CN; with no mixing of different spin environments, as did Jensen, and Chistyakov, whom Jensen relied on. C&W: "There are many important trends and correlations to be found among these results [for ionic radii]." Shriver & Atkins: "The sizes of ions, ionic radii, generally increase down a group, decrease across a period, increase with coordination number, and decrease with increasing oxidation number." etc. It's like extracting trends from data despite the 20% differences, in order to make useful generalisations (acknowledging the need for caution) rather than highlighting the 20% differences in the data and concluding that no useful or general trends can be observed. Sandbh (talk) 00:12, 7 February 2020 (UTC)

@Sandbh: How can you extract a trend from data where the range of variation exceeds the magnitude of the trend you are looking for? Anything you find will just be noise. Do you have values for the 4d and 5d metals that distinguish low-spin from high-spin? Our article ionic radius only gives such for 3d, where they differ significantly. Double sharp (talk) 00:01, 8 February 2020 (UTC)

@Double sharp: By using comparable data. I don’t know if I have that data. I hope the literature is not so uniformly “stupid” as to use uncomparable data. Sandbh (talk) 10:18, 8 February 2020 (UTC)

@Sandbh: OK, I looked it up and see why now: the 4d and 5d metals are usually low-spin in complexes, so I made the right choice above. But still: notice that the magnitude of the increase in size is not constant, but constantly wiggles a bit. If it is wiggling around zero, then I put it to you that the wiggle is not significant, and the important takeaway is that the increase has been cancelled out pretty much by a contraction. Which is what the literature says for 4d vs. 5d. By looking only at the sign you are still observing noise. As is everybody who counts TM groups showing an increase (or not), rather than getting that key takeaway.

For the series X-Y-Z I could just as well have plotted (Y-X increase) minus (Z-Y increase) to bring home the point about the increase dropping sharply after the 1st row. Then putting La in group 3 creates a big outlier. Double sharp (talk) 10:23, 8 February 2020 (UTC)

Periodic law (revisited)

I’m satisfied that the periodic law, combined with our understanding of the actual electron configuration filling sequence, provides a robust argument for La, as the first d element after Y, going under Y (whereas Lu is the third element in which a d electron appears). Double sharp is more concerned with the n + l or Madelung rule, which is only an approximation. According to the n + l rule, La should have an 4f electron (only it doesn’t).

It has a low-lying 4f state that contributes. That's good enough for chemistry, in which elements are often in what would be excited-state configurations were they alone. According to your periodic law Th is the second 6d element because Th has the advantage of incumbency over Rf when it comes to the 6d² configuration. I know what will follow: a double standard in which Th as an f-block element is defended on the grounds of its ions and excited-state configurations that contribute in the metal, but La and Ac with similar excited-state credentials are blocked. While meanwhile Lu and Lr are let in with absolutely core-like, inactive f-orbitals in an unprecedented step. Double sharp (talk) 12:02, 3 February 2020 (UTC)

@Double sharp: My understanding of the situation follows.

La is the first element with a 4d electron so it goes under Y according to the periodic law, and the aufbau principle as manifested in real life rather than the idealised n + l rule. I’d regard the presence of a low-lying 4f state as a tipping point argument, in the absence of more fundamental arguments.

La does not form a cation having an 4f electron; OTOH the Lu³⁺ cation has the configuration [Xe]4f¹⁴. The poor shielding of the 14 f electrons results in a large contraction of the size of the Lu cation, and this impacts it chemistry, making it the least basic of the lanthanides.

Ce is the first 4f element so it starts the f-block. The other block starting elements are H, B, and Sc.

Th as the second 6d element would normally go under Hf, as occurred historically.

Subsequently (as proposed by Seaborg) it was realised that Th 6d², Pa 5f²6d¹, and U 5f³6d¹ in fact represented the start of new series analogous to the Ln. Thorium thereby came to be relocated under Ce.

It was then determined that the presence of f character in Th influenced its crystalline structure and that Th could form a +3 cation having an [Rn]5f¹ configuration. The f-electron count for condensed thorium is thought to be up to 0.5 due to a 5f–6d overlap.

The presence of any f-character in La is not considered to be of comparable significance: "...its 4f character, if there is one, is in any case very small (B. Coqblin 1977, The electronic structure of rare-earth metals and alloys, Academic Press, p. v).

A few authors have referred to some properties of Lu being influenced by the presence of its filled 4f shell: Langley 1981; Tibbetts and Harmon 1982; Clavaguéra, Dognon and Pyykkö 2006; Furet et al. 2008; Xu et al. 2013; Ji et al. 2015. The most surprising of these is likely to have been Clavaguéra and colleagues, who reported a pronounced 4f hybridisation in LuF3 on the basis of three different relativistic calculations. Their findings were questioned by Roos et al. (2008) and Ramakrishnan, Matveev and Rösch (2009).

Citations for all but Furet et al. can be found in our IUPAC submission. Furet E, Costuas, K, Rabiller, P & Maury O 2008, "On the sensitivity of f electrons to their chemical environment, Journal of the American Chemical Society, vol. 130, no. 7, 2180–2183

Sandbh (talk) 21:46, 4 February 2020 (UTC)

@Sandbh: My understanding follows instead:

Lutetium utterly lacks 4f character. All but one study conclude that those orbitals are core-like, and that one is questioned. OTOH, lanthanum certainly has 4f character, since 4f is a low-lying configuration well within the range that chemical bonding can excite an atom to. (It is actually lower in energy than d⁹s² for silver.) Otherwise cubic La complexes would be terribly difficult to explain on symmetry grounds. This is utterly decisive: lanthanum is the beginning of the f-block. This is exactly like all the heavy element delayed collapses: 5f doesn't start in the gas phase until Pa, 6d until Rf, 5g until E125. Not the slightest problem, they are all the same. Do you not realise how much of a double standard it is to keep insisting on differentiating electrons, but backpedaling and saying "whoops, actually this 5f excited state is important for thorium only"? When is the differentiating electron just an inconvenience like for thorium and lawrencium, and when is it prohibitive like you seem to want it to be for lanthanum and actinium? Where is the consistency? Double sharp (talk) 00:06, 5 February 2020 (UTC)

@Double sharp: I agree the 4f electrons in Lu are core like. That does not mean the presence of those fourteen f electrons in Lu³⁺ has zero impact on the chemistry of Lu. Quite the contrary. Lanthanum, OTOH, has zero 4f electrons to start with. There is no back pedalling in the case of Th, as I will explain shortly. Differentiating electrons are the first order sorting mechanism, per Jensen. They do not resolve La and Lu. For La the presence of any f-character is minimal. For Lu, its fourteen f electrons have a sizeable impact on its chemistry. I raised other considerations in my first response. Thorium causes some problems which, on closer examination and consideration of other factors, go away. Sandbh (talk) 01:34, 5 February 2020 (UTC)

@Sandbh: The 14 f electrons in Lu³⁺ have as much impact on Lu chemistry as the 14 f electrons in Hf⁴⁺ have on Hf chemistry. Or the 14 f electrons in Ta⁵⁺ on Ta chemistry. As do the 10 d electrons in Ga³⁺ chemistry. Every single one of them are the same thing: the effect of a filled core-like subshell in providing incomplete screening. That happens once a block is finished, which is exactly why Lu needs to go into the d-block. And it is totally different from that of the 14 f electrons in Yb²⁺ because then the 4f subshell is still available for chemical reactions, proving that at Yb we are in the f-block and at Lu we have left it.

Jensen did not say that differentiating electrons were the first-order sorting mechanism. He wrote of the "kinds of available valence electrons". And given the way d- and f-block elements move freely between configurations, for La through Yb that includes 4f, 5d, 6s, and 6p due to having so many configurations so close to each other: chemical bond energy is sufficient for such excitations. The amount of energy required for La to display 4f¹ is well within that of chemical bond range. Now, does anyone actually have a figure for how much energy Lu requires to breach the 4f shell? I certainly cannot find that figure listed in the NIST tables. (Not saying it can't happen, since the table is not so complete: here we are told that "New and more complete observations of Lu I and Lu II are needed". But I bet it is far more than the energy required for La to put something in its 4f shell, since now we are breaking open a full subshell.) I put it to you that these two considerations are decisive: La has direct 4f involvement as a valence subshell, just like Th for 5f, that just happens to not be occupied in whatever configuration happened to be the ground state. (Same for 5s in Pd.) 4f in Lu acts like a core subshell, just like for Hf, Ta, W, and so on. There is no difference between my approaches for La and Th.

The one time I have to appeal to other factors is for a very different situation altogether: group 2 vs 12, where there is a genuine ambiguity. And I try not to sweep it under the rug as best as I can: I am happy to call Ca through Ra strictly also d-elements, just putting them in the s-block since Zn, Cd, and Hg are more d-element-like and the d-block can't hold eleven columns. When those higher oxidation states of Cs are discovered I am willing to call Cs strictly also a p-element as well but still display it in the s-block as eka-Rb. The s-block is weird anyway, so it can stomach these odd cases better than any other one. Double sharp (talk) 16:33, 5 February 2020 (UTC)

@Double sharp: Bear in mind my focus here is only on the composition of group 3. In the case of the f-block, its start is delayed until Ce. It therefore finishes at Lu. This can be seen in the configurations of the applicable trivalent cations, from Ce f¹ to Yb f¹³, and Lu f¹⁴.

Yes, my mistake. Jensen said, "Assignment to a major block based on the kinds of available valence electrons (i.e., s, p, d, f, etc.)." In La this is s and d. In Lu this is s and d. Thus, for example: "…lanthanum and lutetium, both of which have just three (sd) valence electrons." (Freeman et al. 1984, Handbook on the lanthanides and actinides, p. 166). So Jensen does not work here. Everything else I wrote still stands. I think you need to be a bit careful saying the s-block is weird, since it is supposed to be the epitome of regularity and periodicity. Sandbh (talk) 04:53, 6 February 2020 (UTC)

@Sandbh: False premise. La has f-involvement just like Th does: it's only that you implicitly admit chemically active unoccupied subshells for Th and Lr by looking at the condensed phase, and refuse to consider them for La and Ac, creating an effective double standard. Jensen noted much the same thing while criticising Lavelle: you seem to be making Lavelle's mistake, characterised by Jensen as "he ignores the evidence for irregular conﬁgurations and the loose correlation between these configurations and chemical behavior and instead relies solely on their ground-state valence configurations coupled with apparently arbitrary criteria for when they are or are not of significance when it comes to assigning the elements in question to either the d- or the f-blocks." So in La the valence orbital types include f, but in Lu they do not.

The s-block is weird precisely because it looks like the epitome of regularity and periodicity from the schoolkids' perspective. This is actually very weird because it means that:

Incomplete screening effects are minimised because of the hard noble gas core;
Secondary periodicity does not arise for the same reason;

This is weird because every other element has this. You like to refer to predominance, so consider this: in school we like to look at elements like group 1 and 2, maybe the first row, and we see that our usual tricks like simple cations and stable octets work perfectly there. And then we go elsewhere and it all stops working. Since most elements have this stop working, perhaps we might consider that the elements we know and love are, in fact, the weird ones? And primogenic repulsion supports that for period 2, while absence of screening effects and secondary periodicity supports that for the s-block. Double sharp (talk) 12:32, 6 February 2020 (UTC)

@Double sharp: I observe Occam's razor and only consider secondary criteria when primary criteria are inconclusive. La is a d-element, as is Th and Lu. La, Th and Lu fit well where they are in a convention table for all of the other secondary reasons I've previously listed. Sandbh (talk) 23:28, 6 February 2020 (UTC)

@Sandbh: Precisely. And not only do I do the same thing, I also make sure my primary criterion (chemically active subshells) is actually relevant to the elements' chemistry, which yours (differentiating electrons) isn't. Jensen and Schwarz have already debunked the latter. Double sharp (talk) 00:10, 7 February 2020 (UTC)

Debunking differentiating electrons

@Double sharp: Where did J & S debunk differentiating electrons? Sandbh (talk) 07:38, 7 February 2020 (UTC)

Jensen, quoting Jørgensen: 'There is not the slightest doubt that no simple relation exists between the electron configuration of the ground state of the neutral atom and the chemistry of the element under consideration. Thus iron and ruthenium differ much more from each other chemically than do nickel, palladium, and platinum, though the configurations are analogous in the former case but differ in the latter. The most spectacular discrepancy between the spectroscopic and chemical versions of the periodic table is that helium is an alkaline earth element from the standpoint of spectroscopy, since its configuration does not terminate with with np⁶ like the other noble gases. Hence, it is not too surprising that the almost invariant trivalency of the lanthanum series has little to do with the ground states of the neutral atoms.'

Schwarz: 'The second reason for differences between chemically bound transition-metal atoms and free atoms in vacuum is that the electronic motions in free atoms are not disturbed by adjacent atoms. Most free atoms have open valence shells, where the electrons can arrange differently. The orbit−orbit and spin−orbit angular-momenta couplings result in a large number of different electronic states with different energies. For instance, the 3d⁵4s¹ configuration of a free Cr⁰ or Mo⁰ atom comprises 504 different states with 74 different degenerate energy levels, scattered over several hundred kJ/mol. ...

'The qualitative behavior of chemical elements can be rationalized with the help of the dominant electronic valence configurations of the atoms embedded in a molecular or crystal environment. These may be correctly called the “electronic configurations of the chemical elements”. However, what is listed in respective tables of chemical textbooks under this headline is something else, namely, what physicists call “the configurations from which the J-level ground states of free unbound atoms in vacuum derive”. ...

'The third exception concerns the free neutral transition-metal atoms in vacuum, including the f block. Their ground-state configurations depend in an involved manner on the often-discussed averaged d−d and d−s Coulomb-repulsion energies and also on the individual orbit−orbit (term) and spin−orbit splittings, even if the latter are small. The correct quantitative explanation is vital for the interpretation of atomic vacuum spectra, but exceeds the scope of general chemical education. There are only a few special topics in chemistry that require the correct understanding of free atoms in vacuum (e.g., atom-molecular gas-phase reactions) or of orbit−orbit and spin−orbit couplings of bonded open-shell atoms (e.g., the chemistry of the transition, lanthanoid, and actinoid metals; spin-flip enhanced reaction mechanisms; so-called spin-forbidden processes). [Nota bene, bonded open-shell TM atoms show different configurations from ground-state free ones.]

'Finally, it is misleading to present free atoms as prototypes for the microscopic description of chemical elements in compounds. The common qualitative textbook explanations of the atomic ground states (correctly: J levels) are incorrect. Therefore, we plead for teaching the correct atomic-orbital order (sequence 6) together with the regular exception, sequence 8, for the s block. One need no longer apologize for irregularities.' Double sharp (talk) 00:07, 8 February 2020 (UTC)

I have added some bolding. Double sharp (talk) 19:48, 8 February 2020 (UTC)

@Double sharp: Jensen undermines his own quote when his #1 criteria for block assignment is, “Assignment of the element to a major block based on the kinds of available valence electrons and/or valence vacancies (i.e., s, p, d, f, etc.).” Jorgensen did not imply there was no relationship between electron configuration and the chemistry of an element. Instead, he said there was no simple relationship. Nor did he say anything about differentiating electrons, and their relationship to blocks. His point was that you could not necessarily tell all of the oxidation states that any particular element could manifest. That is all.

Schwarz similarly did not have anything to say about differentiating electrons, nor their connection to the aufbau principle and the n+l rule. Sandbh (talk) 10:57, 8 February 2020 (UTC)

@Sandbh:

Jørgensen is obviously not only talking about common oxidation states. These differ in group 10 just as they do in group 8, taking his example. What he is talking about is the totality of chemistry, which is something you have so far in these arguments been totally unable to grapple with, respectfully. It is a simple fact that group 10 is more homogeneous in chemistry than group 8, but ground-state electron configurations match better in group 8 than 10!
Jensen has mentioned "valence vacancies", not just electrons. Surely that includes 4f for La. In fact, considering valence electrons and vacancies basically means considering chemically active subshells, as Droog Andrey and I advocate.
What on earth are you talking about wrt Schwarz? He already explained very well why ground-state gas-phase configurations are irrelevant chemically. The fact that he doesn't use the words "differentiating electrons" is irrelevant since those depend on ground-state gas-phase configurations. And if you actually read the article (I gave a link) you would see him discussing the energy level order of subshells as well. Double sharp (talk) 12:17, 8 February 2020 (UTC)

@Sandbh: And here is Glenn T. Seaborg himself on my side that the Ln contraction is exceptional and that we should consider chemically active subshells (i.e. those that are involved for ions and compounds) instead of just ground-state gas-phase electron configurations. I have added some bolding:

'It is important to realize that the electronic structures listed in Table 6 are those of the neutral (unionized) gaseous atoms, whereas it is the electronic structure of the ions and compounds that we are chiefly concerned with in chemistry. The relationship of the electronic structure of the gaseous atom of an element to that of its compounds can be rather complicated. For example, in the case of the actinide and lanthanide elements, one would not necessarily predict the predominance of the III oxidation state from the electronic structures of the gaseous atoms; there are usually only two so-called "valence electrons," the 7s or 6s electrons, which might indicate a preference for the II oxidation state.

Apparently, specific factors in the crystal structure of, and the aquation (hydration) energies of, the compounds and ions are important in determining the stability of the III oxidation state. Thus, the characteristic tripositive oxidation state of the lanthanide elements is not related directly to the number of "valence electrons" outside the 4f subshell, but is the somewhat accidental result of a nearly constant small difference between large energy terms (ionization potentials on the one hand, and hydration and crystal energies on the other) which persists over an interval of fourteen atomic numbers. Therefore, if we could somehow have a very extended Periodic Table of Elements containing numerous "f" transition series, we might expect that the 5f, rather than the 4f, elements would be regarded as more nearly representative of such f series.'

Respectfully, your stance is Sandbh vs the world. Double sharp (talk) 19:47, 8 February 2020 (UTC)

@Double sharp: I could not find anything in Seaborg saying the Ln contraction is exceptional. I liked where he said, "The relationship of the electronic structure of the gaseous atom of an element to that of its compounds can be rather complicated." This is much more useful than Jensen, quoting Jørgensen: 'There is not the slightest doubt that no simple relation exists between the electron configuration of the ground state of the neutral atom and the chemistry of the element under consideration." I liked Seaborg's two tables showing the Ln as 58 to 71, and the other two showing the f-block as Ce to Lu, etc. How did you find these tables? Sandbh (talk) 06:12, 10 February 2020 (UTC)

@Sandbh: Regarding the exceptional nature of the 4f contraction, see the last bit that I already quoted: "Thus, the characteristic tripositive oxidation state of the lanthanide elements is not related directly to the number of "valence electrons" outside the 4f subshell, but is the somewhat accidental result of a nearly constant small difference between large energy terms (ionization potentials on the one hand, and hydration and crystal energies on the other) which persists over an interval of fourteen atomic numbers. Therefore, if we could somehow have a very extended Periodic Table of Elements containing numerous "f" transition series, we might expect that the 5f, rather than the 4f, elements would be regarded as more nearly representative of such f series." In other words, the main reason why we care so much more about the Ln contraction than any other one (constant +3 oxidation state) is an exception. We all know that the s, p, and d series do not show this. And as Seaborg notes, the 5f series doesn't show this, and higher f-series that we might expect for the extended periodic table don't show it either.

The whole point is that there is no simple relationship between ground-state electron configurations and chemistry. DE's are based only on ground-state electron configurations, and therefore the relationship between them and chemistry is foggy. As Seaborg wrote, 'it is the electronic structure of the ions and compounds that we are chiefly concerned with in chemistry'. As Schwarz wrote, 'The qualitative behavior of chemical elements can be rationalized with the help of the dominant electronic valence configurations of the atoms embedded in a molecular or crystal environment. These may be correctly called the “electronic configurations of the chemical elements”. However, what is listed in respective tables of chemical textbooks under this headline is something else, namely, what physicists call “the configurations from which the J-level ground states of free unbound atoms in vacuum derive”'. In other words, look at electron configurations over all chemically relevant environments, which do not include ground-state gas-phase ones and your favourite DE's that are based on them.

I found the La tables there understandably mistaken, given the era. Same as all the Zn tables from the immediately previous era. As we can see from figures 2 and 4, the old mistaken idea of the f-block as degenerate members of the d-block had not died yet, and so what came below Y was instead La and all the succeeding elements, not only La, and this placement no doubt influenced the mistaken idea that La should go up there as the placeholder for all of them. We are past this, I hope. (Oh, and he duplicates Al in group 3 and group 13 in figure 2. ^_^) Double sharp (talk) 11:34, 10 February 2020 (UTC)

PS: Another interesting passage in Seaborg was, "Some spatial classifications of the elements appeared in which the heaviest elements, starting with thorium as the homolog of cerium, are listed as the chemical homologs of the rare-earth elements, but the reason in these cases appears to be mainly connected with the symmetry of and the ease of making such an arrangement (Cjounkovsky and Kavos (1944): Talpain (1945)."

@Double sharp: Well, consider this passage: "The excitation energies of the free atoms and ions correlate with many properties of their compounds: redox potentials, energy of cohesion of the metals, and thermodynamic stability…" from here. Surely it is reasonable to observe that there are good correlations to be drawn between the electron configurations of the elements in their gas phase, and their properties and those of their compounds on the ground, noting that such correlations can sometimes be complex, obscure, tricky or buffeted by irregularities? Sandbh (talk) 00:52, 11 February 2020 (UTC)

@Sandbh: But the author doesn't refer to the ground-state electron configurations of the gas-phase atoms that you restrict your consideration to. She refers to the excitation energies, which implies that excited states are being considered and an interplay of configurations. As indeed she does on p. 41. Double sharp (talk) 23:11, 11 February 2020 (UTC)

@Double sharp: The abstract sums it up well enough for me:

"A number of properties of d-elements, lanthanides, and actinides depend on the initial dq-, fq- and final dq–1-, fq–1-electron configurations. These properties include the ionisation potentials of the free atoms and ions, electron affinity, redox potentials, excitation energies, and enthalpies of the decomposition and disproportionation of the halides, oxides, chalcogenides, and pnictides of the lanthanides and actinides, the oxidation state in compounds with variable oxidation states, etc."

Sandbh (talk) 23:26, 11 February 2020 (UTC)

@Sandbh: It sums it up in my favour. She's already mentioned two electron-configurations in it: fⁿ and f^n-1. They can't both be the ground state, so it can't be supporting your stand. This is clearly pretty much what I mentioned about the interplay between fⁿ and fⁿ⁺¹ configurations in the Ln and An. And guess what, La through Yb show it, Lu mathematically cannot. Double sharp (talk) 23:31, 11 February 2020 (UTC)

@Sandbh: You're guilty of that yourself. You exclude La as an f-element because it lacks a 4f electron, and demand that the f-block should start at cerium. But then you notice that thorium also lacks an f-electron. Since your own logic for La would demand that thorium also be excluded as an f-element, you quickly make special exemptions for it on the grounds of chemically more relevant configurations where 5f appears in it. (Meanwhile, those configurations for lanthanum and actinium are quietly ignored.) If you were being consistent, rather than being concerned with the symmetry that demands that each block begins as a complete vertical column, you would be forced to begin the 5f block at protactinium by your logic. And this is what Seaborg's forerunners did not rule out, suggesting elements all the way up to element 99 as possible starting points for the 5f series (yes, a protactinide series was considered possible among other things), to be confirmed or disproved by experimental investigation of their chemistries! So you are the one demanding symmetry that each block starts in a vertical column, that those pioneers did not demand, but simply treated as a hypothesis to stand or fall on later discoveries! Which is why your reaction to La and Ac is "yes, that is prohibitive", whereas your reaction to Th, Lr, and presumably E121 when we discover it is to scramble to find other reasons to avoid exposing the inconsistent use of DE's. Just like Lavelle's argument that Jensen criticise, respectfully. If you were really consistent about it, you would be noting that your logic demands that Th is not an f-block element (and hence a protactinide series), and the Lr is not a d-block element. But you won't do that, because "there is no other place [Lr] can practically go" as you said. Well, so what happened to drawing Nature as She was rather than how we would like Her to be?

When Seaborg formulated his actinide concept, not only was the electron configuration of the Ln and known An not really known for sure (Ce was thought to be 4f²6s²), but he also explicitly noted that the important thing was chemistry and that it should trump the exact ground state configurations. To quote him: "It may be, of course, that there are no 5f electrons in thorium and protactinium and that the entry into a rare-earth like series begins at uranium, with three electrons in the 5f shell. It would still seem logical to refer to this as an actinide series." And why? Because of the predictions for Am and Cm that don't make sense without an actinide concept, with Cm refusing mostly to go past the IV state and Am having difficulty as well. The chemistry rules, not the little waves here and there of which among the dozens of close configurations happens to luck out and barely become the lowest. That's exactly why a Lu table is so much superior to a La one holistically. Double sharp (talk) 11:42, 10 February 2020 (UTC)

@Double sharp: I have nothing to feel guilty about! :) As we wrote in out IUPAC submission, a block starts upon the appearance of the first applicable electron. Everything else falls into place after that, guided by the periodic law and the n+l approximation. I don't have to justify Th's place under Ce, although it is interesting to comment upon the marked 4f nature of Th. Sandbh (talk) 00:58, 11 February 2020 (UTC)

@Sandbh: As I wrote above: you're still assuming symmetry to force a block to begin in a vertical column, even if your first criterion of DE's says it doesn't. So why is this symmetry inviolable when you seem to consider it fine to violate the symmetry of rectangular blocks? Double sharp (talk) 23:11, 11 February 2020 (UTC)

I'm grooving with the Seaborg vibe :) Sandbh (talk) 06:17, 10 February 2020 (UTC)

@Sandbh: It appears that the both of us can read the same article and both come away with completely different impressions of whose arguments they are supporting. Which maybe supports R8R's contention on your talk page: "I also fear, and I hope to be wrong at that, that the discussion with Double sharp is not helping you much---not because DS is not giving you reasonable arguments but rather because, as it appears to me from the sidelines of your discussion, you two cannot truly hear each other. I would be inclined to think that a complete consideration would include his arguments too, and then try to compare each one hand-by-hand by the same metrics. If I were to summarize in one sentence how your paper could be improved, it's that---it could use a comparison of both sides of each argument by the same metrics. I don't know if that would yield the same result or whether it would yield a definitive result at all, but if a result was to be gained this way, it would stand a much greater chance to persuade me, even if into the option I don't usually fancy. The same, I believe, is also to be said of your intended readers." Double sharp (talk) 11:42, 10 February 2020 (UTC)

REM

I’m satisfied with the rare earth argument and the regularity of its horizontal and vertical trends, consistent with the other 18 groups and the actinides, but I’m not satisfied with how I’ve explained its relevance.

Because it doesn't have any. It is predicated on a category we made up that is not wholly based on chemistry (partly natural occurrence) and blurry in its boundaries. The logic is moreover not applicable to any other category we made up other than the group-based ones. Double sharp (talk) 12:02, 3 February 2020 (UTC)

@Double sharp: We have an article on the rare earth metals. Books have been written on the chemistry of the rare earths e.g. Topp NE 1965, The chemistry of the rare-earth elements, Elsevier, Amsterdam. As with classification schemes generally, there is some variation and overlapping of properties within and across each category. That is to be expected. Sandbh (talk) 07:01, 4 February 2020 (UTC)

We also have articles on transition metals, platinum group metals, refractory metals, noble metals, etc. Every one has wobbly boundaries (noting what you said about Au as an honorary PGM), and not a single one of them can be stretched out into a straight line. At the very least that questions the relevance of your own argument about the stretching by your own standards. Double sharp (talk) 19:32, 4 February 2020 (UTC)

@Double sharp: All those categories can be stretched out into lines, of increasing Z, consistent with their appearance in Z order in the periodic table. PGM = 44 45 46 77 78 79; etc. In an Lu table, the REM appear as 21 39 71; 57 to 70. In an La table they appear as 21 39 57 to 71. Sandbh (talk) 01:16, 5 February 2020 (UTC)

@Sandbh: Ah, so now we are allowed to connect Pd to Os even if they're not next to each other. That's already backpedalling from your statement in #Rare earth series: 'The first option can be "bent", in ascending numerical order, to read Sc 21 to Lu 71.' Now, since you have returned to reasonably allowing people to read the periodic table in the order they read English(!), note that in a Lu table, the REM appear as 21, 39, (*) 71 with an asterisk leading to 57 through 70. So, that is just 21, 39, 57-71 by the simple rule of reading footnotes. There's always an asterisk in an 18-column form (as long as it actually takes a stand on group 3) that lets you reconstruct a 32-column form from it, and people know how to read asterisks and find footnotes and do the gluing. And at this rate every category can be stretched out into lines of increasing Z just because the periodic table goes in increasing Z, even a stupid one like Be-O-P-S-V-Mo (atomic numbers from the Lost numbers sequence), so this still ends up saying nothing. Double sharp (talk) 16:38, 5 February 2020 (UTC)

@Double sharp: I had to go back to my article to see what I'd written [lines and arrows added]:

"The rare earth series (Sc, Y and the lanthanides La–Lu) appear listed in order of their atomic numbers in a 32-column periodic table with Group 3 as Sc-Y-La-Ac. If Group 3 is shown as Sc-Y-Lu-Lr, the minority of the rare earths appear in order of their atomic number whereas the majority appear in a backwards order. Thus, in the first instance they appear as…

| Sc21
| Y39
| La57 Ce58 Pr59 Nd60 Pm61 Sm62 Eu63 Gd64 Tb65 Dy66 Ho67 Er68 Tm69 Yb70 Lu71
+-------------------------------------------------------------------------->

…whereas in the second instance, as follows:

                                                                      Sc21 |
                                                                       Y39 |
La57 Ce58 Pr59 Nd60 Pm61 Sm62 Eu63 Gd64 Tb65 Dy66 Ho67 Er68 Tm69 Yb70 Lu71 | 
-------------------------------------------------------------------------->v

The second option is awkward, or highly anomalous at best, since the horizontal, vertical, and diagonal trends that characterise the periodic table are based on an increasing sequence of atomic numbers."

The PGM look like:

Ru44 Rh45 Pd46
+------------+
             |
-------------+
| 
+------------>
Os76 Ir77 Pt78

Here, the majority do not appear in backwards order. In fact there is no backwards order really, since the two horizontal triads are aligned.

Of course, I can word the last line of my extract better. Sandbh (talk) 04:20, 6 February 2020 (UTC)

@Sandbh: There's nothing backwards about the REM even in a Lu table, even if I still think the argument is silly. It goes like this:

                                                                      Sc21 |
                                                                       Y39 |
+--------------------------------------------------------------------------+
|
+-------------------------------------------------------------------------->
La57 Ce58 Pr59 Nd60 Pm61 Sm62 Eu63 Gd64 Tb65 Dy66 Ho67 Er68 Tm69 Yb70 Lu71 |

Why do you allow yourself to do that for the PGM, but not for the REM? Just take each line and read it, left to right. If not, any category which starts earlier in each period is suspect. Good riddance to the post-transition metals, then. Double sharp (talk) 12:27, 6 February 2020 (UTC)

@Double sharp: In the PTM the majority do not appear in "backwards" order, or uniquely –x spaces behind the first member of the series, if you will.

@Sandbh:. Yes they do. The first member is Al in group 13, in all future periods they start in group 12. Double sharp (talk) 00:36, 8 February 2020 (UTC)

@Double sharp: There are 12 PTM. How many are in negative spaces behind Al? Sandbh (talk) 10:04, 8 February 2020 (UTC)

@Sandbh: Ah, so that's what you mean: just the first element in each row, not the number of early-starting rows. Fine, not in this case, then. But I can look at the definition that starts in group 11, and suddenly it is inconclusive. At the extreme and only considering true metals (i.e. not Bi) we may end up with {Cu, Ag, Au, Zn, Cd, Hg} on the left, and {Al, Ga, In, Tl, Sn, Pb} on the right. Now where are we? This choice is just as arbitrary as your choice between REM definitions. (You do know that Wulfsberg treats Bi, Po, At and sometimes even Sn as nonmetals in his tables, right?)

Anyway: you are shifting the goalposts. First it is about stretching in order. Once we point out that it doesn't work for the PGM, you back up and say it's actually about vertical placements. When are we going to allow readers of the periodic table to use their common sense that they exercise when reading English? OK, the REM start much earlier in period 6. Big deal, it's just like reading indented paragraphs. This is a pure graphic-design argument that has nothing to do with chemistry. Double sharp (talk) 10:14, 8 February 2020 (UTC)

Tempted to add: try "spectroscopically s² elements". Since spectroscopic stuff is one of the only times your favourite DE's become important. Well, in your table, they start with He, and everyone else is suddenly 30 columns to the left. ^_-☆ Double sharp (talk) 10:17, 8 February 2020 (UTC)

Here's another angle for your consideration:

Situation

A
The rare earth metals, in a conventional periodic table, effectively appear as follows:

Sc21
Y 39
La57 Ce58 Pr59 Nd60 Pm61 Sm62 Eu63 Gd64 Tb65 Dy66 Ho67 Er68 Tm69 Yb70 Lu71

B
Whereas In a table with Lu in group 3 they appear as follows:

                                                                      Sc21
                                                                      Y 39
La57 Ce58 Pr59 Nd60 Pm61 Sm62 Eu63 Gd64 Tb65 Dy66 Ho67 Er68 Tm69 Yb70 Lu71

Analysis

Option A
The REM appear in order of Z i.e. as Group 3 (21-39-57) and 58-71 (i.e. the old school definition of lanthanides). Chemically, in terms of their trivalent cations, this can be explained as group 3 having NG cores, and Ce to Lu having [Xe]f1 to f14 cores.

Alternatively, you can treat them as just 21-71, and leave the group 3 concept out. Chemically, in terms of the trivalent cations, this can be explained as Sc, Y and La having NG cores, and Ce to Lu having [Xe]f¹ to f¹⁴ cores.

Option B
The REM appear either as:

Group 3 (21-39-71) and 57-70; or
57-70 and group 3 (21-39-71).

Chemically, in trivalent cation terms, this can be either explained as:

Sc and Y having [NG] cores; Lu having an [NG]f14 core; La having an [NG] core and Ce to Yb having [Xe]f¹ to f¹³ cores; or
La having an [NG] core, Ce to Yb having [Xe]f¹ to f¹³ cores; Sc and Y having [NG] cores; and Lu having an [NG]f¹⁴ core.

Alternatively, you can treat them as 21-39, and 57 to 71, and leave the group 3 concept out. Chemically, in terms of the trivalent cations, this can also be explained as Sc, Y and (reaching back 14 places) La having NG cores, and Ce to Lu having [Xe]f¹ to f¹⁴ cores.

Question
I think I’ve answered my own question, after my head stopped spinning, but which of these two options is easier to present? Sandbh (talk) 23:20, 6 February 2020 (UTC)

@Sandbh: You're making it too hard. In a Lu table, the REM are just the 4f metals plus group 3. (Yes, La is a 4f metal, as I have demonstrated far too many times here already.) Double sharp (talk) 00:09, 7 February 2020 (UTC)

@Double sharp: In terms of differentiating electrons it’s not. Differentiating electrons are mainstream; everything else is noise by comparison, IMO of course.

In archive 40, you wrote, “I think saying that a block starts when its characteristic electron appears in the ground state only is too coarse."

I responded, “It’s consistent with all my responses above. It's the simplest rubric I can think of that produces consistent results viz. "The best education is found in gaining the utmost information from the simplest apparatus". (Whitehead AN 1929, The aims of education and other essays, The Free Press, New York, p. 37).

You replied, “But if the cost is that a block then has to extend to the point where its characteristic electrons are core electrons, then I'd rather have weakly involved excited states at the start instead.”

As I explained earlier, while Lu was originally thought to have an f differentiating electron, the fact that it didn’t, and that the f block then extended to the point where it’s characteristic electron become a core electron, made no difference to the chemistry of interest.

If you want to prioritise block details in the terms you’ve described, when it makes no difference to the chemistry of interest, that’s fine. I’ll stick to the chemistry. We can agree to disagree. Sandbh (talk) 09:16, 7 February 2020 (UTC)

@Sandbh: I trust the quotes I have given from Jørgensen and Schwarz have explained why it is that differentiating electrons have very little to do with actual chemistry. The fact that La and Lu both lack a 4f differentiating electron is completely inconsequential. We have to look at chemical activity of subshells, because that is at least something actually relevant to chemistry. And when we do that, we find 4f character for La and not for Lu. Double sharp (talk) 00:09, 8 February 2020 (UTC)

@Double sharp: You’ll see from my response that J & S were of no value. The universal impact of the 14 f electrons in the Lu3+ cation on the chemistry of Lu dwarfs any marginal f character in La. Sandbh (talk) 11:05, 8 February 2020 (UTC)

@Sandbh: This is a total canard. J & S have addressed the heart of the issue, but you refuse to see it even when I spell it out for you. And the universal impact of the 14 f-electrons in Lu is the same as that in Hf, Ta, W, etc., all the way to Rn thanks to the Ln contraction. They are core electrons! And it's not even the first time I've said this.

I'm tired of this endless double standard. You throw out a barrage of arguments that look like they might support the La table, and flip non-stop between them the moment one of them looks like it is in trouble. And then you selectively read the literature in order to not see refutations. And you never consider whether any of your criteria are truly fundamental by putting them to the test of the rest of the table, cloaking this masterpiece of inconsistency under the garment of minimising change. Which is more or less like taking the La table as an axiom and throwing out whatever you want to save it. All I can say is: this is not science. There is no way we can proceed if you refuse to follow scientific principles, actually put your theories to the test, and at least compare all possibly relevant criteria and no others equally regardless of whether they seem to favour La or Lu. If you don't do that, then I say: go ahead and get what you want published. But don't thank me for the critique in the acknowledgements, because I disagree with so much of your paper that I don't want it to look like I supported the final product. Double sharp (talk) 12:26, 8 February 2020 (UTC)

234

I’ll add the +2+3+4 maximum oxidation states pattern as something else observed by the La form but not by the Lu form.

I can come up with an infinite number of things that are only displayed in a periodic table if we put some set of elements into a vertical column. And none of those will be important, fundamental considerations worth paying attention to until and unless I actually demonstrate some reason why it should be fundamental. Given that I think everyone would agree that the possible existence of Hg^IV doesn't weaken Tl's placement in group 13, I'm not seeing it here. Double sharp (talk) 12:00, 3 February 2020 (UTC)

@Double sharp: Henry Bent was the source of this one (in his Fresh energy for the periodic law). He asked the question whether it would be possible to capture the LSPT from chemical data without knowledge of group membership for any elements whatsoever. He started with DIM's line and the elements' maximum oxidation states. He does get to the LSPT using this method and quotes DIM, "the forms of oxides and…atomic weights…give us the means to erect an unarbitrary system as complete as possible."

Bent does manage to extract some quasi-regularities in the LSPT, on this basis, but he missed the most regular one of all i.e. +2 +3, +4 because of Lu under Y!

The DIM heritage, quote, and the Lu irony is what makes this one important. You alerted me to the fact that Hg(IV) has not been reproduced. Sandbh (talk) 06:34, 4 February 2020 (UTC)

I know Hg(IV) has not been reproduced. But my point is: if it was, does it really impact the placement of Tl in group 13? And why is 234 so important anyway given that you will not find regularities throughout the table for 012, 123, 345, 456, 567, or 678? Why does it become fundamental and not just a neat coincidence? The 012 one being weak affects the alkali metals, that paragon of great group trends. ^_^ Double sharp (talk) 07:52, 4 February 2020 (UTC)

@Double sharp: I thought it was significant since it shows the La form is more regular than the Lu form, in this particular context. I'd describe its occurence as a manifestation of the periodic law, rather than a coincidence. It's particularly interesting to consider why this pattern arises, too. A pattern does not need to be reproduced elsewhere, in order for it to be relevant. It does raise an interesting question, as you said, why it doesn't occur so well for the 012, which leads into questions about the structure of the periodic table. Sandbh (talk) 01:08, 5 February 2020 (UTC)

@Sandbh: Certainly, it leads to the question why this matters at all. We are all agreed that the alkali metals are one of the poster children of great group trends, and I hope we agree that that is, in fact, a good manifestation of the periodic law. And yet group I shows this so badly: there isn't such a pattern recurrence for group IB (for which +1 is never the maximum oxidation state), and the 012 pattern goes away when the noble gases from Kr onwards become chemically active. Still hoping for the day the ArF⁺ salts are synthesised in the solid phase and I can start saying "Ar onwards", which will lower the pattern to literally two occurrences in the whole table. And once the helium compounds are discovered we can bump it down to one, at which point it is not even a pattern anymore. That gives me two questions about this whole exercise:

What kind of a fundamental pattern is this when the poster child of group trends is on the verge of not showing it at all? I can come up with a billion regularities that are conditional on one form of the periodic table or another: for example, the outward form looks more symmetrical in Scerri's old version with H-F-Cl and He-Ne-Ar and four columns on each side flanking the transition elements. They all stand or fall depending on whether they are fundamental. And if they are actually fundamental, it is not too much to ask for their repercussions on the whole table.
Why on earth are the indiscretions of the heavier noble gases (snooping around with that upstart commoner fluorine, who just latches on to everything and never lets go, oh my) relevant when contemplating the trend of the alkali metals?

Double sharp (talk) 16:22, 5 February 2020 (UTC)

@Double sharp: I don't have answers at hand to many of your questions. For me, the only relevance of the 234 pattern is to the group 3 question. This cuts across all tables. It doesn't work for the Scerri table you referred to me, for example. That the failure of the 234 pattern originated in Bent's successful construction of the LSPT—supposedly the epitome of regularity and symmetry—from only DIM's line and the elements' maximum oxidation states, is priceless. Sandbh (talk) 01:28, 6 February 2020 (UTC)

@Sandbh: I can come up with infinitely many patterns that are only relevant to one particular question in the periodic table, and none of them will mean anything unless you give some reason why it is important. The LSPT has many patterns that fail in the current table or Scerri's old table. The same can be said of the current table vs. the other two, or Scerri's old table vs. the other two. What is missing is a consideration of why the pattern is significant, and without them, this argument doesn't have anything to stand on. Double sharp (talk) 12:25, 6 February 2020 (UTC)

@Double sharp: I doubt you could come up with a pattern as significant i.e. with a direct link to the very same property used by DIM to construct his PT, or as precise. Sandbh (talk) 23:09, 6 February 2020 (UTC)

@Sandbh: And this isn't quite one of them either, since DIM evidently had sanity prevail when it came to putting O and F to head their groups. And he quite evidently cared only about the maximum valence of the actual elements under consideration, not their neighbours, or else putting the Zn group in group II becomes questionable. Double sharp (talk) 00:08, 7 February 2020 (UTC)

@Double sharp: I agree. A few exceptions in the margins don’t detract from the direct link. Sandbh (talk) 07:50, 7 February 2020 (UTC)

@Sandbh: Yes they do when the exceptions are in the groups we universally regard as the epitome of great group trends. Group I works terribly badly under your scheme (which prioritises looking at irrelevant neighbouring groups, as Mendeleev never did); group II still badly because of their group IB neighbours; group VII badly because (1) the first and only halogen to centre a 678 pattern is iodine and (2) manganese ends up missing from group VIIB, which gets rid of the one member of that group that Mendeleev actually was aware of. Double sharp (talk) 00:13, 8 February 2020 (UTC)

@Double sharp: Those exceptions don’t detract from the headlines. Group 1 functions quite nicely as a neighbour of group 2. Group 11 is a neighbour of groups 10 and 12. Group 17 is irrelevant to the fact of the 234 pattern existence. Mn is irrelevant too. The 234 link is significant since it shows the La form is more regular than the Lu form, in this particular context—maximum oxidation number—which was a primary focus of DIM. Sandbh (talk) 09:53, 8 February 2020 (UTC)

@Sandbh: For the last time: the maximum oxidation states, without looking at neighbours like you push in, were important to Mendeleev precisely because those exhibited periodicity throughout the whole table without much exception! If they were only relevant for one group, like your criterion is, he would either have found some other basis for periodicity, or not found one at all! So the moment you draw a line and say "everything is irrelevant for this criterion apart from what it says about group 3", it means "this means nothing for the periodic table". Double sharp (talk) 10:01, 8 February 2020 (UTC)

Ln contraction

I’ve argued that the lanthanide contraction fits naturally within the f-block, in an La table, whereas it runs over two blocks in an Lu table. I’ll add this as a congruency based argument.

See Droog Andrey's reply. Double sharp (talk) 12:02, 3 February 2020 (UTC)

He, Be, Mg, Sc, Al etc

We have had some subsidiary discussion in which Double sharp has argued that my arguments would require He over Be; Al over Sc; or Be, Mg over Zn. My position is that there are several other arguments for He over Ne, and Be and Mg in group 2, and Al in group 3 and that despite the popularity of the La form over the Lu form by a wide margin, arguments for such changes have never gotten up. Sandbh (talk) 06:51, 3 February 2020 (UTC)

So we can now take any argument, oblivious to what else it would demand, and advocate in isolation for any placement. And as long as the literature is united, it must be right. Then why are we here? Double sharp (talk) 07:54, 3 February 2020 (UTC)

@Double sharp: I hope the situation turns out to be more sophisticated than that. I recall while we were talking about He, Be, Mg, Sc, Al etc you were arguing that one or more of my arguments for La would imply the merits of one or more of the other movements in question. My response was that there were other arguments for the current situation of He over Ne, Be and Mg in group 2, and Al in group 13, related and unrelated to my case for La, that would work against these movements. But I won't know for sure until my library day, and I have an opportunity to unpack what we discussed.

One impression I did form is that changes to the PT should be minimal to achieve the intended outcome. Presumably Lu in group 3 would suggest He over Be, but that would breach my suggested principle. Each change proposal stands on its own. So, if there is a case for one or more of these moves on the basis of either La or Lu in group 3, that's fine but don't drag me into to it so to speak or suggest that if either La or Lu go in group 3 it would follow that one of the other moves must follow, therefore this speaks against La or Lu in the first place. It's analogous to arguing that if we do something, then it will follow that the sky will down which it won't of course; the PT is much more resilient than that.

@Sandbh: That's why I'm consistent. I argue for Lu in group 3 based on blocks and recognise that this suggests He in group 2. I then have two logically consistent options:

Decide that blocks are not so good an argument after all (modus tollens);
Decide that He should be in group 2 indeed (modus ponens).

This is just basic philosophy and logic. Since blocks are pretty fundamental (since chemically active subshells rather than differentiating electrons control chemistry), I choose option 2, and shunt helium over to group 2. You seem to want to have your cake and eat it too: have your arguments, claim they are fundamental considerations, and not look at where they lead for the rest of the periodic table. With respect, that is trying to pick the actions and then the consequences. You don't get to do that. Double sharp (talk) 11:53, 3 February 2020 (UTC)

Of course, as a respected colleague, you are free to argue as you see fit.

The literature is generally right, in my experience. When I was doing my Masters in Human Resource Management, I was told my opinion didn't count---if I wanted to at least pass---so I had to support all my opinions and arguments with citations. When I write for academic journals, since I don't have any science qualifications, I generally always support my arguments with citations. In a way I'm pleased I don't have any science qualifications because I can ask questions without preconceived notions of what can, can't or shouldn't work wrt to the periodic table. Having said that if I'm going to challenge something or advance a position I do generally seek to support my argument with a citations. Some of my other colleagues interpreted this as preaching to them, until I explained my background to them. The citations I do provide have helped others too, even professional chemists.

In saying the literature is generally right, that doesn't mean there is no room to question, challenge, reinterpret or develop the literature. And it is sometimes wrong, contradictory, silent or confusing (I blame a lot of that on "publish or perish"). Take the notion that elemental metals reduce their electrical conductivity as the temperature increases. Wrong! Pu increases its electrical conductivity when heated in the temperature range of around –175 to +125 °C. Or that H behaves like a metal. Wrong! Hydrogen generally always finds a way to complete its valence shell, in this way behaving as a nonmetal. Or that the Ln contraction runs from La to Lu. Wrong! It starts at Ce and finishes in Lu. Or that there are metals, metalloids, and nonmetals. Wrong! This notion of an intermediate class has been the source of decades of unnecessary confusion, and mumbo jumbo like all metalloids are semiconductors. Wrong! Metalloids are much more easily thought of as chemically weak nonmetals etc (this will be elaborated in my forthcoming FoC article, "Organising the metals and nonmetals). Sandbh (talk) 09:56, 3 February 2020 (UTC)

In fact, the contraction goes all the way from Cs to Hg. You can take a part of it (say, from La to Lu) to explain something, but the boundaries are to be selected arbitrarily. Droog Andrey (talk) 10:36, 3 February 2020 (UTC)

@Droog Andrey: +1 Double sharp (talk) 11:44, 3 February 2020 (UTC)

@Sandbh: And equally: take the notion that only group 3 among the early transition metal groups lacks characteristic transition metal properties of multiple common oxidation states. Wrong! The same is true for Zr, Hf, Nb, and Ta. Double sharp (talk) 11:56, 3 February 2020 (UTC)

@Droog Andrey:@Double sharp: I understand. In my view, it's useful to be able to divide the contraction by (a) magnitude, thus (1) Ce to Lu; (2) La; (3) Ba; and (b) knock-on effects (Hf +). I don't regard that as being arbitrary. Sandbh (talk) 00:58, 4 February 2020 (UTC)

@Sandbh: Where is the big difference in magnitude? We just see a monotonic decrease all the way, and the difference from La to Ce is no different qualitatively and quantitatively from the difference from any other lanthanide to its Ln neighbour. Double sharp (talk) 19:49, 4 February 2020 (UTC)

@Double sharp: Thank you. If I read you correctly, that's an inaccurate description of the notion. The notion is, "multiple oxidation states", rather than "common" such states. The literature distinguishes group 3 from group 4 due to the well-established chemistry of Ti, Zr and Hf in lower oxidation states, especially for Ti, noting these states are nevertheless uncommon. The literature further distinguishes group 3 from group 4 according to the predominant ionic chemistry of the former v the predominant covalent chemistry of the latter. Could you please see my supporting quotes, including the one by Rayner-Canham and Overton, re the importance of ionic v covalent, that I posted a few minutes ago. Sandbh (talk) 00:58, 4 February 2020 (UTC)

@Sandbh: Then the literature you quote has certainly never heard of CsScCl₃, not to mention the recent explosion of work done on Ln(II) compounds. Nothing wrong with that; G & E aren't aware of Cm(VI) in their book either. Presumably the burgeoning on Ln(II) chemistry came after the books you cite were published. But it significantly weakens your point. Knowledge about group 3 has moved on from "only a +3 state". (On my phone right now, will link later.) Edit: links appear in section on G&E 2nd ed. Double sharp (talk) 07:47, 4 February 2020 (UTC)

@Double sharp: This does not change the fact that groups 1-3 are predominately ionic and groups 4 to 12 predominately covalent. Sandbh (talk) 00:51, 5 February 2020 (UTC)

@Sandbh: See our replies below. Respectfully, this distinction is nonsensical. Double sharp (talk) 16:07, 5 February 2020 (UTC)

On a lighter note: wow, we passed 500k! ^_^ Double sharp (talk) 17:27, 5 February 2020 (UTC)

And on a side note: why is the notion of lower oxidation states suddenly dropped when it is obvious that it no longer works as a La argument? It would be fairer to continue to consider both, noting that one of them supports Lu and the other (as much as it means anything at all) is somewhat of a La argument (although it can still be blown out of the water by simply focusing on one set of compounds or another, as I did by looking at fluorides instead of the chlorides we considered for the IUPAC submission). Double sharp (talk) 00:54, 8 February 2020 (UTC)

@Double sharp: I didn’t see the announcements in the world’s chemistry journals that +3 is no longer the predominant oxidation state in La and Lu, and that it is now +2. I don’t look at one set of compounds, I look at the chemistry of the element or group as a whole. Sandbh (talk) 09:39, 8 February 2020 (UTC)

@Sandbh:

And yet you have no problem referring above to well-established lower oxidation states for the Ti group above, even outright saying the point was "multiple" oxidation states rather than multiple "common" oxidation states. Why not for the Sc group, then?
"I don’t look at one set of compounds, I look at the chemistry of the element or group as a whole." – and yet you only look at one oxidation state, one item on the continuum from ionic to covalent, and one differentiating electron (until it gets to difficulties with Th and Lr when you backpedal). What is this if not a double standard? You want one of everything, so one basic principle for the PT might be a good start, respectfully. Double sharp (talk) 10:32, 8 February 2020 (UTC)

Predominately ionic

What the hell is going on with this? We know that groups 3 and 12 are much less "transition" than, say, 6 to 10. That's pretty normal. Why should we make 3 vs. 4 a special case? Yes, a lot of philosophy could be cited about the sharp edges and meanings of classifications, but what's the matter? Droog Andrey (talk) 10:30, 5 February 2020 (UTC)

+1 Exactly, there is not a big difference between group 3 and 4 here. +4 is too high for ionicity, OK, so look at the same elements in the +2 or +3 states and they suddenly become more ionic like uranium by Fajans' rules. Everything is continuous. Meanwhile, "predominantly ionic" continues to be complete nonsense, as can be seen by asking: is fluorine predominantly ionic? Is caesium predominantly ionic? Is uranium predominantly ionic? Is thallium predominantly ionic? None of these questions have a good answer, it depends too much on the chemical environment. Just because some literature has used unfortunate terminology that literally means nonsense does not give it a free pass from being nonsense. Double sharp (talk) 15:57, 5 February 2020 (UTC)

@Droog Andrey:@Double sharp: I don't know. I'm not saying any more than the chemistry of groups 1 to 3 is predominantly ionic, whereas the chemistry of groups 4 to 12 is predominately covalent. It's like saying in my street that, predominately, the houses are made of brick (say forty brick and ten wood). Whereas in the next street down from us the houses are predominantly made of wood (say forty wood, and ten brick). The most common oxidation state of Tl is +1 and the compounds of Tl in this oxidation state may be covalent, as for example in thallium acetylacetonate, but more frequently they are ionic (Durrant & Durrant 1962, Introduction to advanced inorganic chemistry, p. 558). Sandbh (talk) 00:42, 6 February 2020 (UTC)

@Sandbh: So, two follow-up questions:

By this logic, is not the placement of Tl as a p-block element weakened? Because due to typically higher oxidation states, the p-block elements are mostly pretty weak in their ionicity, see for example Ga and Sn. By these standards, Mendeleev's initial placement of Tl as eka-Cs seems to look better.
So you admit that oxidation state matters, as by itself the +3 state of thallium is assuredly not so ionic. (It is much more electronegative.) So why not do as Allred did, and consider different oxidation states separately? Remember, organothallium chemistry has the +3 state much more prominent, so saying the most common oxidation state of Tl is +1 demands a caveat about what distribution of compounds we are talking about! ^_^ And from there we can stop trying to crush everything down to a yes-or-no binary answer to "what predominates", and realise, of course, that there was a continuous trend all along that Fajans formulated in 1923. Double sharp (talk) 12:23, 6 February 2020 (UTC)

@Droog Andrey:@Double sharp: Actually I do know, but not the reason why it matters to Double sharp. For example, the chemistry of group 1 is predominantly ionic. Double sharp says this is meaningless in that the chemistry of group 1 depends on the environment. I agree and I'm sure we could find some degree of covalency in Group 1 if the conditions were extreme enough. That does not negate, however, the statement the chemistry of group 1 is predominately (i.e. not exclusively) ionic. Here's another example. Group 1 predominately form +1 cations. In some circumstances some of them can form -1 anions. Nice. Interesting. It nevertheless remains true that group 1 metals predominately form +1 cations. I hope this helps. Another example. The population of Australia is predominately urban. Etc. Sandbh (talk) 00:52, 6 February 2020 (UTC)

Sandbh (talk) 00:52, 6 February 2020 (UTC)

@Sandb: This is still wrong, respectfully. Well, take Cs compounds with every other element. Most of them are metals, up to group 12, and the bonds of Cs with those metals will be metallic. So "group 1 metals predominately form +1 cations" is only true when they are bonding with the more nonmetallic elements. Which is a wider class than for anybody else, admittedly, because with the group 13 elements already they form M⁺ (some Zintl ion), and it takes an incredible amount of electropositivity to make the arsenides ionic (even lanthanum apparently cannot do it). But most elements are not in the p-block. Double sharp (talk) 12:23, 6 February 2020 (UTC)

@Double sharp: I see. The compounds that Cs forms with metals are electrically conducting alloys, comprised of a mixture of Cs cations and the other metal's cations. Like C & W say, "the chemistry of these elements is principally that of their +1 ions...The chemistry of these elements is mainly that of ionic salts in the solid state and solvated cations" etc. Sandbh (talk) 23:05, 6 February 2020 (UTC)

@Sandbh: That's not ionic bonding. That's metallic bonding. Double sharp (talk) 23:55, 6 February 2020 (UTC)

@Double sharp: Would you count them as chemical compounds? Sandbh (talk) 07:46, 7 February 2020 (UTC)

@Sandbh: The world certainly does, see intermetallic compound. Double sharp (talk) 00:35, 8 February 2020 (UTC)

@Sandbh:@Double sharp: There's not a problem that caesium compounds are predominantly ionic. The problem is: why that specific predominance (among a heavy lot of others) becomes so important? Why we don't rip apart Groups 13 and 14 on the basis that, for example, Group 14 compounds are predominantly coloured while for Group 13 they are not? Droog Andrey (talk) 17:23, 7 February 2020 (UTC)

@Droog Andrey:@Double sharp: "For chemists…the most important feature of an element is its pattern of chemical behaviour, in particular, its tendency toward covalent bond formation (or its preference for cation formation)." (Rayner-Canham Overton 2010, p. 29) Sandbh (talk) 09:16, 8 February 2020 (UTC)

@Sandbh: So what happened to the maximum oxidation states you like to talk about when it comes to supporting the 234 bad argument? Or do we have yet another double standard where you pick and choose the criterion most likely to save the La table in each context? Double sharp (talk) 10:29, 8 February 2020 (UTC)

@Double sharp: What has the 234 argument got to do the with the ionic chemistry of Cs? Sandbh (talk) 12:01, 8 February 2020 (UTC)

@Sandbh: Sorry, this is poorly phrased and placed, and I apologise for it. What I meant to say is something that still makes me uncomfortable about this. In the 234 argument you seem to be focusing on maximum oxidation states if I read you rightly, and here you take ionic vs covalent. In case they contradict each other, as for Be-Mg-Zn, who wins? (The 123 pattern works better with Be and Mg in group 2, but they are more covalent like group 12.) Or will you jump once again to ground-state gas-phase configurations for that one? Or decree that this is off-limits because it's not strictly about group 3, never mind that a fundamental basis for the table has to be relevant for everything (that's why in our submission we argued "well, what about the s-block" against considering carbonyl valencies)? That's why I want to ask: please set down your criteria, a precedence order for them, and reasons why each one is important. That's the only way you can get a consistent basis for the PT. Double sharp (talk) 12:28, 8 February 2020 (UTC)

@Double sharp: Hmmm. The 123 horizontal triad fails at He, in an La table and an Lu table, so that doesn't help with the group 3 question. There is a 123 pattern for Li-Be-B, and Na-Mg-Al, and K, Ca, Sc. This does not change in either table, so does not help. I wouldn't say horizontal triads are necessarily fundamental, noting however their use by DIM and Newlands, and Dias' opinion about them connecting the whole table. I'd say they were more of a piece of the puzzle.

Nelson examined periodicity in carbonyls and on this basis supported Lu in group 3. He argued that the number of outer electrons possessed by an atom, and the number required for it to achieve an inert gas configuration exhibit an almost exact periodicity, which it didn't, as we argued. We further queried what happens to the s block if one takes this approach. We said we're not aware of s-block carbonyls, but this would seem to suggest that Mg (which needs 6 electrons to achieve the [Ar] configuration) cannot be placed above Ca (which needs 16 to achieve the [Kr] configuration), and that Sr (which needs 16 to get to [Xe]) cannot be placed above Ba (which needs 30 to get to [Rn]).

I don't see any issues with our logic here, but happy to discuss further.

More to follow re criteria etc. Sandbh (talk) 07:03, 9 February 2020 (UTC)

@Sandbh: This is an exact demonstration of why I feel your logic is biased. When examining a Lu argument, namely that of Nelson, you are willing to apply modus tollens. The logic goes like:

The carbonyl approach predicts Be-Mg-Zn (since they all need 6 electrons to get to the next noble gas configuration), i.e. P implies Q.
Be-Mg-Zn is not good, for other reasons, i.e. not Q.
Therefore the carbonyl approach is not good, i.e. not P.

But you seem unwilling to apply modus tollens to a La argument such as isodiagonality, where I say:

Isodiagonality works better with Al in group 3, so that Al is really diagonally adjacent to Be and Ti, i.e. P implies Q.
But Al over Sc is not good, for other reasons, i.e. not Q.
Therefore the isodiagonality approach is not good, i.e. not P.

Or when I apply it to horizontal triads for oxidation state, where I say;

Such triads work the worst for groups I, II, and VII, so they should not be considered homogeneous, i.e. P implies Q.
And yet those groups are widely considered the most homogeneous, i.e. not Q.
Therefore those triads are not particularly important in the grand scheme of things, i.e. not P.

Why is it that me referring to what happens outside group 3 is irrelevant when using modus tollens for a La argument, but you can do that with impunity when attacking a Lu argument like that of Nelson? Double sharp (talk) 21:26, 9 February 2020 (UTC)

Classification science

A small, relaxed contribution:

“At any given time, during the historical development of a scientific discipline, classification of available evidence offers itself as the explanandum that asks for a theory (or alternative theories) able to explain it. But this is just one segment in a potentially unending chain of recursive relationships between classification and theory. Theory and classification indeed change over time. As a consequence, the theory that provides explanation for the data organized in a classification at a given time can influence subsequent classificatory effort, and so on. “By means of this a discipline advances: each new pattern raises questions that call for explanations, and each verified phenomenon or fact gives a new pattern” (p. 163). What counts as a fact or a theory is a matter of temporal relativity. The authors’ “concern is that we do not replace observation with theory and think that we have made some progress. Science is founded upon empirical observations, no matter how these are tied up with local and cross-disciplinary theoretical commitments or stances. Once we abandon this aspect of science…science becomes little more than a matter of worldviews and epistemic statements of faith” (p. 163).”

Minelli, A.: The nature of classification: Relationships and kinds in the natural sciences—By John S. Wilkins and Malte C. Ebach. Systematic Biology. 63 (5), 2014, pp. 844–846

Sandbh (talk) 11:30, 3 February 2020 (UTC)

"Perhaps in time the so-called Dark Ages will be thought of as including our own" – Georg Christoph Lichtenberg.

Exactly, that's why arguments based on the predominant form in today's literature, or today's categories, are not useful. You have to look at fundamental properties anew. Double sharp (talk) 12:07, 3 February 2020 (UTC)

@Double sharp: I agree with the sentiment, but not your interpretation of it. Arguments based on the predominant form in today's literature, or today's categories, may or may not be useful, rather than being not useful. What's important is the merit of any new perspective. Sandbh (talk) 23:50, 3 February 2020 (UTC)

@Sandbh: Well, that's your perspective. My perspective is that if we are seeking a fundamentally best periodic table, it's not enough to just appeal to tradition. To read the tradition, a thousand times yes; to understand why the tradition made their choices, ten thousand times yes, indeed! But to use something just because it keeps some tradition in some way means nothing. You must analyse the tradition and draw your own conclusion independent of it, even if it is based on all you learned from it. It even means less than nothing when it is not clear what the tradition itself is, such as for the boundary of the REM we use; and when it is not clear why the way in which the tradition is claimed to be kept means anything, as for your argument about unspooling the REM as a continuous line. Double sharp (talk) 19:56, 4 February 2020 (UTC)

@Double sharp: Rather than keeping tradition I'm upholding what represents an accumulation of scientific thought. Like Jones said, "Though classification is an essential feature of all branches of science, there are always hard cases at the boundaries. The boundary of a class is rarely sharp…Scientists should not lose sleep over the hard cases. As long as a classification system is beneficial to economy of description, to structuring knowledge and to our understanding, and hard cases constitute a small minority, then keep it. If the system becomes less than useful, then scrap it and replace it with a system based on different shared characteristics." I don't see sufficient merit in changing the status quo, as an accumulation of scientific thought. Please see my response in the REM subsection. Sandbh (talk) 02:59, 5 February 2020 (UTC)

@Sandbh: Would we ever have gotten rid of Be-Mg-Zn if we had done that? Double sharp (talk) 17:13, 5 February 2020 (UTC)

@Double sharp: Yes, it was gotten rid of with the development of electronic periodic tables. Sandbh (talk) 00:19, 6 February 2020 (UTC)

@Sandbh: But if we followed your quote's advice, then since Be-Mg-Zn is mostly an OK classification, and the hard cases are a small minority, it should have been kept. Double sharp (talk) 12:13, 6 February 2020 (UTC)

@Double sharp: You have to consider how the quote works in real life. There is no drama over Be-Mg-Zn since Be and Mg are s metals, whereas Zn is a d10s2 metal. We've discussed this before, in the arena. Sandbh (talk) 22:58, 6 February 2020 (UTC)

@Sandbh: The little problem with that is that at the time Be-Mg-Zn was popular, there was enough drama for authors to apologise when they moved Be and Mg over Ca. And it was certainly "beneficial to economy of description, to structuring knowledge and to our understanding", because everything else is the same, and Be and Mg are indeed more like Zn than like Ca. So the system did not become "less than useful", and yet we still went and scrapped it. Why? Because there are other factors, like figuring out something deeper that is driving the chemistry we see. All right, then; we have already figured out that chemistry has a lot more to do with generally considering chemically active subshells rather than focusing only on ground-state configurations, so there is enough merit to change to Sc-Y-Lu. Simply put: how do you know we're not in a Be-Mg-Zn situation? Right now we see only the Ca table, so if anyone suggests a move back to the Zn one, we will hear "not enough merit for the sea change needed". Well, I put it to you that if the Lu table were to win, nobody would be suggesting a move back to the La one for exactly the same reason! But as long as the La one is around, you will hear constant arguments to scrap it. Double sharp (talk) 00:00, 7 February 2020 (UTC)

@Double sharp: It's interesting to see Jensen's paper has 65 citations. Judging from Google Scholar, none of these 65 citations were about supporting Be-Mg over Zn. Jensen is in the wilderness on this one. Sandbh (talk) 06:47, 9 February 2020 (UTC)

@Sandbh: You're missing his point. He's not supporting Be-Mg-Zn. He's saying that this was the more common classification historically.

Indeed, prior to the introduction of electronic periodic tables, the similarity between Be and Mg and Zn and Cd was often considered to be greater than the similarity between Be and Mg and the rest of the alkaline earth metals (Ca–Ra). Many inorganic texts written before the Second World War placed their discussion of the chemistry of Be and Mg in the chapter dealing with the Zn subgroup rather than in the chapter dealing with the Ca subgroup, and the same is true of many older periodic tables, including those originally proposed by Mendeleev (34, 35). Even as late as 1950, N. V. Sidgwick, in his classic two-volume survey of The Chemical Elements and Their Compounds, felt that it was necessary to justify his departure from this scheme in the case of Mg (36).

And that's all I am saying. The system was useful, with hard cases a tiny minority, and yet we scrapped it. Why? Because our understanding progressed and the consensus changed. Eventually that may well happen with the triumph of Sc-Y-Lu, and looking at the chemistry and the actually important things such as chemically active subshells, that would be a most excellent outcome IMHO. Double sharp (talk) 21:29, 9 February 2020 (UTC)

Ionic vs. covalent

One more contribution:

"For chemists…the most important feature of an element is its pattern of chemical behaviour, in particular, its tendency toward covalent bond formation (or its preference for cation formation)."
Rayner-Canham G and Overton T, In Descriptive inorganic chemistry (2010, p. 29)

I wonder how they deal with fluorine, say? Depending on what it's bonded to it either forms (more or less polar) covalent bonds, or anions. Double sharp (talk) 00:10, 4 February 2020 (UTC)

C & W at least say that most metal halides are predominantly ionic. Sandbh (talk) 01:37, 4 February 2020 (UTC)

Then they've forgotten the salient point that said ionicity depends on the oxidation state involved, see the uranium fluorides from UF₃ going up to UF₆. And even then they've noticed that ionicity vs covalency of a halide depends on metallicity of the counter-cation, i.e. electropositivity, though the point about ionic radius and hence polarisability is not in your quote. I am not even saying anything new here; Kazimierz Fajans codified this in his rules all these years ago back in 1923. Double sharp (talk) 07:42, 4 February 2020 (UTC)

@Double sharp: I'm sure they took that into account, consciously or subconsciously, when they made their general statement. Such a statement does not need to detail its supporting considerations. Sandbh (talk) 03:05, 5 February 2020 (UTC)

@Sandbh: I'm sure they didn't, because that's not something supporting their statement, it's something refuting it. If they had thought about that they might have chosen their words a little more carefully and said "metal halides are predominantly ionic unless the metal is in a high oxidation state". Think WF₆ and ReF₇. And in case you want to call this "Double sharp v the world" again, the world has a term for this: fluoride volatility. This is used when separating radionuclides, and here the important gap in oxidation state is not the 3 vs. 4 you like to focus on, but 4 vs. 5. So much for discontinuities: in different contexts they move and exemplify a larger continuity. Double sharp (talk) 16:03, 5 February 2020 (UTC)

@Double sharp: The expression "predominantly ionic" needs no further qualification. If I have six snooker balls, 4 red, 1 yellow, and 1 blue, I can say they are predominantly red. I don't have to add, "unless the ball is yellow or blue". Or the chemical elements are predominately metals, etc. Sandbh (talk) 00:25, 6 February 2020 (UTC)

@Sandbh: But you don't have that. You have a lot of snooker balls, with a correlation that the bigger they are, the bluer they are. So they go along with from some small red ones (e.g. CsF) through some medium-sized purple ones (e.g. BeF₂, TiF₄, SnF₄) all the way to the large blue ones (e.g. WF₆). Not to mention the other related factor of electronegativity (e.g. TiF₄ vs. ZrF₄, GeF₄ vs. SnF₄). As a result, saying "most are red" is (1) not the full story, because there is some other factor that is clearly at work controlling the colour, and (2) is not even clearly true; just think about how many metals show an oxidation state over 3 or 4, and how many show multiple oxidation states whose fluorides behave differently (UF_n, n = 3, 4, 5, 6). It's not for nothing that compounds of fluorine divides low-oxidation state from high-oxidation state metal fluorides. Double sharp (talk) 12:12, 6 February 2020 (UTC)

@Double sharp: We've discussed this before in the arena. 4 out of 6 = a predominance. It's equivalent to saying of all Ln compounds, most are ionic in nature, taking everything into account, including e.g. all possible oxidation states, and all possible EN differences. Sandbh (talk) 22:58, 6 February 2020 (UTC)

@Sandbh: It's not much of a predominance if it fractures so well along EN and oxidation state lines. That tends to mean you have two different classes here and arguing about predominance is just the tyranny of the majority group (which in this case is not even much of a majority, segueing into my next point). Also, 4 out of 6 (even if it was relevant) is not much of a predominance either. If a predominance is not skewed so far as to at least 90% or so you cannot neglect the other one. Like you do for U and Tl, only considering the +6 and +1 states respectively, and forgetting how important the +4 and +3 states are too respectively. I look forward to seeing this approach used on Tc, where it is extremely hard to say what the most common oxidation state is because it likes converting between them so much. That in itself tells me that it's reducing the complexity of the situation far too much. You have to at least look at all common oxidation states and notice the pattern between them. And once you do that, the whole misapprehension about "predominately ionic" is blown out of the water. Double sharp (talk) 00:04, 7 February 2020 (UTC)

@Double sharp: It's a good enough, useful generalisation. I'll rely on the fact that 4 > 2, and the wide use of the concept of "mainly" etc in the scientific literature to make useful generalisations and characterisations, analogous to e.g. most elements are metals. In the specific case of the Ln I'll continue to rely on the 100% agreement in the literature that the chemistry of the Ln is mainly (i.e. not exclusively) ionic. Mainly is good enough to make a useful generalisations, acknowledging the exceptions. Sandbh (talk) 00:32, 7 February 2020 (UTC)

@Sandbh: One more time: something like 51% vs. 49% is totally not predominant behaviour. (This is the sort of situation we are in for technetium with a bunch of equally common oxidation states.) Something like 70% vs. 30% is still not it because the minor oxidation state can be a big part of chemistry. Crack open any inorganic book about the p-block elements, it'll tell you that for the heavy ones the important one is the interplay between the group oxidation state and the one two oxidation units lower. See, both are considered. You appear to want to reduce the chemistry of the elements to something tiny: one oxidation state, one typical EN difference, one differentiating electron, one of everything controlling everything. What a magnificent situation this will be:

“

Once upon a time there was a state that — by European standards — was really quite small. The state was a constitutional monarchy. Its population consisted of one king, of course, one prime minister, one head of the security service, one minister with responsibility for the police, and one public prosecutor.

The country had just one criminal, a single political prisoner and a lone political refugee.

The army was made up of one general who commanded one colonel, a lone major, and a single captain.

Needless to say, there was just one trades union; on its books there was one builder and one specialist in demolition, one professor and one student, one academician and one completely illiterate citizen.

It was just the same in every other area of life. The country counted among its inhabitants just one alcoholic and one drug addict, one pimp and just one professional lady of the night, one AIDS sufferer and one who had gone down with syphilis.

Next to the only individual in the country to own a really luxurious villa lived the only homeless man — in a large rubbish skip. The country did indeed have some ethnic minorities — the census returns reported a single Jew, one Tatar, one Pole and a person from the Caucasus region, one Russian and a lone Albanian. So it was with sexual minorities: just one gay man and one lesbian.

The appropriate forces of law ‘n’ order – no more than one man in each, of course — kept a close watch on the country’s only paedo, as well as on the one guy who had a secret fondness for bouts of bestiality. The same strict balance could also be observed in the arts. The country was quite happy with its only composer, it needed no more than one artist, one actor and one writer. One journalist wrote for the one newspaper. There was employment for just the one architect.

There were — it should perhaps be pointed out at this stage — vague rumours circulating to the effect that not everything had always been quite so perfect in the country.

For example, people were saying that apparently there were at one time several professors delivering lectures to several students, and then these students got it into their heads to shut themselves in one of the lecture halls together with their professors and draft an inflammatory petition.

But that’s another story.

”

— Uładzimir Arłou, The Most Noble Order of the White Mouse, translated by Jim Dingley

(I think I like your country's literature, Droog Andrey! ^_^ Maybe not surprising, as I am a fan of E. T. A. Hoffmann.) Double sharp (talk) 00:20, 8 February 2020 (UTC)

@Double sharp: Yes, of course, 51 > 49. Is 51 predominately greater than 49? No, I’d say it's barely greater. I’d say something like 70% vs. 30%, at a 2:1 ratio, would represent a predominant majority. The 30% could still be important, of course. For example, weeds take up 70% of my lawn, and therefore represent the dominant form of growth in my lawn. The remaining 30% occupied by grass is important, but not predominant. Group 13 is mainly known in the +3 oxidation state but the +1 oxidation state becomes more important for thallium. I can tell this from our oxidation state article. Yes, I do seek to reduce the chemistry of the elements to their most common oxidation states, in order to map the broad contours of the situation; to typical EN differences for the same reason; and to differentiating electrons in order to delineate the s, p, d and f blocks. As another example, the fact that there are the four seasons of spring, summer, autumn and winter represents a controlling insight into the weather (at least where I live). Sandbh (talk) 09:08, 8 February 2020 (UTC)

@Sandbh: But you're not even consistent about it. You do it for La and Ac and claim that placing them in the f-block is verboten. Then you look at Th, think "ah, that's a bit inconvenient", and save yourself by going to an uncommon oxidation state (+3) and retreating away from differentiating electrons. And while you like talking about how Nature is supposedly like and not how easy She is to draw, you then insist that Lr must go in the f-block under Lu because there is nowhere else that it can practically go(!). IMHO, you are making exactly the same mistake as Lavelle: inconsistency. At least when my criteria have a little problem (the Ca group), I accept the inconsistency, and it actually points to something real in the chemistry. Now, remind me, exactly how much does the DE anomaly between Nb and Ta mean? Absolutely nothing. Is Pb categorically different from its lighter congeners because of its different major oxidation state? No, Ge shows it already, Sn more so, so it is a continuum. And the stability of Pb(IV) anyway depends on ligands, so the only sane thing to do is to mark both 2 and 4 as important and consider their relative importance down group 14. As everyone does. Except you, who seem to want to reduce everything to one dimension. Sandbh vs the World, respectfully. Double sharp (talk) 09:56, 8 February 2020 (UTC)

@Double sharp: I don’t claim La and Ac in the f-block are verboten. I argue they are better placed in the d block, in a chemical table. I do so on the basis of shared chemistry; differentiating electrons; the periodic law; a pattern inconsistency in the REM; a unique 234 pattern; and isodiagonality. These are linked arguments. An Lu table is less regular in all these aspects. Th is as anomalous in an La table as in an Lu table. Lr is superficially a “problem” but this goes away in the context of e.g the differentiating electron argument. Yes, Ge (most stable oxidation state +4) is categorically different from Pb (+2), in that context. The d/e anomaly between No and Ta means as much for an La table as for an Lu table. Sandbh (talk) 11:36, 8 February 2020 (UTC)

@Sandbh: Shared chemistry supports Lu, DE's are chemically irrelevant, you misread the periodic law, your pattern is only graphic design, the 234 pattern is ungeneralisable, and isodiagonality supports Al in group 3. Your case for La convinces me about 0%. All it is is a bunch of one-off arguments glued together, with no hint as to which ones are the more important ones, and no heed to what nonsense they have to say for the rest of the periodic table. The only commonality with them is that they all support the La table in what IMHO are just increasingly desperate ways having less and less to do with actual chemistry. Since R8R and Droog Andrey have echoed some of my points, not to mention Jensen and Schwarz, I think the world would agree. At least I critically analyse and accept the tiny sparks of nonsense my single highest criterion appears to throw up (He in group 2, the ambiguous position of some s-block elements), and see that it is in fact not nonsense and has some chemical repercussions in the real world. So all is well. Double sharp (talk) 12:38, 8 February 2020 (UTC)

If you claim Ge is categorically different from Pb, why do you put them in the same column? You have DIM to appeal to if you want to put Pb under Ba. But I bet you won't do it, in order to not rock the boat too much. So this is just like Lavelle: La must go under Y, ultimately because that is the way the majority draws it. Respectfully, we would never have gotten rid of Be-Mg-Zn with that logic. Double sharp (talk) 12:41, 8 February 2020 (UTC)

@Double sharp: Err, the periodic law and the real world aufbau principle (the latter which explains why we got rid of Be-Mg-Zn)?

@Sandbh: Precisely, our understanding progressed, and we went for a new basis that pointed to Be-Mg-Ca. As it will progress from just looking at chemically irrelevant gas-phase differentiating electrons to configurations in all chemically relevant environments, which will end up meaning looking at chemically relevant subshells and Sc-Y-Lu. Not only Jensen, Jørgensen, and Schwarz, but also Seaborg mentioned this. Double sharp (talk) 21:31, 9 February 2020 (UTC)

RELOCATION NOTICE

Since I was no longer able to load the thread onto my ipad, I've temporarily moved the content that used to appear between here and the following section to here, pending a longer term home. Sandbh (talk) 05:07, 16 February 2020 (UTC)

All the outstanding chat between DS and I is still located in this main page, as at the time of the move.

I guess we could preemptively put part of this straight into Archive 42, too. Double sharp (talk) 10:53, 16 February 2020 (UTC)

I've gone ahead and done that. In order to not destroy everyone's computers, I guess the remainder of the thread must go into Archive 43 when it finally finishes. (Which, given that my reserve of free time should drop soon enough and wasn't that high to begin with, will probably be soon.) Double sharp (talk) 23:52, 21 February 2020 (UTC)

Isodiagonality and group 3

Rayner-Canham has written extensively on isodiagonality.

The three examples of Li and Mg, Be and Al, and B and Si, are commonly cited.

La table
The following isodiagonal relationship can be observed:

  2  3                  4

 =========================

 Ca Sc.................Ti

 Sr  Y..................Zr

 Ba La Ce Pr Nd etc

all three elements (Ca-Y-Ce) are strongly basic
similarities between Ca and the lanthanides (inc. Ce) are well known;
Y is a member of the rare earths, as are the lanthanides;
all three elements exhibit predominantly ionic chemistry.

Lu table
The following diagonal is observed:

 2  3  4

 ========

 Ca Sc Ti

 Sr  Y   Zr

 Ba Lu Hf

Ca and Y are strongly basic; Hf is amphoteric;
Ca and Y exhibit a predominately ionic chemistry whereas Hf exhibits a predominately covalent chemistry;
Y and Hf can form intermetallic compounds with Pt, noting this capacity does not extend to Ca.

Conclusion
In a chemical table, from an isodiagonality perspective, La seems to be preferred. An Lu table introduces another irregularity.

I was surprised when I discovered this. I posted it here as I couldn't get the courier-text trick to work in the main thread. Sandbh (talk) 06:55, 8 February 2020 (UTC)

@Sandbh: Actually we have Na-Ca-Y-Hf in both La and Lu tables. In 32-column PT there's no diagonal after Na-Ca, but there is Rb-Ba-La-Th, again in both La and Lu versions. But if we compare La-Rf and Lu-Rf, the latter will stand much better. So the diagonal argument supports Lu table. Droog Andrey (talk) 23:36, 11 February 2020 (UTC)

@Droog Andrey: Yes, Na-Ca-Y-Hf is in both 18-col tables. In the 32-column La table, Na-Ca-Y-Hf disappears, and we see Na-Ca-Y-Ce. In the Lu table Na-Ca-Y-Hf remains. In both forms of the 32-column table there is no Rb-Ba-La-Th; you may have wanted to refer to K-Sr-La-Th. I don't know why you refer to La-Rf or Lu-Rf; these are not contiguous diagonal relationships. Sandbh (talk) 02:29, 12 February 2020 (UTC)

@Sandbh: Sorry, I thought about K-Sr-La-Th indeed. As for Lu-Rf vs. La-Rf: just look closer at the 18-column table. Droog Andrey (talk) 05:32, 12 February 2020 (UTC)

@Droog Andrey: No matter. Before I posted my first answer I printed two 32-col tables, one La and one Lu. After examining them I folded them into 18-col tables. In every case of isodiagonality it's possible to trace a zig-zag path. For example, with Li3-Mg12 the zz path is Li3-Na11-Mg12. With Be4-Al13, the zz path is Be4-Mg12-Al13.

In an La or Lu table it's not possible to zz La-Rf. In both tables it's possible to zz Lu-Rf. I don't see your point. Sandbh (talk) 23:16, 12 February 2020 (UTC)

@Sandbh: In an 18-column La table, the zigzag is ₅₇La-₈₉Ac-₁₀₄Rf. Double sharp (talk) 23:23, 12 February 2020 (UTC)

@Double sharp: That's not a zz path since there is no contiguity with Z. There is a chasm of 14 elements between Ac and Rf. The best that can be done is ₅₇La-₈₉Ac-₉₀Th. Sandbh (talk) 01:14, 13 February 2020 (UTC)

@Sandbh: Diagonality means "one period lower, one column to the right". So we have Na-Ca-In-Pb in 8-column, but Na-Ca-Y-Hf in 18-column, and Na-Ca-Y-Ce in 32-column. We also have:

K-Sr-Tl-Fl in 8-column,

K-Sr-La-Rf in 18-column La,

K-Sr-Lu-Rf in 18-column Lu,

K-Sr-La-Th in 32-column.

Droog Andrey (talk) 12:34, 13 February 2020 (UTC)

@Sandbh: I don't see why "contiguity with Z" recommends itself above other criteria for relevance of diagonal relationships. The name literally has "diagonal" in it, so elements in it should actually appear along a diagonal in the periodic table layout you're analysing. Why do you allow Ca to Y in a Lu 32-column table, even though there is a big chasm between Sr and Y there? Why is the placement of Al not a strike against the Be-Al diagonal? Double sharp (talk) 13:48, 13 February 2020 (UTC)

@Double sharp:@Droog Andrey: Oh dear. This looks like an example of extrapolating my argument beyond its boundaries.

Na-Ca-In-Pb is invalid since Ca and In are not next to each other in Z contiguity terms

Na-Ca-Y-Hf is ~~invalid since Y and Hf are not next to each other in Z contiguity terms~~ valid Sandbh (talk) 02:41, 15 February 2020 (UTC)

Na-Ca-Y-Ce is good

K-Sr-Tl-Fl is invalid

K-Sr-La-Rf is invalid

K-Sr-Lu-Rf is invalid

K-Sr-La-Th is valid.

I recognise Ca-Y (says he, quickly getting out his 32-col table to check :) in an Lu 32 table since there is contiguity in Z.

I recognise Be-Al (as does the entirety of the literature) since there is Z contiguity via Mg.

Are there are any more "mind-bending" counter-arguments? You guys must have missed something! I must be wrong somehow! Sandbh (talk) 04:45, 14 February 2020 (UTC)

@Sandbh: If you insist that Y-Hf is invalid, why do you refer to it in your argument? Droog Andrey (talk) 18:34, 14 February 2020 (UTC)

@Droog Andrey: My bad ×2. Now corrected. Sandbh (talk) 02:41, 15 February 2020 (UTC)

@Sandbh: This is yet another of those arguments that ends up supporting Al in group 3. Read his paper; he focuses more on Al-Ti than Al-Ge (mentioning the latter only as a minority view based on only some synthesis attempts), and his periodic table figure even has Al in group 3 to show this diagonal! Double sharp (talk) 09:48, 8 February 2020 (UTC)

@Double sharp: Al in group 3 is a non-starter for other reasons we’ve discussed, including its p differentiating electron. I must be onto something if the best you can do is attempt to distract the audience :) Sandbh (talk) 11:47, 8 February 2020 (UTC)

@Sandbh: Only for you is modus tollens irrelevant. So much for a philosophical perspective. Double sharp (talk) 12:39, 8 February 2020 (UTC)

I've moved this to the main thread, as the Courier text seems to be working fine. Double sharp (talk) 20:18, 8 February 2020 (UTC)

@Double sharp: Thank you.

I've added a space in front of this sentence. It shows as courier new in preview mode but won't in published change mode.

I wanted to add that this was a nice example of something Jensen referred to: arguing against "the relevance of such evidence using the time honored technique of first setting up a nonexistent straw man…and then attacking it".

It's not a straw man. It's just modus tollens.

Sandbh claims that isodiagonality is relevant for element placement. (P)
Isodiagonality supports Al over Sc. (Rayner-Canham may not have argued it explicitly, but he explicitly devotes more time to Al-Ti as isodiagonality than Al-Ge, and he shows an Al over Sc table.) (P implies Q.)
Sandbh seems to agree that Al over Sc is not correct. (Not Q.)
Conclusion: isodiagonality is not so relevant after all. (Therefore Not P.)

Double sharp (talk) 22:21, 8 February 2020 (UTC)

@Double sharp:

Sandbh waits in the automatic clay pigeon thrower, ready to set out his group 3 solution that hinges on moving Al over Sc

The reception committee for Sandbh's group 3 solution, locked and loaded

Your application of modus tollens i.e. "the rule of logic which states that if a conditional statement (‘if p then q’) is accepted, and the consequent does not hold (not-q) then the negation of the antecedent (not-p) can be inferred" doesn't apply here, since you left out the context. Here's the scenario:

Given a choice between an La table and an Lu table, we see that there is an extra isodiagonal relationship in an La table; or
Or, Al is a p-block element so it stays over Ga. That said, we see an La table features an extra isodiagonal relationship.

A close analogy is that when you go down a few rungs on the family tree, and try and sort out something at that level, you can't go back up the family tree and seek to undo it. You have to accept where you are, figure out the context, and go from there.

That's all. I don't want to be the clay pigeon that says, "Here's a solution to the group 3 question and it requires Al over Sc", nor do I need to be. Since I get to set the context.

Sandbh (talk) 10:23, 27 February 2020 (UTC)

@Double sharp: The usual ignorance of basic facts. It seems like I need to preface every one of my arguments with every single fact and principle of classification science under consideration. Really?

Isodiagonality is relevant for element placement ceteris paribus. While there is isodiagonality between Al and Sc, Al is a p-block element so it stays in the p-block.

Next mind-bending argument? Sandbh (talk) 00:52, 17 February 2020 (UTC)

@Sandbh: On what basis do you claim that Al is a p-block element, noting that such a basis on your list must trump isodiagonality? Double sharp (talk) 14:12, 17 February 2020 (UTC)

@Double sharp: Well, on the basis its s²p¹ electron configuration. Let's recall that the literature recognises the diagonal relationship between Be and Al, notwithstanding Be = s and Al = p. There is no conflict here, that I can see. You seem to think there is. Care to elaborate on why the literature must be wrong? Sandbh (talk) 01:36, 18 February 2020 (UTC)

As well, Rayner-Canham did not argue for Al over Sc. Habashi (a metallurgist) did, but not on isodiagonality grounds per se. Being a metallurgist, many of his arguments ignore periodic trends going down a group, as well as the fundamental nature—from a classification science perspective—of the s-p-d, and f-classification. There may be a case for Al over Sc in a metallurgical periodic table.

It occurs to me there are now at least nine chemical arguments for La:

Liu et al.;
isodiagonality;
horizontal triads;
Atkins et al. Q & A;
trends going down Group 3;
monocations of Sc, Y, La and Lu;
Laing's comparing the pairs Ca-Sc and Sr-Y with Ba-La;
the Ln contraction starts in Ce and ends in Lu, noting your objections; and
Restrepo's stoichometry findings, noting your concerns and that I've asked him about these;

I recall you disputed Laing so I'll have to go back and look at what you said; library day will be tomorrow :) Sandbh (talk) 22:04, 8 February 2020 (UTC)

A table that claims La is closer to Au and Hg than the other 4f metals is just plain silly and discountable;
Most of the elements don't display this, so what? And some elements display it better if you put them in "wrong" places.
Not generalisable to the rest of the periodic table, therefore irrelevant. Most of the elements don't display this.
Already debunked; at the 4d-5d scale, your increases are just noise.
Supports Lu, because group 3 is a d-block group and should follow the d-block trend. If you dispute this, off to Be-Mg-Zn we go logically.
Not sure why this is relevant since Sc, Y, La, and Lu are almost never in the +1 state.
It's obviously irrelevant, just compare Be-B and Mg-Al with Ca-Sc, it's much closer than Ca-Ga.
You have noted my objections, though actually addressing them would be a good start rather than just always saying "this is a tipping point argument" and continuing to argue from something that I have already demonstrated is quite irrelevant chemically (DE's);
You have noted them here too.

Scorecard: 0/9 according to any sensible criterion that demands that properties trotted out as fundamental concerns for element placement on the PT be actually relevant to all or at least almost all the elements, not just "picking and choosing" for an arrangement you like. Double sharp (talk) 22:15, 8 February 2020 (UTC)

@Double sharp: Comments from teacher :)…

La, Au, Hg. You know this. [A] All three metals are in the same period; [B] La shows similarities to main group metals in groups 1 and 2; remind me again of the emerging interest in the +2 oxidation state of the Ln, and compare this to Hg, which looks like it is one of the very few 5d metals with +2 as the predominant oxidation state; [C] Like La, Au has a +3 common oxidation state; Au has the capacity to act as a main-group metal in its common +1 oxidation state; it also shows similarities to the halogens, which are main group metals; and [D] Hg is a post-transition metal, i.e. main group metal, with +2 as the common oxidation state cf La.
Are you kidding? Au and Hg, in their main-group-like states, are strongly post-transition. La is strongly pre-transition. Au is one of the worst metals in the periodic table and Hg is not far behind, whereas La is chemically strong. Just like Ce through Lu, in fact. Double sharp (talk) 21:39, 9 February 2020 (UTC)
Diagonal relationships in the periodic table were recognized by both Mendeleev and Newlands. Most of the elements don't display the properties of the noble gases. Therefore the NG don't mean anything, just like the conclusion at the end of your scorecard sentence. Per Rayner-Canham, "Isodiagonality is, in some ways, a general attribute of the properties of the chemical elements. For example, the metal-nonmetal divide forms an almost diagonal demarkation (Edwards and Sienko 1983). Similarly, the elements often considered to be semimetals fall on a roughly diagonal border between the metals and nonmetals (Hawkes 2001)."
And the Be-Al relationship shows up much better in their 8-column tables than in our 18-column form, because then it is actually a diagonal. So what? Just because something is common somewhere in the periodic table does not make it a fundamental law for it. Relativistic effects are today recognised by every single authority on the heavy elements from late period 6 onwards. That doesn't make them fundamental for the periodic table because they are totally irrelevant for the first 5. Double sharp (talk) 21:48, 9 February 2020 (UTC)
Mendeleev used horizontal triads when he predicted the properties of the then undiscovered elements Al, Ga, and Ge. He discussed his technique using the horizontal triad As, Se, Br to estimate the atomic weight of selenium. Dias (1989; 1990; 1991) asserts that, “A periodic table is defined as a partially ordered set forming a two-dimensional array which complies with the triad principle where any central element has some metric property that is the arithmetic mean of two flanking [i.e. horizontal] member elements."
But he never used them like you do when considering maximum valences. Otherwise he would have noticed that periodicity in those values simply did not work for what were otherwise the most homogeneous of his groups. Double sharp (talk) 21:48, 9 February 2020 (UTC)
Ionic radii. This stands up on the basis of comparable properties. You argue against "the relevance of such evidence using the time honored technique of first setting up a nonexistent straw man…and then attacking it". The ionic radii in question are those of Shannon (1976), with 50,522 citations. All the people behind these citations are wrong, of course!
If they say that ionic radii generally increase down the table, like Atkins does, they are absolutely right. That is generally what happens in the absence of a contraction. And indeed, it happens in the presence of most contractions as well, albeit diminished, and I'm sure they all know that effect of a contraction. In particular, I'm sure they all know that the lanthanide contraction, being the longest contraction thus far in the periodic table, almost exactly wipes the 4d to 5d increase out. And I'm sure they know that the increase wobbles about over a period. And I'm sure they learnt back in high school about significance, and realised that it doesn't really matter if the increase is actually a slight decrease going down from a few 4d elements to their 5d congeners, because the wobble around zero means that the sign is not significant. Therefore there is a very clear-cut reason why the general trend has been overthrown for this specific case that I'm sure all these authors are aware of. Therefore the failure of the ionic radius to increase for Y³⁺ to Lu³⁺ is not a mark against it because the same happens for the early 5d elements, where we have the exact same failure from Zr⁴⁺ to Hf⁴⁺, and for Nb⁵⁺ to Ta⁵⁺, for the exact same reason. So the problem is not that those authors are wrong, but that you seem to be wrongly taking their general statement which permits itself exceptions under extreme circumstances (one of which before us), and elevating it to a law. Double sharp (talk) 21:48, 9 February 2020 (UTC)
Trends going down Group 3: Another paper tiger.
Not a rebuttal. Double sharp (talk) 21:48, 9 February 2020 (UTC)
To be read in Monty Python's voices: "That's not a rebuttal." "No, it's a figure of speech though." "I didn't think it was a very good argument." "No, it's the end of the thread, they must be running out of ideas." ;) Double sharp (talk) 22:01, 9 February 2020 (UTC)
The +1 state is used to measure the ionisation energies of the elements, from which general trends are derived.
The only problem with that is that this argument is about the chemistry of the +1 state, not just abstractly taking away that first electron. Whatever happened to sticking to characteristic oxidation states and properties? Double sharp (talk) 21:48, 9 February 2020 (UTC)
Laing's pairs. There's no argument here since B and Al are p metals while Sc is a d metal.
See my earlier post about your selective and biased use of modus tollens from my perspective. Double sharp (talk) 21:48, 9 February 2020 (UTC)
Ln contraction. While I note your objections, there is nothing about them needing to be addressed, since the fact of the Ln contraction running from Ce to Lu, and the congruence of this with a Ce to Lu f-block, is not in question.
It is obviously in question. You look only at the +3 cations, forgetting that it works just as well for atomic radii as for ionic radii, when all three electrons are still there. For no other contraction is there a characteristic oxidation state like that. Double sharp (talk) 21:48, 9 February 2020 (UTC)
Restrepo. Interim comments by me:

@Double sharp:

Horovitz and Sârbu (2005), on the basis of 18 mainly physical properties, argued that Sc and Y are rather dissimilar to the lanthanides. They found that Yb, Lu, Eu and La were outliers. Eu and Yb are understandable given their low values of density and melting point compared with those of their immediate neighbors (indicating a 2+ oxidation state). That left La and Lu. They plumbed for Lu under Y given it was more of an outlier than La. We queried this conclusion noting the absence of any consideration or comparison of the merits of La.

In two earlier studies by Horovitz and Sârbu, based on physical, chemical, and structural data, there was more support for La under Y. And La was next door to clusters including Hg and Au =:o

I will read the paper later. But note: "next door" means different clusters. (A classification that puts La closer to Hg and Au than the other lanthanides, and Sc and Y, is by the consensus of just about everybody who ever used "group 3" or "rare earths" as a category nonsensical.) Also, I notice that Zr gets in as a main-group metal in one cluster (p. 481, hence probably Hf would as well but for some edge effects given their great similarity), supporting my point that main-group properties don't suddenly stop at group 3, but continue to be seen in 4 and to some extent 5 and even 6. Double sharp (talk) 12:15, 10 February 2020 (UTC)

Liu et al. found that, "Except La, all other lanthanide elements (inc. Lu) are classified into one cluster colored in pink, which reflects the strong similarities between lanthanide elements." Y has its own colour.

A classification that puts La closer to Hg and Au than the other lanthanides, and Sc and Y, is by the consensus of just about everybody who ever used "group 3" or "rare earths" as a category nonsensical. Double sharp (talk) 12:15, 10 February 2020 (UTC)

In the introduction to Scerri's Red Book, he wrote: "…there are in fact two big ideas in chemistry. They are chemical periodicity and chemical bonding, and they are deeply interconnected (p. xiii)." I contend this adds support to Restrepo's approach.

But Restrepo's approach makes it impossible to see relationships between elements with different characteristic valences. Since Mendeleev noted diagonal relationships as part of periodicity and so do you, it supports the idea that his approach is not complete. ^_^ Double sharp (talk) 12:17, 10 February 2020 (UTC)

Scorecard: 0/8. Very disappointing; careless, could do better. Your homework is to write a 5,000 word assignment explaining why the authors of the 50,522 articles citing Shannon were wrong :) Sandbh (talk) 05:23, 9 February 2020 (UTC)

@Double sharp:

In Essential trends in inorganic chemistry (Mingos 1998) writes:

"This book explores and interprets in some detail the properties of the elements in the family tree, which has been defined by the Periodic Table. It achieves this exploring the relationships between the atomic and molecular properties of the individual members in the family tree. Therefore, two large chapters are used to define vertical and horizontal and diagonal trends in the properties of the elements and their compounds and a further chapter discusses isoelectronic and isostoichiometric relationships."

"The modern use of the Periodic Table also utilizes horizontal and diagonal trends as well as the vertical relationships which were originally highlighted by Mendeleev. Therefore, the aim of this book is to illustrate how a modern chemist utilizes the Periodic Table to classify and interpret chemical phenomena."

It's interesting to see that Mingos includes diagonal relationships as an "essential trend" and that the modern use of the PT includes this trend, as per DIM, to classify and interpret chemical phenomena. I take this as further good support for the relevance of my isodiagonality argument, in a chemical PT. Sandbh (talk) 04:00, 27 February 2020 (UTC)

DS' simple case for Lu

Whereas I have actually strong ones for Lu:

Lu lacks 4f involvement but La has it, so chemically active subshells imply Sc-Y-Lu without any further ado.
The resulting trends are more homogeneous, be they the trends in the d-block, the shape of the periodic table, the general changes of electron configurations (in all chemically relevant states), the general addition of a contraction before the first element in the next block, etc. etc. etc.

That's it. I would've said that this is unarguably chemically relevant and not minutiae, but it appears that you are keen to argue it even if it is self-evident that looking at all chemically relevant configurations must surely be more relevant than the minutiae of which one happens to be the gas-phase ground state. These are the ones that convinced me finally that Sc-Y-Lu was the better form: (1) implies that Lu as an f-block element is suspect, and looks at all configurations: gas-phase, condensed-phase, you name it. It's holistic. And (2) confirms that the result is OK. If (1) ordered something and (2) turned out not so good, that would be bad: but it works even for He over Be, so I'm logically consistent. Which, with all due respect, I don't see you being. Double sharp (talk) 22:24, 8 February 2020 (UTC)

@Double sharp:

1. Any 4f involvement in La is marginal. The 14 f electrons in the Lu³⁺ cation, are manifestly more significant in terms of their impact on the chemistry of Lu.

@Sandbh: Not this canard again. The 14 f electrons in Lu are important, yes. In the same way as those of Hf are important. And those of Ta are important. And so on and so on and so on. As core electrons. Blocks are supposed to be about valence electrons and vacancies. Otherwise, the 3d block must extend until Kr as the repercussions of the 3d contraction are still being felt till then. Double sharp (talk) 21:37, 9 February 2020 (UTC)

2. That the trends of the d-block are less homogenous is due to the delayed start of the filling of the 4f shell. The shape of the periodic table is an outcome of the real-world aufbau filling sequence (and the associated differentiating electrons) not the imaginary or idealised n+l rule. All chemically relevant states are not as relevant as the characteristic or predominant states.

@Sandbh: They are for sure more relevant than the gas-phase electronic configurations which are neither characteristic nor predominant in actual compounds. Double sharp (talk) 21:38, 9 February 2020 (UTC)

I haven't based my arguments exclusively on gas-phase configuration, as you know.

@Sandbh: No, but when you use them, you inconsistently flip between when they are decisive (for La and Ac) and when other factors can overthrow them (like for Th and Lr). As Jensen commented about Lavelle: "When it comes to the question of why La and Ac should remain in the d-block rather than being reassigned to the f-block, Lavelle offers no new chemical or physical evidence other than his constant reiteration of the fact that both elements contain d-electrons in their ground-state valence conﬁgurations, but no f-electrons. Yet in the cases of both Lu and Th, for which this is equally true, he proceeds to inconsistently argue that this fact is of no consequence when it comes to assigning them to the f-block. As with the case of the revised conﬁguration for Lr, which counts when it comes to not placing this element in the d-block but is irrelevant when it comes to placing it in the f-block, this arbitrary and naive use of electron conﬁgurations, to the exclusion of all other evidence, is logically inconsistent and leaves one with the impression that the only true argument that Lavelle has for the major premise of his diatribe is that La and Ac should remain in the d-block because that is where IUPAC places them in its ofﬁcial periodic table and therefore all rational discussion of other possibilities is strictly forbidden." You've made a better case than Lavelle by bringing in other properties as well, but (1) they are often weak arguments and (2) we still don't know which of your criteria you consider to be the most important and fundamental. Without such an order, how can we distinguish it from a scattergun firing of arguments? Respectfully, I think Jensen's strategy (which I have pretty much adopted) of first looking at valence subshells (either with electrons or vacancies), then confirming our assignment with periodic trends, comes the closest yet to the Holy Grail of finding one fundamental principle behind periodic table drawing. Yours doesn't seem to be anywhere near that. Double sharp (talk) 21:37, 9 February 2020 (UTC)

The La and Lu question is better viewed as follows:

In terms of Scerri's continuum of periodic tables the three versions appear broadly as follows:

Towards the Platonic end

Tetrahedral ADOMAH in a cube
ADOMAH
LSPT
Lu table

Somewhere near the middle

La table

Towards the chemistry end

The continuum puts things into perspective; each form has its purpose. Each one is worth exploring. Frex, the LST prompted surprising research on the He over B question. In this spirit, I say give people a toolbox, not a hammer. Sandbh (talk) 06:10, 9 February 2020 (UTC)

@Sandbh: I say that whatever minuscule advantage the La form has does not overthrow the decisive advantages of the Lu one for harmony of blocks and chemically active subshells that control them. The La form is an unsatisfactory compromise between showing no secondary effects (He-Be, Sc-Y-Lu) and getting drowned in them (Rayner-Canham), with one particular secondary effect (delayed collapses, and only for La/Ac, because the Lr one gets ignored) blown out of proportion above all others. (Maybe because it is the only one that can easily be drawn.) Teach students the Sc-Y-La trend alongside the Sc-Y-Lu trend, for sure; it makes sense for comparative chemistry. And do the same for Be-Mg-Ca vs. Be-Mg-Zn, which is a real ambiguity in electronic structure. But there is no advantage significant enough to overthrow the bald facts that 4f is an active, valence subshell in La, but is stuck in the core for Lu just as much as it is for the rest of the 6th period. Double sharp (talk) 21:37, 9 February 2020 (UTC)

DS' current reassessment of the old IUPAC submission

Here are my revised views of the arguments from our old submission, now that I learnt more in 2018 from Droog Andrey about the issue and about Lu's total lack of 4f involvement:

Lu arguments:

Argument	Summary	Type	Analysis	Status
1958: Electron configurations	4f shell complete in Lu	Commonality	Strong, since 4f is core-like in Lu. 3d is not a valid comparison as it still contributes to bonding in Zn.	Substantiated Core argument
1965: Similarity of Lu with Sc, Y	Lu is closer to Sc, Y than is La	Commonality	True, but not the full story. This does not address relevance of similarity v. linearity and requires more fundamental considerations to deal with. Since there is no big discontinuity from groups 1 to 6, just a continuous easing into more and more transition-like behaviour we instead note that group 3 appears to be a standard d-block group, in which case the group 4+ trend ought to be followed, and this becomes correct. This is something that affects many of the other arguments: Sc-Y-La follows a group 1 and 2-like trend, Sc-Y-Lu a group 4-to-8-like trend. The reason why the latter is preferred is for the increased d-block homogeneity.	Substantiated (though incomplete) Core argument (once completed)
1967: f-character of La	Literature suggests this could explain some properties	Commonality	Indeed, significant for La and nonexistent for Lu	Substantiated Core argument
1982: Separation groups	Y, less so Sc, chemically closer to Lu than to La	Commonality	True, but not the full story. We have to address the continuity of the group 2 to 4 trend to show that this is the expected periodic trend that follows group 4.	Substantiated (though incomplete)
Irregular electron configurations	Gas phase electron configs support Lu under Y	Commonality	Gas phase configurations are usually chemically irrelevant	Irrelevant
Electron configuration analogy	Consistent atomic number difference of 32 between heavy d block metals	Trend similarity	True; breaking this results in an inconsistency of cores and a breaking of the post-contraction pattern	Substantiated Core argument
Ionization potentials	IE 1 + IE 2 for Sc-Y-Lu similar to groups 4–8, unlike Sc-Y-La	Trend similarity	Correct, but why first two IE?	Inconclusive
Atomic radii	Periodic trends favour Sc-Y-Lu	Trend similarity	Correct. But strictly speaking this comes after the core arguments, when we confirm that the periodic trends it gives make sense.	Substantiated
Ionic radii	Trends favour Sc-Y-Lu	Trend similarity	No data nor references given, but easy to supply by looking at the d-block trend and how it becomes more homogeneous this way. But strictly speaking this comes after the core arguments, when we confirm that the periodic trends it gives make sense.	Substantiated
Redox potentials	Comparison of periodic trends favour Sc-Y-Lu	Trend similarity	Ditto	Substantiated
Electronegativities	Allred-Rochow trends favour Sc-Y-Lu	Trend similarity	Pauling EN favours Sc-Y-La. Corrected "chemical" electronegativity (Kulsha-Kolevich) favours Sc-Y-Lu as more consistent with d-block trends. But strictly speaking this comes after the core arguments, when we confirm that the periodic trends it gives make sense.	Inconclusive, though somewhat suggestive
Melting points	Sc-Y-Lu trend fits better with groups 4–10	Trend similarity	Correct. But strictly speaking this comes after the core arguments, when we confirm that the periodic trends it gives make sense.	Substantiated
Crystal structures (elements)	Sc, Y, Lu are HCP but La is double-HCP	Commonality	Structures in other d-block groups vary, too	Meaningless
Crystal structures (oxides etc)	M₂O₃ etc for Sc, Y, Lu are = whereas La different	Commonality	Structures in other d-block groups vary, too	Meaningless
Excited state spectra	Spectra for Sc, Y, Lu differ from La	Commonality	Empty d-bands in Ca, Sr and Ba precede d block proper and differ from spectra for Be, Mg. But does illustrate the point that 4f is a valence vacancy for La, so has some chemical relevance. Be-Mg-Zn is a true ambiguity that has to be resolved at the 2nd order by trends for periodic table placement, and the Ca group should be considered in comparative chemistry discussing the TMs.	Reflection of a stronger argument
Superconductivity	Sc, Y, Lu incapable of superconductivity in bulk at normal pressure whereas La is	Commonality	Lu may or may not also be capable, but most recent work suggests that it is not for reasons related to band structure (chemically relevant)	Inconclusive but suggestive
Conduction band structures	Sc, Y, Lu have conductivity bands with d block like structure but La does not	Commonality	X-ray isochromats of Gd to Lu all show similar structures. But it does offer an illustration of Lu displaying more d-elementishness than La.	Weak but suggestive
1985: Seven properties	Density triads, and some mechanical and thermodynamic properties support Lu under Y	Periodic trends/Commonality	Density triads OK, but only because we have already established where the d-block goes, so only confirmatory. The other properties are inconclusive	Inconclusive
2005: Physical properties	Sc, Y dissimilar to Ln; as Lu is also an Ln outlier it should be in group 3	Commonality	Lu is hardly an outlier, and Y is more or less like an Ln	Groundless
2006: Characteristic electron configurations of ions	Configurations of ions are more important than those of gas phase atoms	Other	Incomplete, even if going in the right direction towards all relevant subshells; on the face of it, looking at these alone looks like it should support -La-Ac	Argument supports -La-Ac, and is incomplete
2011: Triads	Y-Lu-Lr is a triad; Y-La-Ac is not	Other	Sc-Y-La form triad but not Sc-Y-Lu	Inconsequential
2012: Split d block	Sc-Y-La-Ac yields symmetry deficit in 32-column version	Other	In itself this is not a criticism. It only becomes so because a comparison of the two options shows that the symmetry deficit of the La form does not increase explanatory power appreciably, and in fact decreases it in many cases.	Incomplete
2013: Carbonyls	Periodicity in carbonyl valencies supports Lu under Y	Commonality	Not representative; breaks down in s block	Unsubstantiated
2014: Lu as a TM	Lu shares many properties and similarities with period 6 TMs	Commonality	Correct; Lu is more d-elementish than La, and makes the d-block more homogeneous	Substantiated
Name matches position	La, Ac in f block is consistent with names	Commonality	This is not about chemistry	Baseless and irrelevant
2015: Dimer spectroscopy	Spectra of Lu M₂ dimers is more like those of other period 6 transition metals, so Lu is better fit under Y than is case for La.	Commonality	Correct, but this is not a form the Ln are usually in chemically, so relevance is weak	Weak but suggestive
Relativistic contraction of 6s shell	Lu falls on period 6 TM trend line and off the lanthanide trend line	Commonality	Pt and Au fall off the period 6 TM trend line; the other lanthanides with a d electron (La, Ce, Gd) also fall off the lanthanide trend line; but it is true that Lu falls off far more, and fits better with the period 6 TM trend line than even the "corrected" one-d-electron trendline leading on from La, Ce, and Gd	Weak but suggestive
Aluminide dimers	AlLa dimer different bond compared with AlSc, AlY, AlLu	Commonality	Bonds of other groups' compounds vary, too	Meaningless, incomplete
Heat of vaporization	Sc-Y-Lu trend fits better with early d block than does Sc-Y-La	Trend similarity	True, though this is just one property among many others and might well be combined with them	Substantiated
IE of Lr	Experimental determination of Lr IE has no implication	Other	Agree with Jensen	Meaningless

La arguments:

Argument	Summary	Type	Analysis	Status
1970: Six properties	Basicity increase down a group is a general principle	Trend similarity	La is more basic than Y; Lu is less basic than Y. As far as it goes this is true, but the contraction before 4f is especially strong. Contractions usually weaken basicity (note Al vs. Ga) for the elements coming after them and there is no reason why this should not be so here. Since we have previously determined the 4f block through chemical activity of the f-subshell, the violation of this principle is justified.	Incomplete
1974: Integrity of the f block	Double periodicity in the f block is apparent	Periodicity	True, but misleading (4f is active at La but not at Lu), and incomplete since based on gas-phase configurations [Note 1]	Irrelevant
2004: La-Ac remains the most popular form	Popularity of La-Ac calls into question the merits of Lu-Lr	Popularity	True	Inconclusive, given lack of critical examination in literature
2008: A pair out of place	Lu-Lr would mean La-Ac become only case of a vertical pair with no outer electrons in common with their block	Commonality	True, but based on gas-phase configurations and hence not relevant. La-Ac makes Lu-Lr the only case of a vertical pair in a block where their characteristic electrons are core electrons, which is even worse since the table is supposed to be based on valence electrons. [Note 2]	Irrelevant
2016: Condensed-phase v gas-phase electron configurations	Condensed phase configurations are more pertinent to the chemistry of the elements, and support Sc-Y-La-Ac	Commonality	True, but their invocation means playing with fire for Be-Mg-Zn. Also incomplete: you want to look at all chemically relevant configurations, not just condensed-phase only or gas-phase only.	Incomplete
Blocks	Concept of periodic table blocks supports Sc-Y-La-Ac	Commonality	False, because a block's members should have its characteristic electrons as valence electrons or at least valence vacancies. This is true for La-Ac in the f-block but not for Lu-Lr in the f-block. [Note 3]	Baseless
Chemical behaviour	Group 3 chemical behaviour is like groups 1–2; Sc-Y-La trends fit better with groups 1–2; Sc-Y-Lu trends fit better with groups 4–10; ergo Sc-Y-La preferred	Trend similarity, commonality	Group 3 chemical behaviour is in actuality inconclusive between group 2 and 4; it is quite intermediate if you look at all aspects of chemistry. Therefore this argument is not strong enough to overturn the delineation of blocks by 4f involvement of La.	Groundless

Double sharp (talk) 22:53, 8 February 2020 (UTC)

(And so we pass 600K!) Double sharp (talk) 00:18, 9 February 2020 (UTC)

@Double sharp: Some comments below.

Note 1: Double periodicity is based on the ions rather than the free gas phase.
Note 2: "…since the table is supposed to be based on valence electrons." Valence configurations are a consideration but not the ultimate basis of the table. The chemistry involved, as per your ultimate analysis, also has to be taken into account.
Note 3: "…a block's members should have its characteristic electrons as valence electrons or at least valence vacancies." Per note 3, there is no such intrinsic requirement. Sandbh (talk) 05:52, 25 March 2020 (UTC)

@Sandbh: Comments:

Re note 1: Rokhlin and Wiberg as quoted in that section focus on gas-phase configurations. I overlooked Shchukarev's different argument above, but I have now addressed this below. In our old submission we agree that "the most important periodic property of the Ln and An is their valency", and that is exactly why the double periodicity supports La-Yb as the f block. For the 4f row especially, we should expect a half-filled 4f shell to confer stability and lead to increased stability of the +2 state (not touching the 4f shell) as we approach it, as we indeed see for Sm and Eu. As we approach the end of the block, the f orbitals should become more core-like by simple high-school chemistry (higher effective nuclear charge), and the +2 state should increase in stability, as we indeed see for Tm and Yb. Lu is clearly not getting its +3 state from the f orbitals anymore. All this is exactly analogous to 3d, which we both agree is Sc through Zn, only if we start the f block at La and end it at Yb. With the 5f row, the double periodicity of first half vs. second half is weak (as normal once you pass the first row), but the block-end effects are even stronger.
Re note 2: If we only consider chemistry, there is no way to decide between Be-Mg-Ca and Be-Mg-Zn, among other things. That's why valence electrons have to be brought in as something that explains the chemistry.
Re note 3: Similarly to note 2, this requirement is obvious if the blocks are supposed to mean anything and not just be formal devices. Double sharp (talk) 05:58, 25 March 2020 (UTC)

Sandbh's criteria

@Double sharp: Earlier, you posted:

"That's why I want to ask: please set down your criteria, a precedence order for them, and reasons why each one is important. That's the only way you can get a consistent basis for the PT."

It looks something like this, with # denoting an IUPAC argument.

Important arguments/criteria

D/e’s are important, per giving shape to the blocks
- And since this is where I start disagreeing with you, having quoted many papers in support of DE's being generally chemically irrelevant, it is not a surprise that my disagreement with your logic runs to almost the whole of it. Double sharp (talk) 11:27, 10 February 2020 (UTC)

-- Our criterion that a block starts when the first electron of its name enters the applicable sub-shell #

-- One less d/e anomaly in an La table

-- The Ln contraction proper starts in Ce and ends in Lu

The periodic law and the actual afbau process

The ionic v covalent distinction, per Rayner-Canham.

-- Ionic radii trends going down Sc-Y-La and Sc-Y-Lu compared to groups 1 and 2, and 4+ #

Internal regularity

Supporting arguments/criteria

One more 234 triad in an La table (regularity)
Isodiagonality seen in Ca-Y-Ce but not Ca-Y-Lu (importance per Rayner-Canham)
Laing's comparing the pairs Ca-Sc and Sr-Y with Ba-La # (DIM extrapolation)
Restrepo's stoichometry findings (importance re connection with chemistry)
Monocations of Sc, Y, La and Lu (noting many correlations made to 1st IE)
Rare earth metals (consistency, regularity)

Sandbh (talk) 05:48, 10 February 2020 (UTC)

The metallic elements

@Double sharp:

These extracts are from: Parish RV 1977, The metallic elements, Longman, London

I was looking through Parish to see if I could get a better appreciation of the homogeneity issue i.e. are the vertical trends down group 3 more relevant than the horizontal trends along the 5d row, etc. No real joy there.

And I'm not surprised, given his considering 4d and 5d metals are something different from the 3d metals, rather than going group-by-group like Greenwood and Earnshaw. Double sharp (talk) 12:07, 10 February 2020 (UTC)

I did discover a treasure trove instead.

"The chemistry of the s-block metals is the simplest of any group of elements in the Periodic Table, because each element displays only one oxidation state: +1 for the alkali metals (lithium to caesium), and +2 for beryllium, magnesium and the alkaline earth metals. A great deal of their chemistry is explicable in terms of simple ionic bonding and the number of covalent compounds is small, lithium, magnesium and, particularly, beryllium providing the most examples." (p. 34)

Note use of the expression, "A great deal of their chemistry…etc".

"…of the 3d -metals, scandium, (along with yttrium and lanthanum) bears a much closer resemblance to the 4f-metals and all these metals are more conveniently treated with the latter in Chapter 6." (p. 48)

"The metals of the 4d- and 5d-series form a strong contrast with those of the 3d-series. The metals themselves are generally very hard, high-melting and unreactive, and are often used for these properties. In their compounds a wide range of oxidation states is shown, but all are characterised by the formation of bonds of high covalent character, and there are no simple ionic compounds. Only in a few cases are even the simple aquated cations known, other ligands, often anions, being bound in preference to water. Within each Group, the 4d — and 5d—metals are often closely similar, especially in the earlier Groups, and this gives rise to difﬁculties in separation and identiﬁcation. It is, for example, not easy to obtain samples of hafnium or zirconium uncontaminated by the other. These similarities are the result of the ‘lanthanide contraction’. In Group III, yttrium and lanthanum show the differences in their chemistry which would be anticipated from the difference in ionic radii, ionisation energies. etc., but the interpolation of the fourteen lanthanide elements between lanthanum and zirconium, with the resultant increase in effective nuclear charge, reduces the radii and increases the ionisation energies to values close to those for hafnium. These effects are seen to build up through the 4f series…" (p. 112)

Note reference to Y and La showing the expected trends, and the reference to the interpolation of the Ln.

This is circular if you apply it to the group 3 question. By saying that the Ln are interpolated, you are implicitly assuming that they come between La and Hf. Which means that this is useless for actually determining whether the 4f block should start at La or Ce. Well, if you think it starts at La, then the trend at Lu is totally expected because the 4f series is over. Well, if you think it starts at Ce, then the trends in group 3 and 4 are totally expected because La comes before the 4f series, but Hf comes after it. Either way, it is perfectly rationalisable. So you have to appeal to some other factors, hopefully chemically relevant ones (whence chemically active subshells and certainly not those tiresomely irrelevant DE's), that determine the start of a block. And this is where we part, because you insist on chemically irrelevant DE's (which you then massage away to get rid of the annoying problem that according to them, 4f begins at Ce but 5f begins at Pa), and I insist on chemically relevant active valence subshells (which you then misread all the time by dragging in the canard about the core 4f subshells at Lu). After this fundamental difference there is not much common ground to be had. Double sharp (talk) 12:01, 10 February 2020 (UTC)

"The f-block consists of two series of elements in which the 4f- and 5f-orbitals are ﬁlled. However, the chemistry and properties of these two series are so very different that, as with the d-block, it is more convenient to treat them separately. The 4f-elements are therefore considered in this Chapter, and the 5f-elements in the next. The 4f elements (alias lanthanons, lanthanides or lanthanoids) have a very simple chemistry since with but few exceptions only one oxidation state is displayed, viz. +3. In this respect they resemble the s-block elements, and indeed there are pronounced similarities to calcium, which often occurs in lanthanide minerals, and to strontium and barium, particularly in the complicated solid—state structures found." (p. 142)

Note reference to resemblance to s-block elements and pronounced similarities to calcium, and to Sr and Ba.

For minerals the important broad-strokes classification is Goldschmidt's. In which, indeed, the Ln and An occur as lithophiles, just like groups 1 and 2. Unfortunately for the prospects of this as a La argument, so do the elements of groups 3, 4, and 5. Double sharp (talk) 12:02, 10 February 2020 (UTC)

"Two features are particularly striking in the chemistry of the 4f—elements, Viz. (a) the uniformity of the +3 oxidation state and the small number of other oxidation states, and (b) the irregularity of structures and occurrence of high coordination numbers. In the compounds described here, coordination numbers of six, seven, eight, and nine have been mentioned, and in other compounds ten- and even twelve-coordinate metal ions are found, eg. in La2(SO4)3.9H20 and (NH4)2Ce(NO3)6. It is tempting to think that the f-orbitals must be involved in the bonding, since the maximum number of hybrid orbitals which can be constructed from an s-p-d -set is nine, and to obtain eight bonding orbitals directed towards the corners of a cube (as in C602) requires at least one f-orbital. There is, however, no evidence to suggest that the f-orbitals are involved at all in the bonding, and even ligand-ﬁeld effects are extremely small. All the compounds appear to be essentially ionic, with very little covalency involving even the 6s- or 6p-orbitals. The curious structures and high coordination numbers are similar to those found with other large cations (e.g. salts of Ba2+ or Pb2+) and are presumably a result of the optimisation of electrostatic forces. The large internuclear distances necessitated by the radii of the cations will cause the electrostatic energy per pair of ions to be relatively small, despite the high cationic charge, and many such pairs must be formed to achieve a suﬂiciently large lattice energy. Similarly, the large radii diminish considerably the polarising effect of the +3 charge which would otherwise be expected to lead to considerable covalency." (p. 151)

Note no evidence for f orbital involvement, including in La. Sandbh (talk) 11:25, 10 February 2020 (UTC)

Despite my strong scepticism about this whole idea (especially given the 1977 date of the book), I'll bite: if there is no 4f involvement in any lanthanide, then there isn't any in Lu either, and so we are back to square one. The whole point is that 4f is a reserve area for electron; it prevails in indirectly bonding MO's, but electrons may appear in it in chemically relevant configurations and jump out from it to involve themselves in the bonding. Again, this is something that happens for La and not Lu. Double sharp (talk) 12:04, 10 February 2020 (UTC)

P.S. I should like to see how Parish proposes to explain cubic complexes without 4f involvement. Double sharp (talk) 16:17, 18 February 2020 (UTC)

More about the transition metals: a case study for why DS chose to adopt Jensen's criteria

This will probably get called fogging, but I will put it up anyway because it well illustrates my policy: before elevating something to a principle of the periodic table, we work backwards from it and see what more fundamental stuff we can derive it from to get to the bottom of it. (Which is why my approach accepts only chemically active valence subshells confirmed by periodic trends.) We start to understand more clearly why the TMs in later and later periods start showing characteristic transition properties more and more sluggishly if we step backwards and look at the more fundamental reasons why this is happening. (Which makes sense, because we want to go to the most fundamental reason possible for the periodic table.) This surely beats the alternative of fogging (to use Sandbh's word) about how the gap is supposedly between groups 3 and 4 all the time, when it is plain as day that by slightly shifting our focus it can move as far as the line before group 2, or the line after group 7 even. (Yes, seriously. Ca-Sr-Ba have significant pre-transition character. But Tc-Re-Bh have +7 as the most major oxidation state, although Tc admittedly likes interconverting between them a lot; we may draw parallels with what happens with a lot of p-block main-group elements, with one characteristic group oxidation state, but another common lower one!)

Generally speaking, if something happens in one element of the 3d transition series, it will only happen one or two elements later in 4d and 5d (e.g. the melting-point trend: cf. the positions of Cr vs. Tc/Re, which Greenwood and Earnshaw note IIRC). This is, in fact, a diagonal relationship (note compensations for charge/radius, per Fajans' rules); it becomes a straight-down relationship from 4d to 5d because of the 4f contraction, of course. (From La to Yb, naturally. ^_^)

The end result is: in the 3d row, titanium is the first one with bona fide low oxidation states in water. (They are still readily oxidised to the +4 state and are not the predominant ones, of course; for more stability and dominance you really need to wait till vanadium with its +4 state.) But in the 4d and 5d rows: lower oxidation states of zirconium and hafnium reduce water outright. For niobium and tantalum, the lower oxidation state is readily oxidised, and the group state dominates. The "crooked diagonals" here are Sc to Zr-Hf; Ti to Nb-Ta; and V to Mo-W (this set is the one with stronger lower oxidation states, although for tungsten this is not so stable.)

If we dare to go to the 6d metals, we get a double whammy. Firstly, the 5f contraction's action is not so strong as the 4f one, and so we still have some increase in atomic radius. But secondly and more importantly, 6d is relativistically strongly destabilised. The end result is absolutely predictable: even at seaborgium, Sg(IV) is more unstable than W(IV) and should be readily oxidised to Sg(VI). The first time we get a lower oxidation state well-defined enough to exist in water and display acidic/amphoteric/basic properties is probably for bohrium (+6), which should be readily oxidised to the group state of Bh(VII). Hassium is the first one where the group oxidation state is not among the most stable ones! (As we should have guessed, from the dominance of +7 for technetium and rhenium, even though lower oxidation states are well-defined there.)

So, now that we understand what is going on, we pencil in: "due to the increased activity of d-subshells relative to s-subshells down the table going from 3d to 4d (avoiding primogenic repulsion) and 5d to 6d (relativistic destabilisation), main-group character persists for longer and longer at the start of each transition series, but incipient transition behaviour still begins at about the same time". And now we understand what is going on, instead of endlessly talking about a dichotomy, raising it to a principle of the periodic table, when in fact it is the job of the principles behind the periodic table to explain that dichotomy. And, lo and behold, we have returned to the true fundamental basis: chemically active valence subshells. And the number of electrons in them in total, which gives group assignments and controls valency. Notice, of course, that the little surface fluctuations of ground-state DE's never came into it. In fact, I did not need to reference DE's even once here to explain this. By Occam's razor, they fly away.

While looking up stuff for this comment, which will no doubt end up being referred to as fogging anyway, I came across my descriptive chemistry of the d-block from archive 27, and I found this extremely revealing comment: 'Suppose I talk to you about an element M which is usually tetravalent. Now I tell you that MCl₄ is a volatile molecular liquid that hydrolyses readily and completely to MO₂ even when in contact with moist air; that oxoacid salts of M^IV do not exist, only hydrolysed species being formed; that supposed "MO²⁺" ions sometimes alluded to in the literature are really polymeric –M–O–M–O– species; and that it has no simple cationic chemistry. Looking at how you are interpreting the literature to make the case for the metalloids as nonmetals, I am sure you would say that M should be classified as a nonmetal, although perhaps a weak nonmetal, analogous to silicon and germanium. Except that M is, of course, titanium.' Mendeleev was right: valence is very important. And it controls ionic vs covalent and all such dichotomies so much that it even transcends distinctions of elements that are metallic vs. nonmetallic as simple substances. The "breakpoint" simply occurs at a particular z/r ratio per Fajans. But that simply shows that "ionic vs covalent" is not the basic dichotomy to use here, as it is a consequence of valence and Fajans' rules. Instead we must look back at the recurring pattern of valences and atomic radii. And then look at what causes it, which yields chemically active subshells and electron configurations in all chemically reasonable environments. Only with such a regression are we ever going to get to something like a sound basis for the periodic table. Everything else can be traced back to that and is secondary. That's why looking at periodic trends is only a confirmation that we have not been barking up the wrong tree.

TL;DR: go back to the most basic relevant phenomenon you can think of for chemistry and use it as the basis for drawing your PT. That's why we go to chemically active subshells, with control everything that happens next, incl. ionic vs covalent, metallishness, valences, diagonal relationships, contractions, trends, etc.: everything should be as simple as possible, so we go back to the first basic relevant cause. But not further to the chemically irrelevant ground states: simple as possible, but not simpler. Double sharp (talk) 17:46, 10 February 2020 (UTC)

Jensen's criteria, recapitulated:

Assignment of the element to a major block based on the kinds of available valence electrons and/or valence vacancies (i.e., s, p, d, f, etc.).

Assignment of the element within a given block to a particular group based on the total number of available valence electrons.

Verification of the validity of the resulting block and group assignments through the establishment of consistent patterns in overall block, group and period property trends.

Verification that the elements are arranged in order of increasing atomic number as required by the periodic law.

Frankly, the only place I differ with him on these criteria is where he says here that criteria 1 and 2 alone do not resolve the group 3 question. As he himself points out here, "[La and Ac] have low-lying empty f orbitals, which is more than can be said for Lu and Lr". The debate should never even have gotten past step 1. It's only for the problem of Be and Mg that there is a serious issue that requires going down to step 2, noting that the d-electrons of group 12 at least contribute meaningfully to bonding. (Yes, I disagree with his stance on group 12, but that doesn't forbid me from agreeing with him on group 3.) Double sharp (talk) 21:43, 10 February 2020 (UTC)

+2 in group 3 and +3 for Ti

@Double sharp:

It's said, rightly or wrongly, that group 4 is the first in which we see the really characteristic transition metal properties of variable oxidation state, colour, and paramagnetism.

We can see this in titanium, where our article says, "The +4 oxidation state dominates titanium chemistry, but compounds in the +3 oxidation state are also common."

For scandium, our article says, "In the chemical compounds of the elements in group 3, the predominant oxidation state is +3. Compounds that feature scandium in oxidation states other than +3 are rare but well characterized."

For organometallic chemistry our organoscandium chemistry article says, "As with the other elements in group 3 – e.g. yttrium, forming organoyttrium compounds – and the lanthanides, the dominant oxidation state for scandium in organometallic compounds is +3. Most organoscandium compounds have at least one cyclopentadienyl (Cp) ligand. The dominant species are CpScX2, Cp2ScX and Cp3Sc."

From this, I conclude that:

The dominant oxidation state in group 3 is +3. Group 3 compounds in lower oxidation states are rare but well characterised.

It is in group 4 that the really characteristic transition metal properties are first commonly seen.

Is that a fair appraisal of the situation? Sandbh (talk) 01:16, 11 February 2020 (UTC)

@Sandbh: No, because it overlooks that the change happens later in each period. For the 4d elements, Zr and Hf are strongly pre-transition with only the +4 oxidation state as a major one. Lower oxidation states are rare but well-characterised. The same is more or less true for Nb and Ta in group 5 stuck in the +5 state. The 6d elements suffer a double whammy from a weaker An than Ln contraction plus relativistic destabilisation, so much so that maybe Hs in group 8 is the first one where characteristic transition properties are seen.

Therefore I claim that by your standards, transition properties in groups 4 and 5 are not characteristic: each group has four elements and only one in each shows them seriously. A much better thing to look at to understand this is to see the shift move later in each period: group 4 for 3d, group 6 for 4d and 5d (more or less), group 8 for 6d. Double sharp (talk) 07:54, 11 February 2020 (UTC)

@Double sharp: Thank you. Do you agree that it is in Ti that the really characteristic transition metal properties are first commonly seen? Sandbh (talk) 09:42, 11 February 2020 (UTC)

@Sandbh: Yes, that is fair to say. The lower oxidation state +3 is easily oxidised to +4, but undoubtedly well-defined and stable in water. Double sharp (talk) 11:43, 11 February 2020 (UTC)

Block homogeneity and similarity

@Double sharp:

Here’s another question, at the end of this post.

Context: With La in group 3, the vertical trends resemble those in groups 1 and 2. With Lu in group 3, the vertical trends resemble those of groups 4 and 5.

You argue that since a comparison of vertical trends going down group 3 as Sc-Y-La or Sc-Y-Lu is inconclusive (true), the homogeneity of the 5d series becomes the decider. On this basis Lu is the go, since Lu resembles a 5d metal more than does La (true).

@Sandbh: Ah, so you finally admit that that's true, instead of hiding behind Restrepo who by his methodology will have overlooked the important issues here. ^_^ Double sharp (talk) 00:11, 14 February 2020 (UTC)

Among other things, I've argued for looking at group 3's neighbours. Group 3 (whether La or Lu) has a predominately ionic chemistry, as is the case for K-Rb-Cs in group 1, and Ca-Sr-Ba in group 2. Groups 4 and 5 have a predominately covalent chemistry.

As noted, similarity is one of the key concepts of the periodic table, historically addressed by assessing the resemblance of chemical elements via their compounds. Mendeleev’s studies were mainly based on compounds; he highlighted the need to rely on compounds and their proportions of combination rather than on properties of chemical elements.

Through DIM’s similarity lens, we have:

Group 3 as Sc, Y, La: Predominately ionic compounds, like their group 1 and 2 counterparts.

Group 3 as Sc, Y, Lu: Predominately ionic compounds, unlike their group 4 and 5 counterparts.

I further noted the diagonal similarity trend between Ca-Y-Ce that occurs in an La table:

all three elements (Ca-Y-Ce) are strongly basic;
similarities between Ca and the lanthanides (inc. Ce) are well known;
Y is a member of the rare earths, as are the lanthanides;
all three elements exhibit predominantly ionic chemistry.

There is no such trend for Ca-Y-Hf, which occurs in an Lu table:

Ca and Y are strongly basic; Hf is amphoteric;
Ca and Y exhibit a predominately ionic chemistry whereas Hf exhibits a predominately covalent chemistry;
Y and Hf can form intermetallic compounds with Pt, noting this capacity does not extend to Ca.

DA: @Sandbh: See http://www.himikatus.ru/art/phase-diagr1/Ca-Pt.gif

As noted, diagonal relationships in the periodic table were recognized by both Mendeleev and Newlands. Per Rayner-Canham, "Isodiagonality is, in some ways, a general attribute of the properties of the chemical elements. For example, the metal-nonmetal divide forms an almost diagonal demarkation (Edwards and Sienko 1983). Similarly, the elements often considered to be semimetals fall on a roughly diagonal border between the metals and nonmetals (Hawkes 2001)."

I further noted that Sc-Y-La maintain a +2 +3 +4 maximum oxidation state (MOS) pattern that periodically recurs elsewhere in the periodic table, at least up to Z = 100, whereas this pattern is not seen in Sc-Y-Lu. I said that the relevance of this is that DIM similarly assigned great importance to the MOS of the elements, as seen in their compounds.

On the basis of shared chemistry, the diagonal similarity trend, and the 234 pattern, among other reasons,* I support La in group 3.

* such as a block starts with the first appearance of the applicable electron, consistent with the n+l rule

You essentially seek to refute my arguments on the basis that:

there is no such thing as "predominant chemistry" (though such a notion is common in chemistry)

DS: It's common only when we all know what context we're talking about. Predominant ionicity vs. covalency hardly a fundamental principle because it comes from EN differences, which are part of periodicity and perfectly explained by (you guessed it) looking at subshells. When we don't know what context we're talking about, such as in the really most basic texts, we hear a rather different story:

“

The implication of all this is that there is no clear-cut division between covalent and ionic bonds. In a pure covalent bond, the electrons are held on average exactly half way between the atoms. In a polar bond, the electrons have been dragged slightly towards one end.

How far does this dragging have to go before the bond counts as ionic? There is no real answer to that. You normally think of sodium chloride as being a typically ionic solid, but even here the sodium hasn't completely lost control of its electron. Because of the properties of sodium chloride, however, we tend to count it as if it were purely ionic.

Lithium iodide, on the other hand, would be described as being "ionic with some covalent character". In this case, the pair of electrons hasn't moved entirely over to the iodine end of the bond. Lithium iodide, for example, dissolves in organic solvents like ethanol - not something which ionic substances normally do.

”

— Jim Clark, Chemguide (when this is discussed under, you guessed it, a page on electronegativity)

Besides: why should one property among many possible ones be elevated to the level of something fundamental for drawing the PT? Well, ionic vs. covalent (a spectrum) is possible, and it is a consequence of chemically active valence subshells. So is formation of aqueous cations, so is physically strong metallicity, so are maximum oxidation states. But there's no good reason why we should pick one above all the others. They are all consequences of something more fundamental. Mendeleev might have had nothing better than maximum oxidation states and atomic weights, but now we know better what controls them, and we can reflect something more fundamental and improve on him rather than being stuck at the scientific knowledge of 1869. And it is our job to find out what the more fundamental thing is and see what it tells us. If it tells me something that I thought was true, then I'm happy that I was right. If it tells me something that I didn't think was true, then I'm even happier to learn something new. Which is why I moved from the Lu table to the La table at first, and then back to the Lu table again. And why I moved from He over Ne to He over Be. So it goes in science. Double sharp (talk) 19:55, 12 February 2020 (UTC)

RV: This is illuminating. To me it seems you are unable to grasp the concept of a generalisation or a tendency. I quote Rayner-Canham: "For chemists…the most important feature of an element is its pattern of chemical behaviour, in particular, its tendency toward covalent bond formation (or its preference for cation formation)." You don't address this quote. You instead engage in some fogging by saying there is a continuum of covalent to ionic. Or by saying it depends on the context. While I agree about a continuum, this is not the issue here. I agree about the context, which in this case is "general behaviour", considered as whole. Thus, "Australia is a dry country". To which you would respond that this is not true since there is a continuum of dry to wet in Australia. True! But not the point. Or you would say, "it depends on the context". Frex which time of the year? True, this can vary according to the seasons. But that is not the point of a generalisation. And then you would say, why should the dry-wet distinction be elevated to something fundamental? Which is not the point. The dry-wet distinction is one characteristic that I can use to distinguish Oz from other countries. Maybe there are 999 other ways of distinguishing Oz. But that doesn't concern me since I know the dry-wet distinction is quite a helpful and recognisable one for comparative purposes. When I migrated to Australia with my parents, for example, my father chose our destination city on the grounds of its weather. He had had enough of the cold European winters. Sandbh (talk) 03:20, 13 February 2020 (UTC)

@Sandbh: For sure, it is a characteristic. But why is it the most important one? If all you want to do is choose your destination on the grounds of its weather, then sure, all you need is that little bit of data. But if you want to actually understand the fundamentals behind climate and how to predict what the weather of some place on Earth will be like, you must go deeper. I claim that when drawing the periodic table, we are in something much closer to the second situation than the first. It's not good enough to simply note that there are periodicities in what we externally can see, because there are so many of them. You need to go deeper to see what is driving them and use that as the fundamental basis for the PT. Otherwise, you are just taking one among many equally significant properties and elevating it above all the others to a position it never should have taken.

I don't engage in fogging, unless speaking the truth is fogging. The undeniable truth is that there is a continuum between covalent and ionic bonding based on electronegativity, and tendencies towards forming bonds more to one end of the spectrum or another are simply due to EN. Depending on the types of compounds under consideration, it may be most convenient to draw the line in different places. The line is clearly not in the same place for chlorides as it is for fluorides, for example. And clearly not in the same place for hydrides and chlorides. Or arsenides and chlorides. And you miss out the last one of the "big three" bond types that are typically covered in introductory chemistry courses and books: metallic bonds, which naturally make up a huge subset because so many elements on the PT are metals. So clearly the whole idea of "predominantly ionic vs. covalent" is (1) ill-defined, (2) wishy-washy (we may draw it in different places depending on our focus), (3) incomplete (where are metallic bonds?), and (4) clearly not fundamental. You would do better going straight to EN like Wulfsberg emphasises. It's one step closer to being fundamental, and it shows by how much better a predictor it is of chemical behaviour. Not that it is perfect, either. Double sharp (talk) 18:41, 13 February 2020 (UTC)

@Double sharp: Well, you look at something and say, what about the 999 other properties? I look at something and say, gee this is a pretty common distinction in chemistry, let's run with that, and see where it takes me. And then you say because I haven't considered the other 999 properties, my findings must be irrelevant. DIM would never have discovered the PT using your approach.

You engage in fogging by throwing up an irrelevancy such as the continuum between ionic and covalent. This has nil to do with the literature-based distinction, as I've cited several times, between predominately ionic and predominately covalent. And you mention more detailed minutiae such fluorides, chlorides, arsenide, and metallic bonds. Yet the entire literature is able to make generalisations at the highest level and say that e.g. the chemistry of Group 1 is predominately ionic. And you are the voice in the wilderness saying to the entire chemistry and classification science communities that they are all wrong. Good luck with that. Sandbh (talk) 05:27, 15 February 2020 (UTC)

@Sandbh: In DIM's day, of course he had to look at properties by themselves! There was nothing better then; atoms were not known, electrons were not known, subshells were not known. Mendeleev could not have done better than what he did in his day. But we can, obviously. (Or else, why are we not still using an 8-column table with the Ln spread like he thought might happen?) We now have enough knowledge to get at what is fundamentally driving periodicity. That's why I insist that we draw our table based on the most fundamental thing we can get to make it as objective as possible. There are lots and lots of properties and there's no reason why one should trump the other, but if we can see what is driving those properties, we get somewhere. And Mendeleev realised that, hence his focus on atomic weight as something fundamental for PT-drawing that was then confirmed by the fact that it made the trends match. Yup, he said that, straight from his Faraday lecture.

“

The elements, if arranged according to their atomic weights, exhibit an evident periodicity of properties.
Elements which are similar as regards their chemical properties have atomic weights which are either of nearly the same value (e.g. platinum, iridium, osmium) or which increase regularly (e.g. potassium, rubidium, cesium).
The arrangement of the elements, or of groups of elements, in the order of their atomic weights, corresponds to their so-called valencies as well as, to some extent, to their distinctive chemical properties -as is apparent, among other series, in that of lithium, beryllium, [boron], carbon, nitrogen, oxygen and [fluorine].
The elements, which are the most widely diffused have small atomic weights.
The magnitude of the atomic weight determines the character of the element, just as the magnitude of the molecule determines the character of a compound.
We must expect the discovery of many yet unknown elements - for example, elements analogous to aluminium and silicon, whose atomic weight would be between 65 and 75.
The atomic weight of an element may sometimes be amended by a knowledge of those of the contiguous elements. Thus, the atomic weight of tellurium must lie between 123 and 126, and cannot be 128.
Certain characteristic properties of the elements can be foretold from their atomic weights

”

— Dmitri Mendeleev's Faraday lecture

This all sounds much like what I'm saying. Except, of course, that I am writing generations later, science has progressed, and I talk about chemically active valence subshells and the number of electrons in them, confirmed by the arrangement being in increasing atomic number, instead of atomic weights. But what I want from that is the same.

Since when are metallic bonds "minutiae"? All this literature is assuming a certain context within which it makes sense to talk about ionic vs covalence as a predominance. It must be, or else you get bogged down into the issue that Cs bonds with most elements on the PT are metallic. Depending on what you are thinking of, it may make more sense to draw the line in other places (e.g. where the nuclear physics specialists draw covalent-vs-ionic wrt fluoride volatility). But that in itself makes the distinction not fundamental. I'm sure every text that mentions Fajans' rules implicitly understands this. It is an effect of other factors and therefore it should not be our basis for drawing the PT. Double sharp (talk) 20:24, 15 February 2020 (UTC)

@Sandbh: Oh, and Rayner-Canham agrees with me: "A related phenomenon, the change in bonding type across periods, similarly lies upon a diagonal (Mingos 1998). The pattern is usually for a change from ionic (to the left) to small-molecule covalent (to the right) with a species that can be assigned as possessing network covalent bonding at the transition point. For Period 2 and 3 fluorides, this intermediate bond type occurs with BeF2 and AlF3, and similarly for hydrides with (BeH2)x and (AlH3)x. For oxides, the transition is displaced right by one group so that it occurs with B2O3 and SiO2." Of course, it's only truly diagonal for some bits of the table (mostly in period 2 and 3 indeed), but the idea is right: the point of the change can move a lot. Double sharp (talk) 10:40, 16 February 2020 (UTC)

just because a diagonal relationship is common somewhere in the periodic table does not make it fundamental (though the literature uniformly recognises the occurrence and validity of such diagonal relationships)

DS: The literature also recognises that most elements are not in chemically significant diagonal relationships, and in fact for the most part stops talking about them past the famous ones from period 2 to period 3 (and mostly only the first few, Li-Mg, Be-Al, and B-Si). Double sharp (talk) 19:11, 12 February 2020 (UTC)

Periodic table trends (arrows show an increase)

RV: Here you are engaging in fogging and evading. I never said a diagonal relationship is fundamental. You and I both know that the periodic table is characterised by horizontal and vertical trend and this results in diagonal trends across the PT. Quoting R-C again "Isodiagonality is, in some ways, a general attribute of the properties of the chemical elements. For example, the metal-nonmetal divide forms an almost diagonal demarkation (Edwards and Sienko 1983). Similarly, the elements often considered to be semimetals fall on a roughly diagonal border between the metals and nonmetals (Hawkes 2001)."

Yet, the best you can do is to attempt to downplay the significance of these diagonal trends. Really? I've added our periodic trends graphic in case you've forgotten it. Sandbh (talk) 03:20, 13 February 2020 (UTC)

@Sandbh: Diagonal similarities are merely the result of downward and rightward trends approximately cancelling each other out. They don't play a major role for the placement of the periodic table because:

The elements involved in them do not have the same number of valence electrons, and therefore by Jensen's criteria cannot be placed in the same group. If you want to follow Mendeleev and look only at the effects (which was great for him, since he only knew about the effects, but surely we've progressed since then): they have different maximum oxidation states. Why are those suddenly not important here but very important for the 234 argument?
These diagonal trends are combinations of two different orthogonal trends. As such they are totally dependent on the rate at which each trend is running. In period 2 to 3 you get diagonals, sure. In 4d to 5d you mostly get straight lines downward because the Ln contraction has mostly destroyed the expected increase in atomic radius, and so charge/radius is unchanged going straight down instead. In the heavy elements we have a "knight's move relationship" because of the inert pair effect (e.g. Ag-Tl, Cd-Pb, In-Bi, Sn-Po), that you drew yourself in your article. Why is any of these more important than the others? They are all just local manifestations of periodicity. Not global ones.

P.S. Metallicity is not exactly diagonal, even. In periods 4 through 7 it seems to be running faster than the diagonal down by knight's moves. The last element with more metallish than nonmetallish properties in 4p is Ga; in 5p it's Sb; in 6p it's jumped all the way to At; and in 7p to Og. That's two elements at a time until we literally run into the right end of the PT. If you want to insist that Sb is not a true metal, then the jump from 5p to 6p becomes even more astonishing. The whole point is that the horizontal and vertical trends are running at different rates in the periodic table. Double sharp (talk) 14:16, 13 February 2020 (UTC)

@Double sharp: I look forward to your removal of our periodic trends image from Wikipedia since, as a generalisation it has no value according to you. And send a note to Rayner-Cahham debunking his comment that "Isodiagonality is, in some ways, a general attribute of the properties of the chemical elements." Oh, and write a note to Scerri asking him to withdraw Rayner-Canham's article from FoC because it was obviously written by a charlatan. Sandbh (talk) 05:12, 14 February 2020 (UTC)

@Sandbh: I never said that generalisations have no value. I only attack ill-defined generalisations like "predominantly covalent" or "predominantly ionic". If we were talking about electronegativity, then I would say "yes, definitely, that has value". While simultaneously noting that for the purposes of drawing the PT we need to go another level or two deeper, of course.

Yes, it's false that isodiagonality is a general attribute of chemical elements. It's blatantly obvious that the big relationship down from 4d to 5d is straight down, for instance. And that the big relationship in the heavy B-subgroup elements is the knight's move one (e.g. Ag⁺-Tl⁺, Cd²⁺-Pb²⁺, etc.). No, I don't need to send Rayner-Canham a note about it, because he clearly knows that himself: his Inorganic Chemist's Periodic Table only shows Li-Mg, Be-Al, and B-Si as important diagonal relationships. For the B-subgroup elements he, surprise, surprise, shows the knight's-move ones instead. Oh, and he puts Al in group 3 which he draws as Al-Sc-Y-Lu-Lr. And he's also clearly aware of many other important relationships (diagonals, knight's moves, isoelectronic series, A vs. B subgroups). And in that article he pragmatically notes that different ones are important in different parts of the table, writing about Tl: "As a final note, the bottom member of Group 13, thallium, has very different chemistry to either yttrium or indium. The chemistry of thallium is more appropriately linked to that of silver through the ‘knight’s move’ relationship". Is it not obvious that these are the secondary linkages and that the primary ones are the groups and periods, like the introduction on my first link to his table states? Why make a mountain out of a molehill and act like it's terribly important that the molehills are local? Double sharp (talk) 11:46, 14 February 2020 (UTC)

Double sharp works on his molehills of insignificance

Meanwhile ignoring the stampede of inconvenient contextuality and literature support

@Double sharp: I love your introduction of molehills! :)

I'm looking forward to adding a "periodic table of predominantly ionic and covalent chemistry", to our periodic table article, as this will be so easily supported by the literature.

@Sandbh: Which will not stop it from being nonsense, since you're not critically examining the literature. If we give the literature credit for not saying things that are completely nonsensical, there must be some sort of implied context that makes it make sense to talk about predominant ionicity and covalency of compounds, and that line will surely be different for a nuclear chemist worried about fluoride volatility and an organometallic chemist. Without that context, we'll quickly produce nonsense. And of course we'll notice some elements that look glaringly misplaced, but as long as they are not near group 3 I bet they will be ignored. Not to mention what happens when an element has two main oxidation states, both about as equally common, with different ionicities per Fajans' rules (e.g. manganese, uranium), but of course Sandbh will ignore one of them in this quest to turn a continuum into a sharp discontinuity at any cost. Double sharp (talk) 20:45, 15 February 2020 (UTC)

Let me now highlight some things you left out in your references to RC, among other things.

As RC said, "From the perspective of this series, however, the more important task is to define and clarify isodiagonality as one of the valid linkages among the chemical elements." As I wrote in my FoC article, "The power of boundary overlaps comes from recognizing the interesting chemistry that they flag rather than squabbling about where one class starts and another ends (Schultz 2010). They can be regarded as linch-pins, in addition to horizontal, diagonal, and vertical relationships, that hold together and affirm the facts and parts of the periodic table as a complex structure (Scerri 2012)." French (1937) felt that the diagonal linkages were so significant that he proposed slanting (‘‘warping’’) the periodic table. RC again, "Isodiagonality is, in some ways, a general attribute of the properties of the chemical elements." Your claim that, "Yes, it's false that isodiagonality is a general attribute of chemical elements" lacks any peer support. Of course, all these people are wrong. Really?
- You underlined the point yourself. Isodiagonality is one of the valid linkages. Depending on where you are it may be of very high relevance (e.g. Li-Mg) or of essentially no relevance at all (e.g. Sn-Bi). So it's clearly not a fundamental basis for the PT. As we expected, since it comes from a secondary mixing of horizontal and vertical trends. Double sharp (talk) 20:45, 15 February 2020 (UTC)

Consider the following: "Chemical similarities between the first-row elements and those diagonally to their lower right (e.g., Li-Mg, Be-Al, BSi) have been recognized since at least the 1860’s[!]. As an illustration of the anomalous chemical behavior of the first row elements relative to their heavier congeners, the "diagonal rule" is still included in the descriptive chemistry sections of many general and inorganic chemistry textbooks, and practical uses of the concept have been recently described. From here.

And it speaks volumes that the "diagonal rule" as presented is mostly used for the 2nd-3rd period linkages only. And it is hilarious that you don't quote the rest of the article, which notes correctly that this is simply a result of linkages in charge/radius (which is the parameter that I keep stressing per Fajans' rules), and that the conventional diagonal relationships are not the best possible matches. Indeed, he notes (and is not the only one) that Li-Ca often fits better than Li-Mg. And Mg-Y vs. Mg-Sc. And Sc-Th vs. Sc-Zr. In the first two cases we have a "knight's move" relationship instead and in the last case we even have a "camel's move" relationship in a La table and an incredibly long-striding leaper's move relationship in a Lu table. But you don't quote that, because as you write below when criticising me, "that would undermine your case". Double sharp (talk) 20:45, 15 February 2020 (UTC)

Since when did "the big relationship down from 4d to 5d being straight down" obliterate any prospect of a diagonal relationship? How about V-Mo-Re, as drawn, discussed, and cited by RC? A figment of his imagination?

Anyone can see that the Mo-Re relationship, while existing, is small potatoes compared to Mo-W. Whatever happened to your focus on predominant behaviour, once again? Double sharp (talk) 20:45, 15 February 2020 (UTC)

RC's PT dates from 2002; his subsequent article expanding on isodiagonality is 2011. But that would undermine your case.

Even after he expanded on it, going to cases where it is starting to be only just visible, it still doesn't even come close to dragging in the majority of the elements. Double sharp (talk) 20:45, 15 February 2020 (UTC)

Regarding "he puts Al in group 3 which he draws as Al-Sc-Y-Lu-Lr". How about mentioning the gap between Ba-Lu and Ra-Lr, and what that might mean?

Just that the lanthanides and actinides come between them, and chemically it makes some sense to put them partly as honorary congeners of Y (mostly for the lanthanides), but that he seems to think the linkage from Y to Lu is the primary one. Double sharp (talk) 20:45, 15 February 2020 (UTC)

Of course different relationships "are important in different parts of the table". What does that add? Like RC said, "From the perspective of this series, however, the more important task is to define and clarify isodiagonality as one of the valid linkages among the chemical elements."

Once again: one of the valid linkages. It's not extendable to the whole PT, therefore it's not fundamental for drawing it, just something we note as a cool partial trend after having drawn it. End of story. Double sharp (talk) 20:45, 15 February 2020 (UTC)

Good work on glossing over all these considerations. Sandbh (talk) 04:55, 15 February 2020 (UTC)

the 234 MOS pattern is no more than a neat coincidence (though DIM recognised the importance of MOS when he said "the forms of oxides [i.e. per MOS] and…atomic weights…give us the means to erect an unarbitrary system as complete as possible.")

DS: Never mind that Mendeleev never considered the regularity in the adjacent elements, and never mind that we now know more than he did about what was going on in the Ln, and never mind that he himself broke the MOS pattern when assigning Cu, Ag, and Au to group I. Double sharp (talk) 19:11, 12 February 2020 (UTC)

RV: Yes, here's a nice example of seeking to discredit the central message i.e. "…the means to erect an unarbitrary system as complete as possible." Fortunately, DIM recognised that he was looking for an unarbitrary system as complete as possible, rather than a completely unarbitrary system, and that he was able to exercise some pragmatism with his treatment of Cu, Ag, and Au. Sandbh (talk) 03:20, 13 February 2020 (UTC)

@Sandbh: So why can we not exercise some pragmatism with our treatment of La and Ac, noting that they obviously have low-lying f-subshells that can be involved chemically, and treat the accident of chemically irrelevant wrong DE's for them as just that: an accident? Double sharp (talk) 00:09, 14 February 2020 (UTC)

@Double sharp: I don't think it's that easy. You have to follow your core principles first i.e. periodic law, aufbau, d/e etc. Sandbh (talk) 04:50, 14 February 2020 (UTC)

@Sandbh: Well, I do: chemically active valence subshells. And they support Lu 100%. Those are a theoretical sound basis for periodicity (as it really is, not as you oversimplify it) and faithfully recreate the Aufbau motif all the way up to period 8 (and even then it still holds with very minor changes; the idea of "s, then g, then f, then d, then p" is still correct"). DE's are an oversimplification that we have progressed from.

BTW, since Mendeleev in your quote seems to be taking maximum oxidation states as a core principle, your logic of "you have to follow your core principles first" means that group IB becomes a problem. Which he did not sweep under the rug, preferring to locate them both in group VIII and group I. But you don't even acknowledge that Th is a problem for your overreliance on DE's, instead inconsistently hiding behind what really is symmetry but you don't admit is symmetry to avoid staggering the f-block. Never mind that such luminaries as Bohr and Goldschmidt entertained that as a possibility keeping in view what would then be future data on 5f occupation, of course. I stand by the words "double standard"! Double sharp (talk) 11:49, 14 February 2020 (UTC)

the properties of the individual elements are more important than those of their compounds (though this is contrary to DIM's view)

DS: The properties of compounds also completely support Lu under Y. Lu is a smaller ion and has better coordinating power than La. And I find it hilarious that this argument is coming from you, because if anything DE's are "properties of the individual elements" (sitting in the corner alone by themselves with nobody around), and chemically active valence subshells are "those of their compounds". Double sharp (talk) 19:11, 12 February 2020 (UTC)

RV: More evasion. I can't tell what you are getting at here. According to you, are the properties of the individual elements more important than those of their compounds? Remember all those physical properties you compiled? :) Sandbh (talk) 03:20, 13 February 2020 (UTC)

@Sandbh: No, they are all important. Firstly, on what planet is electronegativity, which I included, a physical property? I indeed said "And I'm even restricting myself mostly to physical properties, and already the difference is so big." And my next sentence was "With chemistry it is the same, as Lu is softer than La as a cation and coordinates better, making it a closer match for Hf through Hg." I would surely have included some more chemical properties, except that I was in a hurry and just stuck to something I could type up as data. For example consider hardness: Lu is obviously closer to the 5d metals than La, because Lu³⁺ is a smaller and hence softer cation. Or coordination ability: Lu is better than La and thus closer to the 5d metals, because Lu³⁺ is a smaller cation. Or basicity of aqueous cations: Lu is closer to the 5d metals because it is the weakest base among all the Ln cations (indeed it's barely amphoteric). And on and on it goes. Chemical properties totally support Lu under Y as well. On the Ac vs. Lr question they are even more decisive. Double sharp (talk) 14:24, 13 February 2020 (UTC)

@Double sharp: Before posting my prior edit, I looked at your table of properties and counted (as I recall) nine physical properties and one chemical property. That is what I meant by, "Remember all those physical properties you compiled?". I didn't take much notice of the following sentence since there was no hard data to back it up and it read like a case of assuming if A is true, then it must follows that B must be true, even though A <> B. You may be reading too much into my replies.

@Sandbh: The only reason "there was no hard data to back it up" is because we have to go qualitative there, because you can't exactly give a rating for coordination power. But come on, this is well-known stuff. Just see Greenwood and Earnshaw on coordination power of Sc vs. Y vs. La, you'll see that the important thing is atomic size. Naturally Lu is better than La because it's smaller. Double sharp (talk) 00:47, 16 February 2020 (UTC)

Now then. I suggest you've taken your eye off the main game. This is that, at least physically, La and Lu are both more like Ln than TM. For Lu I'm relying on the old saw that "Since metallic lutetium resembles closely erbium and holmium, except that it melts at a slightly higher temperature and is essentially non-magnetic, the details of producing, purifying and fabricating it are almost identical with those described under Holmium". Restrepo, writing over 40 years later, (noting the cloud he's under) likewise found Lu in an {Ho,Er,Lu} cluster, on stoichiometric/chemical compound terms. He must be doing at least something right. I note he was able to discern an {Eu,Yb} cluster even though, as you've noted, the difference in shading among the Ln is quite similar.

@Sandbh: The old saw continues to be completely irrelevant. Everyone knows that Lu is a physically and chemically normal late Ln. Just the same way that La is a physically and chemically normal early Ln. We're proposing to cut one off the Ln row to move to the d-block, so it's natural that you look at the other tenants of the d-block apartment complex to see similarity. Your "main game" is inconclusive, that's why we move down to the next most conclusive one when confirming our chemically-active-valence-subshells assignment. Double sharp (talk) 00:47, 16 February 2020 (UTC)

@Double sharp: Of course the old saw is irrelevant yet all of sudden in this passage, the physical properties are important:

@Sandbh: Yes, you did, leaving aside whether it is relevant. (I insist that EN is more relevant, as Wulfsberg uses, and then group 4 predominately patterns with group 3 because of Zr, Hf, and Rf.) But if you were being consistent, you would also notice that groups 1-5 are all predominantly pre-transition in chemical behaviour. And you would notice that group 1-2 have predominantly pre-transition physical properties, whereas Sc and Y, like groups 4 and 5, have predominantly transition physical properties, and therefore Sc-Y-Lu is physically preferred. So if you were being consistent, instead of dismissing commonalities that support Lu as "fogging and selectivity", you would come to the conclusion that actually commonalities do not make group 3 throw more strongly to group 2 than group 4; they are intermediate. Double sharp (talk) 11:56, 14 February 2020 (UTC)

Sandbh (talk) 04:47, 17 February 2020 (UTC)

@Sandbh: You're not understanding what I'm saying. Here I'm talking about the physical properties being close to TM. The fact that La and Lu both are normal-ish lanthanides is irrelevant because it is totally inconclusive: the f-block at face value looks physically and chemically about the same either way. What is important is that Lu has physical properties closer to TM, and that's what I'm talking about here: pre-transition vs transition physical properties. Double sharp (talk) 14:14, 17 February 2020 (UTC)

The question then becomes, which of these two Ln best fit under Y? My considerations are:

ʀ = regularity-based argument

La under Y is closer to the n+l rule. ʀ
- So what is the n+l rule according to you? If it's "subshells fill in order of increasing n+l, and within a series of identical n+l, in order of increasing n", then this is wrong! Lu under Y is closer. Double sharp (talk) 21:06, 15 February 2020 (UTC)

@Double sharp: Really? As you know, and you know I know, the n+l rule is an idealisation of the actual aufbau sequence. The La form is closer to this idealisation (more regular).

@Sandbh: If we are talking "idealisations", why is the delay of the 4f differentiating electron so important that it must go into the idealisation? According to everyone who ever drew the Madelung rule diagram it just goes 6s, 4f, 5d, 6p here. No special hanging up of one 5d electron for La. In fact many even contradict themselves by drawing La under Y and then giving the Lu-supporting normal n+l rule. Double sharp (talk) 10:00, 16 February 2020 (UTC)

@Double sharp: Well, the n+l rule is the idealization. The aufbau pattern is what happens in real life. Yes, many do contradict themselves. Parroting + publish or perish + no real appreciation of what they are talking about. So much needless confusion for students. Sandbh (talk) 01:00, 17 February 2020 (UTC)

@Sandbh: Then why do you refer to the n+l principle below? There will also be much less needless confusion if we go to the Lu table, coupled with a chemically accurate pure n+l rule rather than the unsupported idea that one 5d electron hangs up first. Double sharp (talk) 14:27, 17 February 2020 (UTC)

La under Y upholds the n+l principle that a block starts with the appearance of the first of applicable electron. ʀ
- That's not the n+l principle. Instead it's a principle that seems to be only applied by you. Not only is the end of the block not considered (which is where La under Y fails very badly), but luminaries such as Bohr and Goldschmidt considering the start of the 5f series did not accept this principle. And when Seaborg finally argued for the 4f and 5f rows to start together, it was because of chemistry, nothing to do with DE's. Of course it wasn't, since Th has the wrong DE. Double sharp (talk) 21:06, 15 February 2020 (UTC)

@Double sharp: Really. I seek to match the n+l rule, as closely as possible with respect to when a new block starts, as per the n+l rule. Well, no doubt you have a better rule. Sandbh (talk) 06:55, 16 February 2020 (UTC)

@Sandbh: Can you show me anyone at all in the literature who makes an exception in the n+l rule to let one 5d electron hang up first? Mostly this rule is just used to predict the right configuration anyway, not the right DE. And surprise, surprise, a Lu table with its implied n+l rule shows less anomalies there than a La one! Double sharp (talk) 10:00, 16 February 2020 (UTC)

@Double sharp: I've seen references in the literature to the n+l rule and, by comparison, the anomalies seen in the aufbau process/pattern, and I think I've seen augmented n+l rules tables, but I don't have them at hand. Yes, agree about d/e and right configuration. Really? An La table has one less d/e anomaly and one less n+l anomaly (obviously) than an Lu table. Could you recheck your assertion? That seems odd. Sandbh (talk) 01:10, 17 February 2020 (UTC)

@Sandbh: I said mostly this rule is just used to predict the right configuration anyway, not the right DE. Mostly, a configuration like Mo [Kr]4d⁵5s¹ is considered to be anomalous even though it has the right 4d differentiating electron Nb, because filling 42 electrons according to the idealised n+l order suggests [Kr]4d⁴5s². By that metric, which is what most people talking about anomalous configurations are actually mentioning, a Lu table is obviously less anomalous than a La one because the Ln and An are predominantly fⁿs², not f^n-1ds². Double sharp (talk) 14:27, 17 February 2020 (UTC)

La under Y preserves the real meaning of the term lanthanide, where La was the prototype Ln, and Ce to Lu were the Ln proper.
- That's just semantics. If Lu had been discovered earlier it would have been the prototype Ln instead. Double sharp (talk) 21:06, 15 February 2020 (UTC)

@Double sharp: Of course, it being the most dense of the Ln, having the highest atomic weight, and being the least basic. Brilliant! Sandbh (talk) 06:55, 16 February 2020 (UTC)

@Sandbh: La is similarly extreme in the other direction. BTW, this sounds a lot like saying that Lu is the least representative Ln, which should consistently lead to the conclusion that it is the one you should take out and put under Y. ;) Double sharp (talk) 10:00, 16 February 2020 (UTC)

La under Y is congruent with the f-block running from Ce to Lu. ʀ
- And why do you think the f-block starts at Ce? Because that's where the first 4f electron comes in? Not only is that awkward for Th, but by the time you get to Lu the 4f shell is a core subshell. So I say: the f-block clearly can't end at Lu (it must end earlier), and DE's can't be what defines where the f-block starts (or else Th is in trouble if we treat it fairly, like Bohr and Goldschmidt did, though you refuse to do it). An f-block running from La through Yb is much more congruent with chemistry, but that occurs in a Lu table. Double sharp (talk) 21:06, 15 February 2020 (UTC)

@Double sharp: Noting you like to discount the relevance of gas phase configurations I have to laugh at your continuing focus on Th, and it's indisputable f character. LOL! An La-Yb f-block is more congruent with chemistry. Woe is poor Lu, and its status as a lanthanide, banished to the d-block. 06:55, 16 February 2020 (UTC)

@Sandbh: Yes, I don't believe gas phase configurations have real relevance. But you do, which is why I keep dragging out that of Th to show how you are using a double standard on it. And you seem to agree just above that Lu is a worse prototype for the Ln than La. So who should we banish to the d-block? Clearly Lu if you were being consistent. Double sharp (talk) 10:00, 16 February 2020 (UTC)

Lu has more TM character than La, but is still an Ln: that is the primary consideration.
- So is La. Therefore, since you have to fish one out to put with the TM's, it should be the one more like a TM, i.e. Lu. Double sharp (talk) 21:06, 15 February 2020 (UTC)

@Double sharp: The main consideration is that Lu is more of an Ln than a TM. There are more issues to consider than your response. Sandbh (talk) 06:55, 16 February 2020 (UTC)

@Sandbh: But that is even more true for La. Double sharp (talk) 10:00, 16 February 2020 (UTC)

The PT is primarily concerned with the elements as basic substances (P as Z = 15), and secondly as simple substances (P as black, red or white etc). That was the case in DIM's day; it's still the case today. The numerous TM-like physical properties of Lu are of secondary importance, compared to the regularity of the aufbau process. ʀ

- Which is even more regular when considering chemically active valence subshells (which are actually relevant and present with the elements as basic substances, because they consider all chemically relevant configurations). Then Lu is totally recommended, because not only does it have numerous TM-like physical properties, but its chemistry is much more like a TM than La. Double sharp (talk) 21:06, 15 February 2020 (UTC)

@Double sharp: Tricky. More to follow.

@Sandbh: Need I add that treating simple substances as secondary suddenly makes the case for He in group 2 stronger? ;) Double sharp (talk) 10:00, 16 February 2020 (UTC)

@Double sharp: Yep, fine by me. Helium has never been my focus. Sandbh (talk) 04:51, 17 February 2020 (UTC)

The chemistry of group 3 is atypical for a transition metal group or could be described as marginally TM-like. Since La is not as close to the TM as Lu, La fits better into group 3.
- The chemistry of group 4 and 5 is almost equally atypical. Double sharp (talk) 21:06, 15 February 2020 (UTC)

With the TM character of Lu being greater than that of La, Lu fits naturally into the position after Yb, as a linking or bridging element. Here, Lu stands out as representing the culmination of the direct impact of the f-block contraction. The contraction is seen thereafter as a knock-on consequence of the progressive filling of the 4f sub-shell, from Ce to Lu.
- By the time of Lu the 4f shell is a core subshell, so this is nonsensical. If La is a worse TM than Lu, why do you insist that it be the one placed with the TMs? Far better to treat La as the bridging element starting the f-block with rather s-like character (as is normal at the borderlines of blocks), whereas Lu continues the character of a borderline d-element like Sc or Y better. Double sharp (talk) 21:06, 15 February 2020 (UTC)

The previously noted observation that, while trends going down group 3 as La or as Lu are inconclusive by themselves, the chemical behaviour of groups 1 to 3 is largely ionic, whereas that of groups 4-5 is largely i.e. at the highest level of generalisation, covalent. This lends support to La in group 3, since the trends going down the group are then similar to those going down groups 1 to 2, whereas this is not the case for Lu in group 3.
- You know, this argument doesn't stop being nonsense no matter how many times you repeat it. And even if it did somehow stop being nonsense, there are equally many ways in which group 3 rather resembles 4 and 5 if you consider properties, e.g. coordination chemistry, physical properties, lack of generally "true TM" character. It's really intermediate, as everyone could have guessed, but you are too focused on making everything discontinuous. Double sharp (talk) 21:06, 15 February 2020 (UTC)

In Group 3, Y and La show the differences in their chemistry which would be anticipated from the difference in ionic radii, ionisation energies etc.
- Only if you prioritise the s-block above all others. Literally everywhere else in the periodic table, you would expect an attenuated differences because this is an even period. But no, Sandbh insists that group 3 must somehow follow the s-block. Double sharp (talk) 21:06, 15 February 2020 (UTC)

Nature sees fit to delay the start of filling of the 4f shell until Ce. La under Y better reflects this situation.
- But that's not the situation. 4f is active in La. I know your quote from Parish, but I should like to see how he or anyone would like to explain cubic complexes without 4f orbitals active. Nature also sees fit to put the first 5f electron in the ground state of Pa (gas-phase), but we're still waiting for you to admit your double standard on that. Double sharp (talk) 21:06, 15 February 2020 (UTC)

@Double sharp: There are no f electrons in La, either in the gas phase or the condensed phase. Sandbh (talk) 06:55, 16 February 2020 (UTC)

@Sandbh: But there are low-lying excited states of La with 4f occupancy. With chemical repercussions, e.g. cubic complexes (I should like to see how Parish deals with that). That's the important thing. Double sharp (talk) 10:00, 16 February 2020 (UTC)

The 5d metals become less homogenous with La under Y. Rather than losing any sleep about this, we know that this is due to the inter-positioning of the Ln between La and Hf, in accordance with the aufbau process.
- Here we go round the circle again. Look, if you insist that La goes under Y, you can certainly explain the cleft between groups 3 and 4 this way. Indeed, if you think the f-block only starts at Ce, then it makes perfect sense that La isn't affected by contractions but Hf through Hg are. The only problem is that chemistry and physics says that f-block already starts at La, DE's aside, because of cubic La complexes and everything Gschneidner noticed. Double sharp (talk) 21:06, 15 February 2020 (UTC)
There is a possibility of some marginal 4f involvement in La; however this is dwarfed by the impact of the 14 f electrons in Lu³⁺, a phenomenon not possible in La³⁺. Of course this impact is seen in Hf onwards, however Hf belongs to the transition metals, rather than the Ln, and there is no Hf⁺⁴ cation.
- HfO₂ is mostly ionic, so there goes your last claim. And as usual, the whole point of speaking of f-involvement is that it be valence f-involvement. Otherwise Hf through Rn are all f-elements too by consistency. Double sharp (talk) 21:06, 15 February 2020 (UTC)
Whatever loss of homogeneity is seen in the d-bock as a result of placing La under Y rather than an Lu is insignificant compared to the heterogenous range of properties already seen in the d-block, and of a second order nature compared to higher considerations such as the aufbau process, and the n+l rule. ʀ
- Aufbau process and n+l rule according to everyone but you support Lu. And the d-block is indeed not so homogeneous, but adding La to it makes it always the extreme case of chemical strength and reactivity. Double sharp (talk) 21:06, 15 February 2020 (UTC)
La introduces a new isodiagonal relationship; Lu does not.
- Groundless, given the general irrelevance of isodiagonality outside its favourite haunt of the 2nd and 3rd periods. Double sharp (talk) 21:06, 15 February 2020 (UTC)
La maintains s series of horizontal +2 +3 +4 triads up to at least Z = 100; Lu does not. ʀ
- Long since debunked as irrelevant, but still trotted out. Double sharp (talk) 21:06, 15 February 2020 (UTC)
In an La table, the element n in the 4f series, in its most common +3 oxidation state, has n f electrons.
- Ah, finally we get to a halfway decent argument. Except that such a consideration doesn't work for the s, p, and d blocks, so it can't be the deciding factor for the f-block. Double sharp (talk) 21:06, 15 February 2020 (UTC)
Placing La and Ac in the f-block would be only case where a pair of elements that belong in the same column are placed such that they have no outer electrons in common with that block. ʀ
- Placing Lu and Lr in the f-block makes them the only elements for which the characteristic electron shell (that matches the block name) is a core subshell. Even the noble gases slowly become chemically active and their reluctance towards chemistry comes directly from the composition of those characteristic valence subshells (which are full already). Double sharp (talk) 21:06, 15 February 2020 (UTC)
Spectroscopically, an Sc-Y-La-Ac table has one fewer term symbol discrepancy than is the case with an Sc-Y-Lu-Lr table. ʀ
- This is just ground-state electron configurations all over again. Which means that it basically locks Lu and Lr out of the d-block and into the f-block on the grounds that Lr has a p electron due to relativity(!), which is hilariously irrelevant since p is neither d nor f, and best of all, that weird configuration seems to not affect Lr chemistry in the only common state of +3 at all! Double sharp (talk) 21:06, 15 February 2020 (UTC)

I'm not aware of any comparable regularity-based Lu arguments. Double sharp, could you please pick me up on this if you know of any comparable regularity-based arguments in favour of Lu.

Sandbh (talk) 03:58, 15 February 2020 (UTC)

Madelung according to everybody, a regular d-block (not interrupted halfway), and the fact that a La-Ac table makes Lu-Lr the only pair of elements in a block who don't actually have their characteristic electrons as valence electrons. Double sharp (talk) 21:06, 15 February 2020 (UTC)

the block starting rule does not apply to Th (though we did not extend the rule past the first occurrence of the applicable electron).

DS: That's a mistake in hindsight. Saying "Ce satisfied the f-block criterion, therefore we don't need to make a fuss that Th and E122 don't" is as much a mistake as saying "the blocks start "on time" according to the simple Madelung rule for s, p, and d in the ground state gas-phase configurations, so we don't need to make a fuss that the f and g-blocks do not". Both are assuming regularity/symmetry/whatever you want to call it when it must be proven! You have only two logically consistent options in both cases: (1) argue that the criterion is flawed, or (2) agree with the criterion and adjust the table accordingly. You don't get to listen to it when you like it and say that it trumps symmetry then, and then ignore it when you don't like it and say that symmetry trumps it then. Double sharp (talk) 19:11, 12 February 2020 (UTC)

RV: More fogging. The rule stands as it is, well enough. It has nothing to do with symmetry. Why is there a need to extend it? Sandbh (talk) 03:20, 13 February 2020 (UTC)

@Sandbh: It has everything to do with symmetry. You've taken something (Ce with its 4f electron in the ground state) and used it to immediately declare that others must follow (Th and E122). How is that not implicit use of symmetry to argue that a block must begin in a vertical column rather than staggered like Prof Poliakoff who you quote suggested could happen? Or many pioneers such as Goldschmidt considering the start of the 5f series considered? Double sharp (talk) 14:26, 13 February 2020 (UTC)

@Sandbh: I use the periodic law and the aufbau process. I don't prejudge the outcome of these as to their symmetry or asymmetry. Sandbh (talk) 05:17, 14 February 2020 (UTC)

@Sandbh: Insisting that Th is an f-block element just because Ce is is prejudging the outcome based on symmetry. Double sharp (talk) 11:57, 14 February 2020 (UTC)

@Double sharp: Broken record time: I use the periodic law and the aufbau process…I use the periodic law and the aufbau process…I use the periodic law and the aufbau process…Regularity is not symmetry…Regularity is not symmetry…Regularity is not symmetry…etc. Sandbh (talk) 03:55, 17 February 2020 (UTC)

@Sandbh: No, you don't use the periodic law, just your own misunderstanding of it. You selectively use evidence that appears to support a spurious "one 5d, all 4f, then nine 5d" Aufbau process, then blithely ignore how the same evidence supports an even more spurious "two 6d, all 5f, then eight 6d" process in the next row. And regularity is absolutely a case of symmetry, no matter how many times you deny it. An arrangement with more regularity is more symmetrical and vice versa. Double sharp (talk) 14:27, 17 February 2020 (UTC)

@Sandbh: To quote Seaborg again: after he discusses places where chemists thought the first 5f electron might appear, he states

“

Some spatial classifications of the elements appeared in which the heaviest elements, starting with thorium as the homolog of cerium, are listed as the chemical homologs of the rare-earth elements, but the reason in these cases appears to be mainly connected with the symmetry of and the ease of making such an arrangement.

”

Yup, Seaborg said it first, not I. If your criterion is "where does the first 5f electron appear", then the 5f block has to begin at Pa according to modern knowledge. This seems to have been the criterion used by pioneers such as Bohr, Goldschmidt, and many others. They were being consistent: if you think ground-state electron configurations (which I surmise was what was being looked at) are the fundamental thing, then you must be consistent between how you treat 4f and 5f. If 5f happens to start late, your hand would be forced to begin the 5f series late. If you don't do it, you are appealing to symmetry. Seaborg said it, not I. And that's exactly a double standard: you refuse to allow symmetry for La and Ac, but you appeal to it non-stop for Th and Lr.

Seaborg insightfully realised that there are more important considerations than differentiating electrons. You have to consider where the "half-filled" and "fully-filled" subshells are supposed to be, among other things, and the chemistry must match that prediction. So he correctly noted that the fact that Th had no 5f electrons was no obstacle to starting an actinide series at Ac, but he did it not because of inconsistent special pleading using arguments that you reject when I apply them to La, but on chemical grounds. A thoride series makes predictions that simply do not gel with the chemistry we observe because of where it should start and end. From Am onwards the actinides become better homologues of actinium and the rare earths above them, suggesting that both series match in terms of where 4f filling has started and where the double periodicity ends up. This is an excellent insight that shows that chemistry trumps differentiating electrons. And notice that, although some earlier authors placed Th under Ce, something he agreed with and supported, he does not treat them as pioneering forerunners who got it right even though they agreed with him, because they did not do it for a good reason. This is how science looks like. You must put your theory to the test against the facts. And you cannot willy-nilly grab lots of bad arguments just because they support your theory. And you must be consistent about how you treat your theory vs. other people's theories. But you're not doing any of that. Double sharp (talk) 18:57, 13 February 2020 (UTC)

@Double sharp: 10/10 for fogging and taking things out of context, once again. I don't give a damn about symmetry. Nope, 5f is irrelevant. A block starts when the first applicable electron appears. After that we apply the periodic law and the real aufbau context. Do you think Seaborg would be so stupid to criticise articles based on symmetry and then give his own examples of La tables? How about adding Seaborg's context: "Cjounkovsky and Kavos (1944): Talpain (1945)", and checking those articles first, before posting? Both articles are based on symmetry first. The second starts with the n+l rule as it was real! Hilarious! No wonder Seaborg criticised them. The spin you put on Seaborg's words without checking what he really said, and the context he said it in, is remarkable. Look at figure 5, the modern periodic table. The Ln are Ce to Lu. The An are Th to Lr. How about cutting out that table and keeping it with you as a permanent reminder? Look at Seaborg's futuristic table. Golly. That's also an La table! How far sighted was Seaborg? Sandbh (talk) 11:17, 14 February 2020 (UTC)

@Sandbh: 11/10 for not reading what I'm writing and contradicting yourself, as usual.

"I don't give a damn about symmetry. Nope, 5f is irrelevant" – there's a contradiction right there. You say 5f is irrelevant because 4f already decreed that the f-block starts at Ce, therefore the next row must start at Th. Except that, surprise, surprise, that is symmetry.

"Do you think Seaborg would be so stupid to criticise articles based on symmetry and then give his own examples of La tables?" No, he's not so stupid. As I wrote myself: "notice that, although some earlier authors placed Th under Ce, something he agreed with and supported, he does not treat them as pioneering forerunners who got it right even though they agreed with him, because they did not do it for a good reason. This is how science looks like." It's not enough to get something right, you also have to get it right for the right reason, and Seaborg understood this. His La tables are based on other considerations than symmetry. And it's perfectly reasonable that they're La tables given the era, as if you look at some of them you will notice that the old idea that the f-block is a degenerate branch of the d-block had not yet died out (as all 15 Ln appear under Y with La selected as the prototype). Now that that idea is dead, we may progress even further. Seaborg was progress over past thinkers, but he's not the final word on the PT. As is obvious if you look at later predictions of the chemistry of eighth-period elements which is totally inconsistent with Seaborg's pure-Aufbau table. (Nonetheless, looking at chemically active valence subshells still works perfectly all the way up to E172. ^_^) Double sharp (talk) 11:46, 14 February 2020 (UTC)

Sorry to interject, but one particular sentence caught my eye here. "A block starts when the first applicable electron appears." If we want to escape Double sharp's pretension on that all arguments should not be viewed from one angle only (which I support, I find that important as well), we would have to think when a block ends, since the end is no less important than the beginning, and it seems that under identical assumptions that the proper place according to this logic would be ytterbium, Yb = 6s² 4f¹⁴. This gives us a 13-element block, which hints that the original statement should not be quite that categorical.

So if I were the IUPAC you submitted this paper to and I were to read it, I would dismiss this statement on this ground. You asked above for cases of what could be viewed as asymmetrical treatment in your thinking, and this is one illustrative example.--R8R (talk) 11:59, 14 February 2020 (UTC)

@R8R: Thank you for phrasing this so clearly. ^_^

@Sandbh: As I was getting at in Archive 40: "But if the cost is that a block then has to extend to the point where its characteristic electrons are core electrons, then I'd rather have weakly involved excited states at the start instead." I put it to you that the end of a block is just as important to its start, and it is totally nonsensical to have supposed "f-block elements" for which the f-electrons are core electrons like Lu and Lr. Anyone can see that this is far worse than having an anomalous ground-state configuration for La and Ac (not that this was a big problem in the first place, cf. passim on Th and Lr), because it flies in the face about what a block is supposed to represent. Double sharp (talk) 13:31, 14 February 2020 (UTC)

@R8R:@Double sharp: With great respect, I feel I must be onto something when you need to take this—a 13 element wide f block—line. That is what I call "the sky will fall down" or "catastrophizing"—thinking about the worst thing that could happen when it never will. I note the approved within IUPAC table features a 15-element wide f-block. Does anybody object? A few do but that is based on a misunderstanding, as set out in my draft.

@Sandbh: I absolutely object to a 15-element-wide f-block, as it includes Lu and Lr with core-like f-electrons. Double sharp (talk) 14:27, 17 February 2020 (UTC)

@Double sharp: Well, count your self as one of the few who lose sleep about it. It doesn't seem to matter to anyone within IUPAC. It's just more of a chemical table, focussing on the chemistry of the Ln. And, it's nonsense to call it an f-block; it has notionally 14-block elements and one one d-block element. That said, it still causes confusion, given the lack of IUPAC guidance. There's no excuse for that. Sandbh (talk) 02:22, 18 February 2020 (UTC)

Symmetry or asymmetry does not concern me. I go where Nature leads me.

@Sandbh: It suddenly concerns you the moment you relabel it as regularity. Double sharp (talk) 14:27, 17 February 2020 (UTC)

The line about "to the point where its characteristic electrons are core electrons" reminds me of group 12. Therefore we need to start the d-block in group 2! IUPAC will throw that one out.

@Sandbh: Nonsense. The d-electrons in group 12 are not core electrons; there is effective overlap of 3d orbitals into the bond in compounds like ZnCl₂ (just confirm interatomic distances). That doesn't exist for 4f in Lu or 5f in Lr. Double sharp (talk) 14:27, 17 February 2020 (UTC)

The end of a block is relevant, I agree. Historically, it was thought that Ce was f1, that Yb was f13 and that Lu was f14. Recall that, historically, La was followed by the lanthanides, Ce to Lu, and that the occurence of the Ln was attributed to an "interruption" caused by the filling of the inner 4f sub-shell. They were called Ln in reference to their similarity to La; the latter was not a Ln per se, only the prototype.

It was subsequently discovered that the 4f sub-shell became full at Yb, and that Lu was 4f14 5d1. What happened? Was there panic at the prospect of a 13-element wide f-block? No. The discovery made zero difference to the chemistry involved. So La stayed where it was under Y and Lu stayed where it was at the end of the f-block, and everyone realised that this was simply the result of an accelerated filling of the 4f sub-shell.

History and its (staggering) momentum, supports La in group 3, in the particular context of this entire thread. Sandbh (talk) 00:37, 17 February 2020 (UTC)

@Sandbh: It also supported Be and Mg in group 12 within living memory (if rather old living memory). We may obviously progress from history, no matter how much momentum it has, or we would all still be using an 8-column table. Double sharp (talk) 14:27, 17 February 2020 (UTC)

@Sandbh: I’d like to respond to your response in once piece if that okay with you.

First of all, the IUPAC table does not have a 15-element f-block. In fact, it does not have blocks at all. And if we were to overlay the concept of blocks onto their table, I can’t see why there wouldn’t be a 14-element block, with the last lanthanide and actinide (whether La and Ac or Lu and Lr) being in d-block. Regardless, it doesn’t have any blocks whatsoever.

There is an important line in your response that I don’t quite understand, and a lot depends on what exactly you meant there. What did you mean when when you said, “Symmetry or asymmetry does not concern me. I go where Nature leads me“? I can read this in two manners.

First, you may have said that you don’t care about having a symmetric periodic table, whether symmetry is -La-Ac or -Lu-Lr. If that was what you meant, then more power to you. However, I’m afraid that it may not have been your intention to say so, as I was not arguing for a nicer representation.

Second, you may have said that you don’t care about the symmetry of argument itself, and I believe that invalidates any argument. Even if you arrive to a right conclusion, you must still do it in a manner that does not display obvious fallacies of thought for it to really count. If you apply an argument to one option, and it seems to support the option, you still need to check the other to say the support is in favor on the former as opposed to the other; if you do not comment on the other option, the argument is inconclusive.

I don’t believe that I’m saying something you couldn’t have said yourself but I am rather sorry to arrive at the thought that this may be the case. To clear things up, let me rephrase one question I asked above that I still haven’t had an answer to: what is the exact argument or set of arguments that collectively, when applied equally to both, overall supports the stretchable Sc-Y-La-...-Lu line while, all things considered, dismissing the notion of the contiguous blocks?

The phrase “where Nature leads me“ is equally confusing. Strictly speaking, it doesn’t lead you anywhere; it’s up for you to go one way or another. People tend to vary in interpretation of things, and that’s why you need a solid basis of thinking that accounts for various biases. Without a doubt, you have one, as do I, or Double sharp, or anybody else. What I’d like to hear is that you share this line of thought and could say how it is reflected in your argument and if it perhaps needs a tweak.

I also note that this argument (“we learned about electronic configurations; nothing has changed”) does not agree with your argument according to which -Lu-Lr is worse because it adds one more discrepancy with its 7p electron to the existing handful. So what if nothing has changed?

The momentum of history, as you described it, is also highly confusing at best and flawed as it occurs to me. So there was a historical argument that supported -La-Ac, it was later disproved, but still there were others reasons to keep it (“nothing changed”): so why bother recalling the disproved argument and saying it’s okay it’s gone because there are also other arguments? How much is the original argument worth then if it’s really the other arguments that matter? And if it’s the other arguments that really matter, what does history have to do with it? Arguments exists regardless of history. I think that popular usage is a valid argument, and that physical/chemical arguments matter is also a question that merits a discussion, but these are separate arguments and they should be treated as such, not conflated.

As for the symmetry of the argument in this case, consider the following situation. If chemistry involved does not change as we learn more about electronic configurations, then had it been known all along that the electron configurations really are and the decision had been made on that basic that we should go with -Lu-Lr, could we keep it? Nothing has changed. What kind of response would you give? Would you stick to -Lu-Lr or would properties, according to your argument, still favor -La-Ac? The former would show your preference to history, the latter to properties, and the dichotomy itself shows that the two, again, should not be conflated. I really do think you need to consider that, because your arguments may appear deficient in a sense of such considerations, but if those considerations are made, your argument will only be improved, something this discussion is in dire need of. Better arguments lead to better discussions, and that this discussion doesn’t represent an example of such a discussion is best illustrated by your scoreboard exchange with Double sharp (although there are many more examples).

On a related note, there’s a proverb that says, “The truth is born in argument”. Do you think that you and Double sharp are having that kind of discussion?—R8R (talk) 16:53, 18 February 2020 (UTC)

@R8R and Sandbh: Well, I admit that I have played some role in increasing the resemblance of this to a flame war with the rhetorical scorecards and bolding (thankfully not ALL CAPS ^_^ yet). But I feel like I have found legitimate inconsistencies and mistakes in Sandbh's logic that are being skated over. I do think that the argument has sharpened my approach and made it come some way closer to the truth (e.g. what's going on with the s-block). However I don't see Sandbh making any substantative changes in logic even when the flaws are pointed out: the only thing I see, at most, is a statement to the effect that the exposition needs to be improved (for things like the Sc-Y-La-...-Lu trend argument that you and I have both found wanting). Double sharp (talk) 20:27, 18 February 2020 (UTC)

P.S. I think R8R's argument in his second-last paragraph is right on the mark. As is my continued pointing out that if we were having this argument in the early part of last century, the crushing weight of history would be for Be-Mg-Zn. Double sharp (talk) 20:28, 18 February 2020 (UTC)

As I understand it, it is more important for you that Lu resembles the properties of the rest of the 5d series better than is the case for La, notwithstanding the occurrence of the other thirteen lanthanides between La and Lu. Since Lu is a better 5d metal than La, it follows that Lu should go under Y. This will make the d block as homogenous as possible.

I've said that an La table is more homogenous in terms of differentiating electrons. It’s therefore important for you to discount the relevance of differentiating electrons. You’ve questioned why d/e homogeneity is important for me whereas when it comes to the homogeneity of the d-block and the individual properties of Lu being a better 5d metal than La, this does not seem as important to me.

Is that a fair summary of the situation? Sandbh (talk) 03:25, 12 February 2020 (UTC)

@Sandbh: You mistake my motive. The reason why I discount the relevance of DE's is not because they happen to support the La table. That's not how science works. I did not start with my conclusion and hunt for arguments to support them. I discount them because I prioritise chemistry and ground-state gas-phase configurations, that your DE's depend on, are irrelevant there. Chemically bound atoms generally do not show the configurations they show when in the gas phase by themselves! Chemically active valence subshells are obviously (cf. the literature I quoted + common sense) the important thing here, since there are lots of relevant configurations (with fine structure splitting) and the fact that among many relevant configurations one of them happens to be the gas-phase ground state is more or less just an accident given how close they are.

My starting point is that chemically active valence subshells, being the main motor behind the chemistry we see, should be given first priority as a basis for the PT as it is the most fundamental cause we can get to for periodicity. Only once we have decided, ideally impartially based on predictive power and fundamentalness, on our criterion, do we look at whether it supports La or Lu. In this case, the answer is clearly Lu.

Then we go back and confirm that the resulting trends make sense, because I chose the criterion on the basis of how well it explains the regular periodicity of the elements. (Which is regular precisely because of its high degree of symmetry.) That's why I look at the trends in groups and periods. Then we find:

Taken completely by themselves, Sc-Y-La and Sc-Y-Lu both make reasonable-looking trends. However, the situation in the s-block with a "preemptive" filling of the s-orbital is unique, and we are clearly not in it in group 3. Group 3 is clearly a d-block group with an energy level structure similar to that of groups 4 through 12: (n-1)d, ns, and np at similar energy levels. It has the characteristic physical properties of the early transition metals, and if its chemical credentials as TMs are weak, then so are those of Zr/Hf/Rf, Nb/Ta/Db, Sg, and Bh. The break happens later and later each period, so there's no fuss there since peripheral groups often show a smooth transition to the next block (just like group 12 showing quite p-block-like properties, but that doesn't stop it from being a d-block group). So Lu is preferred.
Then we consider the trend across the period, and indeed, the 5d row is much more regular with Lu in it than with La in it, all fogging about papers giving chemically ridiculous classifications (e.g. La more similar to Au and Hg than the Ln, are you kidding me?) aside.

Then we rest our case. But, and I cannot stress this enough, this second bit is confirmatory. We don't start by looking at trends anymore now that we know what causes them. We go to the root cause and use that as a fundamental principle. We just check the trends that it produces because that will give a further confirmatory check. If the trends are what we think they should be, well and good. If an unusual one comes out, then either (1) we can learn from it, or (2) perhaps our fundamental idea was not so fundamental, and back to the drawing board we go. With He over Be I think we have the first case, given important considerations for atomic properties. Double sharp (talk) 19:11, 12 February 2020 (UTC)

@Double sharp: Good. I acknowledge your motive.

Before proceeding I'd like to check what you mean by saying, "My starting point is that chemically active valence sub-shells, being the main motor behind the chemistry we see, should be given first priority as a basis for the PT as it is the most fundamental cause we can get to for periodicity."

That looks circular to me. We look at the chemistry and that informs us of the chemically active valence sub-shells. That is all. Thus, the chemically active sub-shells inform the chemistry which is informed by the chemically active sub-shells…etc. You're confusing a phenomenon with a cause. It's the same as saying the chemically active valence sub-shells in the group 1 metals are the s sub-shells. That doesn't say anything about the cause. If anything the cause is an outcome of the aufbau process.

@Sandbh: There is nothing circular about it. The phenomenon is the facts of chemistry and the cause is which subshells are active and their occupancy. We can get that just by looking at excited-state and chemically bound electron configurations up to the range of chemical bonding (so within 10 eV; in most cases, like 4f in La, you don't even have to go anywhere near that high). And of course they inform the chemistry because that's where the valence electrons and vacancies come from. Take Zn for example. The facts of chemistry is what Mendeleev could see about Zn: that it was a divalent metal, similar to Mg in chemistry, blah blah blah. Looking at its configurations and how 3d contributes to the bonding is not the phenomenon, it's the cause for the phenomenon. Double sharp (talk) 14:32, 13 February 2020 (UTC)

@Double sharp: It seems to me that the chemically active sub-shell influences chemistry, but is not the fundamental cause. This is governed instead by the aufbau process, which maps which electrons build up each atom. Once the electrons are settled into their atoms, they can have a second order fight as to which of their sub-shells will be chemically active, having regard to the stability of filled and unfilled shells, inter-electronic repulsions etc, and whether any empty shells are within the energy range (up to 10 eV) of mundane chemical reactions. Now, the aufbau process is not a fundamental cause either, since it has no first principles derivation. I guess the aufbau process is more of a top down external view whereas the chemically active sub-shell is more of an internal bottom up view. Atoms aren't made of a random collection of electrons; there is a primary order to their configurations. Without this, there can be no secondary outcome of chemically active subshells. Sandbh (talk) 23:41, 14 February 2020 (UTC)

@Sandbh: What is aufbau according to you? Differentiating electrons, i.e. "add a proton and an electron, that's the next element"? That's completely irrelevant chemically: the energies involved for such a process are those of nuclear physics. It would be marginally more relevant to start with a naked cation and gradually add electrons. Except that chemistry is not strong enough to create something like U⁹²⁺, even though physically generating that is no big problem. That's why I reject this idea, as building up of atoms happens at energies that are just plain irrelevant to chemistry in general. Instead I just look at which electrons are active in each atom, separately for each Z. That's chemically relevant and displays the n+l order as it should.

On first-principles derivation of the n+l rule: this paper contains one (1979). Note, to apply it to make predictions, you also start by setting a Z value. You don't compare Z with Z − 1. ;) Double sharp (talk) 00:18, 15 February 2020 (UTC)

@Double sharp: As at 2019, the…[n+l] rule has not yet been derived from quantum mechanics or other fundamental physical principles. In 1969, on the 100th anniversary of the periodic table, chemist Per-Olov Löwdin declared this derivation to be one of chemistry’s major theoretical challenges. It still is, 50 years on. See here.

@Double sharp: Aufbau is the actual filling sequence as opposed to what it should be according to the n+l rule. Everything else you said is irrelevant. I suspect aufbau and your own approach to active electrons are very close. Are you saying that the chemically active electrons match aufbau? Sandbh (talk) 04:40, 17 February 2020 (UTC)

@Sandbh: Amazing: I link to a first-principles derivation (published!) of the n+l rule, and the best you can do is simply parrot the assertion that none exists yet! At least criticise it if you think something is wrong with it! The actual filling sequence, up to the seventh period, is indeed exactly what the n+l rule says it should be if you consider chemically active valence subshells (not only electrons)! Double sharp (talk) 14:27, 17 February 2020 (UTC)

@Double sharp: A derivation of n+l is of considerable interest within the philosophy of chemistry community. If such a thing had been achieved it would've been all over that community, not to mention widely circulated among physicists. It is amazing that you did not appreciate this. Sandbh (talk) 02:51, 18 February 2020 (UTC)

@Sandbh: Well, there are Wong's or Klechkovsky's papers deriving n+l. It is amazing that you do not appreciate that now that I have linked you an actual paper where n+l is derived, your only logical follow-ups are either to (1) admit that the rule has been derived, or (2) show me somewhere from a reliable source where Wong's and Klechkovsky's derivations are criticised. Double sharp (talk) 11:51, 18 February 2020 (UTC)

Now then, more generally :), we will have to disagree. You say, "I prioritise chemistry, and ground-state gas-phase configurations that your DE's depend on are irrelevant there."

I place importance on the periodic law, as informed by the aufbau process; and d/e's, which shape the layout of the periodic table. Oh, and chemistry. Per Stewart:

Block identity works on the following basis:

predominant differentiating electron;
s is characterised, except in H, by highly electropositive metals; and by the fact that its outer electrons do not withdraw completely into the core until the next subshell of s elements is added; instead it contributes to bonding in the subsequent p, d and f blocks;
p by a range of very distinctive metals and non-metals, many of them essential to life; and by the fact that, when its orbitals are all filled, the six electrons with the two s electrons form an almost impregnable octet in the noble gases;
d by metals with multiple oxidation states; and by the fact that, as its orbitals fill up, they withdraw increasingly into the core until withdrawal is complete in Zn, Cd, Hg;
f by metals so similar that their separation is problematic; and by the fact that withdrawal into the core starts immediately, leaving only one (or two) electrons to combine with s electrons in bonding. I note that the nature of the 4f electrons explains the similarity among these elements.
- This is a textbook example of "confusing a phenomenon with a cause" as you accuse me of doing. Double sharp (talk) 14:32, 13 February 2020 (UTC)

Pre Bohr, we could not explain the shape of the periodic table nor why its chemistry was it is. With the d/e concept we could, at a first order or so level.

Exactly, we progressed. Why must we be stuck there and not progress even further? Double sharp (talk) 14:32, 13 February 2020 (UTC)

Per Scerri:

"…for the purpose of selecting an optimal periodic table we prefer to consider block membership as a global property in which we focus on the predominant differentiating electron."

There is some nice fogging, and selectivity here: "…and if its [Group 3] chemical credentials as TMs are weak, then so are those of Zr/Hf/Rf, Nb/Ta/Db, Sg, and Bh", with your exclusion of the transition metal chemistry of Ti. As we did agree (!), "…it is in Ti that the really characteristic transition metal properties are first commonly seen."

@Sandbh: Whatever happened to your focus on "predominant" behaviour? Group 4 has one element with common TM chemistry (Ti) and three without it (Zr, Hf, Rf). Group 5 has one element with common TM chemistry (V) and three without it (Nb, Ta, Db). I get the picture: if picking "predominant" behaviour seems to support La, it is a broad-strokes understanding, and if it seems to support Lu, it is fogging and selectivity. Double sharp (talk) 14:20, 13 February 2020 (UTC)

@Double sharp: It never went away, did it? I've always maintained that groups 1-3 are predominantly ionic; and groups 4 and 5 are predominately covalent. Sandbh (talk) 00:41, 14 February 2020 (UTC)

@Sandbh: Yes, you did, leaving aside whether it is relevant. (I insist that EN is more relevant, as Wulfsberg uses, and then group 4 predominately patterns with group 3 because of Zr, Hf, and Rf.) But if you were being consistent, you would also notice that groups 1-5 are all predominantly pre-transition in chemical behaviour. And you would notice that group 1-2 have predominantly pre-transition physical properties, whereas Sc and Y, like groups 4 and 5, have predominantly transition physical properties, and therefore Sc-Y-Lu is physically preferred. So if you were being consistent, instead of dismissing commonalities that support Lu as "fogging and selectivity", you would come to the conclusion that actually commonalities do not make group 3 throw more strongly to group 2 than group 4; they are intermediate. Double sharp (talk) 11:56, 14 February 2020 (UTC)

@Double sharp: I can't be accused of something I never did. We haven't discussed comparing physical properties (PTM v TM) in the context you're referring to AFAI can recall. Nor have we discussed the predominate pre-transition chemical behaviour of groups 1-5.

Certainly the presence of a d-electron in the bulk group 3 metals makes a physical difference, as G & E noted. I agree, physically speaking, that group 3 is intermediate. G&E also note group 3 were chemically largely atypical TM metals. Oh, and OMG(!) they say, "In the main, the chemistry of these elements concerns the formation of a predominately +3 oxidation state…and give a well-defied cationic aqueous chemistry." They are deluded, of course. Sandbh (talk) 03:50, 17 February 2020 (UTC)

@Sandbh: No, they haven't said anything laughable. "Predominately +3 oxidation state" makes perfect sense, you can in principle list all compounds and under any sane probability distribution applied to them, it's clear that most are in that state. (Likewise, of course, for an element like uranium I would say "predominant +4 and +6 oxidation states".) "Well-defined cationic aqueous chemistry" makes perfect sense too, we can see Sc³⁺, Y³⁺, and Lu³⁺ aqueous cations (La³⁺ too, of course). It's only "predominately ionic or covalent" that don't make any sense because they are too dependent on the distribution of counter-anions and therefore are very much context-dependent. It is, in fact, intimately based on oxidation states and atomic radii!

I'm not accusing you of discussing anything. I'm saying that if you were consistent you should be discussing those things! But you're not. Double sharp (talk) 14:27, 17 February 2020 (UTC)

More selectivity: "Then we consider the trend across the period, and indeed, the 5d row is much more regular with Lu in it than with La in it…". Yes, completely overlooking the intervening thirteen lanthanides between La and Lu. The elements in group 13 show some irregularity due to the double impact of the d-block contraction, and the f-block contraction. For some reason, we should not show the impact of the f-block contraction on the regularity of the 5d metals. Really? Let's pretend the f-block starts at La, so we won't have to show this. And since we won't be able to call the it the f-block contraction, we'll have to call it the Ln contraction.

We can call it the f-block contraction just like how we call the d-block contraction the d-block contraction. Never mind that there is no predominant oxidation state for the 3d elements like you always throw out there to artificially exclude La from the f-block one. And then we have a regular impact of the f-block contraction on every 5d metal: Lu through Hg. Including the first group of the d-block (group 3), just like we include the first group of the p-block (group 13). Double sharp (talk) 14:20, 13 February 2020 (UTC)

And we will talk over the fact that the fourteen 4f electrons in Lu³⁺ have at least an order of magnitude greater impact on the chemistry of Lu compared to the possibility of any marginal 4f involvement in La. Sandbh (talk) 04:54, 13 February 2020 (UTC)

As core electrons. The 3d electrons in Ga³⁺ have much more effect (making it actually more acidic than Al³⁺) than the zero 3d electrons in Sc³⁺, too. I know what I expect to see next: more fogging about how the core electrons in Lu are somehow totally different from those in Hf through Rn. Double sharp (talk) 14:20, 13 February 2020 (UTC)User:Sandbh/nonmetals#Droog_Andrey_and_Double_sharp

Epilogue

I've just finished carefully reviewing the R8R section. I'll put my brief impressions here, and update things as I get through the rest of the thread. Nothing of what follows is intended to distract from my respect for all concerned.

Respectfully, from my perspective I see just a lot of faulty logic everywhere, which makes me think that R8R was truly right when he said that the two of us can no longer hear each other. But OK, I will respond to this epilogue for anybody else in the future doing an archive binge like I used to do. ;) Double sharp (talk) 07:48, 10 February 2020 (UTC)

The nature of boundaries

Concerns have been raised that I rely too much on sharp boundaries, and subjective things like cats being a natural class etc. It follows that my arguments cannot be sustained. I responded by quoting Jones, on classification science:

"Though classification is an essential feature of all branches of science, there are always hard cases at the boundaries. The boundary of a class is rarely sharp…Scientists should not lose sleep over the hard cases. As long as a classification system is beneficial to economy of description, to structuring knowledge and to our understanding, and hard cases constitute a small minority, then keep it. If the system becomes less than useful, then scrap it and replace it with a system based on different shared characteristics."

I need to expand on this in the article, as I did in "Organising the metals and nonmetals".

The Be-Mg-Zn arrangement was similarly beneficial. Upgrade to differentiating electrons was done because it is closer to an underlying, fundamental truth than just comparing properties. Eventually we will arrive at a holistic view of looking at all chemically relevant configurations per Jensen, Jørgensen, Schwarz, Seaborg, and Wulfsberg, and the La table can finally die like the Zn one did as the relic of an early misunderstanding. Double sharp (talk) 07:46, 10 February 2020 (UTC)

Fogging

This occurs when Double sharp attempts to counter one of my arguments with, as I see it, a fog of irrelevancy. For example, I argue the chemistry of group 3 is predominantly ionic. The fogging technique is to say that this is a false dichotomy (i.e. the distinction between ionic and covalent); it has lot to do with counter-anions, and oxidation states. For example "just compare uranium chemistry as we jack the oxidation state up from +3 to +4 to +5 to +6". It is true that ionic character is influenced by these things, but that has nothing to with my stated, broad generalisation.

On the contrary, it has everything to do with it. You have to go down and look for the most fundamental cause you can get of the phenomena you observe. Because you have to base the PT on something as fundamental as possible. Double sharp (talk) 07:46, 10 February 2020 (UTC)

Here are some more examples:

(a) "Respectfully, I put it to you that Zr, Hf, Nb, and Ta by this standards have weak credentials as transition metals, just as weak as Sc for that matter." Here, Zr, Hf, Nb, and Ta are the fog; the elephant in the room is Ti, which has reasonable credentials as a transition metal.

Never mind that the heavy members of group 4 and 5 are the majority in their groups. Ti and V are literally only the first elements in them. But of course, if it is inconvenient for the La form, it must be a fog of irrelevancy. If we actually examine why this is the case, we actually get enlightened about the relative energy levels of d and s subshells here. Which shows, again, that everything goes back to the fundamental principle of chemically active valence subshells. You elevate its consequences to fundamental principles, but never go back to see what is causing them. Whereas I am of the position that a fundamental basis for the periodic table ought to be as fundamental as possible. (But not more so, so no, DE's are out as chemically irrelevant.) Double sharp (talk) 21:27, 10 February 2020 (UTC)

(b) "…its [f-block] initial filling is delayed, which is something common throughout [t]he table." Here the fog is, "which is something common throughout [t]he table" In fact the s, p, and d-blocks have no delay. s, starts at H; p starts at B; d starts at Sc, as expected. The surprise is the delayed start of filling of the f-block, which starts at Ce rather than La.

As I said a few times, it is absolutely common for heavy elements. The 5f row has the f-filling delayed two elements, rather than one as in the 4f row. Lu has the p-configuration already lying quite low, and then for Lr the d filling is really delayed. And then for E121 (5g doesn't start filling till later, at around E125), and for E139 (5g is still active, 6f seems to become the highest angular-momentum core subshell only around E143), and for E153 (the 7d elements start at E157), and for E163 (the "8p" = hybrid 9p/8p ones start at E167). That's why The important thing is not where the first characteristic electron appears, but where it finally sinks into the core. Which is pretty much what Seaborg was saying when he argued that even if not only Ac and Th, but also Pa, lacked any f-electrons in the ground state, but the actinides still had the same chemistries we know and love, we would still be justified in drawing an actinide series because it would explain the position of Cm³⁺ (attaining a 5f⁷ configuration from losing three electrons). And, might I add, it would explain Lr³⁺ where the fourteen 5f electrons are firmly core ones. The same argument works in the real world where Ac and Th both lack those f-electrons. Double sharp (talk) 07:46, 10 February 2020 (UTC)

You can't do that

For example, "nobody uses that as a criterion in the literature for this divide". That may be so. And so what? That doesn't meant I can't put it forward as peer-reviewed (which it most certainly will be) OR.

@Sandbh: It's simply an observation that something serious chemists don't use is probably not terribly important. Double sharp (talk) 07:46, 10 February 2020 (UTC)

@Double sharp: I see. In your world there will never be OR, as serious chemists haven't used it therefore there will never be anything in OR. Sandbh (talk) 06:29, 16 February 2020 (UTC)

@Sandbh: It is possible to come up with useful OR here: for example, simply take what criteria serious chemists actually used and critically examine them. That's where I got Jensen's criteria and chemically active valence subshells from. (In particular, many who insist on blocks as the important basis is implicitly being inconsistent when considering helium. And many who put the standard n+l rule and a La table are also implicitly being inconsistent!)

You must also critically examine your own criteria. Yes, it's possible that you have somehow come up with some fundamental basis that every single serious chemist missed. But realistically, they have probably as a whole thought about the problem far more than we have. And they have probably gotten all the simple arguments. So if a simple property fails to be used as something important in the literature for the whole PT and chemistry, then it is already quite suspect. We should try to find out why this is the case, and often the answer is not very far away: it produces nonsense when applied to other elements. Build on the literature, yes, but give them some credit! If something simple is absent there's probably a reason that a moment's thought will reveal. Double sharp (talk) 10:35, 16 February 2020 (UTC)

The sky will fall down

I'm arguing for Sc-Y-La. Double sharp responds by saying this would require Be-Mg to go over Zn, or Al to go over Sc. My response is that the PT is arranged more pragmatically than that. Only the minimum sufficient change is made, at the time it is perceived to be worthwhile e.g. with the understanding of how the aufabu process actually worked, which resulted in the periodic table moving away from chemistry and more towards physics, and the demise of Be-Mg over Zn. Sandbh (talk) 00:43, 10 February 2020 (UTC)

@Sandbh: In other words, a biased refusal to use modus tollens against La. Double sharp (talk) 07:46, 10 February 2020 (UTC)

What follows takes me up to the end of 1.2.4 Basis for blocks.

Out of context reframing

This happens when I present an argument in one context that is repacked into another irrelevant context. There is some fogging here, too. For example, I refer to the Ln contraction per se running from Ce³⁺ f¹, where it starts, to Lu³⁺ f¹⁴, where it finishes. It starts at Ce due to the delayed filling of the 4f sub-shell. In an La table the Ln contraction matches the start and finish of the f block.

This is repacked into an irrelevant context, as follows:

"No, but you exclude it [Ln³⁺] from the Ln contraction trend as the member when n = 0 in the 4fn configuration. It ought to be included in the trend line as just another lanthanide ion, because the contraction is measured by the difference in size between two lanthanides with adjacent values of n, of which n = 0 and n = 1 counts just as well."

It's perfectly in context because that's what the Ln contraction is there for. Each Ln ion is smaller than the previous, that's why it's called a contraction. And each Ln atom is smaller than the previous too. That's an atomic radius contraction that works all the way across a period. Double sharp (talk) 11:58, 10 February 2020 (UTC)

@Double sharp: Nice evasiveness, inability to answer the question, and taking me out of context again. So, is there an f electron caused contraction in La? 06:26, 16 February 2020 (UTC)

@Sandbh: Yes, we have an f-block contraction starting there, looking at atomic radii! Just as there is an f electron caused contraction in Th and a d electron caused contraction in Lr! Double sharp (talk) 10:31, 16 February 2020 (UTC)

@Double sharp: A nonsense answer needs no response from me. Sandbh (talk) 04:57, 17 February 2020 (UTC)

@Sandbh: And why is it a nonsense answer? Because for you the lack of 4f involvement in La on the grounds of its DE is an absolute axiom? Respectfully, this whole thing is futile until you critically examine your favourite DE's and how useless they really are for chemistry. Double sharp (talk) 14:29, 17 February 2020 (UTC)

Using a toothpick to leverage the World

"When one holistically considers what orbitals are chemically active, one sees that 4f is already an active valence subshell in La (whence cubic complexes among other things), but is clearly core in Lu."

Any 4f character in La³⁺ is very minor. Compared to the impact of the fourteen f electrons in Lu³⁺, it's microscopic. Like the Sun and the Moon. Sandbh (talk) 01:26, 10 February 2020 (UTC)

@Sandbh: I just see a refuted canard being dragged out again and again. Those 14 electrons in Lu are core electrons. By that logic the 4f block has to end at Rn, because the incomplete screening of 4f is visible all the way there. Double sharp (talk) 07:59, 10 February 2020 (UTC)

@Double sharp: Yes, I follow your perspective. From a classification science perspective, we can distinguish between the direct cause i.e. the f-electron-caused contraction from Ce-Lu, in contrast to the indirect knock on effect running from Hf to Rn. Sandbh (talk) 00:39, 11 February 2020 (UTC)

@Sandbh: I see no difference between the cause of lower-than-expected atomic size in Lu and in Hf. From Y to Lu we add fourteen core 4f electrons which provide incomplete shielding from the nucleus and almost exactly cancel out the expected increase in atomic radius from period 5 to period 6, exactly as from Zr to Hf. The situation is different from La through Yb because there the 4f electrons are valence electrons and may participate in chemistry.

When we analyse period 6, we note that the number of outer shells does not increase when we go along it, but the atomic charge grows and hence the atomic radius shrinks, as the shielding from the [Xe] core is approximately equal for each element. There's no gap here between blocks, we see a smooth contraction all the way from Cs to Hg. Exactly like what happens across period 2 or period 3: this is a horizontal effect. What changes from periods 4 onwards is that inner subshells start filling that join the core after their block: thus for Ga through Kr, the core is [Ar]3d¹⁰ (whereas it was [Ar] for K through Zn). Similarly, in period 6, the core is [Xe] from Cs to Yb, but it is [Xe]4f¹⁴ from Lu to Hg, and then [Xe]4f¹⁴5d¹⁰ from Tl to Rn. It is when a subshell drops into the core and becomes chemically inactive as a valence subshell that controls when a block should stop. That's just simple logic: if "f-block" means anything at all, it should mean that the elements in it have some f-involvement in chemistry. Respectfully, Lu and Lr simply don't have any: for them they are core electrons. La and Ac at least have f-contributions even if they are not the ground states: the excited states with populated f-orbitals are well within reach of chemical bond energies. Double sharp (talk) 11:54, 11 February 2020 (UTC)

@Double sharp: We should clarify what you said about "from La through Yb because there the 4f electrons are valence electrons and may participate in chemistry." La has no valence 4f electrons. What 4f valence electron participation there may be, is likely to be confined to Ce, as I understand it. Sandbh (talk) 22:53, 11 February 2020 (UTC)

@Sandbh: La has a 4f subshell that valence electrons may enter. Sure, they don't do it in the gas-phase ground state. But a La atom in a compound is probably not in that ground-state anyway, so there is no problem. Same situation as for 5f in Ac and Th. Double sharp (talk) 23:05, 11 February 2020 (UTC)

My citations are wrong

My citations are commonly undermined. For example:

"Citation is not an ultimate truth but just another opinion."

Yes, I agree. There's no categorical argument for the resolving the group 3 question, so I have to rely on qualitative and quantitative arguments, supported by citations.

And how exactly does this square with 3? You offer your own opinions, the literature does the same too. So far, your response to the chemical relevance criterion of Jensen, Droog Andrey and I, which categorically argues for Lu, is simply to ignore it and keep standing by DE's through increasingly contorted misreadings of the sources I keep piling up to demonstrate the irrelevance of DE's. Double sharp (talk) 07:59, 10 February 2020 (UTC) ♠

@Double sharp: What did you mean by "3" in your lead sentence? Sandbh (talk) 03:17, 18 February 2020 (UTC)

@Sandbh: The section "You can't do that", back when it had that number. Double sharp (talk) 11:52, 18 February 2020 (UTC)

You're not being fair

For example:

It feels like La-Ac is being accepted from the start as the null hypothesis and that Lu-Lr is not being treated fairly. Indeed, some arguments for La-Ac made here would support things like Al-Sc or Mg-Zn or Tl-Lr or He-Be.

My article, as it says, is premised on accepting Scerri's position that group 3 can't be resolved on the basis of physical (including spectroscopic), chemical, and electronic properties and trends. So it seeks to address the question from a perspective external to Group 3, rather than on the individual physical, chemical, or electronic properties of La or Lu. Apart from the symmetry argument, I don't know of any other philosophical arguments for Lu. That's just how it is; this has nothing to do with fairness.

I know we've descended into arguments based on physical (including spectroscopic), chemical, and electronic properties, as our way of working through things. Which is fine by me. Sandbh (talk) 02:02, 10 February 2020 (UTC)

@Sandbh: And yet, as I demonstrated wrt the carbonyls argument, you hold Lu arguments to a higher standard than La arguments. Double sharp (talk) 07:59, 10 February 2020 (UTC)

This takes me up to the end of 1.2.10 Lanthanide contraction.

Indiscriminate use of logic

Also a form of fogging.

For example, I said:

"With the f block as Ce to Lu, the range is 0 to 14. With La to Yb the range is 0 to 14, as you say, my oversight. I would not count La as an f-block metal, since the 4f subshell has not started filling yet. So the second option is not comparing like with like."

Double sharp responded: "So Th is not an f-block metal either, by that logic."

We had already covered this in our IUPAC submission, when we wrote: "A block starts when the first electron of its name enters the applicable subshell. Thus, the s block starts at group 1 with H, the p block starts in group 13 with B, the d block starts in group 3 with Sc, and the f block starts at Ce."

If follows then that Th goes under Ce.

This represents an example of indiscriminate use of logic, oblivious to what other arguments may be at play. Sandbh (talk) 02:24, 10 February 2020 (UTC)

Firstly, I now disagree with that definition of block because of the widely demonstrated irrelevance of DE's. This is much simpler to explain by delayed collapse effects becoming more and more pronounced as the table is descended, which is why what happens at La and Lu blossoms into a bigger problem at Ac, Th, and Lr. It appears your only argument for Th as an f-block metal is to align it with Ce immediately above, because only for this element and Lr do you momentarily align with me on saying that actually chemically active subshells are relevant. Respectfully, that is by your standards Nature as you would like Her to be rather than how She is. Double sharp (talk) 07:59, 10 February 2020 (UTC)

"The best education is found in gaining the utmost information from the simplest apparatus."

— Whitehead AN 1929, The aims of education and other essays, The Free Press, New York, p. 37 Sandbh (talk) 23:25, 13 February 2020 (UTC)

@Sandbh: That's precisely why a Lu table is better. It's simpler and doesn't make a mountain (splitting the d-block and decreasing simplicity) out of molehill (since even trends in a vacuum do not significantly favour the La table, and chemistry taken as a whole favours the Lu one). Double sharp (talk) 23:34, 13 February 2020 (UTC)

@Double sharp: The La form accords with the observation that a block starts with the appearance of the first relevant electron. What's the equivalent for the Lu form (I'm not sure there is one, is there?). Sandbh (talk) 00:48, 14 February 2020 (UTC)

@Sandbh: We are in a block when its characteristic subshell is the highest angular-momentum valence subshell. (And when we have the s-orbital filled preemptively for the other ones, to take care of group 2.) Double sharp (talk) 07:56, 14 February 2020 (UTC)

@Double sharp: Eh? So, the "characteristic" subshell of the d-block is the d subshell? Sandbh (talk) 11:29, 14 February 2020 (UTC)

@Sandbh: That's right. Double sharp (talk) 11:58, 14 February 2020 (UTC)

@Double sharp: And the predominant differentiating electron in the d-block is a d electron? Sandbh (talk) 06:21, 16 February 2020 (UTC)

@Sandbh: I don't care because DE's are chemically largely irrelevant. The important thing is that every d-element should have the d-subshell at least contributing to the bonding (which is true for the Zn group as well, just look at the interatomic distances in ZnCl₂ say: we see that there must be significant overlap of Zn 3d with Cl). Lu and Lr in the f-block makes them spit in the face of this otherwise totally correct generalisation: the distance for LuCl₃ is bigger than for ZnCl₂, and Lu 4f is smaller than Zn 3d! Double sharp (talk) 10:31, 16 February 2020 (UTC)

Who's seeking to overthrow what?

My article attracts a fair amount of commentary along the line of it seeking to overthrow the Lu form. For example: …the La form has does not overthrow the decisive advantages of the Lu [form]" In a related manner, Double sharp presents the Lu form as the null hypothesis.

As we all know, the La form is the predominant form, by a wide margin. My article presents an argument in support of the better regularity of the La form compared to the Lu form.

I don't need to overthrow anything. Sandbh (talk) 02:47, 10 February 2020 (UTC)

An author before WWII would not have to overthrow anything if he wanted to continue with the Be-Mg-Zn table. But it was overthrown as people learnt that actually there is something more fundamental for the PT. As it should happen eventually for the Sc-Y-La table: an overthrowing as we learnt more. This is science. Tradition counts for nothing once we learn something that invalidates it. Double sharp (talk) 07:59, 10 February 2020 (UTC)

Sandbh flip-flops and is inconsistent

For example:

I said, "I haven't based my arguments exclusively on gas-phase configuration, as you know."

Double sharp responded:

"No, but when you use them, you inconsistently flip between when they are decisive (for La and Ac) and when other factors can overthrow them (like for Th and Lr). As Jensen commented about Lavelle: "When it comes to the question of why La and Ac should remain in the d-block rather than being reassigned to the f-block, Lavelle offers no new chemical or physical evidence other than his constant reiteration of the fact that both elements contain d-electrons in their ground-state valence conﬁgurations, but no f-electrons. Yet in the cases of both Lu and Th, for which this is equally true, he proceeds to inconsistently argue that this fact is of no consequence when it comes to assigning them to the f-block. As with the case of the revised conﬁguration for Lr, which counts when it comes to not placing this element in the d-block but is irrelevant when it comes to placing it in the f-block, this arbitrary and naive use of electron conﬁgurations, to the exclusion of all other evidence, is logically inconsistent and leaves one with the impression that the only true argument that Lavelle has for the major premise of his diatribe is that La and Ac should remain in the d-block because that is where IUPAC places them in its ofﬁcial periodic table and therefore all rational discussion of other possibilities is strictly forbidden."

I aim for consistency. Per the periodic law and aufbau, Ce starts the f-block. Lu, which turns up 13 elements later, represents the third occurence of a 5d electron. Its fourteen f electrons have a dramatic impact on its ionic radius, and therefore its chemistry. It follows that Th goes under Ce. Yes, Th does not have an f electron in its gas phases, but it has about 0.5 of an f electron in the condensed phase, and this impacts its crystalline structure, and we know of the presence of an f electron in the Th³⁺, including its colour in aqueous solution, despite the instability of this cation. It's no ticket to front row seats at the f-stadium, unlike Ce, but it's impressive nevertheless. You know all of this already, of course.

Here we go again. La is forbidden as an f-element even though the same arguments allow Th. Meanwhile Lu is let in on the basis of core-like f-electrons that would allow Hf through Rn all as f-elements. Double sharp (talk) 07:59, 10 February 2020 (UTC)

@Double sharp: Eh? Th falls into line, under Ce as the first f element. Lu has a predominately ionic chemistry as do the rest of the Ln. The chemistry of Hf and the rest of the 5f metals is covalent. Chalk and cheese. Sandbh (talk) 07:11, 13 February 2020 (UTC)

@Sandbh: This is an excellent example of "Sandbh flip-flops and is inconsistent". "Th falls into line": here we see Sandbh arguing from symmetry and regularity, which is acceptable for forcing Th into the f-block despite its lack of a 5f DE and a 5f electron in the ground state (gas-phase), but suddenly becomes unacceptable for La and Ac. (I wonder how Sandbh plans to handle how the first element with a ground-state 5g electron should be E125, the seventh element in the 8th period; but the first one with a ground-state 6g should be E173, the first element in the 9th period. Never mind that E125 seems to be a normal early superactinide acting like eka-U or eka-Np, but with 5g more of a "reserve" place like 4f is for La, and E173 seems to be a normal alkali metal more reactive than even Cs.)

"The chemistry of Hf and the rest of the 5d metals is covalent": the same mistake, elevating an effect to a cause driving the PT, ignoring that it is simply a result of periodic trends controlling electronegativity: predominant oxidation states and atomic radius, which go back ultimately to chemically active valence subshells. Notice also the sudden flip. First you want to argue that Lu must be in the f-block because of its 4f electrons (never mind that they are core electrons); the moment you realise that this also puts Hf through Rn into the f-block, you suddenly flip to a new criterion of ionic vs. covalent. Also notice that I said Hf through Rn (including the 6p elements as well, since the 4f insertion is equally still contributing there), and Sandbh thinks Tl is predominantly ionic. (So probably the same for Pb as well.)

Prediction for the next episode: another flip to another argument about why this is "fogging". Respectfully, if this isn't a double standard, I don't know what is. You are using different criteria for different elements. Double sharp (talk) 14:06, 13 February 2020 (UTC)

@Double sharp: Eh? Th falls into line having regard to the periodic law and the aufbau process. The sky will not fall down with the first appearance of a g electron. I have never argued that Lu must be in the f-block because of its 4f electrons. Where do you get these fantasies from? The moment I realise what? Another fantasy. What is this nonsense about me regarding Hf to Rn as part of the f-block? Absurd! Yes, Tl is predominantly ionic! Read our article on it: "Thallium tends to oxidize to the +3 and +1 oxidation states as ionic salts." Sandbh (talk) 23:24, 13 February 2020 (UTC)

Thorium: See, this is exactly the issue. Thorium falls into line only because you decreed that a block should start in a vertical column. You only look at the first appearance of the characteristic electron in the ground-state configurations, and then just assume regularity holds. Just like how it would be if we assumed the pure n+l regularity held, of course. But that is a Lu argument and therefore it cannot be allowed.

@Double sharp: I saw this in the literature a while ago but did not then realise the importance of it :( At face value I see where you are coming from. I don’t decree the appearance of the first electron of relevance. Such appearances are a matter of objective fact. I haven’t read that much of Bohr but I recall he outlined the blocks or whatever he called them back then, on the same basis. I do presume regularity holds having regard to the precedent of the periodic law, the distinct identity of the blocks, and the actual aufbau sequence. I do note the irregularities and seek to minimise these where practical. I don’t start with the fiction of n+l and then attempt to “correct” anomalous configurations because they don’t agree with the n+l fairy tale. Sandbh (talk) 02:02, 14 February 2020 (UTC)

@Sandbh: Nope. Bohr thought that 4f started at Ce indeed, but on the basis of the TM-like chemistry of Ac through U, he thought that 5f really started shortly after U, and accordingly drew a staggered f-block in his table. That's consistent. Your approach starts with a fiction of blocks starting in a vertical column, which doesn't tally with your emphasis on DE's.

The appearance of the first 4f electron in Ce is an objective fact but also an irrelevant one because we've progressed since then and now know that excited states are also important: as Schwarz and Seaborg stated, chemically bound atoms are usually not in those ground states! The more important thing is that 4f is low enough in energy to contribute in La, and 5f in Ac, explaining cubic complexes and other physical properties that Gschneidner pointed out. I never started with n+l here, I started with chemically active valence subshells like Jensen. They do happen to follow n+l mostly in the first 7 periods, though the rule misses the point that the big caesura isn't between different n+l values, it's between a p orbital amd the next higher s one (or 1s-2s for period 1). And I don't correct La to save n+l, I see it corrects itself in real chemistry. Double sharp (talk) 07:53, 14 February 2020 (UTC)

@Double sharp: My emphasis on DE's is consistent with the n+l rule and the aufbau process. The explanation for cubic complexes is contentious, as you know, per my earlier quote (which you conveniently chose not to mention). There is no need to rely on discerning chemically active sub-shells. The DE explanation is much simpler. Per Einstein: "Everything should be made as simple as possible, but not simpler." Per Whitehead: "The best education is found in gaining the utmost information from the simplest apparatus." Per Scerri: "…for the purpose of selecting an optimal periodic table we prefer to consider block membership as a global property in which we focus on the predominant differentiating electron." Einstein, Whitehead, and Scerri are all wrong, of course. As are Earnshaw and Harrington; Cotton & Wilkinson; Remy; Shannon (1976), with 50,522 citations (all of whom are unable to compare like-with-like, and not realising that Shannon's measurements must be noise compared to the differences in high spin low spin ions); Rayner-Canham; Schulz; French; and so on. Sandbh (talk) 06:08, 15 February 2020 (UTC)

@Sandbh: I should like to see how Parish proposes to explain cubic complexes without 4f orbitals. I agree with Einstein's quote: your DE's are chemically irrelevant, so they are too simple to be simple. You must use the simplest apparatus indeed, but the simplest one that is actually relevant. So of course, Einstein and Whitehead are right (though yes, Scerri is wrong here IMHO). And Shannon knew, of course, that ionic radii depend strongly not only on high-spin vs. low-spin, but also coordination number, and helpfully provided graphs showing it (pp. 759ff). And I'm sure that everybody writing that stuff knew enough about significance to recognise that on such grounds the only conclusion you could make for the 4d-5d increase, given how close to zero it was, was that the contraction almost totally obliterates the difference, and that sign differences here are noise. Absolutely no one makes a mountain out of the molehill that in some d-block groups 4d-5d shows a very tiny increase and in some groups an equally tiny decrease. The important thing is just that the increase is almost zero. That's all you can say at this level of significance, and that's all I bet they do say, since it's the common thing to say about the post-lanthanides. Double sharp (talk) 21:11, 15 February 2020 (UTC)

G electrons: The sky will not fall down only because you are basically holding it up with sheer force of will like Atlas. In actuality the arguments pushing for a La table push for a lot of weird placements as well (B-Al-Sc, Be-Mg-Zn, etc. etc.), but on the grounds of minimising change you sweep them under the rug. If you used any consistency at all, then yes, the sky would fall down. BTW, you haven't addressed the point that the first g-electron appears earlier in the 9th period than in the 8th period, according to calculations. What are we going to do then? Declare E173 to be an s-element anyway even though the only valence electron outside the core is 6g¹? While I sympathise with that idea myself by considering chemically active valence subshells (we should have 6g+7f+8d+10s+10p_1/2 for the most part here, interpreting Fricke's comments on E184), isn't that totally inconsistent with your own view about what matters for La and Ac? Perhaps we must indeed await the coming of Hercules to build his pillars, this time of simple logic, to stop having to hold the sky up to make sure your arguments don't make the rest of the table written in it fall down. Unfortunately, Hercules supports the Lu table, because his name contains "Lu" and not "La", so the offer will have to be rejected, and we must go for the other variant of the myth where Hercules feigns that he has to adjust his cloak and runs off with the apples instead. ;)

Lutetium: Let me quote you directly: "And we will talk over the fact that the fourteen 4f electrons in Lu³⁺ have at least an order of magnitude greater impact on the chemistry of Lu compared to the possibility of any marginal 4f involvement in La." That sounds a lot like you're arguing for Lu in the f-block instead of La on the basis of greater 4f involvement. Never mind that that involvement is core involvement, of course. Naturally, I then pointed out that this was a total canard, since Hf through Rn also have core 4f electrons of equal relevance to those of Lu (see among many other places "6. Using a toothpick to leverage the World"). As expected, you then ran away to another argument, showing yet another double standard: to quote you, "From a classification science perspective, we can distinguish between the direct cause i.e. the f-electron-caused contraction from Ce-Lu, in contrast to the indirect knock on effect running from Hf to Rn." Never mind, of course, that the causes of the Y-Lu and Zr-Hf size similarities are exactly the same. So do you even remember what you write? That seems to be a prerequisite for actual consistency of usage of arguments.

@Double sharp: I feel I do remember what I write. The principles that guide me are not that many. Now, you were arguing that the f character in La, marginal as it is, exceeded that of Lu. Therefore Lu should go under Y. I said the basis of this argument pales compared to the influence of the 14 f electrons in Lu³⁺ on its chemistry. That’s all. I never used this as an argument for Lu in the f block. You then go off on an absurdist sky will fall down tangent saying this means Hf to Rn must be 4f elements too. Really. You extend my argument into out of context territory. And yes, from a classification science perspective we can distinguish between the cause/development of the f-block contraction, f electron by f electron, until this stops at Lu3+. And we can see the knock on consequences going along the rest of period 6 even though the number of f electrons is now constant. If you can see some flip-flopping here please elaborate. Sandbh (talk) 02:33, 14 February 2020 (UTC)

@Sandbh: You keep harping on the f-block contraction by taking the atoms in the +3 oxidation state. The little problem with that is that there is no such characteristic oxidation state anywhere else on the PT, vide infra: "Harping on +3 as a predominant oxidation state as an excuse to keep La out of the 4f contraction is fogging, since no such analogous thing exists for the 3d contraction. Or the 5f contraction (because of the early An). Or the 4d or 5d contractions. Or the 2p contraction, for that matter." That's a quote from me. To be fair you must look at atomic radii and suddenly there is no good reason to exclude La anymore, not that there ever was one in the first place. Lu³⁺ has 4f influence only in the sense that it has 4f core electrons, which is irrelevant. And since you're arguing that that makes its f-character more significant than La's, I don't see the difference between that and "using it as an argument for Lu in the f block", which you claim you won't do. But I understand: if I use modus tollens against a La argument, it's "an absurdist sky will fall down tangent", but when you use it against a Lu argument as you did for Nelson's carbonyl one, it's suddenly OK! Double standard, much? Double sharp (talk) 13:39, 14 February 2020 (UTC)

@Double sharp: Please don't put words into my mouth. I harp on about the 4f contraction, period. Not the f-block contraction, although I have commented on, but not harped on, 5f. I don't need to look at La in this context. The contraction is caused by the presence of 4f electrons in the trivalent cations of Ce-Lu. Note the absence of La, which you already know about already, but gloss over. Oh yes, the 14 f electrons in Lu 3+ are irrelevant. Wow! That sounds like new chemistry. Time for a letter to the Nature journal. Please don't refer to modus tollens and Nelson's carbonyl argument in summary form, and presume I understand what you're talking about. Like I said earlier, "Yes, Nelson's argument was not consistent, on the grounds he was arguing for it. You agreed. When you give Be or Mg or Al arguments you ignore more fundamental grounds (that I presume are implicit, hence I don't state them) such as that Al is a p-block metal, therefore it can't go over Sc. Sandbh (talk) 04:22, 17 February 2020 (UTC)

@Sandbh: You cannot consistently claim that the important thing indicating the start of the 4f contraction is the appearance of 4f electrons in trivalent cations, and then talk about contractions in other blocks, because there is no characteristic oxidation state there! The only fair thing is to look at atomic radii, and when we do that we find that there is suddenly no reason to exclude La from the series! I never glossed over that, but addressed this!

There is nothing new about the fact that the 14 f electrons in Lu³⁺ are core electrons and that core electrons are largely irrelevant except for providing incomplete shielding effects! There is no new chemistry here! Everybody understands this, see all the talk about the effects of the 3d contraction in Ga through Kr, or those of the 4f contraction in Hf through Rn (also in Lu just the same way)!

You are inconsistent in the order you put your fundamental arguments. When arguing that Al is a p-block metal so it can't go over Sc, despite the fact that Al-Sc often shows more similarities than Al-Ga, you are saying differentiating electrons trump (your preferred focus in) chemical behaviour. (Of course, there are also many ways in which Al-Ga is a more useful comparison, except that all your arguments against Sc-Y-Lu on chemical grounds "look at the group 2 trend" have successfully zapped them as well, since Al is quite pre-transition-like! ^_^) When arguing that Th is an f-block metal despite the fact that 5f hasn't started filling looking at ground-state electron configurations, you are saying (your preferred focus in) chemical behaviour trumps differentiating electrons. So when are you going to learn consistency? Double sharp (talk) 14:36, 17 February 2020 (UTC)

@Double sharp:

Re consistency.

For Al there is no up front issue, since it has a p electron.

For Ce there is no issue.

For Th there is an up front issue, since it has a d d/e. Should it therefore go under Hf? Additional considerations come into play, such as the n+1 rule, regularity, the close match in some significant properties with Ce, the presence of 0.5 of an f electron in solid Th, the existence of the blue Th3+ cation, etc. Like Jensen's 4-stage waterfall model.

How does that look? Sandbh (talk) 02:45, 18 February 2020 (UTC)

@Sandbh: Self-serving for the La table, as always. If you were really consistent you would then say that for La there is an up front issue, since it has a d/de. Should it therefore go under Y? Additional considerations come into play, such as the n+l rule as the whole literature has it, regularity (which is obviously increased with a Lu table), the close match in significant properties with all the other lanthanides, the presence of 4f involvement in La compounds (cubic complexes cannot otherwise be explained), the effects of 4f character on La metal (Gschneidner), etc. Double sharp (talk) 11:53, 18 February 2020 (UTC)

@Double sharp: That's it! The nub of the issue is that I make an argument and you extrapolate it out of context!

DS: La has more 4f involvement than Lu. Therefore Lu should go under Y, and La should start the f block.
S: What 4f involvement there is in La is marginal. Furthermore the impact of 14f electrons on the chemistry of Lu³⁺ is at least an order of magnitude more important.
DS: Therefore the 14f core in Hf onwards means these elements must also be treated as f-block elements!
S: No, that is an unjustified extrapolation that is irrelevant to, and goes beyond the context of, our argument that only deals with La and Lu. The applicability of an argument to A and B does not necessarily extend to C, even though C may share some properties with B.

I hope you can see what you are doing here. Sandbh (talk) 03:04, 14 February 2020 (UTC)

@Sandbh: No, it is you who artificially set down contexts not to be trespassed for your La arguments. Somehow the contexts disappear for Lu arguments, since you are totally fine asking "what happens to the s-block" for Nelson's carbonyl argument wrt Lu, but you're clearly not fine with me asking "what about Be and Mg? what about Al?" regarding your arguments.

How it actually goes is as follows (I've left your responses untouched):

DS: La has valence 4f involvement, Lu doesn't have any. Therefore Lu should go under Y as a d-block element, and La must start the f-block.
S: What 4f involvement there is in La is marginal. Furthermore the impact of 14f electrons on the chemistry of Lu³⁺ is at least an order of magnitude more important.
DS: That is totally irrelevant because the 14 f-electrons in Lu are core electrons. By that logic one would have to accept Hf through Rn as f-block elements on the basis of an equally relevant f-subshell. Or Ga through Kr as d-block elements.
S: No, that is an unjustified extrapolation that is irrelevant to, and goes beyond the context of, our argument that only deals with La and Lu. The applicability of an argument to A and B does not necessarily extend to C, even though C may share some properties with B.
DS: You will never find a fundamental criterion for the PT unless you test it against all elements. Since you don't allow your arguments to apply to other elements, they are groundless. Why are we allowed to do such testing when debunking a Lu argument but not when debunking a La argument, anyway?

Now, are you going to address your double standard on when modus tollens can be used? Double sharp (talk) 13:36, 14 February 2020 (UTC)

@Double sharp: Hey, they're my arguments so I get to set the contexts. Go your hardest then with your out of context arguments. It does not matter that the 14 f-electrons in Lu are core electrons. The fact is that Lu is a lanthanide, and all of their chemistry is impacted by their f electrons. Hf through Rn are not Ln. Do you follow? Sandbh (talk) 04:08, 17 February 2020 (UTC)

@Sandbh: No, you don't get to set the contexts. You want something as a fundamental basis for the PT, that sets the context already. An argument that doesn't address the whole table is absolutely useless for that and must be rejected out of hand! Hf through Rn have chemistry impacted by their f electrons causing incomplete shielding; La through Yb have chemistry impacted by direct involvement of, or promotion of, electrons in and out of the 4f subshell. Of the two, Lu follows the first type. Therefore there is nothing out of context about this reductio ad absurdum. You cannot consistently say that the 14 f-electrons in Lu matter but the equally relevant ones of Hf through Rn do not! Double sharp (talk) 14:32, 17 February 2020 (UTC)

Thallium: Ionic salts in the +3 oxidation state of thallium? Are you joking? (checks article) Wow, that is rubbish. (I've deleted the uncited statement.) Not even Tl₂O₃ is "predominantly ionic", so what hope does any counter-anion other than the ever-dependable fluoride have? As I said before, "Being from the literature does not give you a free pass for a bad argument, you know. ^_^" Well, this isn't even from the literature. Double sharp (talk) 23:49, 13 February 2020 (UTC)

@Double sharp: Here you go: The most common oxidation state of Tl is +1 and the compounds of Tl in this oxidation state may be covalent, as for example in thallium acetylacetonate, but more frequently they are ionic (Durrant & Durrant 1962, Introduction to advanced inorganic chemistry, p. 558). Sandbh (talk) 02:02, 14 February 2020 (UTC)

@Sandbh: Everyone can see that that is because of the lower oxidation state (inert pair effect stabilises +1 gradually going down group 13). It doesn't mean that Tl is suddenly a terrible anomaly for group 13 that we had better move off to group 1 under the alkali metals like Mendeleev did in his 1869 table. That's why you must go one step deeper and actually analyse these things. Double sharp (talk) 13:40, 14 February 2020 (UTC)

@Double sharp: Another fine example of responding to me out of the original context, which is when I said, "Yes, Tl is predominantly ionic!". Of course you could only focus on the +3 part of our WP Tl article, where it said "Thallium tends to oxidize to the +3 and +1 oxidation states as ionic salts." Never mind that +1 is the most common state. Sandbh (talk) 04:30, 17 February 2020 (UTC)

@Sandbh: Sure, +1 is the more common state for inorganic chemistry, in which Tl definitely is more electropositive. Except, organothallium compounds prefer +3, where it certainly is not. Which is important, because the examples of organometallics (where Li and Mg are polar covalent, mostly) and fluorides for nuclear chemists (where the big gap in oxidation state is between +4 and +5) show that different chemists with different specialties will implicitly assume different breakdowns for ionic vs. covalent because they are working from different distributions of compounds. Which is part of why this metric is quite nonsensical out of context; the most useful thing to say here is, as I keep saying, not forcing the winner to take everything when it is something like 51-49, but seeing how ionicity and covalency can be explained by more fundamental trends. That should have been obvious the moment things like this started fracturing under such clear-cut lines, really.

Parable: if a scientist sees that out of a flock of 100 chickens, 60 have big feet and 40 have small feet, he doesn't immediately conclude that "chickens mostly have big feet" and bar all discussion of the cause for it, because that is not what a scientist does. He first looks for what might possibly be causing the difference between the two groups. A scientist who doesn't seek to get to the bottom of such a situation is not worthy of the name. And if he finds that the presence of big feet is correlated with getting more food, then he should be concluding "eating more food increases chicken foot size", because there is obviously an easily guessed mechanism for this to happen. If he finds that the presence of big feet is correlated with the chickens having stomach upsets more often, then he should obviously realise that there's no obvious direct causal relationship, and it's more likely that these are two side effects of something more fundamental. If he finds that the chickens with bigger feet were all born when Mercury was in retrograde, then he should strongly suspect that there is nothing really going on here because there is no plausible mechanism in which Mercury's orbit as viewed from Earth could possibly impact this. More likely it is just because the chickens with bigger feet were mostly born earlier and grew more and Mercury happened to be in retrograde then. But, as he is a true scientist, he then goes and applies this to other flocks of chickens to see if his theories work out. Well, here your flocks of chickens are the chemistries of elements, and foot size corresponds to any property you would like. You keep coming out with at best secondary effects "stomach upsets" like DE's and overly reduced predominance, and at worst irrelevant effects "Mercury was in retrograde" like fogging about 4f in Lu (which is somehow categorically different from 4f in Hf through Rn simply because we labelled Lu as a lanthanide!). I go to the fundamental cause.

Now how do you plan on explaining this with your black-and-white insistence of reducing everything to one predominant one and not caring what dries how they change? I can do it without breaking a sweat from chemically active valence subshells, because Kaupp did it for me already. As we go down the table, there is an increasing energy gap between ns and np (hybridisation defect). This is aggravated by electronegative substituents, because Bent's rule says "atomic s character concentrates in orbitals directed toward electropositive substituents" (yes, the same Henry Bent who supported He over Be). So by using more electropositive alkyl groups rather than fluorides and oxides, we immediately get a vast improvement in stability of the higher oxidation state. So, once again, we see that chemically active valence subshells win the day in explanatory power with how much they can encompass. The preference for +1 in inorganic Tl goes back to them (hybridisation defect + relativistic effects), and the switch to +3 for organic Tl also goes back to them (amelioration of hybridisation defect). That is the sign of a powerful basis for the PT: how much it can explain. Your dogmatic insistence on "ionic vs. covalent" and refusal to analyse what is behind that, plus the same thing for DE's and the supposed "rule" about where a block should begin (combined with sticking your fingers in your ears and saying what amounts to "lalala, I can't hear you over my screams of regularity, never mind that that is just the hated symmetry by another name"), can explain none of this rich chemistry, respectfully.

Also, you still don't address the inconsistency here from above. First you say that Lu cannot be compared with Hf-Hg, because Lu is "predominantly ionic" according to you whereas Hf-Hg are "predominantly covalent". Then I note that I said Hf-Rn, and of course Tl is "predominantly ionic" even according to you. (Probably Pb too, given how it favours +2.) So we now have a case of Sandbh switching between arguments whenever he feels one is in danger. No consistency is needed as long as something can be brought forward to support the La table, which is fundamental and primary purely because of the crushing weight of the literature, and paradoxically by differentiating electrons even though the crushing weight of the literature is either for (1) chemically active valence subshells if they actually analyse the situation properly, or (2) anomalies in the Madelung rule building up an atom from scratch (in which Mo is an anomaly because it's d⁵s even if it has the right DE from Nb), which both support Lu. I'm sure that if we were arguing this a century earlier it would all be about me on the side of the new-fangled electronic structures of Be-Mg-Ca and you defending Be-Mg-Zn with increasingly tortured arguments. ;) Double sharp (talk) 19:54, 17 February 2020 (UTC)

@Double sharp: Hey, you said, "Well, this isn't even from the literature." I quoted an explicit example from the literature. Nobody said anything about "Tl is suddenly a terrible anomaly". Yes, brilliant, let's set up a paper tiger of moving Tl to group 1, and then knock it down. Yes DIM did it back then but as you keep reminding me, we know more these days! More fogging and irrelevancy. Sandbh (talk) 06:18, 16 February 2020 (UTC)

@Sandbh: Well, at first you said +3 for Tl was also mostly ionic! I explained that that was rubbish, and so you're back to +1 only again. Never mind that +3 for Tl is still a big part of its chemistry, particularly for organothallium compounds. Good, so you agree we know more these days than Mendeleev did. So why can't we also note that we know more these days than Bohr did and abandon DE's to the irrelevance heap, as Seaborg, Schwarz, and Jørgensen explained? And why can't we actually analyse ionicity/covalency to Fajans' rules and go back to the real periodicity underlying it, i.e. charge and atomic radius? Double sharp (talk) 10:43, 16 February 2020 (UTC)

Omnibus bombardment

For example, Double sharp wrote that:

"Shared chemistry supports Lu, DE's are chemically irrelevant, you misread the periodic law, your pattern is only graphic design, the 234 pattern is ungeneralisable, and isodiagonality supports Al in group 3. Your case for La convinces me about 0%. All it is is a bunch of one-off arguments glued together, with no hint as to which ones are the more important ones, and no heed to what nonsense they have to say for the rest of the periodic table. The only commonality with them is that they all support the La table in what IMHO are just increasingly desperate ways having less and less to do with actual chemistry. Since R8R and Droog Andrey have echoed some of my points, not to mention Jensen and Schwarz, I think the world would agree. At least I critically analyse and accept the tiny sparks of nonsense my single highest criterion appears to throw up (He in group 2, the ambiguous position of some s-block elements), and see that it is in fact not nonsense and has some chemical repercussions in the real world. So all is well."

There is a lot to unpack here. I see uncited opinions; fogging; selective quoting; unfounded undermining—the periodic table is "only" a graphic design; misattribution; more fogging, and myopia.

I've rec'd other respected external professional feedback on a summary of my article, and the response was, " I think you have presented a balanced description of the issue." Of course, DE's only shape the periodic table. And, as we know, Scerri observed, "…for the purpose of selecting an optimal periodic table we prefer to consider block membership as a global property in which we focus on the predominant differentiating electron." He must be wrong, of course. So much for d/e's.

Yes, I agree. DE's are flawed and incomplete. Double sharp (talk) 07:59, 10 February 2020 (UTC)

I apply the periodic law in conjunction with the real aufbau process, not the misleading n+l approximation. Of course, the periodic table is only a graphic design, nothing more. The 234 pattern is not generalisable, and I never said it was; rather, I compared the two patterns in the La and Lu forms. That Al is isodiagonal with Sc does not undermine my argument. We addressed Jensen's contributions in our IUPAC submission. I've addressed Droog Andrey's major contribution which, to his credit, and as I said, stumped me for a while.

A good chemist is able to hold the three different perspectives in their head, and recognise they all have value depending on the context, rather than insisting there is one correct answer. Thus, I can appreciate the La form, the Lu form, and the IUPAC form, concurrently. (I’m not a chemist)

It's a question of the right tool for the job rather than one size fits all.

Well, do you think there is one correct answer for H, Be, Mg, and Al? Double sharp (talk) 12:18, 10 February 2020 (UTC)

@Double sharp: It's context dependent. Frex, Habishi's metallurgist's table in which Al is over Sc, but not B. Sandbh (talk) 23:11, 13 February 2020 (UTC)

@Sandbh: So how does that square with your statements "The world has moved on from the days of Be and Mg over Zn" and "Al in group 3 is a non-starter" on this very talk page? Double sharp (talk) 23:51, 13 February 2020 (UTC)

@Double sharp: Well, I haven't been talking about a metallurgy kind of table. I've been talking about the table that's near the middle of Scerri's continuum of tables, with the Platonic LST at one end and Rayner-Canham's unruly table at the other. Sandbh (talk) 04:55, 14 February 2020 (UTC)

@Sandbh: But how do you know that something near the middle of this continuum would not be better off reflecting the many ways in which Al is similar to group 3? Do you know that the pair Al-Sc shows more chemical similarities than the pair Al-Ga according to Rayner-Canham? Double sharp (talk) 11:59, 14 February 2020 (UTC)

@Double sharp: I don't. Sandbh (talk) 03:57, 17 February 2020 (UTC)

@Sandbh: So you don't have a leg to stand on. All you have is an idea of something compromising between the boundaries, and what your most important criteria are seems to be what you feel like using at the moment in order to get your favourite arrangement of La and Ac under Y but not affecting anybody else. Contrast me: when I find that one criteria above any other really stands out as something that can make a great basis for the PT, but it has the side effect of insisting on He over Be, I am consistent and move it even if I thought at first that He-Be-Mg was chemically insane. (Now, of course, my trust in that criterion has been rewarded by predictions of He being like Be in its rare compounds, and in those graphs of periodic trends. Just like Mendeleev.) Double sharp (talk) 14:38, 17 February 2020 (UTC)

The IUPAC table represents one of these tools, taken from more of a chemistry perspective, where He sits over Ne, and group 3 is shown as Sc-L-[La to Lu].

Most chemistry text-book authors drill down into the electronic filling sequence, and present the table as Sc-Y-La, because it's not until Ce and Th where f electrons first make their presence felt in a substantial rather than peripheral manner. The split-d block issue doesn’t become an issue because of the dominance of the 18-column form of the table.

Maybe this is simplistic but it serves its purpose, at least in the first instance.

Meanwhile, for my respected colleague Double sharp everything points to the about 100% relevance of Lu, leaving effectively 0% for the La form. Sandbh (talk) 04:17, 10 February 2020 (UTC)

Because it does according to my analysis. The best fundamental argument of chemically active valence subshells confirmed by periodic trends is surprisingly more decisive for He over Be and Lu under Y than for Be and Mg. I was extremely surprised by this, but I'm consistent and stick to it. Double sharp (talk) 07:59, 10 February 2020 (UTC)

The crushing weight of history

Earlier, I wrote that, "History and its (staggering) momentum, supports La in group 3, in the particular context of this entire thread."

I thought I'd covered this before, but maybe not.

Historically, the Ln were known to be chemically very similar.
Originally, the 4f sub-shell was thought to be complete only at Lu.
So, with the popularity of electronic periodic tables, La was placed under Y since La did not have an f electron, and the Ln ran from Ce to Lu.
It was later recognised that the 4f shell was prematurely completed at Yb, and that Lu was in fact 4f¹⁴5d¹.
Nothing happened however, since the chemistry of Lu, as a lanthanide, remained 100% unchanged.
So La remained under Y in recognition of the delayed start to the filling of the 4f sub-shell, and the unchanged chemistry of Lu.
The resulting separation of the d-block in the 32-column form never became an issue in light of the overwhelming popularity of the 18-column form.
As Reger, Scott and Ball (2010, p. 295) put it, "perhaps" the correct shape of the 32-column periodic table should feature a split d block given the electron configurations of La and Ac, but that "we avoid these structures by splitting the f block from the rest of the periodic table. This also has the advantage of being able to print a legible periodic table on a single piece of paper." (They show La below Y in the rest of their book.)
A survey conducted by Scerri and me, of some 200 chemistry books from 1970 onwards, showed that for every six books, four were La, one was Lu, and other other one was IUPAC style.

A few tables of the 1920s and 30s showed Lu under Y for reasons of perfect regularity (Janet) or because Lu occurred in the “yttrium” group (along with Sc and Y) rather than the “cerium” group (which included La).

But this never took off.

That Sc, Y and Lu occurred in the so called yttrium group, and that La occurred in the "cerium" group did not imply anything particularly significant; it is simply a reflection of the increasing basicity of these elements as atomic radius increases. Taking the alkaline earth metals as another example, Mg (less basic) belongs in the "soluble group" and Ca, Sr and Ba (more basic) occur in the "ammonium carbonate group". Moving Lu under Y because they occur in the same chemical separation group failed to consider separation group patterns elsewhere in the periodic table. Further, the separation group behaviour of Y can be ambiguous, and Sc, Y, and La appear to show complexation behaviour different to that of Lu (as previously cited).

However lacking arguments in support of La may be, they have (so to speak) the advantage of incumbency. Whatever arguments there are in favour of Lu are like, if I may be so crude, a squashed gnat on the windscreen of an eighteen-wheeler going at full speed.

Chemists are such a tyrannically conservative bunch that there will be virtually no chance of getting them to consider electron configurations based on the solid/ionic rather than the gaseous state.

These are just chemistry-based observations based on practicality and pragmatism, of course. Sandbh (talk) 06:20, 17 February 2020 (UTC)

@Sandbh: Just because something is the predominant form does not make it right. Where is the critical analysis of this in the literature? By these standards we would never have gotten rid of Be-Mg-Zn, but we did! Double sharp (talk) 14:39, 17 February 2020 (UTC)

Article redrafting

That's just about it for me. The next iteration of the article to follow, for submission to FoC.

Thank you to @Double sharp:@Droog Andrey:@R8R:@Дрейгорич: for a tremendous and productive peer review experience. Sandbh (talk) 04:55, 10 February 2020 (UTC)

@Sandbh: No prob. Although I am in no way a chemist. Just a hobbyist who loves the periodic table, so I'm talking from an inexperienced point of view, perhaps the average educated reader. ― Дрейгорич / Dreigorich Talk 05:04, 10 February 2020 (UTC)

@Дрейгорич: If you actually read most of this, I'd be somewhat interested to hear if you think Sandbh or I was more convincing. Since you think your POV is inexperienced, that means you're the closest thing we have to a neutral reader. I mean, we have done this argument before with Sandbh on the Lu side and me on the La side instead ^_^, but we changed our minds, and maybe we are too invested in our respective current sides. P.S. I am in no way a chemist either. Just someone who has spent entirely too long thinking about this problem. Double sharp (talk) 11:56, 10 February 2020 (UTC)

@Sandbh: I will admit I'm on team Lutetium myself due to Aufbau, and I'm aware that most tables draw either La or put all 15 below. The entire conversation ended up being FAAAAAAAAR too long for me to read through, although interesting points were raised on both sides (and maybe more). I learned quite a bit. ― Дрейгорич / Dreigorich Talk 16:39, 10 February 2020 (UTC)

@Double sharp: You as well, oops. ― Дрейгорич / Dreigorich Talk 20:56, 10 February 2020 (UTC)

@Sandbh: Do you plan to add anything to address my argument about chemically active valence subshells (cf. Jensen, Jørgensen, Schwarz, Seaborg; I add valence because otherwise I expect some fogging, to use your term, will appear about the 4f core subshells of Lu, that are of the same relevance for this as the 4f core subshells of Hf through Rn, i.e. zero)? Double sharp (talk) 11:56, 10 February 2020 (UTC)

@Double sharp: Nothing planned at this stage. It is something I'll consider though as I work on the next iteration. Sandbh (talk) 00:31, 11 February 2020 (UTC)

(700k!) Double sharp (talk) 23:40, 11 February 2020 (UTC)

Double standard

Having read all 700k+ of this discission, I've got the same feeling as Double sharp had:

I'm tired of this endless double standard. You throw out a barrage of arguments that look like they might support the La table, and flip non-stop between them the moment one of them looks like it is in trouble. And then you selectively read the literature in order to not see refutations. And you never consider whether any of your criteria are truly fundamental by putting them to the test of the rest of the table, cloaking this masterpiece of inconsistency under the garment of minimising change. Which is more or less like taking the La table as an axiom and throwing out whatever you want to save it. All I can say is: this is not science. There is no way we can proceed if you refuse to follow scientific principles, actually put your theories to the test, and at least compare all possibly relevant criteria and no others equally regardless of whether they seem to favour La or Lu. If you don't do that, then I say: go ahead and get what you want published. But don't thank me for the critique in the acknowledgements, because I disagree with so much of your paper that I don't want it to look like I supported the final product.

Indeed, it seems that Sandbh lacks attention to patterns and general trends explained by Double sharp with great patience of job. As an experienced chemist, I insist that deep understanding of these interrelations is required to discuss the foundations of chemistry, even in the context of historical review. Otherwise this is not science to send an article, but conscience to withdraw it. Droog Andrey (talk) 07:51, 12 February 2020 (UTC)

@Droog Andrey: Thank you! As you are an experienced chemist and I am not one at all ^_^, and especially since it was you who gave me a much better understanding of group 3 back in Archive 33, your agreement means a lot to me. Nice pun at the end, BTW. ;)

@Sandbh: So out of the four people who have expressed their views here: we now have two people who think your article is incomplete and misses the important chemical perspectives (me and Droog Andrey), one who at least thinks your article feels imbalanced and runs to a hasty conclusion (R8R), and one who at least seems to think that "maybe we don't have enough evidence to overthrow the Aufbau Sc/Y/Lu/Lr arrangement" (Dreigorich) based on glancing at our long thread. Surely this suggests that a rather significant overhaul of the chemistry-focused section of your article would be a reasonable course of action? I agree with Droog Andrey's 9 January comment: "An overall impression is that the article provides enough opinions from literature, but lacks analysis of chemistry". Double sharp (talk) 22:32, 12 February 2020 (UTC)

@Double sharp:@Droog Andrey:@R8R:

I agree my article is incomplete.

A double standard is not science.

My general impression has been, rightly or wrongly, that I set out an argument and Double sharp argues against it using a different context, or goes into detail one or two levels down, and on either or both of those grounds, eventually ends up saying I adopt a double standard. A variation on this is to identify an inconsistency at one or two levels down and argue that because of this inconsistency, my more general argument is therefore invalid. I feel I do analyse the chemistry involved but only down to the level of generality involved, and no further. Chemistry is full of such generalisations, otherwise it becomes unworkable. That said we're always mindful of the exceptions and boundary overlaps and we assign them a commensurable level of significance: "Get on with the overall story and it's themes rather becoming unnecessarily distracted by less important details".

I believe I haven't entered into any double standards, but if I have, please set out one example here and I'll address it.

Here's four. ^_^

Your treatment of Th and Lr, vs that of La and Ac.
Your treatment of the 14 core 4f electrons of Lu, which is totally different from how any other element's core electrons are treated (e.g. 4f in Hf through Rn, 3d in Ga through Kr).
Your use of modus tollens against Lu arguments (Nelson), but refusal to allow them as rebuttals of La arguments (whenever I say that "your argument raises questions about Al in group 3 or Be and Mg in group 12").
Inconsistency over when an oxidation state is relevant. Somehow Ti(III) is relevant when considering transition metal chemistry of Ti, but absolutely irrelevant when it comes to undermining the "predominately covalent" nature of group 4, in which we can always bring the oxidation state lower and by Fajans' rules covalency will go down just like it does from Tl(III) to Tl(I). Just compare TiCl₂ vs. TiCl₃ vs. TiCl₄.

Double sharp (talk) 19:05, 13 February 2020 (UTC)

@Double sharp: Here we go. I ask for one example, and get 4 instead, most of which are written too abstractly for me to address. I can barely follow the 4th example. Here is what I say:

As a generalisation, Group 4 has a predominately covalent chemistry.
The +4 oxidation state dominates Ti chemistry, but compounds in the +3 oxidation state, in which Ti has a transition metal chemistry, are also common.
It is in Ti that the really characteristic transition metal properties are first commonly seen (I know we agree on this one).

Could you please now take it from there in giving me an example of how I have used this as a double standard. Sandbh (talk) 23:08, 13 February 2020 (UTC)

@Sandbh: Easy. [1] First you generalise by saying "group 4 has a predominately covalent chemistry" (which means ignoring the lower oxidation states +2 and +3, which are more ionic, cf. for example TiCl₂ and TiCl₃). [2] Then you claim "really characteristic transition metal properties are first commonly seen" in Ti, which is only true for the +3 oxidation state that is not predominant! That's a double standard right there. [3] Is +3 relevant or not for determining predominant/characteristic behaviour?

@Double sharp: Nice progress! 1. Agree. 2. Agree. 3. +3 is not relevant for determining predominant/characteristic behaviour. I never said +3 is predominant. From our Ti article I said, “The +4 oxidation state dominates Ti chemistry, but compounds in the +3 oxidation state, in which Ti has a transition metal chemistry, are also common.” You and I have agreed (!) that, "It is in Ti that the really characteristic transition metal properties are first commonly seen".

Now, what double standard are you referring to in respect of these factual statements? Looking forward to your response in that we can hopefully further develop a mutual understanding. Sandbh (talk) 01:40, 14 February 2020 (UTC)

@Sandbh:. Simple. In (3) you claim "+3 is not relevant for determining predominant/characteristic behaviour". But then you say "It is in Ti that the really characteristic TM properties are first commonly seen". But that is only on the basis of the +3 state, which you previously said was not relevant for determining characteristic behaviour. Why don't we sweep it under the rug as Jensen proposed to do for Hg^IV when it was thought that that was a thing? Double sharp (talk) 12:01, 14 February 2020 (UTC)

What follows is my perspective: group 4 has four elements, only Ti has more or less common characteristic TM properties (using "is it stable in water" as a benchmark). Zr, Hf, and Rf don't. So as a generalisation, group 4 doesn't show characteristic TM properties (neither does group 5). So if we speak of commonalities from group 3 to the neighbouring groups 2 and 4, we see that its behaviour is perfectly intermediate between them, since all groups have incipient TM behaviour but chemically are not very good at it. (Physically they get better and better gradually, of course.) Why is "predominately covalent/ionic" more important than this? For me, the only consistent answer is: they are useful only as confirmations, they are not the fundamental thing. We choose something fundamental that controls all the chemistry and trends from behind the scenes as our basis for drawing the PT. Then we confirm that it indeed predicts the right answer, of course.

If you think the first three are too abstract, here are rephrasings:

You allow Th to stand as an f-block element, and Lr to stand as a d-block element, despite having the "wrong" differentiating electrons. But La and Ac, with similar credentials, are not allowed by you to stand as f-block elements.
You treat the core electrons of Lu as relevant for the 4f-block membership you push for it, while simultaneously ignoring the equally relevant core electrons of Hf through Rn.
You are perfectly fine with asking the question "what happens to other elements if we take that approach?" when it criticises a Lu argument (Nelson on carbonyls, where you and I argued that it doesn't work for the s-block), but any time I use it to criticise a La argument (usually by asking "what happens to Be or Mg or Al"), you dismiss it as irrelevant. Double sharp (talk) 23:25, 13 February 2020 (UTC)

@Double sharp: I've been banging on about Rayner-Canham's quote, "For chemists…the most important feature of an element is its pattern of chemical behaviour, in particular, its tendency toward covalent bond formation (or its preference for cation formation)." I neglected to add that as well as attributing this to Professor Rayner-Canham (121 Chem ED publications), he wrote that book with Tina Overton, former Distinguished Professor of Chemistry at Monash University, now the Director of the Leeds Institute for Teaching Excellence (51 publications). They are both wrong, of course. Sandbh (talk) 11:35, 18 February 2020 (UTC)

@Sandbh: Tendency, which is a continuum, and is of course just electronegativity. None of this all-or-nothing ridiculous notion of "predominately ionic" / "predominately covalent" that I've refuted many times. As usual, the literature is not wrong and chooses its words carefully, and you take it out of context and become laughably easy to prove wrong. Double sharp (talk) 11:55, 18 February 2020 (UTC)

@Double sharp:

In (3) you claim "+3 is not relevant for determining predominant/characteristic behaviour". Correct
But then you say "It is in Ti that the really characteristic TM properties are first commonly seen". Correct; as you have agreed"
But that is only on the basis of the +3 state, which you previously said was not relevant for determining characteristic behaviour. Correct

Where is the contradiction between my first and second statements? Ti +4 does not show TM behaviour. Ti +3 does. Our titanium article says, "The +4 oxidation state dominates titanium chemistry, but compounds in the +3 oxidation state are also common." Correct

Where is the double standard?

@Sandbh: It's right there. If you say that +3 is irrelevant for characteristic behaviour, then the characteristic behaviour of Ti is based only on the +4 state and is hence main-group, because +3 then cannot be common. (Contradiction between #1, #2, and #3 identified.) Therefore group 4 exhibits characteristic main-group chemistry, and so we have an equally strong argument saying that group 4 is not different from groups 2 and 3 countering your one about supposed ionicity/covalency having a rupture between groups 3 and 4.

P.S. You somehow don't seem to have a problem acknowledging "schizoid" chemistry that differs significantly between oxidation states in Cu, Ag, and Au. With a bit of critical analysis of the literature you might realise that this is totally normal in the periodic table that elements behave differently in different oxidation states. And perhaps you might graduate to the idea that if different oxidation states of an element show different characteristic behaviour, there ought to be something deeper explaining why. You can already do it for group 11, albeit using a flawed idea of what that "something deeper" really is, so it shouldn't be that hard! Double sharp (talk) 20:12, 17 February 2020 (UTC)

@Double sharp: You read things into what I say that are not there.

I say, [1] "It is in Ti that the really characteristic TM properties are first commonly seen" which you agree. Just in case, this is not the same as saying that [2] Group 4 has characteristically TM behaviour.

I say [3] the chemistry of groups 1-3 is predominately ionic, unlike the predominately covalent chemistry of Groups 4+.

[1] and [2] are my points of difference. That's all.

Get it? Sandbh (talk) 03:03, 18 February 2020 (UTC)

@Sandbh: So we have a double standard indeed. If you are willing to use [3] as an argument saying "the rupture is between groups 3 and 4", then by the logic of [1] and [2] you should be equally willing to use

[4] The chemistry of groups 1-5 is predominantly pre-transition, so there is no strong gap there.

And we should be equally willing to use:

[5] The physical properties of group 3-5 are predominantly strongly metallic, unlike the structurally weak metals of groups 1-2.

But somehow, we never see those, because they make for good Lu arguments. Double sharp (talk) 12:10, 18 February 2020 (UTC)

@Double sharp: It’s like I have a red billiard ball and a red basketball. They are both red; I choose to focus on the size difference. From a chemistry view, physical properties of the elements are not so important. Do you see a double standard? I don’t. Sandbh (talk) 09:27, 19 February 2020 (UTC)

@Sandbh: That succeeds in wriggling out of [5], but not of [4], so the double standard remains. Not to mention that physical properties are also important to periodicity. ;) Double sharp (talk) 21:44, 19 February 2020 (UTC)

@Double sharp: [4] is equivalent to them both being balls. Sandbh (talk) 01:50, 20 February 2020 (UTC)

@Sandbh: Nope. It's a perfectly relevant illustration of how most often there is no difference or the difference is a continuum. Meanwhile, physical properties i.e. [5] are still an important part of periodicity. Do you actually want a compromise table somewhere in the middle of the spectrum from LSPT to Rayner-Canham, or just to support La under Y no matter what? Double sharp (talk) 07:57, 20 February 2020 (UTC)

You also asked me:

Why is "predominately covalent/ionic" more important than this?

Answer: This pervades the whole of the PT. TM behaviour is limited.

It is so obviously correlated with other properties that no scientist worth the name should claim it as fundamental for how we draw it. It's based on EN, it's based on atomic size, that's what we have to look at. Meanwhile, the main-group vs. transition distinction is embraced as fundamental by practically every chemistry text in the world... Double sharp (talk) 20:12, 17 February 2020 (UTC)

You note that I:

"…allow Th to stand as an f-block element, and Lr to stand as a d-block element, despite having the "wrong" differentiating electrons. But La and Ac, with similar credentials, are not allowed by you to stand as f-block elements."

Answer: Yes, and you know why. Primarily the periodic law, the aufbau process, and that the La form is more regular/closer to the n+l rule.

@Sandbh: Total nonsense. The n+l and the aufbau process rule according to everyone else but you says "6s, 4f, 5d, 6p", no exceptions, and pushes for Lu. The relevant anomalies according to everyone else but you are about the configurations built up as a whole, not the electron that differentiates us from the previous element (never mind how ill-defined that is when multiple electrons change, e.g. V d³s² vs. Cr d⁵s), and that pushes strongly for Lu. And the periodic law according to everyone else but you works on periods as well as groups (Mendeleev said it too), and that pushes strongly for Lu. Of course, it's not as simple as looking for the first element, and it has to be in the right block, and surprise, surprise, La has 4f valence involvement and Lu does not. Double sharp (talk) 20:12, 17 February 2020 (UTC)

@Double sharp: I conclude you don't know what you're talking about in this narrow field. Like Scerri told us about needing to do some more homework. Listen to what he said. I did. Try, for example, his argument with Parsons, based on the n+l rule, and tell me what doesn't work. That'd be a good start. Have a look at our article on quantum numbers, too. Sandbh (talk) 03:10, 18 February 2020 (UTC)

@Sandbh: I did, thanks to Droog Andrey. Your reference to Scerri and Parsons is quite rich since their chapter in Mendeleev to Oganesson is a chapter that argues for Lu in group 3, and they even use a lot of the arguments I have been using. They state that "arguments drawing on changes in electron configuration suggest the need to replace lanthanum with lutetium but are, by no means conclusive"; that suggests immediately that the important thing is what Landau and Lifschitz (one can hardly find brighter luminaries arguing for a Lu table) noted correctly, that the 4f shell is complete with Lu and it therefore must be part of the 5d series (not La, without the 4f shell). Then they note that "the chemical and physical data...also support the replacement of lanthanum with lutetium" (citing Chistyakov and Jensen), and I have already reanalysed it after Droog Andrey's kind explanations on why "look at group 2" (which is essentially our only argument in our submission) may easily be refuted. Then they go for their conclusive argument: that a La table drawn in order of increasing Z requires a split d-block, and nowhere else in the PT does this occur. Then they go on and say that the n+l rule is violated for a La table but not a Lu table! Why? Because we have La as the first element where n+l=7, but with La as a supposed d-block element we end up first with n=5 before going to n=4! So, indeed, a La table is totally inconsistent with the n+l rule as everyone in the literature has it! You are a lone voice in the wilderness arguing about differentiating electrons and with an altered n+l rule! Oh, and even better, they agree with me about hypocrisy applied to thorium: they write "Similarly, we draw attention to the fact that there are anomalous cases such as the thorium atom, which features no f-orbital electrons—yet nobody disputes that this element belongs in the f-block of the periodic table."

Of course, if we wanted completeness, we would have to critically analyse the n+l rule to see if it is really right. It could be, of course, that there is a real situation of "one 5d, fourteen 4f, nine 5d". But just look at chemically active valence subshells and you'll see that it isn't so: La has 4f valence involvement and Lu doesn't. Score: DS 11/10, Sandbh −1/10. ;)

As for helium, I agree with Scerri and Parsons that it doesn't create this sort of anomaly because we all know that it really is an s-block element anyway even when moved over Ne: whereas a La table makes the bold claim that La is a d-block element. But I would support He over Be anyway to make the fundamental nature of blocks clearer. Double sharp (talk) 12:10, 18 February 2020 (UTC)

@Double sharp: I’m glad you read it.

Yes, electron configuration arguments by themselves are insufficient.

On L & L I defer to our IUPAC submission:

“The authors do not satisfactorily resolve the group 3 question. They effectively show lutetium as a period 6 d block element, in the position immediately to the left of hafnium, but also show La occupying a position immediately above Lu and below Y (p. 256). While they were not specifically addressing the group 3 question, such a configuration appears to be at odds with the general principle of one element per periodic table position or, at best, leaves the question of the constitution of group 3 unanswered. They apply the same approach to Cu-Ag-Au, and to Zn-Cd-Hg, resulting in these metals being treated as main group elements belonging to groups 1 and 2, respectively (p. 255). However, groups 11 and 12 are always considered to be d-block groups, since the ten columns from group 3 to 12 correspond to the filling of the ten vacancies in a d subshell. Furthermore, the chemistry of group 11, with the d electrons readily ionised, seems to further weaken such a possibility.”

@Sandbh: So they didn't consistently follow their own argument. That's a shame, but it doesn't make their argument worse, and it doesn't stop us from paying attention to it. (What is their context, anyway? If they were aiming at something like Rayner-Canham's table, this all makes sense!) Double sharp (talk) 22:09, 19 February 2020 (UTC)

The chemical and physical data...support[ing] the replacement of lanthanum with lutetium" (citing Chistyakov and Jensen), did so on the basis of selectivity, as Scerri noted.

@Sandbh: Even when one is less selective the data is still strongly suggestive towards Lu. Double sharp (talk) 22:09, 19 February 2020 (UTC)

On the split d-block table, there is already a split s-block, with He over Ne. In our IUPAC submission we noted “Indeed, Hamilton (1965), shows a periodic table extract (groups 1 to 11, plus footnoted Ln and An, showing Ce, Pr…Lu; and Th, Pa…Lw) with a split d block (the gap is between groups 3 and 4) and says that—without any fuss—this is "the periodic table as it is usually presented". Similarly the Inorganic Chemisty Division of the ACS featured a split-d block table for many years."

That's not a split s-block. Everyone knows that He is an s-block element, so the sequence of elements aligned with their blocks here looks like:

H  He Li Be B  C  N  O  F  Ne ...
s  s  s  s  p  p  p  p  p  p ...

and there is no splitting. But in a La table, the claim is made that La is a d-block element, so the sequence around there looks like:

Cs Ba La Ce Pr Nd ... Yb Lu Hf Ta ...
s  s  d  f  f  f  ... f  f  d  d ...

And we have a split. Many people present it that way, sure. That doesn't mean they are right if they don't critically analyse what they happen to be doing. Double sharp (talk) 22:09, 19 February 2020 (UTC)

As we wrote, “We support this line of reasoning. The 32-column form of the -La-Ac table may be regarded as being asymmetrical but we do not think this is necessarily significant given other examples of asymmetry in physics. The 18-column form strikes us as representing an elegant synthesis of accuracy and symmetry. Accuracy in capturing the relationships among the elements; symmetry in the maintenance of an intact d block. We think the -Lu-Lr table sacrifices accuracy in the pursuit of symmetry.”

@Sandbh: I supported such a statement only on the basis that it seemed from my then more limited understanding of the chemistry involved that the behaviour of group 3 was significantly skewed towards the s-block, and overreliance on condensed-phase configurations. Now that Droog Andrey has demonstrated to me that this is not so, and that condensed-phase configurations by themselves are incomplete and advocate for a lot of silly things elsewhere in the table, I consistently shifted back to Lu-Lr. Double sharp (talk) 22:09, 19 February 2020 (UTC)

Further, an analogous uneven distribution occurs with Groups 1−2, and 12−18, which become spatially separated by Groups 3−11, although this is not as extreme. Here, Groups 1−2 and 12−18, from a chemical point of view, effectively form a joint “sp” block of elements. In structural terms, the larger and more energetic s- and p-block orbitals provide the structural framework of the periodic table, which is internally perturbed by the smaller d and f orbitals.

@Sandbh: There's a big difference between the pre-transition main group elements and the post-transition main group ones, so there is nothing wrong with that. Moreover, the sequence of valence subshell filling supports that d and f orbitals appear between ns and np. There is not a big difference between group 3 and groups 4+, and evidence from chemically active valence subshells shows clearly that there is no such thing as "one 5d, fourteen 4f, nine 5d" like a La table claims, since La is already using 4f as a valence shell. So this split has no leg to stand on. Double sharp (talk) 22:09, 19 February 2020 (UTC)

P.S. I'd argue that the Zn group are dsp elements, see below on ZnF₂ and ZnCl₂. The d-involvement is weak but definitely present. Double sharp (talk) 23:17, 19 February 2020 (UTC)

Scerri and Parsons’ additional n+l requirement namely that…

"In progressing sequentially through the blocks of the PT one should adhere to both parts of the MR, namely that the order of orbital filling should proceed with increasing values of n + l and in cases of equal values of n + l in an increasing order of the quantum number."

...is a "set up to fail" argument.

This is because the La form does not pass the argument, whereas the Lu form does.

Their additional requirement is not a part of the Madelung Rule.

@Sandbh: To quote you: "Wow! That sounds like new chemistry. Time for a letter to the Nature journal." Look at every source talking about the n+l rule. The moment you see the diagonal path, which goes though 3d before 4p before 5s, and through 4f before 5d before 6p before 7s, you are seeing Scerri and Parsons' requirement: orbitals fill in order of increasing n+l, and when n+l is constant they fill in order of increasing n. That's why the path is diagonal. Yet you are disputing this. Really? I've left the very picture you have in your sandbox here in case you've forgotten this utterly basic bit of chemistry. Double sharp (talk) 22:09, 19 February 2020 (UTC)

In comparing the La form with the Lu form one sees this anomaly is an outcome of the delayed filling of the 4f sub-shell.

@Sandbh: The little problem is that it's not chemically relevant to anything. La doesn't have a 4f electron but it still has chemically relevant 4f valence involvement. Double sharp (talk) 22:10, 19 February 2020 (UTC)

To then propose an additional requirement for the Madelung Rule such that the La form does not comply with it is a "set up to fail" argument.

@Sandbh: As demonstrated it's not an additional requirement. It's a totally standard one.

“

The order in which orbitals are filled by the electrons is given by Madelung's rule (also known as the n+l rule): (i) orbitals are filled in order of increasing n+l; (ii) if two orbitals have the same value of n+l, they are filled in order of increasing n.

”

— A Concise Handbook of Mathematics, Physics, and Engineering Sciences (Polyanin and Chernoutsan, 2010)

“

Madelung's Rule: The energy ordering is from lowest value of n+l to the largest; and when two shells have the same value of n+l, fill the one with the smaller n first.

”

— The Oxford Solid State Basics (Steven H. Simon, 2013)

“

...when there are two or more orbitals with the same value of n + l, the order of filling is that of increasing n.

”

— Modern Inorganic Chemistry (William L. Jolly, 1984)

...and every book that ever displayed a diagram like the one I just posted up including 4f before 5d, i.e. absolutely all of them. They are all wrong, of course. It looks like you have a new homework assignment. ;) Double sharp (talk) 22:09, 19 February 2020 (UTC)

In contrast, one can compare the actual differenting electrons of the La and Lu forms, with the n + l rule, and simply observe that that the La form more closely matches the n + l rule.

And that is all that needs to be said. There is no need for an additional requirement to be added to the n + l rule.

Yes, it’s good to see that they write “nobody disputes that this element belongs in the f-block of the periodic table." With the exception of yourself :) Sandbh (talk) 10:26, 19 February 2020 (UTC)

@Sandbh: As usual you don't understand reductio ad absurdum. I am arguing about Th not because I believe it's not an f-block element, but to refute your arguments. Those arguments of yours about when a block begins, if applied consistently, lead to denying Th as an f-block element, which is nonsense. And that is the point I'm making. If you do even a basic study of mathematics you will encounter this, no doubt in the proof that the square root of 2 is irrational. When we begin by writing "suppose it's actually rational", we don't actually believe that, and are using that assumption to deduce something that is obviously false, that a fraction with even numerator and denominator could be in lowest terms. And we don't believe that either, because we know it's nonsense. Double sharp (talk) 22:09, 19 February 2020 (UTC)

@Double sharp: Did you miss when I said:

Scerri and Parsons’ additional n+l requirement namely that…

"In progressing sequentially through the blocks of the PT one should adhere to both parts of the MR, namely that the order of orbital filling should proceed with increasing values of n + l and in cases of equal values of n + l in an increasing order of the quantum number."

...is a "set up to fail" argument.

Their additional requirement is not a part of the MR. Do you now understand what I said? Sandbh (talk) 01:24, 20 February 2020 (UTC)

@Sandbh: Oh I understood what you said. Unfortunately, it's rubbish. Not only that, it's even worse rubbish than anything else you've thus far posted. Literally everyone who ever mentions the n+l rule mentions this requirement. Or else no one would ever be able to tell if 3d or 4s was supposed to go first according to it. See my above quotes and pictures. Of course, every chemistry author in the world must be wrong, according to you! If you want to keep denying it, go ahead. But then, shall I know indeed that this is not science. Double sharp (talk) 07:57, 20 February 2020 (UTC)

@Double sharp: Well, I asked Scerri about this. He agrees with me. Send him an e-mail, as a *world authority* on the periodic table, and tell him he's spouting "astonishing rubbish" :) Alternatively, go back and carefully read what he and Parsons said and my explanation above, paying special attention to the underlined word. Sandbh (talk) 10:55, 20 February 2020 (UTC)

@Sandbh: I already paid attention to the underlined word. That's precisely what makes your argument astonishing rubbish, because that requirement is not additional at all, and certainly not Scerri and Parsons' addition. It is an absolutely standard component of the Madelung rule. Indeed, you're the voice in the wilderness holding only one half of the rule as important and rejecting the other half. Löwdin even goes so far as to call it the (n+l, n) rule. I've already given three quotations. Providing even more is trivial. Here's another one:

“

Madelung discovered a simple empirical rule for neutral atoms. It consists of two parts.

(A) When considering consecutive neutral atoms the electron shells fill up in the order of the quantum number sum (n + l).

(B) For electrons in states of equal (n + l) the order of filling goes with increasing n.

”

— Goudsmit and Richards, 1964

And this one is of especial historical significance, because it was to Goudsmit that Madelung first privately communicated his rule in 1926.

Given that Scerri understood this, I think it is very likely (since you've demonstrated throughout this argument a lack of understanding of basic logic) that you have misunderstood him. Indeed, the important issue here is that assuming the n+l rule (both parts) beforehand is in some sense backwards, because we should really be testing it against the chemistry and physics involved. But the n+l rule is fully borne out by this, given the direct consequences of 4f valence involvement in La. To put it another way: we suspect n+l rule to be the right rule based on what we see till Ba, and we see absolutely nothing important at La that should overthrow it. Double sharp (talk) 14:19, 20 February 2020 (UTC)

@Double sharp: I've added another underline. The key phrase is, "progressing sequentially through the blocks of the PT". Bear in mind their focus was on what happens when you go from the s-block (Ba 6s) to the d-block (La 5d) to the f-block (Ce 4f). That is where their set-up-to-fail argument "progressing sequentially through the blocks of the PT" kicks in. The "through the blocks" qualifier is not a part of the MR. It's quite a subtle addition. Does this make things clearer? Sandbh (talk) 22:45, 20 February 2020 (UTC)

@Sandbh: Progressing sequentially through the blocks, we are still "considering consecutive neutral atoms" as Goudsmit and Richards say Madelung's rule is, and the former got it directly from Madelung. So Madelung's rule says that for Z = 56 (Ba) we just finished 6s. At Z = 57 (La), we have the lowest n+l states as 4f, 5d, 6p, 7s. By (B), the order of filling goes with increasing n, so we expect La as an f-block element. We don't expect a d-block element until Z = 71 (Lu) when 4f is exhausted. Therefore Scerri and Parsons are vindicated. Double sharp (talk) 22:56, 20 February 2020 (UTC)

@Double sharp: You're missing the point. There is nothing in the MR, per se, about blocks. Scerri did not include this argument in the 2^nd edition of his Periodic Table book (2020) for the reason that it doesn't work. Sandbh (talk) 05:14, 21 February 2020 (UTC)

@Sandbh: There is no need to mention blocks: Scerri and Parsons' original argument still works exactly if it says "progressing sequentially through the PT". Double sharp (talk) 12:56, 21 February 2020 (UTC)

@Double sharp: Regarding Th and reductio ad absurdum, and your assertion that, "Those arguments of yours about when a block begins, if applied consistently, lead to denying Th as an f-block element…" this misstates my position. From day 1, this has consistently been that a block starts upon the appearance of the first relevant electron. That is all. It stands alone: s at H; p at B; d at Sc; and f at Ce. If you choose to extend this argument beyond that, don't blame me. 01:44, 20 February 2020 (UTC)

@Sandbh: Chemistry is not a heap of distinct conceptions standing apart alone, but rather interconnected system of conceptions based on experimental facts.

When Double sharp shows that your argument produces bullshit, you'd better learn what's wrong with the argument instead of continuously building artificial borderlines for its applicability. Droog Andrey (talk) 07:03, 20 February 2020 (UTC)

@Droog Andrey:@Double sharp: Hey, it's not my argument and not my BS! Repeat after me: Sandbh's argument is that a block starts upon the appearance of the relevant electron i.e. s at H; p at B; d at Sc; f at Ce. Sandbh's argument stops there. If DS wants to extend my argument such that it therefore needs to apply to the start of each row of a block thereafter, and then wishes to argue about an extended argument that I never signed up to, then he can knock himself out, as long as he leaves me out of it. Understand? What DS is arguing about is not my argument!! Why is this so hard to understand? Sandbh (talk) 11:32, 20 February 2020 (UTC)

@Sandbh: You don't understand logic.

I could equally well say that the f-block must end when the final f electron appears, i.e. at Yb. Say my argument stops there. If Sandbh wants to extend this argument such that it therefore needs to apply to every block, and notes that this is nonsense because it says the d-block ends at Cu, then I could equally well say that this is an extended argument that I never signed up to. But Sandbh has no problem using this refutation himself when I say (in a corrected version of this argument) that Lu is not an f-element because its f-electrons are core electrons, and give the argument without an f-block only restriction:

@Double sharp: If you said, "the f-block must end when the final f electron appears, i.e. at Yb" I'd ask, "is this statement impacted by aufbau irregularities(?)"; and, "is it impacted by where the f-block then starts when the first f electron appears?" I wouldn't argue about the start of the second f-block row, since this not part of your argument. And I wouldn't argue about the d-block because that's not within the scope of your argument. Sandbh (talk) 22:59, 20 February 2020 (UTC)

@Sandbh: You should be arguing about the d-block if I said that. Because the natural scientific response to me going "oh, this is only valid for the f-block" is not "Great Scott! You're right, of course. Let me fight within the f-block only". It is "so what is the reason the f-block is categorically different from the other blocks that gives you a right to say so"? See the next few paragraphs. ;) And you should also argue what this criterion has to do with chemistry and physics, since it is not unheard of elsewhere that an already preemptively filled subshell is still valence later (see group 12 in the d-block), and it would be my burden to prove this doesn't happen for Lu. (Which Droog Andrey and I have done.) Double sharp (talk) 23:07, 20 February 2020 (UTC)

“

The line about "to the point where its characteristic electrons are core electrons" reminds me of group 12. Therefore we need to start the d-block in group 2! IUPAC will throw that one out.

”

— Sandbh

Of course, you don't even do it right, because as I demonstrated Zn 3d is demonstrably involved in the bonding of some Zn compounds!

Or I could say that only electrons in directly valent MOs matter for determining chemically active subshells in the s-, p-, and d-blocks. Say my argument stops there. (I don't say that, of course.) If Sandbh wants to extend this argument to note that it doesn't work in the f-block, then I can say the same thing. Of course, when I don't pose this artificial restriction, Sandbh has no problem coming up with such examples when attacking my statements about "chemically active subshell of highest angular momentum":

“

How does that work for e.g. Nd, which has a condensed phase configuration of 4f3d1s2, and which is not known in the +4 oxidation state? Time to move into the d block?

”

— Sandbh

And you don't do it right either, since Nd⁴⁺ is known.

So by Sandbh's logic, it appears that my arguments would become more convincing if I said "oh, that's for some elements only". The most convincing argument of all must surely be the one that says "this property is relevant for La only and the fact that literally every other element in the table contradicts it is irrelevant because I say so", then. Of course, the whole world begs to differ...

The point is: it's not enough to say: "This is my argument, and this is where it is applicable only. Lo! hearken to me for I have spoken. All ye shall only apply my argument where I say it is relevant. And all ye who proclaim that my argument is BS because it produces BS in regions I excluded it for are heretics. But I may do that myself when attacking your arguments, for I have special Divine Exemption from my side of this crusade." We are doing science, or at least I am doing science, so you have two requirements:

You have to justify why your argument should be the right one and not my artificially-concocted-to-be-BS ones above that happen to support Lu. (I have better Lu arguments than these, of course.) If you can't apply it everywhere, why should that inspire confidence in it as a foundational principle for the PT? And why is the next row not important? If you can't explain why a criterion is chosen to be relevant, then we should be throwing it in the garbage can. So: why is the first electron so much more important than all the others, and why does the next row of the block not matter?
You don't get to have your arguments in a vacuum. You say the criterion doesn't work somewhere. OK, what is the justification from Nature that says we are in a totally new regime there? Otherwise it is an artificial restriction to save face. As Droog Andrey says, "Chemistry is not a heap of distinct conceptions standing apart alone, but rather interconnected system of conceptions based on experimental facts." So is all of logic. You don't get to have mutually contradictory beliefs if you're arguing a stand. If you wish to claim that a clearly identified contradiction is not a problem because the argument cannot be applied there, then you'd better explain what is so categorically different that the argument cannot be applied there. Not should not. This is not a case of "Don't do it because I say so". Double sharp (talk) 14:07, 20 February 2020 (UTC)

"…treat the core electrons of Lu as relevant for the 4f-block membership you push for it, while simultaneously ignoring the equally relevant core electrons of Hf through Rn."

Answer: Yes, and yow know why. I don't have to ignore the core electrons of Hf through Rn, since they are out of context. Hf through Rn are not Ln.

@Sandbh: It doesn't matter that we labelled Lu as a lanthanide, what matters is: are those 4f electrons actually chemically active in Lu? That's the important question for block assignment. The answer is a resounding no: they are just as inactive as in Hf through Rn! Double sharp (talk) 20:12, 17 February 2020 (UTC)

"…[am] perfectly fine with asking the question "what happens to other elements if we take that approach?" when it criticises a Lu argument (Nelson on carbonyls, where you and I argued that it doesn't work for the s-block), but any time I use it to criticise a La argument (usually by asking "what happens to Be or Mg or Al"), you dismiss it as irrelevant."

Answer: Yes, Nelson's argument was not consistent, on the grounds he was arguing for it. You agreed. When you give Be or Mg or Al arguments you ignore more fundamental grounds (that I presume are implicit, hence I don't state them) such as that Al is a p-block metal, therefore it can't go over Sc. Sandbh (talk) 23:40, 16 February 2020 (UTC)

@Sandbh: And how do you know that Al is a p-block metal? Purely because it leads to one less DE anomaly than putting it above Sc? Then unfortunately, since you've referred to Rg as fog, you can't distinguish between these two tables

H                                 He             H                                 He
Li Be              B  C  N  O  F  Ne             Li              Be B  C  N  O  F  Ne
Na Mg              Al Si P  S  Cl Ar             Na              Mg Al Si P  S  Cl Ar
K  Ca Sc ... Cu Zn Ga Ge As Se Br Kr             K  Ca Sc ... Cu Zn Ga Ge As Se Br Kr
Rb Sr Y  ... Ag Cd In Sn Sb Te I  Xe             Rb Sr Y  ... Ag Cd In Sn Sb Te I  Xe
Cs Ba Lu ... Au Hg Tl Pb Bi Po At Rn             Cs Ba Lu ... Au Hg Tl Pb Bi Po At Rn

because they have the same number of DE anomalies up to Z = 100, the deciding vote of Rg being "fog" according to you when I was talking about how Rg 6d⁹7s² being an excellent homologue about Au 5d¹⁰6s¹ casted doubt about whether the odd DE's were really the cause behind the behaviour of group 11. Not only that: if we were to take out the rare radioactives as being of no use to the average chemist (so only the primordials matter), then DE's don't even suffice for deciding La from Lu! This is part of why I find the whole procedure of counting DE anomalies nonsensical. Not only does it have zilch to do with real chemistry (no one has ever seen "add a proton and an electron, there's the next element" in chemistry rather than nuclear physics; the DE itself is not even well-defined all the time, considering V vs Cr; and ground-state configurations are mostly not relevant in real compounds), but it's even so useless that it can't decide on something as obvious to you as where Be and Mg go without referring to the crown of irrelevancy for this issue, Rg, almost the whole table away! And it can only decide on La under Y because Lr got pushed by relativity into a funky configuration in the ground state! Anyone else can see how ridiculous such a reason is. Oh, wait; when most authors talk about anomalous configurations deviating from the Madelung rule, they don't mean DE's. We know that because they think Mo is anomalous because it isn't d⁴s², even if it has the right 4d DE from Nb next door. Well, guess what: that is sufficient to decide on Sc-Y-Lu and He-Be-Mg-Ca without breaking a sweat.

And if we reject that, and focus purely on chemical properties, we're in for a nasty shock: the linkage Al-Sc is often closer than Al-Ga because of the noble gas cores of Al and Sc which Ga doesn't have. And all the counterarguments that say "actually, Al-Ga is equally often closer" have been zapped by your chemical arguments against Sc-Y-Lu which basically become "let's look at group 2". Well: group 3 is mostly pre-transition in chemistry, Al is pre-transition in chemistry, Ga through Tl are post-transition! Well: it doesn't matter that Al is significantly less electropositive than the other group 3 elements, because it fits perfectly with Be and Mg atop group 2! Off to Al-Sc we go with Seaborg and Rayner-Canham on our side! Double sharp (talk) 20:12, 17 February 2020 (UTC)

@Double sharp: There is no d/e difference between the two. I don't even have to get that far since Be over Mg over Ca falls out naturally on periodic law grounds. d/e's are singularly discernable on the basis of a single gaseous atom in a vacuum; the chemically active sub-shells in an element in a compound will vary depending on its environment. Is there a "standard" element with which every element combines, such that this can be determined? Anomalous configurations deviating from the Madelung rule, are equivalent to d/e anomalies. More homework for you. Sandbh (talk) 03:29, 18 February 2020 (UTC)

@Sandbh: That is total nonsense. First of all, we see a classic case of a double standard regarding argument hierarchy. For Al you say the p-electron comes first and beats everything for not putting Al over Sc, never mind that Al-Sc is exactly analogous to Y-La. For Be and Mg, now you say that the periodic law grounds come first so that you don't even have to look at DE's. Never mind that Be-Mg-Zn is as sensible wrt most periodic trends as Be-Mg-Ca taken in isolation; it just follows a p-block-like rather than an s-block-like trend. Second of all, the whole point of chemically active subshells is that we consider things holistically. Chemically active subshells don't change based on the environment even if the configuration does, so your critique is baseless. And last of all, just look at the table of anomalous configurations deviating from the Madelung rule at Electron configuration, cited to Miessler, G. L.; Tarr, D. A. (1999). Inorganic Chemistry (2nd ed.). Prentice-Hall. p. 38. (and using other sources for period 7, I guess):

Electron shells filled in violation of Madelung's rule (red; predictions for Mt through Cn added)
Period 4			Period 5			Period 6			Period 7
Element	Z	Electron Configuration	Element	Z	Electron Configuration	Element	Z	Electron Configuration	Element	Z	Electron Configuration
						Lanthanum	57	[Xe] 6s² 5d¹	Actinium	89	[Rn] 7s² 6d¹
						Cerium	58	[Xe] 6s² 4f¹ 5d¹	Thorium	90	[Rn] 7s² 6d²
						Praseodymium	59	[Xe] 6s² 4f³	Protactinium	91	[Rn] 7s² 5f² 6d¹
						Neodymium	60	[Xe] 6s² 4f⁴	Uranium	92	[Rn] 7s² 5f³ 6d¹
						Promethium	61	[Xe] 6s² 4f⁵	Neptunium	93	[Rn] 7s² 5f⁴ 6d¹
						Samarium	62	[Xe] 6s² 4f⁶	Plutonium	94	[Rn] 7s² 5f⁶
						Europium	63	[Xe] 6s² 4f⁷	Americium	95	[Rn] 7s² 5f⁷
						Gadolinium	64	[Xe] 6s² 4f⁷ 5d¹	Curium	96	[Rn] 7s² 5f⁷ 6d¹
						Terbium	65	[Xe] 6s² 4f⁹	Berkelium	97	[Rn] 7s² 5f⁹
						Dysprosium	66	[Xe] 6s² 4f¹⁰	Californium	98	[Rn] 7s² 5f¹⁰
						Holmium	67	[Xe] 6s² 4f¹¹	Einsteinium	99	[Rn] 7s² 5f¹¹
						Erbium	68	[Xe] 6s² 4f¹²	Fermium	100	[Rn] 7s² 5f¹²
						Thulium	69	[Xe] 6s² 4f¹³	Mendelevium	101	[Rn] 7s² 5f¹³
						Ytterbium	70	[Xe] 6s² 4f¹⁴	Nobelium	102	[Rn] 7s² 5f¹⁴
Scandium	21	[Ar] 4s² 3d¹	Yttrium	39	[Kr] 5s² 4d¹	Lutetium	71	[Xe] 6s² 4f¹⁴ 5d¹	Lawrencium	103	[Rn] 7s² 5f¹⁴ 7p¹
Titanium	22	[Ar] 4s² 3d²	Zirconium	40	[Kr] 5s² 4d²	Hafnium	72	[Xe] 6s² 4f¹⁴ 5d²	Rutherfordium	104	[Rn] 7s² 5f¹⁴ 6d²
Vanadium	23	[Ar] 4s² 3d³	Niobium	41	[Kr] 5s¹ 4d⁴	Tantalum	73	[Xe] 6s² 4f¹⁴ 5d³	Dubnium	105	[Rn] 7s² 5f¹⁴ 6d³
Chromium	24	[Ar] 4s¹ 3d⁵	Molybdenum	42	[Kr] 5s¹ 4d⁵	Tungsten	74	[Xe] 6s² 4f¹⁴ 5d⁴	Seaborgium	106	[Rn] 7s² 5f¹⁴ 6d⁴
Manganese	25	[Ar] 4s² 3d⁵	Technetium	43	[Kr] 5s² 4d⁵	Rhenium	75	[Xe] 6s² 4f¹⁴ 5d⁵	Bohrium	107	[Rn] 7s² 5f¹⁴ 6d⁵
Iron	26	[Ar] 4s² 3d⁶	Ruthenium	44	[Kr] 5s¹ 4d⁷	Osmium	76	[Xe] 6s² 4f¹⁴ 5d⁶	Hassium	108	[Rn] 7s² 5f¹⁴ 6d⁶
Cobalt	27	[Ar] 4s² 3d⁷	Rhodium	45	[Kr] 5s¹ 4d⁸	Iridium	77	[Xe] 6s² 4f¹⁴ 5d⁷	Meitnerium	109	[Rn] 7s² 5f¹⁴ 6d⁷
Nickel	28	[Ar] 4s² 3d⁸ or [Ar] 4s¹ 3d⁹ (disputed)(*)	Palladium	46	[Kr] 4d¹⁰	Platinum	78	[Xe] 6s¹ 4f¹⁴ 5d⁹	Darmstadtium	110	[Rn] 7s² 5f¹⁴ 6d⁸
Copper	29	[Ar] 4s¹ 3d¹⁰	Silver	47	[Kr] 5s¹ 4d¹⁰	Gold	79	[Xe] 6s¹ 4f¹⁴ 5d¹⁰	Roentgenium	111	[Rn] 7s² 5f¹⁴ 6d⁹
Zinc	30	[Ar] 4s² 3d¹⁰	Cadmium	48	[Kr] 5s² 4d¹⁰	Mercury	80	[Xe] 6s² 4f¹⁴ 5d¹⁰	Copernicium	112	[Rn] 7s² 5f¹⁴ 6d¹⁰

Clearly, molybdenum shows an anomalous configuration from the Madelung rule, but does not represent a DE anomaly. The two are not equivalent. DEs are local: they only care about an element and its neighbour. Anomalous configurations are actually global wrt how they view the n+l rule. The only problem is that they misguidedly focus on gas-phase configurations instead of going holistically and considering all the relevant ones, but that provides the killer blow for the La table: La has well-defined 4f valence involvement per Gschneidner and per common sense (cubic complexes), Lu doesn't have any, and the n+l rule outside the s-block holds absolutely perfectly up to E138 considering chemically active valence subshells! And ignoring that the g-block goes on a bit too long, perfectly up to E172! Double sharp (talk) 16:24, 18 February 2020 (UTC)

(*) See Scerri, Eric R. (2007). The periodic table: its story and its significance. Oxford University Press. pp. 239–240. ISBN 978-0-19-530573-9. Double sharp (talk) 12:15, 18 February 2020 (UTC)

@Double sharp: Sandbh (talk) 11:50, 19 February 2020 (UTC)

Briefly, you’re not seeing the wood for the trees. An La table has 12 d/e anomalies; an Lu table has 13. Same goes for the total n+l discrepancies in the blocks of each table: 12 in an La table; 13 in an Lu table. That’s all. Mo is irrelevant. Mo does however count towards the 20 deviations from the n+l rule. Do you follow? Sandbh (talk) 11:48, 19 February 2020 (UTC)

@Sandbh: You're the one not doing that, respectfully. Whenever authors discuss Madelung discrepancies, the important thing is almost always deviations from the n+l rule, and DE anomalies never come into it. No one ever discounts Mo as an anomaly. And no one ever thinks Zn is an anomaly even if it adds a 4s rather than a 3d electron from its previous neighbour Cu. Looking at n+l anomalies is exactly global, as it pertains to the whole filling sequence. They're the forest here if we insist on looking at ground-state configurations. DE's reduce that even further to just an element and its previous neighbours. They're the trees here. Double sharp (talk) 22:09, 19 February 2020 (UTC)

Please don't get my wrong. My intent is to stay at a more philosophical or general level. I do have to descend into more detailed levels from time to time in order to note what I consider to be details that one or both of you have not considered.

Regarding "maybe we don't have enough evidence to overthrow the Aufbau Sc/Y/Lu/Lr arrangement", an Lu table is not a real life aufbau arrangement; it is an imaginary n+l arrangement.

I agree the way the article is currently written that it may give rise to the kinds of impressions you have raised. Clearly I need to take this on board and better set out its intended scope.

Double sharp: I really like what you say on your talk page, "The drawing above and its reasoning have been heavily influenced by copious discussions on WT:ELEM. Among frequent participants in those discussions I thank most of all Sandbh, R8R, and Droog Andrey for their contributions (and making me think ^_^), even if we disagree." That is a powerful acknowledgement rather than taking away your bat and ball, and going home.

@Sandbh: Thank you. I stand by that statement. Your contributions and arguments here certainly help sharpen my thinking about these issues. It's just that I still disagree with you and think your use of logic needs work. ;) Double sharp (talk) 00:01, 14 February 2020 (UTC)

@Double sharp: Hee hee! Sandbh (talk) 00:50, 14 February 2020 (UTC)

One thing that does stand out for me is Double sharp's intimation that my arguments don't have enough gravitas to "overthrow" the Lu form. For the record, I am not seeking to overthrow anything, since the La form is predominant within the literature. What's more, I've explained that each that each form has its purpose. There is no single tool; there is instead a toolbox. "Use the toolbox young Double sharp; do not be seduced by the dark tool" :) Sandbh (talk) 00:21, 13 February 2020 (UTC)

@Sandbh: It is strange that you call "details" what is usually come from generalization, and "general level" what is usually come from some specific case.

You know, a scientist use paper, pencil and eraser, while a philosopher only use paper and pencil. Double sharp is trying to provide you an eraser.

That whole discussion looks like:

- Hey guys, La table rules because of A and B!

- Sorry body, A is bullshit because of D, and B is not better because of D and E!

- Hah, I don't need your D and E, my A and B still stand, look at the literature where A and B are mentioned!

- But you need to analyse what you take from literature!

- I do: just look how La table rules with A and B!

Droog Andrey (talk) 13:49, 13 February 2020 (UTC)

@Droog Andrey: You're missing some steps at the end: ^_^

- I do: just look how La table rules with A, B, and F!

- But I already refuted A and B, and the same refutation applies to F!

- It's just fogging. Look how La table rules with A, B, F, and G!

- And to G as well! And since you said "look at the literature" earlier, no one in the literature thinks F and G are important!

- That doesn't matter. Look how La table rules with A, B, F, G, and H!

- You are using arguments for H that you criticise when I use them for D and E!

- That doesn't matter either. Look how La table rules with A, B, F, G, H, and I!

Respectfully tongue-in-cheek, ^_-☆ Double sharp (talk) 19:09, 13 February 2020 (UTC)

@Droog Andrey:@Double sharp: I appreciate your interest but have no idea what you're talking about. If you have point to make could you please express it in the form of simple example. Sandbh (talk) 22:55, 13 February 2020 (UTC)

@Sandbh: Very simple. You start with some arguments that support La in group 3, and one of us rebuts them by noting that there's some factor that makes them either wrong or irrelevant. Naturally, what next happens is that you reject them, e.g. "Too hard. D/e's are so much easier", and keep on pushing the same old arguments as if nothing had ever happened, quoting the literature selectively and missing the big picture (and in particular, only analysing it critically when it says something supporting the Lu table, never when it supports the La table). And every so often, a new argument comes in, often refutable by the exact same things that refuted the old ones, but the refutations are dismissed as irrelevant. Sometimes the new arguments (e.g. for Th in the f-block and Lr in the d-block) make use of logic that is totally OK for you when you apply it, but totally not OK for you when we apply it to La and Ac in the f-block. None of that matters, and new and equally bad arguments just keep pouring in. ;) Double sharp (talk) 23:56, 13 February 2020 (UTC)

@Droog Andrey:@Double sharp: Rather than generalisations, an explicit example of a double standard would be more helpful. Sandbh (talk) 06:05, 16 February 2020 (UTC)

@Sandbh: I've already given four. You've started talking about #4, so here are the other 3 from above:

You allow Th to stand as an f-block element, and Lr to stand as a d-block element, despite having the "wrong" differentiating electrons. But La and Ac, with similar credentials, are not allowed by you to stand as f-block elements.
You treat the core electrons of Lu as relevant for the 4f-block membership you push for it, while simultaneously ignoring the equally relevant core electrons of Hf through Rn.
You are perfectly fine with asking the question "what happens to other elements if we take that approach?" when it criticises a Lu argument (Nelson on carbonyls, where you and I argued that it doesn't work for the s-block), but any time I use it to criticise a La argument (usually by asking "what happens to Be or Mg or Al"), you dismiss it as irrelevant.

Double sharp (talk) 10:29, 16 February 2020 (UTC)

The thorium sub-thread

@Double sharp:@Droog Andrey: I’ll see if I can make my logic clearer:

In an n+l table, or an La table, the first row of a block starts when the first relevant electron appears. Thus, the s-block starts with the appearance of a 1s electron at H, the p-block starts with 2p at B, the d-block with 3d at Sc, and the f-block with 4f at Ce.
An Lu table shows the same sequence for the s, p, and d blocks but not for the f-block, which starts with 5d at Lu.
Subsequent block rows continue this regular pattern with two exceptions. In a La table, the start of the second row of the f-block occurs at Th, which has a 5d differentiating electron. In a Lu table, the start of the second row of the f-block occurs at Lr, which has a 7p differentiating electron.
In the n+l and La tables, a block starts with the first appearance of the relevant electron. This cannot be said for a Lu table.

Fire away. Sandbh (talk) 22:29, 20 February 2020 (UTC)

@Sandbh: Basically, the problem can be summarised as "this is all true, but no reason is given why it should be elevated to the criterion, and actual evidence from real properties opposes it".

No reason is given why it is important that the first row of a block should start when the first relevant electron appears in the ground state. If you want to use it as a criterion, you'd better explain its relevance to the trends of real chemical and physical properties. I simply see that the chemistry and physics of La is best explained by significant f-involvement which we even have direct evidence in terms of the low excitation energy for it, despite the lack of that 4f electron in the ground state. So your criterion seems to be irrelevant to chemistry and physics.
And no reason is given why the subsequent block rows should continue the regular pattern. Do the relevant electrons support it? The pattern evidently gets worse and worse as we get to heavier elements. La has significant f-involvement despite not having that 4f electron yet; Ac and Th have significant f-involvement despite not having that 5f electron yet; Lr has significant d-involvement despite not having that 6d electron yet. Meanwhile we have the first few 5g elements where the blocks all take their own sweet time to collapse in a staggered order (E121 has a p-electron, E122 adds a d electron, E123 or E124 may be the first to get an f one, and E125 is probably the first with a g one). So in fact looking at the actual pattern suggests strongly that a symmetry break appears for the heavy elements' ground-state configurations, and it only gets worse as Z increases (why do you think all the blocks from 6f onward are delayed by four elements?). Yes, I see the sky will certainly fall down in a few elements' time if we take delayed collapses too seriously. The funny thing is, in terms of their actual chemistry and physics there is nothing terribly unusual about any of these "delayed collapse" elements for their theoretically correct blocks from n+l! They still show properties that are mighty hard to explain without positing valence involvement of the theoretically correct subshell from n+l, and we have direct or calculated evidence for that for the elements we've actually synthesised among those. That's why chemically active valence subshells are a better criterion for actual chemistry and physics.
P.S. A table following the n+l rule as everyone has it, i.e. an (n+l,n) rule, is a Lu table. Go look up what everyone says the Madelung rule is in any chemistry textbook ever. Or look at any diagram with arrows obviously pointing down the diagonals 1s, 2s, 2p-3s, 3p-4s, 3d-4p-5s, 4d-5p-6s, 4f-5d-6p-7s, 5f-6d-7p-8s. Double sharp (talk) 22:50, 20 February 2020 (UTC)

@Double sharp: Good, we are making progress! I don't give a reason for saying why it is important that the first row of a block should start when the first relevant electron appears in the ground state. I don't need to restate the "bleeding obvious" namely that the periodic table, in chemistry and physics, is organised into blocks.

@Sandbh: It's not "bleeding obvious". It needs to be proven. You need to examine the chemistry and physics and see if the block pattern emerges. Which, judging from the chemistry and physics of the elements involved, it does in favour of the Lu table. Double sharp (talk) 00:10, 21 February 2020 (UTC)

Why the subsequent block rows should continue the regular pattern is another case of the "bleeding obvious". Perhaps less obvious for people unfamiliar with n+1 and the aufbau process. Even you refer to the desirability of increasing regularity and symmetry.

@Sandbh: Again, you have to prove it. You want to talk about differentiating electrons and ground-state configurations, and on that basis I note that once you get to heavy enough elements that relativity happens, the block rows mostly stop continuing the regular pattern if you insist on ground-state configurations. Increasing regularity and symmetry is desirable only if your criteria support it. If they don't, you have to either reject symmetry, or your criteria.

Naturally, the real n+l and Aufbau process supports Lu, as copiously demonstrated by me here. And a Lu table is chemically and physically superior to a La one, as also copiously demonstrated by me here, so here increasing regularity and symmetry is totally justified. Double sharp (talk) 00:10, 21 February 2020 (UTC)

Effectively, now that you mention it, I'm saying that an La table is more regular than an Lu table, in several respects, that's all. Or, an La table is more closely aligned with an idealised n+l table.

Since an Lu table has 13 n+l anomalies, it cannot be an n+l table, per se. Frex Mn according to n+l should be 3+2=5 but is in fact 4+0=4. Concur? Sandbh (talk) 23:38, 20 February 2020 (UTC)

@Sandbh: No. According to everyone else discussing anomalies, DE anomalies are irrelevant. The important thing when people count anomalies is whether the configuration matches what the Madelung rule predicts, which is the forest, rather than just comparing to the previous element, which is the trees. Mn is not an anomaly. Cr is an anomaly. On the basis of this counting, a La table with its modified n+l rule "one 5d, fourteen 4f, nine 5d" is laughably inferior to a Lu one when it comes to n+l anomalies.

Meanwhile, with chemically active subshells taken as a whole and not taking individual configurations, there are in fact no anomalies outside the s-block all the way up to Nh (we may argue about Fl through Og). ^_^ Double sharp (talk) 00:10, 21 February 2020 (UTC)

@Double sharp: Well, if you just want to focus on electron configuration anomalies, there are 20 in either form of table, up to Lr: Cr, Cu, Nb, Mo, Ru, Rh, Pd, Ag, La, Ce, Gd, Pt, Au, Ac, Th, Pa, U, Np, Cm, Lr. Sandbh (talk) 05:26, 21 February 2020 (UTC)

@Sandbh: Drawing a La table, because it changes block assignments, implicitly means you think n+l should be changed for La. That is, it implies that the lanthanides should mostly have a 5d electron hanging up above 4f. Since they mostly don't, we see again the marked inferiority of the La table. Double sharp (talk) 07:56, 21 February 2020 (UTC)

@Double sharp: The only difference between the tables is that in an La table, La-Ac appears in group 3, and Lu and Lr appear at the end of the f-block. In an Lu table, as you know, it's the other way around.

In an La table, La and Ac are 5+2=7 and 6+2=8 as they should be, being in the d-block. Lu 5+2=7 and Lr 7+1=8 look out of place in the f-block, since most of the f-block is 4+3=7 and 5+3=8, as they should be, given the 4f sub-shell is filling. Why does this arrangement implicitly imply that n+l should be changed for La? Why does it imply that the Ln should mostly have a 5d electron hanging up above 4f?

In an Lu table Lu 5+2=7 looks good and Lr 7+1=8 is anomalous, in the d-block. La 5+2=7 and Ac 6+2=8 look out of place in the f-block, since most of the f-block is 4+3=7 and 5+3=8.

Based on this narrow view, there are 2 anomalies in La, and 3 in Lu. Sandbh (talk) 11:59, 21 February 2020 (UTC)

@Sandbh: Meanwhile, we again see DE's being harped on, when the important thing is as usual something else according to everybody else.

Yes, it implicitly implies that if you are starting from ground-state configurations like everyone does. You are drawing, in a La table, one element in the d-block, followed by fourteen in the f-block, and then nine in the d-block. If you think n+l is a basis for drawing the table, then it follows that the n+l rule congruent with the La table is distorted that way! If you're starting from DE's instead, then you're starting from something doubly incomplete and irrelevant. Double sharp (talk) 12:26, 21 February 2020 (UTC)

f-block contraction

It occurred to me that with Lu in group 3 one can no longer refer to an “f block contraction” analogous to the “d block contraction”. Sandbh (talk) 22:55, 12 February 2020 (UTC)

@Sandbh: Yes we can. There's obviously a contraction from La through Yb just as there is one from Sc through Zn, just look at the atomic radii. Then compare the elements before and after, and see that the cancellation of the increase in basicity and atomic radius from Y-Lu, Zr-Hf, Nb-Ta is exactly analogous to that at Al-Ga, Si-Ge, P-As. Harping on +3 as a predominant oxidation state as an excuse to keep La out of the 4f contraction is fogging, since no such analogous thing exists for the 3d contraction. Or the 5f contraction (because of the early An). Or the 4d or 5d contractions. Or the 2p contraction, for that matter. Double sharp (talk) 13:52, 13 February 2020 (UTC)

@Double sharp: With good humour, that's a good example of needlessly muddying the waters. With the f-block as Ce-Lu, we can refer to an "f-block contraction". It starts at Ce and finishes at Lu.

With the f-block as La to Yb, there is no contraction congruous with its block, since the contraction starts at Ce in the f-block and finishes at Lu, in the d-block.

What is a simple observation in the La form turns into an unnecessary misalignment in the Lu form. I look forward to seeing you talking your way out of this one, with another convoluted, "but wait, if you look at it this way…".

"The best education is found in gaining the utmost information from the simplest apparatus."

— Whitehead AN 1929, The aims of education and other essays, The Free Press, New York, p. 37

Sandbh (talk) 22:50, 13 February 2020 (UTC)

@Sandbh: I don't need to talk my way out of it. This whole thing only is a problem for you because you're clinging to the false premise that the f-block begins at Ce and ends at Lu. Never mind that 4f valence involvement exists in La and certainly not in Lu. I wonder where we will be with the 5f contraction, since Th lacks a 5f electron. Oh, wait, I know exactly where we will be: we will next hear an argument about how this doesn't matter, because regularity (which is symmetry by another name) implies that once Ce has its f-electron there can be no further questions for this inconvenient truth. And thus, we again see the double standard in which Th and Lr are not held to the same standard as La and Ac.

P.S. Your quote is exactly part of why a Lu table is superior to a La one. It's the simplest arrangement, no artificial splitting of the d-block needed. And it explains the chemistry better. Double sharp (talk) 23:23, 13 February 2020 (UTC)

@Double sharp: Well, per Seaborg (thank you for that reference) the f-block begins at Ce, as predominately occurs in the literature. Below I've given two examples of f involvement in Lu. Since you are now discounting the relevance of gas phase configurations let us recall the influence of the f electron in condensed thorium and, re the 5f contraction, the blue Th³⁺ cation, as per an earlier post. I have clarified that regularity is not the same as symmetry, and given an example. Feel free to elaborate on my double standard.

The simplest apparatus is not the issue. Per the full quote, "The best education is found in gaining the utmost information from the simplest apparatus." The La form is the simplest apparatus from which the utmost information is gained (including the chemistry). Sandbh (talk) 06:03, 16 February 2020 (UTC)

@Sandbh: Where is he supporting with arguments that 4f begins in Ce? Or is it just that he shows a table like that? He was already OK with saying that 5f "formally (though not actually)" begins at Th, and now that we know more about these elements we know that the same can actually be said already about Ac. You still have a double standard: since you're willing to consider non-ground-states for Th, you should consistently be willing to note them for La and Ac (how else do you explain cubic complexes, BTW? I should like to see how Parish proposes to do it).

The Lu form is obviously a simpler apparatus than the La form. And it fits the chemistry even better, so you get more information from it. Double sharp (talk) 10:46, 16 February 2020 (UTC)

@Double sharp: Seaborg, p. 45: "A periodic table that places the actinide elements and the transactinide elements in positions that best represent our present understanding (1991) is shown in Figure 5." The Ln are Ce to Lu. The An are Th to Lr. Sandbh (talk) 23:13, 18 February 2020 (UTC)

@Sandbh: "Present understanding" according to IUPAC is that the Ln are La to Lu and the An are Ac to Lr. Excluding La and Ac is chemically irrelevant pedantry based on the names "lanthanide" and "actinide". So, Seaborg may not have been on top of the biggest developments in the La/Ac saga, since Landau and Lifschitz already got it right decades earlier. That's not a problem, we can critically analyse the literature. No doubt he had other priorities than getting on top of this saga, like discovering new elements. ;) Double sharp (talk) 23:21, 18 February 2020 (UTC)

Actually, Lu is the start of 5d contraction spanning from Lu to Hg. Droog Andrey (talk) 05:35, 17 February 2020 (UTC)

@Droog Andrey:@Double sharp: Not so much in this context since Lu 3+ which represents most Lu chemistry, has no d electron. It's more accurate to say, in a chemistry based context, that Tl to Rn are recipients of the impact of the 5d contraction since each of them have a full 5d sub-shell, the completion of which happens at Hg +2.

The filling of the 5d shell occurs in a wobbly start over La, Gd, and Lu, before settling down from Hf to Au.

Like Lu, La 3+ has neither a d nor f electron.

In classification science terms I’d say Lu 3+ is a “pile on” member of the f-block contraction, whereas Hf is an incipient recipient of the impact of that contraction (try saying that with a mouthful of marbles) rather than being a pile on player. Sandbh (talk) 23:13, 18 February 2020 (UTC)

@Sandbh: So where are we in the s-block, since M⁺ (M = Li-Fr) and M²⁺ (M = Be-Ra) that represent most s-block chemistry have no s electrons left? Or in the 3d contraction when Sc³⁺ making most of Sc chemistry has no d-electron left? Or Hf^IV and Ta^V which are also dominant for those elements and have d⁰ as well? Are they also excluded from their blocks and contractions? Tl through Rn are impacted by both the 5d and the 4f contractions. Double sharp (talk) 23:18, 18 February 2020 (UTC)

@Double sharp: I guess the p-block elements B to Ne, and Al to Ar feel the impact of the s-block contraction. The d-block contraction is most commonly referred to for its impact on e.g. Ga to Kr etc, rather than its actual occurence so much, within the d-block. Hf and Ta are incipient recipients of the impact of the f-block contraction, rather than causers of the f-block contraction seen so conspicuously as a result of the commonality of the +3 oxidation state across the f-block. Sandbh (talk) 01:03, 19 February 2020 (UTC)

@Sandbh: That's a terribly local way of determining the start of a contraction. Such a common oxidation state exists for no other contraction but the 4f one. It doesn't even exist for the 5f and probably 6f ones. I prefer the global approach that applies to everybody: Lu is just like Hf and Ta, the 4f electrons are core electrons, so the f-block contraction is over and all three are "incipient recipients" as you put it. Your approach, respectfully, is taking the one exception (4f), elevating it to the general rule, and dragging 5f kicking and screaming into it in defiance of the configurations and chemically active valence subshells that Nature has given us. Double sharp (talk) 22:15, 19 February 2020 (UTC)

PT of chemically active subshells

@Double sharp: Could you please post one of these?

User:Double sharp/Idealised electron configurations Double sharp (talk) 00:26, 15 February 2020 (UTC)

@Double sharp: Wow! This is rather good, and deserving of more study. You're putting your money where your mouth is, so to speak, Bravo. Sandbh (talk) 06:23, 15 February 2020 (UTC)

@Double sharp: Preliminary impressions:

Could you please add supporting citations, including for p-d-f involvement in He, Be and Mg; ditto in H, Li and Na; s-p involvement in Pd; and d involvement in Zn-Cd-Hg?
- Re the first: obviously "s+all higher" means those in the same row. I don't posit pdf involvement in H and He, neither do I posit df for Li, Be, Na, Mg. However note that p involvement for Be and Mg is essentially common knowledge when satisfying the octet rule in complexes like beryllocene (will search for Li and Na, shouldn't be hard to find). d is clearly involved in Zn, Cd, Hg even if it isn't ionisable: it has a cohesive effect on the bonding, and there is effective overlap (just look at the interatomic distances in things like ZnCl₂ molecule). As for palladium, the weird configuration is an accident, just find any 18-electron complex of it. Double sharp (talk) 10:38, 15 February 2020 (UTC)
- Lithium 2p involvement (back-donation in MeLi). Still looking for sodium. Double sharp (talk) 11:17, 15 February 2020 (UTC)
  - So far I've already found d-involvement for K-Cs and Ca-Ba mentioned in the paper previously quoted re Cs and Ba as honorary transition metals. So the only one left is Na. Double sharp (talk) 21:21, 15 February 2020 (UTC)

I guess I should copy and paste the table here:

(s+all higher!)¹	(s+all higher!)²	(dsp)³	(dsp)⁴	(dsp)⁵	(dsp)⁶	(dsp)⁷	(dsp)⁸	(dsp)⁹	(dsp)¹⁰	(dsp)¹¹	(dsp)¹²	(sp)³	(sp)⁴	(sp)⁵	(sp)⁶	(sp)⁷	(sp)⁸
H	He																	1s
Li	Be											B	C	N	O	F	Ne	2s2p
Na	Mg											Al	Si	P	S	Cl	Ar	3s3p
K	Ca	Sc	Ti	V	Cr	Mn	Fe	Co	Ni	Cu	Zn	Ga	Ge	As	Se	Br	Kr	3d4s4p
Rb	Sr	Y	Zr	Nb	Mo	Tc	Ru	Rh	Pd	Ag	Cd	In	Sn	Sb	Te	I	Xe	4d5s5p
Cs	Ba	Lu	Hf	Ta	W	Re	Os	Ir	Pt	Au	Hg	Tl	Pb	Bi	Po	At	Rn	5d6s6p
Fr	Ra	Lr	Rf	Db	Sg	Bh	Hs	Mt	Ds	Rg	Cn	Nh	Fl	Mc	Lv	Ts	Og	6d7s7p
119	120	157	158	159	160	161	162	163	164	165	166	167	168	169	170	171	172	7d(8→9)s(8/9)p
(173)		(fdsp)³	(fdsp)⁴	(fdsp)⁵	(fdsp)⁶	(fdsp)⁷	(fdsp)⁸	(fdsp)⁹	(fdsp)¹⁰	(fdsp)¹¹	(fdsp)¹²	(fdsp)¹³	(fdsp)¹⁴	(fdsp)¹⁵	(fdsp)¹⁶
		La	Ce	Pr	Nd	Pm	Sm	Eu	Gd	Tb	Dy	Ho	Er	Tm	Yb			4f5d6s6p
		Ac	Th	Pa	U	Np	Pu	Am	Cm	Bk	Cf	Es	Fm	Md	No			5f6d7s7p
		143	144	145	146	147	148	149	150	151	152	153	154	155	156			6f7d(9s?)8p_1/2

(gfdsp)³	(gfdsp)⁴	(gfdsp)⁵	(gfdsp)⁶	(gfdsp)⁷	(gfdsp)⁸	(gfdsp)⁹	(gfdsp)¹⁰	(gfdsp)¹¹	(gfdsp)¹²	(gfdsp)¹³	(gfdsp)¹⁴	(gfdsp)¹⁵	(gfdsp)¹⁶	(gfdsp)¹⁷	(gfdsp)¹⁸	(gfdsp)¹⁹	(gfdsp)²⁰	(gfdsp)²¹	(gfdsp)²²	(gfdsp)²³	(gfdsp)²⁴
121	122	123	124	125	126	127	128	129	130	131	132	133	134	135	136	137	138	139	140	141	142	5g6f7d8s8p_1/2

(Also: 800k!) Double sharp (talk) 21:13, 15 February 2020 (UTC)

@Double sharp: Still thinking about this one. It raises several issues. I need to get it right. Sandbh (talk) 21:17, 15 February 2020 (UTC)

@Double sharp: Could you clarify what you mean by "chemically active"? Sandbh (talk) 03:44, 18 February 2020 (UTC)

@Sandbh: To participate in chemistry as a valence subshell. So it must have a significant component in bonding MO's, or in deeply buried cases like 4f and 5g, at least as a reserve area where electrons can easily go in and out of from bonding MO's. Double sharp (talk) 08:13, 18 February 2020 (UTC) ♠

@Double sharp: How do we measure or determine such sub-shells? And what is a "significant" component? Sandbh (talk) 12:00, 19 February 2020 (UTC)

@Sandbh: Just look holistically in many different but still chemically normal environments, and analyse the molecular orbitals involved in the bonding, with the caveat I mentioned for deeply buried orbitals like 4f and 5g. You can get this directly or indirectly from interatomic distances (like 3d involvement by Zn-Cl interatomic distances in ZnCl₂). "Significant" is just the mathematician's pedantry: it's possible that a freak quantum fluctuation happens and some crazy thing happens like the 1s core coming out, yes (an orbital that would have a 100% chance of the electrons being found within would have to be drawn the size of the Universe), but it's not terribly likely and we can ignore it and sleep easy. Double sharp (talk) 22:23, 19 February 2020 (UTC)

Gas phase electron configurations

Do gas phase electron configurations still have any relevance to the chemistry of the elements? Sandbh (talk) 10:24, 15 February 2020 (UTC)
- No direct relevance. They have been simplified too much to be really useful. Double sharp (talk) 10:38, 15 February 2020 (UTC)

On relevance:

III. Line Spectra: Atomic Spectra of Rare Earth Elements (1942), here:
"The above survey of normal states and corresponding electron configurations determined from analyses of successive spectra of the rare earth elements is ample proof that these spectra are amenable to analysis and interpretation. Real progress has been limited to the past dozen years, but many interesting and important results have already been obtained. For example, the exceptions to the general rule that all rare earth elements are trivalent can now be understood. Thus the fact that Ce is sometimes quadrivalent, and Sm, Eu, and Yb are sometimes divalent can be expected from the character of their atomic emission spectra. The properties of these atoms depend on the relative strength of binding of electrons of type f, d, and s, and such information can be obtained from the structures of successive spectra."

Sandbh (talk) 05:01, 20 February 2020 (UTC)

@Sandbh: Do you see that they refer to entire spectra and to energies of valence subshells 4f, 5d and 6s, but not to single ground-state configurations? Droog Andrey (talk) 07:11, 20 February 2020 (UTC)

@Droog Andey:Yes. Did you see the electron configurations they listed for the lowest terms in each element's spectra? Sandbh (talk) 11:12, 20 February 2020 (UTC)

@Sandbh: They are just listed without any deep meaning. Droog Andrey (talk) 12:40, 21 February 2020 (UTC)

@Double sharp: How do we explain the tendency of Tl to show +1 rather than +3 chemistry? Sandbh (talk) 22:58, 16 February 2020 (UTC)

@Sandbh: Three points:

Why is that important? How do you explain it with your favourite DE's and gas-phase electrons? (No, saying "it's easier to just lose the 6p electron than throw in two 6s ones as well" is not going to cut it, because that suggests that Lr in group 3 should do that too!) Here again we see the double standard: Lu arguments are criticised by metrics never used for La arguments.

@Double sharp: The electron configuration of Tl is 6s²6p¹. We know that relativistic effects cause the +1 state in Group 13 to become more stable going the group. The "reluctant pair" effect as G&E put it. It is no surprise then, given the electron configuration of Tl, that the +1 state is more stable. We have not seen any evidence for the +1 state in Lu or Lr, which is interesting. Sandbh (talk) 00:10, 18 February 2020 (UTC)

@Sandbh: Incredible. I even say precisely what is not going to cut it (because it would predict the nonexistent Lr +1), but here we see exactly that offered as an explanation, with the refutation just baldly called "interesting"! How is it, you suppose, that the d-elements somehow seem not to be feeling this reluctant pair effect at all? Lu through Re prefer the group oxidation state. Lr through Bh prefer it even more!! Double sharp (talk) 08:13, 18 February 2020 (UTC)

Of course, I can explain it, no problem. The s-p gap grows larger down the table until relativity starts significantly stabilising 7p_1/2, so it really is about chemically active subshells, as usual. If you read Kaupp's paper you will also understand that this is dependent on the electronegativity of the ligands (and the difference in kind between s and p orbitals) per Bent's rule.
And since Tl can still show s activity, if reluctantly in inorganic chemistry (organothallium favours +3 more), (sp)³ is still the absolutely correct diagnosis. Double sharp (talk) 00:30, 17 February 2020 (UTC)

~~While you are here, how do we explain the fact that Pd shows no main group chemistry, whereas its congeners Ni and Pt are so capable? Sandbh (talk)~~

~~@Sandbh: That's a false statement. Where is the main-group chemistry of Ni and Pt? In oxidation-state 0 compounds? Well, Pd has those too. Double sharp (talk) 00:30, 17 February 2020 (UTC)~~

~~@Double sharp: Yes, I was wrong. Sorry. I'll regroup and have another go. Right line of thought, wrong track. Sandbh (talk) 05:03, 17 February 2020 (UTC)~~

Returning to ionisation energy

@Double sharp: Earlier, we had the following exchange:

S: It occurs to me there are now at least nine chemical arguments for La…monocations of Sc, Y, La and Lu…

DS: Not sure why this is relevant since Sc, Y, La, and Lu are almost never in the +1 state.

S: The +1 state is used to measure the ionisation energies of the elements, from which general trends are derived.

DS: The only problem with that is that this argument is about the chemistry of the +1 state, not just abstractly taking away that first electron. Whatever happened to sticking to characteristic oxidation states and properties? Double sharp (talk) 21:48, 9 February 2020 (UTC)

Now, first ionisation energy values are derived from gas phase atoms in a vacuum. The significance of these values are that they are quantitative and refer to the applicable atom only rather than in a chemically combined environment.

These values show periodicity. They are used, with electron affinity, to establish Mulliken electronegativity.

From our electronegativity article:

"The wide variety of methods of calculation of electronegativities, which all give results that correlate well with one another, is one indication of the number of chemical properties which might be affected by electronegativity."

On electronegativity, Leach observed that:

"There are such strong correlations between numerous atomic parameters, physical and chemical, that the term “electronegativity” has the effect of integrating them into a single dimensionless number between 0.78 and 4.00. Consequently, the electronegativity of an element can be used to predict/describe/model much of its empirical physical character and chemical behaviour."

On this basis, I argue that first ionisation energies obtained from the +1 oxidation state represent a rather fundamental consideration for physical and chemical properties. Sandbh (talk) 00:10, 18 February 2020 (UTC)

@Sandbh: As usual you don't read what I write. I have no problem talking about 1st IE. But I reject talking about the chemistry of the +1 state. And here we see Sandbh flushing his own focus on predominant oxidation states down the drain again the moment some uncharacteristic one seems to help the case for La. Double sharp (talk) 07:44, 18 February 2020 (UTC)

@Double sharp:@Droog Andrey:@R8R:

Well, if you read my argument carefully, I said:

"first ionisation energy values are derived from gas phase atoms in a vacuum. The significance of these values are that they are quantitative and refer to the applicable atom only rather than in a chemically combined environment"
These values show periodicity. They are used, with electron affinity, to establish Mulliken electronegativity
From our electronegativity article: "The wide variety of methods of calculation of electronegativities, which all give results that correlate well with one another, is one indication of the number of chemical properties which might be affected by electronegativity."
On electronegativity, Leach observed that: "There are such strong correlations between numerous atomic parameters, physical and chemical, that the term “electronegativity” has the effect of integrating them into a single dimensionless number between 0.78 and 4.00. Consequently, the electronegativity of an element can be used to predict/describe/model much of its empirical physical character and chemical behaviour."
On this basis, I argue that first ionisation energies obtained from the +1 oxidation state [in the gas phase] represent a rather fundamental consideration for physical and chemical properties.

What are you not following? It seems like a s/f argument to me. Patterns in the IE of the elements are one of the first things you will read about in chemistry textbooks, when they address periodicity. Sandbh (talk) 05:21, 19 February 2020 (UTC)

@Sandbh: Sure, there's nothing wrong with 1st IE's. There's also nothing wrong with 2nd and 3rd IE's, and in some cases they might be better (e.g. 3rd IE works better for d- and f-block elements to get rid of the covering s² subshell). In what you quoted I was criticising your use of monocations as an argument, because the +1 oxidation state is irrelevant chemically. Double sharp (talk) 22:19, 19 February 2020 (UTC)

Jensen

@Double sharp:

Comment please:

"While there is certainly a significant correlation between electron configurations and chemical periodicity, the correlation is, as already noted, far from perfect." WB Jensen 2015

Precisely. Good luck taking on "significant correlation". Sandbh (talk) 03:38, 18 February 2020 (UTC)

@Sandbh: Correlation doesn't imply causation. They are similar just because gas-phase configurations are a blurred black-and-white reflection of the sequence of valence subshells that is really driving this. Double sharp (talk) 07:42, 18 February 2020 (UTC)

Th 5f involvement

@Double sharp: Why do you show Th as having potential 4f involvement and criticise me for mentioning this? Sandbh (talk) 22:17, 16 February 2020 (UTC)

@Sandbh: I criticise you for it because it exposes your inconsistency and double standard. You insist throughout on DE's being important, but they say that Th is not an f-element because 5f has not started filling. Instead you backpedal over it and say that, oh, actually, your rule of DE's and nothing else can be overturned specially for Th because of its really obvious 5f involvement. (That is when you're not claiming that Ce's 4f electron forces the rest of the 5f block by regularity aka symmetry to everybody else, while at the same time refusing to accept symmetry as a reason for the Lu table.) While I agree that chemically obvious 5f involvement for Th is more important, it is a double standard that shows that you are not consistently using your own criteria. You have two logically consistent options here: reject DEs, noting as Seaborg did that the actual DE does not really matter all that much, or somehow try to reject the chemical relevance of 5f in Th (good luck with that). Of course, you inconsistently do the first one for Th and Lr, but the second one for La and Ac! Double sharp (talk) 22:37, 16 February 2020 (UTC)

@Double sharp: Could you please desist from associating my arguments with symmetry in light of the fact that I don't give a rat's about symmetry or asymmetry, as I have stated before and you continue to ignore. I let Nature take its course. D/e's are important. So is aubau, and the periodic law, and regularity. I've unpacked my arguments several times, and your own critiques and have yet to see you find a single instance of a double standard. If that was really a wont of mine you would've found some good examples by now. Don't forget ceteris paribus. You seem not to know that one. If you find a double standard by me, I'll 'fess up. I don't try and evade my mistakes. I make them and will continue do so. You seem unable to acknowledge and learn from your own.

@Sandbh: I don't care how much you say that you don't care about symmetry, when your actions speak otherwise. Relabeling it as regularity does not make it stop being symmetry. I found many examples already, but you choose not to logically examine yourself.

Never mind the elephant in the room that La has valence 4f involvement and the best you can do for dredging up scraps of 4f involvement for Lu is (1) dragging out the core electrons and (2) misunderstanding computational chemistry, so we do not have a case of ceteris paribus here and Lu is clearly favoured as the d-block lanthanide. Double sharp (talk) 20:24, 17 February 2020 (UTC)

@Double sharp: Penrose tiling is another example of the difference between symmetry and regularity. Such tiling shows symmetry but not regularity. Despite my examples showing that symmetry and regularity are not necessarily the same thing, there is nothing I can do if you choose to continue to interpret my actions as speaking otherwise. I focus on regularity; if the outcome is symmetry that is fine. I have never relied on symmetry in my arguments. As you know from the draft of my article:

@Sandbh: Penrose tilings show self-similarity. You've still not defined what exactly you claim the difference between symmetry and regularity to be, anyway. Double sharp (talk) 07:57, 18 February 2020 (UTC)

@Double sharp: From our own article: "A Penrose tiling is an example of an aperiodic tiling. Here, a tiling is a covering of the plane by non-overlapping polygons or other shapes, and aperiodic means that shifting any tiling with these shapes by any finite distance, without rotation, cannot produce the same tiling. However, despite their lack of translational symmetry, Penrose tilings may have both reflection symmetry and fivefold rotational symmetry."

Oh, and let us not forget, a square is regular and symmetric; a rectangle is irregular and symmetric." If you disagree, write a letter to Nature, and let the world know. Good luck with that. Sandbh (talk) 08:57, 18 February 2020 (UTC)

@Sandbh: More amazing equivocation. So for the latter "regular" can only be meant in the sense of regular polytope, which is obviously irrelevant to the PT. But this is even funnier, because do you know what the mathematical definition of regularity of a polytope or tiling is? Well, according to our article, it means that its symmetry group(!!!) is transitive on its flags! Double sharp (talk) 11:36, 18 February 2020 (UTC)

Jensen earlier referred to the abuse of (Platonic) symmetry considerations in the construction and interpretation of periodic tables in general, including to the extent of triumphing over the inconvenient facts of chemistry.

An emerging field of thought is the importance of symmetry breaking, rather than pure symmetry:

“...symmetries matter, largely because we like to see them broken sometimes: the laws, particles and forces of physics all have their roots in symmetry-breaking. They create what David Gross of the Kavli Institute for Theoretical Physics at the University of California, Santa Barbara, calls the “texture of the world”. These considerations have led Florian Goertz at the Max Planck Institute for Particle and Astroparticle Physics in Heidelberg to propose the existence of a new particle that is single-handedly capable of cleaning up five of the stickiest problems in physics. “Complete symmetry is boring,” says Goertz. “If symmetry is slightly broken, interesting things can happen.”

As Eugen Schwarz (2019, pers. comm., 8 Dec) stated, “The real, rich pattern of elements’ chemistry does not fit into a clear-cut rectangular grid.” This view is consistent with that of Dias, who asserted that, “A periodic table is defined as a partially ordered [italics added] set forming a two-dimensional array which complies with the triad principle where any central element has some metric property that is the arithmetic mean of two flanking [i.e. horizontal] member elements."

In this context, that you choose to interpret or twist my regularity-based arguments as being symmetry-based is…amusing, extraordinary, dumbfounding, and disappointing.

If you have one such example, I'd be happy to logically examine it, and elaborate.

I contend there are more important issues to consider in the placement of La and Lu than the phenomenon of marginal 4f involvement in La or Lu, such as aufbau and the periodic law. As a marginal phenomenon (relied on out of desperation) it needs to be regarded as such. Sandbh (talk) 00:36, 18 February 2020 (UTC)

@Sandbh: I don't rely on it out of desperation. But because there is obviously nothing more important to chemistry than valence subshells. For valence electrons we already know this is true per every chemistry teacher in the world. And for valence vacancies we know it from everyone who admits sp hybridisation for Be and Mg i.e. everybody. Double sharp (talk) 07:57, 18 February 2020 (UTC)

For the umpteenth time, I'll unpack the Th issue again.

Per our IUPAC submission (and I've seen this in the literature), a block starts upon the first appearance of the applicable electron, per idealised n+l, and actual aufbau.
Consistent with aufbau, the periodic law, and regularity, Th goes under Ce (Yes, Th is n+l anomalous. Yes, Lu and Lr are n+l anomalous. Deal with it. The La form has one less anomaly than the Lu form.)
It's interesting to note the marked 5f character of Th in the condensed state.

Simplest explanation for the greatest teaching and learning dividend.

The end. Sandbh (talk) 07:08, 17 February 2020 (UTC)

The rule for block start is flawed. It causes too many problems with regularity (5f in Th), determination of block end (4f in Lu) and periodic law (La vs. Lu in 5d). So just throw it out and make the things simpler and more transparent to teach and learn. Droog Andrey (talk) 07:22, 17 February 2020 (UTC)

@Sandbh: Exactly. Your first premise is based on a flawed rule, so everything that leads from it is useless. I can go simple while retaining relevance (simple as possible, but not simpler): just look at the subshell occupations listed in my columns. That decides on La, Ac, and Th as f-block elements with significant valence f-involvement in chemistry, and Lu and Lr as d-block elements which have zero significant valence f-involvement in chemistry. There's zero anomalies until you get to the extreme superheavies with their inert pairs and quartets on steroids, and even there we still see the trend continuing and the pattern outline still holding the fort under the stress of relativity. The end. Double sharp (talk) 14:40, 17 February 2020 (UTC)

G'day @Droog Andrey: Nice to hear from you.

What is intrinsically flawed about the first appearance of the applicable electron flagging the start of a block?
- @Sandbh: What do you want out of blocks? I insist they be more than formalities, so an f-block element must have f-chemistry. Under your silly rule (I reject and disown it and am frankly ashamed I ever believed in it, given how much contortion it must go through for Th) we may have a non-f element with f-chemistry (La, pulling the uncharacteristic behaviour out of the s-block) or an f-element without f-chemistry (Lu). Double sharp (talk) 07:57, 18 February 2020 (UTC)
There is no issue with the regularity of Th. It was originally placed under Hf, until a better appreciation of aufbau developed. Even Seaborg placed at it at the start of the f-block, and said, "A periodic table that places the actinide elements and the transactinide elements in positions that best represent our present understanding is shown…". Nothing has changed. Just as the 4f collapse occurs in Ce, so too is it thought to occur in Th.

@Double sharp: “…for the purpose of selecting an optimal periodic table we prefer to consider block membership as a global property in which we focus on the predominant differentiating electron." You were on fire when we were writing on our IUPAC submission. Scerri wanted to arrange a phone hook up between me and the working group, after he got the paper (didn't happen in any event); nothing to be ashamed of there. Sandbh (talk) 09:03, 18 February 2020 (UTC)

@Sandbh: I agree that we noted some important things that show that the standard Lu arguments are incomplete. Unfortunately for you, I've since discovered thanks to Droog Andrey important things that show that they're still right if you complete them with a holistic look at the data (so you can in fact easily address the argument "what about group 2"). So I am just as much "on fire" as ever re this issue, but unlike you, I can actually change my stand when new data comes in. Double sharp (talk) 11:42, 18 February 2020 (UTC)

- Double standard, here we go! 4f can collapse at Ce according to Sandbh because 4f valence involvement in La doesn't matter, but somehow it matters for 5f in Th! The assumption of regularity implies that that is something normal for blocks. Well, not for heavy elements it isn't. You know, the first ground-state 4f electron is in Ce, 5f is in Pa, and some predictions suggest 6f might be E124 instead of E123 (two configurations are very close for E123). One element later in each. The assumption of regularity, once we go to heavy elements that we are discussing here, is groundless. Double sharp (talk) 07:57, 18 February 2020 (UTC)

@Double sharp: According to me, eh? I just quote the literature per out IUPAC submission. We see regularity in the start of each block. We see regularity in the positioning of the 4 and 5f collapse. Of course, the sky will fall down if we persist in this foolishness, just like what was claimed in our search for the Higgs particle. Sandbh (talk) 09:09, 18 February 2020 (UTC)

@Sandbh: No you don't, looking at differentiating electrons. The first 4f electron appears in Ce, the first 5f electron appears in Pa, and the first 6f may have to wait till E124. There is no "regularity" at all here. Neither is there for the d-block once we get to heavy elements. The only way you can cough up "regularity" is to allow in other chemically relevant configurations for Th. Of course, doing so for La and Ac is verboten. The exact same double standard Jensen correctly criticised Lavelle for. Double sharp (talk) 11:42, 18 February 2020 (UTC)

Indeed, This article reports the presence of itinerant f-electrons in Ce and Th, and that the similarity between the two metals, "is especially clear, where for example both elements appear in the fcc structure." Indeed, we know that but for the presence of 4f character in Th it would've had the same structure as Hf.
- @Sandbh: And if not for the presence of 4f in La - well, Gschneidner can tell you better than I. Double sharp (talk) 07:57, 18 February 2020 (UTC)
The irregular block end with Lu is similar to the irregular block end of the d-block. Nothing about the chemistry of Lu has changed since it was realised that Yb completed the 4f shell first.
- @Sandbh: Yes, Lu never had any f-involvement in the first place, so indeed we should realise that we never should have put it in the f block in the first place. The chemical community corrected (eventually) its mistaken placement of Be and Mg in group 12; you seem to want it to double down on the even more obviously mistaken one of La and Ac in group 3 (since, amazingly enough, unadorned chemically active subshells don't even need to analyse the weirdness of the s-block to deal with the group 3 problem, though they do for the group II problem). 3d in Zn is far more active than 4f in Lu, look at interatomic distances. Double sharp (talk) 07:57, 18 February 2020 (UTC)
La represents the first appearance of the 5d¹ electron; Gd the second; and Lu the third. There is no case for skipping La as the first 5d1 member. Sandbh (talk) 01:15, 18 February 2020 (UTC)
- @Sandbh: Because La marks the first appearance of 4f valence activity which is infinitely more important than your focus on incomplete, ill-defined, and irrelevant DEs. Double sharp (talk) 07:57, 18 February 2020 (UTC)

- @Double sharp: The peripheral appearance of 4f valence activity is noise compared to much broader considerations. Sandbh (talk) 09:12, 18 February 2020 (UTC)
  - @Sandbh: Are those the same broader considerations ("block regularity") that you treat as noise compared to the appearance of 5f valence activity in Th?
  - Th represents the first appearance of the 6d² electron; Rf only the second. There is no case, by this logic, for skipping Th as the first 6d2 member. Double sharp (talk) 11:43, 18 February 2020 (UTC)
- @Double sharp: Like I said, if you want to extend my principle that a block starts upon the first appearance of the relevant electron, s = H, p = B, d = Sc, f = La, such that it needs to apply to every column of that block and that your extension (not mine) then becomes illogical from your perspective, then knock yourself out arguing with your self. Sandbh (talk) 11:01, 20 February 2020 (UTC)
  - - @Sandbh: Already addressed above. P.S. I like that slip where you say "f = La". Perfectly true in terms of chemically active valence subshells, of course. ;) Note of course the s-block exemption of weirdness, or else p = Li! Double sharp (talk) 22:53, 20 February 2020 (UTC)

Lu 4f involvement

@Double sharp: Further to our IUPAC submission regarding the f character of Lu, and what you said about the normal range of chemical bond energies being 1 to 10 eV, here are some interesting extracts from the literature:

[1] "Optical properties of two pairs of Ce³⁺-doped scintillating materials, (LiLuF₄, LiYF₄) and LuF₃, LaF₃), are presented. 4f¹⁴→4f¹³-5d transitions of Lu³⁺ are shown to occur between 8–10 eV in the transmission spectra of the Lu-based compounds…Previous investigations have shown that 4f-Lu levels are very close in energy to the 2p F levels forming the valence band in fluoride compounds."
Source: https://www.tandfonline.com/doi/abs/10.1080/10420159908226205

You have to take the c. 10 eV value according to where in the table you are. High values near 10 eV are normally for those strong multiple bonds between 2nd-period elements, e.g. C≡O, N≡N. They are rarely seen elsewhere. Well, for Lu the strongest bond listed here is Lu-O at 7.2 eV, so where are we then? Not to mention that we need to first ionise the Lu to Lu³⁺, which is already what most of the chemical bond energy is doing. You'd think that exciting an f-electron out of there and into a directly valent subshell would be close to creating a Lu(IV) compound, which you don't see...
You cannot have it both ways. Either Parish is right and there's no significant direct 4f involvement, or the 4f electrons are actually in the valence band. But they contradict each other. Double sharp (talk) 10:24, 16 February 2020 (UTC)

[2] "Lutetium monohalides molecules in their lowest lying electronic structure and in a range around the equilibrium internuclear distance of the ground state X¹Σ⁺ are assumed to be ionic with high percentage more than 90%. Because of the high electron correlation in the 4f shell and its weak but noticeable contribution to chemical bonding, 4f electrons should be treated as valence electrons in our accurate ab initio calculations. Moreover, the f orbital has also an important role in the spin–orbit effect in the electronic states."
Source: https://www.sciencedirect.com/science/article/abs/pii/S1386142513011062

Sandbh (talk) 05:45, 16 February 2020 (UTC)

And what you don't quote is "The 5s, 5p, 4d orbitals and the 4f orbitals are found in the same spatial region and should be treated as valence electrons too in order to get a consistent description of electron interactions." This is really normal with computational chemistry, you have to include the outermost layer of core electrons to get something more or less correct. What counts is whether those orbitals actually contribute significantly to the bonding, e.g. effective overlaps. I think the fact that 4f in Lu is appearing with the outer layer of the [Xe] core here says it all: the core is [Xe]4f¹⁴. Double sharp (talk) 10:24, 16 February 2020 (UTC)

@Double sharp: Yes, I left that out as I thought the point had already been made i.e. "Because of the high electron correlation in the 4f shell and its weak but noticeable contribution to chemical bonding". Sandbh (talk) 22:14, 16 February 2020 (UTC)

@Sandbh: @Droog Andrey: By that logic, 5s, 5p, 4d are valence also. Which is silly. Anyone can see that the interatomic distances are too small to allow significant 4f penetration into the bond. You also get noticeable errors neglecting 5s and 5p in Hf compounds, you know (10.1103/PhysRevA.76.030501), as well as 3d in Ga compounds (10.1063/1.477851, strong correlation, even). Anyone can see that chemically that doesn't make them valence subshells. It's really normal that you need one more step down to the top layer of core subshells to get accurate computational results, but it doesn't make them chemically valence subshells as there is not significant overlap with the atoms being bonded to. (Which, BTW, is not true for 3d in Zn; there, there is significant overlap.) Though Droog Andrey as an actual computational chemist is certainly better equipped to explain these subtleties, which I would like to request him to do. ;) Double sharp (talk) 22:35, 16 February 2020 (UTC)

Actually, a lot of "chemically core" electrons should be included in correlation to get reasonable results of quantum-chemical computations. My own computations of certain nickel complexes showed that only 1s2s2p could be treated as "compulationally core" electrons for nickel.

As for 4f in Lu: I just remind that excitation energy of Lu³⁺ is 11.2 eV, while for Tl³⁺ it is only 9.3 eV. Droog Andrey (talk) 06:13, 17 February 2020 (UTC)

Well, yes, for a gaseous single Lu atom in a vacuum. As Double sharp reminds me, context is everything. Sandbh (talk) 06:30, 17 February 2020 (UTC)

In condensed phase the situation is pretty the same: excitation energy for Lu³⁺ is larger than for Tl³⁺. Droog Andrey (talk) 07:12, 17 February 2020 (UTC)

Namely, there are computed orbital eigenvalues (in eV) for Tl(H₂O)₆³⁺ cation of T_h symmetry:

-28.79 (t_g from 5d, occupied)

-24.59 (e_g from 5d, occupied)

-16.53 (a_g from 6s, unoccupied)

And there are computed orbital eigenvalues (in eV) for Lu(H₂O)₆³⁺ cation of T_h symmetry:

-26.84 (a_u from 4f, occupied)

-26.83 (t_u from 4f, occupied)

-25.59 (t_u from 4f, occupied)

-12.66 (t_g from 5d, unoccupied)

So the excitation energy is about 8 eV for 5d->6s in Tl(H₂O)₆³⁺ and about 13 eV for 4f->5d in Lu(H₂O)₆³⁺. Note also that energy splitting is much larger for 5d in Tl than for 4f in Lu, suggesting much larger chemical involvement of the former. Droog Andrey (talk) 13:39, 19 February 2020 (UTC)

[3] In the present work, we report the high pressure behavior, electronic and elastic properties of two lutetium compounds, namely, LuAs and LuSb which crystallize in NaCl structure…
We have also plotted the total and partial density of states for these compounds at zero pressure…The mixing of Lu ‘d’, Lu ’f’ and Sb ‘p’ states at the Fermi level shows the metallic character of these compounds…On the whole, the band profiles are seen to be almost same for the LuSb. The mixing of Lu ‘d’, Lu ’f’ and Sb ‘p’ states at the Fermi level shows the metallic character of the compound.
Source: https://www.sciencedirect.com/science/article/abs/pii/S0927025610005203

@Sandbh: You, of course, do not quote the following: "We can see there is flat band in the valence region at −5.0eV which is due to localized 'f' states of Lu" (my emphasis). The bands just below Fermi level are instead Lu d and pnictogen p. So, 4f is localised, and its contribution is significantly below the Fermi level. Double sharp (talk) 13:56, 18 February 2020 (UTC)

@Double sharp: Well, we have a bit of a conundrum then. Our fermi level article says that, "In band structure theory, used in solid state physics to analyze the energy levels in a solid, the Fermi level can be considered to be a hypothetical energy level of an electron, such that at thermodynamic equilibrium this energy level would have a 50% probability of being occupied at any given time." Sandbh (talk) 22:15, 19 February 2020 (UTC)

@Sandbh: So? -5.0eV is way below it, so those 4f states are essentially always fully occupied. Double sharp (talk) 22:17, 19 February 2020 (UTC)

[4] A curious paper:
603: "From this data follows that the Lu 4f electrons (considered inner valence to a certain approximation) by their spectral parameters differ significantly from the Hf 4f electrons, which become the core."
"The constant term in Eq. (1) can be explained by taking into account the partial contribution of the Ln 4f electrons to the outer valence MO in oxides Ln₂O₃."
604: "According to these data, the Ln 4f shell in lanthanides is rather outer and participates in the MO formation in lanthanide oxides."
"The significant growth of the Ln 4f intensity (photoemission cross-section) going from Lu (Z = 71) to Hf (Z = 72), Ta (Z = 73), W (Z = 74) and further proves that that the Ln 4f electrons in lanthanide oxides are more delocalized than in the case of higher atomic number elements (Fig. 2)."
605. "The 4f electrons in lanthanide oxides were found to be much more delocalized than in the further elements."

Sandbh (talk) 00:11, 20 February 2020 (UTC)

[5] Here's another interesting article, related to [3]:
11881: "The existence of Lu-4f electrons in the band gap can significantly increase the electrons transition probability, namely it can increase the transitions corresponding to the Lu-4f to Nb-4d band and O-2p to Lu-4f band."

Sandbh (talk) 00:11, 20 February 2020 (UTC)

@Sandbh: You may find another 10 papers about 4f involvement in Lu, but, again, it is no more than 5d involvement in Tl. The latter does not make Tl a 5d element, however. Droog Andrey (talk) 07:19, 20 February 2020 (UTC)

@Double sharp:@Droog Andrey: Double sharp, why does your PT not show 5d involvement in Tl? Sandbh (talk) 02:53, 23 February 2020 (UTC)

@Sandbh: Why should it? It's clearly a core subshell. If you're not convinced about 5d in Hg, then note that 5d in Tl must be even lower. Anyway, I'm sure Droog Andrey can give you the figures for a molecule like TlF₃ and see how the 5d overlap is minuscule even for a really small fluoride trying to use 2p. The fact that Lu 4f is even lower than Tl 5d illustrates that 4f is emphatically core for Lu, too.

I agree that technically it should show 6d involvement for Nh (NhF₃ and NhCl₃ have 6d involvement causing them to be T-shaped instead of trigonal planar, see nihonium); but come on, we should know to make relativistic second-order corrections. Double sharp (talk) 10:07, 23 February 2020 (UTC)

@Double sharp: Oh, look, CsF₃ is also T-shaped. If you care about their stability, just compare 2nd and 3rd ionization potentials for Cs and Nh :) Droog Andrey (talk) 07:18, 24 February 2020 (UTC)

@Droog Andrey: Well, in that case there is not any problem at all. ^_^

Since Tl +3 is stabilised by anion formation, we may expect NhF⁻
₄ to be more plausible than NhF₃. But you have mentioned before that in this compound the overlap is Nh 7s with F 2p, instead. ^_^ Double sharp (talk) 11:32, 24 February 2020 (UTC)

Zn 3d involvement

@Double sharp: You often mention ZnCl₂ as an example of 3d involvement by Zn. Do you have a citation?

I have one: "Electronic structure and chemical bonding of the first row transition metal dichlorides, MnCl₂, NiCl₂, and ZnCl₂: A high resolution photoelectron spectroscopic study", here. The authors write:

"For Zn, a closed shell element, the 3d orbitals should be corelike, with little bonding capability."

"Thus, the spectrum in the 3d region is very sharp, with little or no apparent vibrational excitation. This is in accord with the expectation that the 3d orbitals of Zn are core-like, with little bonding capability."

Sandbh (talk) 22:45, 19 February 2020 (UTC)

@Sandbh: Here's some citations for Zn 3d. In many cases it is indeed true that 3d on Zn is almost completely core-like, but not here. The chloride was perhaps not the best choice: I used it in deference to Droog Andrey's use of it (as he notes, the interatomic distances are suggestive, correctly, that there is some significant overlap), but the fluoride is an even stronger case. 3d-2p is an excellent overlap, although 3d-3p can be seen if you look hard. The bolding is mine. ;)

“

The 2ph-TDA calculations manifest the different physics in ZnCl₂ and NiCl₂. CdCl₂ behaves in a similar manner to ZnCl₂ and need not be discussed separately. The calculated spectrum of ZnCl₂ is easy to describe. It consists of three well separated groups of lines. The first group contains four lines which are due to the ionization of the outer valence orbitals 2π_g, 1π_u, 2σ_u and 3σ_g. These orbitals are responsible for the chemical bonding between the Cl atoms and Zn and are admixtures of mainly chlorine 3p and zinc 4s atomic orbitals. The second group contains the closely spaced lines which correspond to the orbitals which derive from the 3d electrons of Zn. These orbitals are strongly localized on the metallic site and are subject to considerable relaxation effects. They behave partly like core orbitals and partly like valence orbitals.

”

— W. von Niessen & L.S. Cederbaum (1981) Many-body calculations on the ionization spectra of transition metal compounds: ZnCl2, CdCl2 and NiCl2 (link)

“

In solid ZnS the Zn 3d levels are essentially core orbitals lying about 7.5 eV below the S 3p nonbonding orbitals. In solid ZnO this energy difference is reduced to about 6 eV and the orbitals at the top of the valence region have significant Zn 3d-O 2p antibonding character. In solid ZnF₂, bonding and antibonding Zn 3d-F 2p orbital sets are clearly evident at the top of the valence region and have an energy separation of about 4 eV. ... The observed difference between ZnS(s) and ZnF₂(s) is probably a result of two factors. First, the F 2p orbitals are more tightly bound than the S 3p and thus closer in energy to the Zn 3d. Second, the Zn 3d orbitals are less stable in the six-coordinate cluster ZnF⁴⁻
₆, occurring in ZnF₂(s), than they are in the (hypothetical) ZnF²⁻
₄ cluster; thus the difference in coordination number between ZnS(s) and ZnF₂(s) may have some effect.

”

— J. A. Tossell (1971) Theoretical Studies of Valence Orbital Binding Energies in Solid ZnS, ZnO, and ZnF2 (link)

I don't dispute that 3d in Zn and 4d in Cd have rather weak involvement. But it is really there. Depending on the ligand and coordination number you may see it more or less, but that's nothing new (look at 6s and 6p in Tl or Pb). With something that can overlap effectively (O, F, to a smaller extent Cl) you will definitely see it. Double sharp (talk) 23:04, 19 February 2020 (UTC)

@Double sharp: Hmmm. In Mendeleev to Oganesson, Jensen has an article called "Richard Begg and the periodic table". Jensen writes:

"The final placement problem involves the status of the Zn group and the question of whether the members of this group should be classified as transition elements and placed in a (12+6) group or as main-block elements and placed in the (2+6) group. As summarized by the author in a previous paper, there is absolutely no evidence that these elements ever make use of either (n-1)d-type electrons or (n-1)d-type orbital vacancies in their chemistry and, though they are frequently lumped with the transition metals in textbooks, they are in fact main-block elements (36, 37). As a result, we encounter for the first time, as pointed out many years ago by Sanderson, a true bifurcation in the group structure of the periodic table – a bifurcation which also underlies the original debate between Abegg and Werner over whether Be and Mg should be placed above Zn or above Ca (38). This is resolved in figure 10 by placing the Ca branch in the (2+6) group and the Zn branch in a (2’+6) group, and in the periodic table in Figure 13.11 by connecting Mg equally to both Ca and Zn by means of primary black tie lines."

36. Jensen WB 2003, “The place of zinc, cadmium, and mercury in the periodic table," JChemEd, 80, 952-961.

37. There have been claims from time to time that it is possible to prepare compounds of Hg(IV) but these have always proven to be unverifiable. See Jensen WB 2008, "Is mercury now a transition element?," JChemEd, 85, 1182-1183.

38. Sanderson RT 1964, "A rational periodic table," JChemEd, 41,187-189.

How do we acquit his assertion, "there is absolutely no evidence that these elements ever make use of either (n-1)d-type electrons or (n-1)d-type orbital vacancies in their chemistry"?

Another question. Supposing Zn does have rather weak involvement of 3d, is this any different from the situation in Lu? Sandbh (talk) 03:19, 22 February 2020 (UTC)

@Sandbh: His assertion is most especially falsified by the second paper I quoted. This is categorically of a different order from Lu: with that one, 4f involvement is always very weak (weaker than 5d in Tl), but for ZnF₂ we see 3d at the top of the valence region(!) having a strong overlap with the similarly small 2p of F. (In general you want a small counteranion for this because 3d is small.)

BTW: Cd is similar to Zn, Hg has a smaller 5d-6s gap even and should have even more d-involvement, and at Cn 6d involvement should be completely normal. Double sharp (talk) 09:52, 22 February 2020 (UTC)

@Double sharp: Thank you. Since the 3d subshell in Zn is full how does it show "rather weak involvement"? Sandbh (talk) 11:54, 22 February 2020 (UTC)

@Sandbh: What's wrong with that? It's full in Cu as well. The point is that there is quite clearly a bonding MO in ZnF₂ near the top of the valence level that has significant 3d participation. Double sharp (talk) 11:58, 22 February 2020 (UTC)

@Double sharp: What's going on here then(?):

603: "From this data follows that the Lu 4f electrons (considered inner valence to a certain approximation) by their spectral parameters differ significantly from the Hf 4f electrons, which become the core."
"The constant term in Eq. (1) can be explained by taking into account the partial contribution of the Ln 4f electrons to the outer valence MO in oxides Ln₂O₃."
604: "According to these data, the Ln 4f shell in lanthanides is rather outer and participates in the MO formation in lanthanide oxides."
"The significant growth of the Ln 4f intensity (photoemission cross-section) going from Lu (Z = 71) to Hf (Z = 72), Ta (Z = 73), W (Z = 74) and further proves that that the Ln 4f electrons in lanthanide oxides are more delocalized than in the case of higher atomic number elements (Fig. 2)."
605. "The 4f electrons in lanthanide oxides were found to be much more delocalized than in the further elements."

Sandbh (talk) 12:03, 22 February 2020 (UTC)

@Sandbh: 4f is nowhere near the top of the valence level, as 3d is in ZnF₂. As Droog Andrey has demonstrated it is of the same order as 5d in Tl, i.e. generally insignificant. Double sharp (talk) 12:13, 22 February 2020 (UTC)

@Double sharp: I've asked you this before and you provided a hand-waving, nothing to see here response of "mathematician's pedantry". Who determines what is "significant" and how? In contrast, GSC's are ubiquitous and DE's clear cut. Sandbh (talk) 04:06, 23 February 2020 (UTC)

@Sandbh: I'll take a difficult-to-apply but effective criterion any day over an easy-to-apply but useless one. Significance is clearly a continuum but you may clearly see steps along that continuum being taken at the right times. Double sharp (talk) 10:09, 23 February 2020 (UTC)

Lu arguments

@Double sharp: Setting aside your concerns about my arguments, what are your arguments, in summary form, for Lu in group 3? Sandbh (talk) 11:55, 19 February 2020 (UTC)

@Sandbh: In order of importance:

La has appreciable 4f valence shell involvement visible in physical (Gschneidner) and chemical (cubic complexes etc.) properties. Lu does not. On the grounds of Jensen's criterion 1 (looking at valence electrons and vacancies, i.e. chemically active valence subshells) this resolves Lu in group 3 immediately without further question.
The result is also more consistent with periodic trends, looking e.g. at the consistent impact of a core 4f shell added from Lu to Hg, making the d-block more homogeneous. (The f-block alone is of course totally inconclusive, but that impacts La as well.) And also e.g. seeing that group 3 is, as normal, totally intermediate between groups 2 and 4, with transition properties slowly going in. Lu tables result in continuous trends, La tables in one-off catastrophic breaks.
We increase regularity and symmetry by avoiding a one-off block split and n+l rule violation in the periodic table. Which is relieving as such a block split has not enough chemical justification to happen, as evidenced by 1. (I am totally OK with an n+l rule violation if there is absolute chemical justification as in period 8. Here there is not any such conclusive one.) This is really a part of 2, but it seems to deserve a number.
History is irrelevant to our starting point; we just start with the properties of the elements as we know them now, with the starting hypothesis of total regularity and symmetry, and changes from that have to be chemically justified. (Since you like the phrase "symmetry-breaking"; in order for it to be breaking we must have started with some.)

The same arguments also work precisely for the other questions I raised, going for He-Be-Mg-Ca and B-Al-Ga. Double sharp (talk) 22:30, 19 February 2020 (UTC)

@Double sharp:

Nice. I've listed some counterpoints for your consideration, in summary form.

Argument 1

A. 4f involvement in La is very marginal.

4f in Lu is even more marginal (less than 5d in Tl). Not only that, but 4f in La is clearly visible in the metal itself and in its compounds (cubic complexes and high coordination numbers). Double sharp (talk) 14:31, 20 February 2020 (UTC)

Having the first row of a block start with an element that does not have an electron configuration with the relevant electron is anomalous, compared to H, B, and Sc. Wither regularity? Where are the citations demonstrating 4f in La is clearly visible in the metal itself and in its compounds (cubic complexes and high coordination numbers).

@Sandbh: The citations appear throughout this page and your archive of the previous discussion every time I refer to Gschneidner and simple symmetry grounds. Not to mention a La table makes La and Ac the only elements outside the s-block exhibiting the wrong "supervalent hybridisation". Whither regularity, either? You're going to have to make a case why your regularity on ground-state electron configurations only is more relevant than mine. And I claim that it's obvious that mine is actually more relevant because (1) it subsumes yours and (2) in chemical environments, generally we are not in ground-state gas-phase electron configurations. Double sharp (talk) 12:03, 21 February 2020 (UTC)

@Double sharp: 4f involvement in La metal is speculation AFAIK. Involvement in cubic complexes and high coordination numbers is either speculation or refuted. There is no smoking gun AFAIK. Sandbh (talk) 12:33, 21 February 2020 (UTC)

@Sandbh: Read Gschneidner's papers cited in our old La submission (back when I did not know better). La 4f is just above the Fermi level. Neither of the chemical considerations has actually been refuted. Again: how does Parish propose to explain cubic complexes without 4f orbitals? Double sharp (talk) 12:57, 21 February 2020 (UTC)

B. Jensen's criteria 1 in fact was: "Assignment to a major block based on the kinds of available valence electrons (i.e., s, p, d, f, etc.)".

Nope. He says "valence electrons and/or valence vacancies" in 2015. Double sharp (talk) 14:38, 20 February 2020 (UTC)

I agree. He updated his definition. My bad. His reference to "valence vacancies" is not the same as your "chemically active valence subshells". For example, in group 12 the valence vacancies equal the number of electrons required to reach the next noble gas configuration i.e. 6. whereas, as you keep asserting, the 3d sub-shell in e.g. Zn is supposedly chemical active, even though it's full. Sandbh (talk) 03:33, 21 February 2020 (UTC)

@Sandbh: The principle is exactly the same. It's just that Jensen has mistakenly overlooked d-involvement in the Zn group. My table is based on exactly his principle except that I make this correction (thus Zn and its congeners are (dsp)¹² instead), and I also make the correction that it's not just the p-subshell that appears in the s-block "prematurely", but also the d-subshell. (Whence "all higher".) For the f-subshell it doesn't seem to happen strongly, but delayed collapse effects are starting here. Double sharp (talk) 12:03, 21 February 2020 (UTC)

C. Jensen's criteria 1 does not resolve Lu in group 3 without further question.

As demonstrated, it does. Double sharp (talk) 14:38, 20 February 2020 (UTC)

On marginal grounds. And Lu in group 3 introduces more irregularities elsewhere. It is ironic that attempts to improve regularity in the outward appearance of the periodic table result in more irregularities among other properties across the table. The biggest clangers for me are probably the periodic law irregularity; the nearest neighbours irregularity; and the double periodicity irregularity, closely followed by Lavelle's argument about two d-metals starting the f-block; isodiagonality, and horizontal triads. Then there would the n+l rule; d/e's; term symbols; the f-block contraction; and the rare earth metals. The history plays a big part too, including the fact that nothing changed wrt to the chemistry of Lu when it was discovered that 4f closed at Yb rather than Lu; and that even if Lu had been discovered first nothing would have changed, due to the atomic weight gap. Sandbh (talk) 03:33, 21 February 2020 (UTC)

@Sandbh: None of these are relevant clangers, because:

There is more to the periodic law than what you admit into it;
Nearest neighbours are inconclusive because a correct holistic look at chemistry reveals that group 3 is normal and intermediate between the two peripheral groups;
Double periodicity when applied properly supports Lu (because otherwise d¹ is the only column that doesn't suffer it outside the s-block, which is at variance with chemical and physical facts);
Lavelle's argument is baseless since La and Ac have well-defined valence f-involvement (and, BTW, a La table means two d-metals are in the f-block: Lu and Lr).
Isodiagonality is not relevant for most of the table. An argument that you have to set artificial boundaries on is worthless.
Horizontal triads reduced to maximum oxidation numbers are not relevant for most of the table. An argument that you have to set artificial boundaries on is worthless.
The n+l rule really supports a Lu table, as I've demonstrated.
DE's are chemically irrelevant.
Term symbols are based on ground-state configurations, which are both (1) incomplete and (2) support a Lu table as far as they go, as I've demonstrated.
The f-block contraction argument is groundless because the 4f electrons in Lu are core-like and simply not behaving the same way as in Yb. They are instead behaving as in Hf through Rn.
The rare earth metals argument is just cosmetics.
The history simply reveals that, since Lu's chemistry never changed, the original placement of La in the d-block was wrong.
The atomic weight gap is groundless because a similar gap appears every single time there is a block insertion. Somehow, it's only permitted to talk about "mind the gap" when it's about the artificial gap you like to push between La and Hf. Double sharp (talk) 12:03, 21 February 2020 (UTC)

@Double sharp: Re #11, "The rare earth metals argument is just cosmetics." "Cosmetic" means to improve or beautify appearance. Since beauty or elegance in science is an important consideration, I agree with you. Sandbh (talk) 22:04, 22 February 2020 (UTC)

@Sandbh: Cosmetics are useless unless it reflects something actual in nature. I could make the periodic table more beautiful by listing the elements in any sort of artistic sculptural arrangement. And it will be useless unless that arrangement actually shows periodicity. (Besides, even if cosmetics were a valid argument, the cosmetic improvement of the REM series, with its changeable definition in reality, pales beside the cosmetic improvement of avoiding the unsightly block interruption of the La table.) Double sharp (talk) 22:08, 22 February 2020 (UTC)

@Double sharp: Or course, since you can't refute or are unwilling to retract your own observation (that's how we learn: from our mistakes), an observation which I support, you have to resort to taking things wildly out of context ("An artistic sculptural arrangement." Really.) or via fogging. In the case of the REM there is an improvement in consistency or regularity with the rest of the periodic table. And yes, considerations of beauty never trump symmetry breaking. Sandbh (talk) 03:47, 23 February 2020 (UTC)

@Sandbh: Funnily enough, Droog Andrey have I have demonstrated many times that the La table destroys a lot of consistency and regularity, and that there is no real symmetry break here in reality. You say that we should be willing to retract our own observations: yes, that's why I'm currently arguing vociferously on the Lu side, whereas I was doing the same on the La side a couple of years ago. What changed? I got new information from Droog Andrey that refuted the good La arguments. Meanwhile, you keep repeating the same arguments over and over again even after we refute them. Double sharp (talk) 12:39, 23 February 2020 (UTC)

@Double sharp: Yes, since you once again are unable to refute or are unwilling to retract your own observation, this time you engage in distraction by heading off into another tangent. Nice work. Sandbh (talk) 04:04, 24 February 2020 (UTC)

@Sandbh: Three points:

Even if perhaps I chose the wrong word here, the point still stands: there is nothing to do with chemistry here, just graphic design. In fact the La table, as Droog Andrey and I have demonstrated, is further removed from the chemistry involved than the Lu one.
"Cosmetic" often has a disapproving meaning, to quote the Cambridge Dictionary linked: "Cosmetic changes, etc. are intended to make you believe that something is better when, really, the problem has not been solved".
Droog Andrey and I have refuted a lot of your observations. I don't see most of them being retracted. Double sharp (talk) 11:35, 24 February 2020 (UTC)

Argument 2

A. The impact of 4f filling on Ce to Lu is substantial, resulting in their common +3 oxidation state, and contributing to their greater-than-expected decrease in ionic radii, and them being called the lanthanides. Here, Hf to Rn are not Ln.

The common +3 oxidation state in Lu is from a different source than that of La through Yb. In La through Yb it comes from fⁿ⁺¹ and fⁿd interplay with promotion back and forth. In Lu 4f is core-like and exactly like in Hf through Rn. Double sharp (talk) 14:40, 20 February 2020 (UTC)

Correct, and noise compared to the chemistry of Lu being than of a lanthanide. Sandbh (talk) 02:54, 21 February 2020 (UTC)

@Sandbh: That is total nonsense. The chemistry of Zn is not far from the main-group metals after it. That doesn't make it a p-block element, because the 3d orbitals are still having significant valence contributions. Double sharp (talk) 12:09, 21 February 2020 (UTC)

Off on a tangent again. There is no proposal to make Zn a p-block element. There is no proposal to move Lu out of the f-block since the chemistry of its trivalent cationic state, arises from its electron configuration of f¹⁴. Compare with Yb f¹³, Tm f¹² all the way back to Ce f¹. Hence the Ln contraction runs from Ce to Lu hence the contraction starts with the first member of the f-block and concludes with the last member of the f-block. Ditto the An contraction. There is no need to drill down as you have done, since the question is resolved at a higher level. That's how a hierarchy of considerations works. Do you understand? Sandbh (talk) 02:48, 22 February 2020 (UTC)

@Sandbh: Something so local doesn't work very well at a high level of the hierarchy because it will nearly always be inconclusive. The whole point of having a hierarchy is that you classify all the easy cases first and only go down for the hard ones.
The f¹⁴ electrons are not valence electrons in Lu. Their relationship to the +3 state in Lu is just that after we remove those outer electrons they form part of a stable [Xe]4f¹⁴ core, which is just like 4f in Hf through Os and completely unlike 4f in La through Yb. Before the ionisation they are there, after the ionisation they are still there, and you can never muster enough energy to get rid of them or get them to show any more than perfunctory (less than 5d in Tl) involvement in bonding. And that's true even in various chemical environments as well. Its trivalence is simply because Lu has easily removed 5d6s² outside and lattice energy considerations suggest removing all three as the easiest thing to do nearly all the time, so exactly like Sc, Y, and Lr. 4f is totally not involved, whereas for La through Yb it is because of electrons flitting in and out of it. The only way it's relevant is when saying that after the outer 3 are removed we have a stable [Xe]4f¹⁴ core which is helpful. But that applies for the whole 5d row with that core, especially Lu through Os which get down to it. By your logic we could just as easily say that the chemistry of the +1 and +2 states of the s-block is totally because of their noble gas configurations, and therefore from Na and Mg onwards they are really p-elements because those are p⁶! Double sharp (talk) 10:03, 22 February 2020 (UTC)

@Double sharp:@Droog Andrey: OK, have a go at this one. Note especially p. 603, where the Lu 4f electrons differ significantly from the Hf 4f core electrons.

From this fine Russian paper:

603: "From this data follows that the Lu 4f electrons (considered inner valence to a certain approximation) by their spectral parameters differ significantly from the Hf 4f electrons, which become the core."

"The constant term in Eq. (1) can be explained by taking into account the partial contribution of the Ln 4f electrons to the outer valence MO in oxides Ln₂O₃."

604: "According to these data, the Ln 4f shell in lanthanides is rather outer and participates in the MO formation in lanthanide oxides."

"The significant growth of the Ln 4f intensity (photoemission cross-section) going from Lu (Z = 71) to Hf (Z = 72), Ta (Z = 73), W (Z = 74) and further proves that that the Ln 4f electrons in lanthanide oxides are more delocalized than in the case of higher atomic number elements (Fig. 2)."

605. "The 4f electrons in lanthanide oxides were found to be much more delocalized than in the further elements."

I'd expect they must be wrong, of course. Surprise me. Sandbh (talk) 05:57, 24 February 2020 (UTC)

@Sandbh: They are right that 4f drowning accelerates starting from Hf onwards, but they are wrong about the significance of 4f participation in chemical bonding. The relative energies of oxygen 2p and lutetium 4f are indeed close, but they do not overlap and correlate nearly the same way as, for example, 2p orbitals of neon atoms in liquid neon. Droog Andrey (talk) 16:21, 24 February 2020 (UTC)

B. Physically and chemically, Lu is more like Ho and Er, than Hf.

Physically and chemically, La is more like Pr and Nd, than Hf. And the resemblance is worse for La vs. Hf than Lu vs. Hf, so this argument even supports Lu. Double sharp (talk) 14:38, 20 February 2020 (UTC)

As would be expected given the intervening 14 elements between La and Hf. Sandbh (talk) 00:52, 21 February 2020 (UTC)

@Sandbh: Backwards logic. You have to prove first that there is such a gap. Double sharp (talk) 12:09, 21 February 2020 (UTC)

C. Holistically, the mainly ionic chemistry of group 3 is more like that of groups 1-2 than the mainly covalent chemistry of groups 4-5.

Out of context, "mainly ionic" is ill-defined. Double sharp (talk) 14:38, 20 February 2020 (UTC)

Double sharp pitches and Sandbh whacks the ball out of the park!

Yet widely recognised in the literature. "For the Ln, the shielding of the 4f-orbitals from external influences by the 5s and 5p electrons is extensive because the 4f-orbitals are greatly contracted throughout the series, leading to an immense domination of the resulting highly ionic chemistry by the trivalent oxidation state." Geoffrey Wilkinson, Francis Gordon Albert Stone, Edward W. Abel 1982, p. 176, Comprehensive organometallic chemistry: the synthesis, reactions, and structures of organometallic compounds, vol. 3 Sandbh (talk) 00:52, 21 February 2020 (UTC)

@Sandbh: Only in context. You push it out of context, when it becomes false. Here we are talking about organometallic chemistry, so with carbon only. Then yes, because of high ionic radius it is true. If we talk about intermetallic compounds instead, it's totally not true. And even here Wilkinson, Stone, and Abel are talking about highly ionic chemistry, which means they understand (of course) that it's a continuum between more or less ionic character in the M-C bond.

Only a Sith deals in absolutes. ;) Double sharp (talk) 12:09, 21 February 2020 (UTC)

@Double sharp: The context given by the authors was, "GENERAL PROPERTIES", not carbon. Oh, and did you miss the immense domination CONTEXT of the resulting highly ionic chemistry? Sandbh (talk) 12:28, 21 February 2020 (UTC)

@Sandbh: The even bigger context given by the authors in their title was "Comprehensive organometallic chemistry" (my bolding). Not to mention that "highly ionic" still implies a continuum. Only a Sith deals in absolutes. ;) Double sharp (talk) 12:52, 21 February 2020 (UTC)

@Double sharp: That's a good fog. As you know, that bigger context is not relevant in this case, since what they were talking about were the general properties of Sc, Y and the Ln, as a prelude to the OMC of these elements. Of course there is a continuum. And we can see that on the continuum the locus of the elements in question is located at the highly ionic end, that's all. In contrast, we can see that Groups 4-5 are on the covalent side of the continuum:

Group 4

1. "The most common and most stable oxidation state…is (+IV)."

2. "The +4 oxidation state for titanium gives rise to largely covalent compounds.

3. "…Zr(IV) and Hf(IV) are mainly covalent…"

-- 1. Lee JD 1996, Concise inorganic chemistry, Blackwell Science, p. 687

-- 2. Nicholls D 1974, Complexes and first-row transition elements, MacMillan Press, London, p. 139

-- 3. Talbot DEJ & Talbot JDR 2018, Corrosion science and technology, 3rd ed., CRC Press, p. 336

Group 5

"The chemistry of the V-Nb-Ta elements is similar to that of the previous triad…"

-- Dickerson et al. 1984, Chemical principles, 4th ed., Benjamin/Cummings, p. 330

And there it is. Sandbh (talk) 02:35, 22 February 2020 (UTC)

D. More broadly, to a staggering degree of difference, the chemical behaviour of group 3 generally resembles that of groups 1−2 rather than that of Groups 4−11.

A false statement, as demonstrated many times here by myself and Droog Andrey. Group 3 merely forms part of the continuous trend from group 1 through group 18.

Only a Sith deals in absolutes. ;) Double sharp (talk) 14:31, 20 February 2020 (UTC)

Well, @R8R: must be wrong too. Recall this conversation:

S: the chemical behaviour of Group 3 generally resembles that of Groups 1−2 rather than that of Groups 4−11

R8R: -- that's indeed the case. Group 3, whether -La-Ac or -Lu-Lr, resembles groups 1 and 2 much more closely than it does resemble groups 4 ~~and 5~~ through 11. This doesn't come as a surprise, however, given that this is not a comparison of the like with the like. A comparison with groups 4 and 5 only would make the difference less staggering and the comparison would be much more even.

Sandbh (talk) 00:28, 21 February 2020 (UTC)

@Sandbh: That's precisely supporting my point. Group 3 is more or less intermediate between 2 and 4. As it is between 1 and 5. Of course if you compare group 3 to all of groups 4-11 you will get a big difference just because of the late TM groups like 10 and 11 which are obviously very far down from group 3, but that's irrelevant. Otherwise I could equally well say that actually group 12 is totally different from group 11 because it more resembles groups 13-18 than groups 1-11. That's (1) not fair because 10-14 vs. 12, 11-13 vs. 12 are quite reasonable comparisons and (2) not good enough to pull apart group 12 from the d-block. A peripheral group is odd for its block just because it's near the edge and the maximum distance to other groups in the block is maximised, there's nothing unusual about that. Double sharp (talk) 12:09, 21 February 2020 (UTC)

Since my words are quoted here, I want there to be no doubt about what I meant with these words. My point was that you can't take two rather similar groups on one hand, a far more diverse set of eight on the other, and call this a fair comparison. I do, too, believe, that the groups form a chemical continuum, so if the comparison is to be run, then on the right hand should be groups 4 and 5, not 4, 5, and 6, 7, 8, and so on. That I put it so mildly is merely a reflection of how I thought the discussion was growing too intense and I hoped that a calmer voice would be a good example to follow. Unfortunately, I was wrong and it had no effect on the discussion whatsoever.--R8R (talk) 19:33, 22 February 2020 (UTC)

@R8R: Sorry. m(_ _) I'll try to be less tetchy about this in future comments. Double sharp (talk) 22:16, 22 February 2020 (UTC)

@Double sharp:@R8R: As R8R's words stand, I agree with him. Going from (a) a comparison of Group 3 with Groups 1−2 and Groups 4−11, to (b) a comparison of Group 3 with Groups 1−2 and Groups 4−5, simply makes the situation less staggering. That is to say, it is still "staggering".

@Sandbh: It simply isn't. Just consider transition properties, mostly absent in all five groups. Or consider physical properties, where the staggering difference is between alkali+alkaline earth and the rest. Or many chemical properties, in which we have also this difference (wrt dissolving in ammonia and organometallics, the divalent Ln, Sm, Eu, and Yb pattern with the alkaline earths and not their Ln partners). You're being selective with the evidence. (P.S. For me, "alkaline earth" means Ca, Sr, Ba, Ra only.) Double sharp (talk) 09:58, 23 February 2020 (UTC)

@Double sharp:@R8R: I'm comfortable that R8R agrees with me. Transition properties are neither helpful nor useful here, given the TM are already widely regarded as taking up groups 4 to 11, with group 3 being atypical per G&E. Nobody thinks group 4 are other than transition metals. Physical properties are of lower relevance to a chemist. Dissolving in ammonia and OMC, are lower order considerations. Ditto, the divalent Ln, Sm, Eu, and Yb pattern with the alkaline earths and not their Ln partners, when a higher order distinction has already been made in the literature wrt to the similar chemistry of groups 1, 2, Sc, Y and the Ln. The evidence I'm considering is RC and Overton's assertion about what is the most important feature for chemist. Nothing selective here. Sandbh (talk) 12:41, 23 February 2020 (UTC)

I note your practice of drilling down into my generalisations, looking for lower order differences, and then saying that my higher order generalisation must therefore be invalid, which it isn't of course.

@Sandbh: You do realise that R8R literally just agreed with me, yes?

You need to critically analyse what you take from the literature. Sure, some authors (mostly older ones) are uncomfortable about group 3 as transition metals. By what we know now, such criteria are so strong that they exclude most of groups 4 and 5 from the transition metals. (Even though G & E correctly defend Ti as a TM, they don't say anything of the sort in favour of Zr and Hf.) So it's still being selective, because you don't stop and analyse what he literature is saying. Again, by this logic we may go ahead and note that the difference between Be and Mg from the alkaline earths is well-known, that many past luminaries put them above Zn, that chemists today still agree that Be and Mg are quite similar to Zn, that Be and Mg have much more covalent character than the alkaline earths and are thus more similar to the Zn group, and therefore Be-Mg-Zn is greenlighted. My point is that by just picking the right properties you can probably engineer something where the big gap is from any group to the next one. You need to explain why the one you picked is the most important one rather than just keep appealing to authority for one that is not even terribly well-defined. Double sharp (talk) 12:47, 23 February 2020 (UTC)

Even your logic is flawed. I can rephrase the statement as a comparison of the pre-transition metals with the transition metals proper (groups 4-11, excluding group 3 which are atypical per G&E). Yes, I know the TM proper are far more diverse. That is not the issue! The high-level criterion under examination is that their overall general chemistry is more often covalent in nature, than ionic. Again, just on this basis, I can see that the overall chemistry of group 3, as a broad generalisation, at the equivalent of the metals v nonmetals level, is down the ionic end of the continuum, in the proximity of the pre-transition metals. Whereas groups 4-11, at the same overall predominant broad level of generalisation, are in the covalent half of the continuum. Diversity and fairness have nothing to do with it. Sandbh (talk) 03:38, 23 February 2020 (UTC)

@Sandbh: But it's still a continuum. Just consider the oxidation states involved and the counter-anions, you'll see that most of the 3d metals (Cr-Zn) prefer an oxidation state that is so low that they have no problem being ionic in it in the typical salts, and form well-defined aqua cations. As usual Fajans' rules are responsible. Double sharp (talk) 09:58, 23 February 2020 (UTC)

@Double sharp: So? That wasn't the point I was raising, was it? Here it is again:

"I can see that the overall chemistry of group 3, as a broad generalisation, at the equivalent of the metals v nonmetals level, is down the ionic end of the continuum, in the proximity of the pre-transition metals. Whereas groups 4-11, at the same overall predominant broad level of generalisation, are in the covalent half of the continuum."

So, what was your point of relevance again?

Further, we earlier had the following exchange:

@Double sharp: How do we measure or determine such sub-shells? And what is a "significant" component? Sandbh (talk) 12:00, 19 February 2020 (UTC)

@Sandbh: Just look holistically in many different but still chemically normal environments, and analyse the molecular orbitals involved in the bonding, with the caveat I mentioned for deeply buried orbitals like 4f and 5g. You can get this directly or indirectly from interatomic distances (like 3d involvement by Zn-Cl interatomic distances in ZnCl2)…Double sharp (talk) 22:23, 19 February 2020 (UTC)

So, how do we assess whether an element has a chemistry mainly in the ionic half or mainly in the covalent half of the continuum? Why, we just look holistically in many different but still chemically normal environments, and analyse the nature of the charge distribution between the element involved and the element/s it is bonding to. And what do we find? Groups 1-3 have mainly ionic chemistry and groups 4-5 have a mainly covalent chemistry. Sandbh (talk) 11:58, 23 February 2020 (UTC)

@Sandbh: Nope. There's a key difference. Chemically active subshells stay almost completely consistent across chemical environments, and the "averaging" of various configurations makes sense for this reason: the changes in ground-state EC are almost totally chemically irrelevant noise, but this reveals the pattern. Whereas ionicity vs covalency do not stay consistent at all across chemical environments. Instead we see an absolutely clear trend from which you can use the different chemical environment to predict ionicity vs covalency: just use the oxidation state, because elements are more electronegative in higher oxidation states (which, if you think about it, is kind of obvious given what electronegativity means). This is not new, Fajans knew it almost a century ago. Therefore "averaging" out the trend doesn't make any sense. Double sharp (talk) 12:43, 23 February 2020 (UTC)

@Double sharp: I'm not seeing the significance of your key difference. That ionicity v covalency do not stay consistent is not an issue for me. What does interest me is the characteristic behaviour or tendency. That the p-block elements have chemically active sp subshells tells me nothing about their diverse chemical behaviour. OTOH, that "The ionic chemistry of oxygen in the solid state is a vast and important subject" tells me quite a bit about the nature of O. Or that nitrogen is a reluctant anion former, tells me quite a bit more. With your focus on chemically active shells you seem to have thrown the baby out with the bathwater. Sandbh (talk) 02:47, 25 February 2020 (UTC)

@Sandbh: Ionicity and covalency not staying consistent is precisely why characteristic behaviour does not make sense for them. In different oxidation states and with different counter-anions they will be very different and it is not sensible at all to say "this element behaves characteristically in a certain way". Why focus on chlorides to create a gap between Sc and Ti, when carbon pushes it to before Sc and oxygen pushes it to after Ti, purely because of greater electronegativity differences? No, you have to look at how the different environments are controlling the different behaviour, i.e. saying "we can expect behaviour skewing one way under certain conditions", and understanding these conditions implies Fajans' rules. Thus we see that this is not fundamental: we have to go a step deeper.

Nitrogen being a reluctant anion-former is in fact failing to see the forest for the trees. That is just because of its charge: it's the same cardinal mistake you're making when focusing on ionic vs covalent, which is impacted so much by oxidation states. You would do better to note that just like the oxygen and fluorine it has a very high electronegativity and favours forming strong multiple bonds. In fact, its very inertness is a manifestation of this tendency. (Note that oxygen is similarly slower than fluorine as an oxidant!) Of course, this is because of chemically active subshells all over again (primogenic repulsion, small size of 2p). And note that like oxygen and fluorine, nitrogen as a donor is a hard base, just like when they are reduced to anions.

Here is how to use oxidation states well: nitrogen in its group oxidation state is strongly oxidising, same as sulfur and chlorine (look at oxoanions, but also elsewhere), whereas carbon and phosphorus are happy in their states. Meanwhile, oxygen, fluorine, neon, argon, and krypton in their group oxidation states are so strongly oxidising they're not known at all. Here we may legitimately use them because the pattern of oxidation state stability persists even if we change the ligands, and N and S are more or less patterning with the heavier halogens. Moreover, the difference with ligands in hardness is mostly N and O vs P and S (and heavier congeners on that side), and multiple bonding instead of catenation is common for N just like it is for O and F, so even if sulfur is borderline, nitrogen is far more connected with the strong ones than the weak ones. I'm not saying anything revolutionary here, much of this is more or less what Wulfsberg already said. Again, the important thing here is not the oxidation state: we have a trend towards greater EN to the rightward and upward corner of the periodic table. (Not to mention another case for helium in group 2; neon would be like fluorine and oxidise whatever oxo groups you attach to it, but the He–O bond should have partial positive charge on the helium rather than the oxygen.) Double sharp (talk) 22:41, 25 February 2020 (UTC)

E. Group 4 is the first group in which there is a common occurence of the characteristic TM properties of colour, multiple oxidation states, and paramagnetism, courtesy of Ti³⁺.

Unfortunately, most of it doesn't, so group 4 is still predominantly a main-group-like group. Group 5, too. Or is a 90-10 split now somehow a victory for the 10%? (Ti is one out of four elements in each group, and +3 is the minor state.) Double sharp (talk) 14:32, 20 February 2020 (UTC)

Ah, you can't refute what I said so you turn the fog machine on. Sandbh (talk) 00:28, 21 February 2020 (UTC)

@Sandbh: In other words: if predominant behaviour seems to support La, it is a broad strokes understanding, but if it seems to support Lu, then it is fogging. Double standard to port, ahoy! Double sharp (talk) 12:09, 21 February 2020 (UTC)

Argument 3

A. The split d-block seen in the rarely used 32-column form is effectively imperceptible in the 18-column form.

In other words, an anomaly can be corrected just by sweeping it under the rug. This must be new science! Double sharp (talk) 14:31, 20 February 2020 (UTC)

Ah, you can't refute what I said so you turn the fog machine on. What I said has nothing to do with a correction.

@Sandbh: It's still the same point. You have no response to this anomaly, so all you can say is that it's "effectively imperceptible in the 18-column form", i.e. that it's OK if we graphically sweep it under the rug. Double sharp (talk) 12:11, 21 February 2020 (UTC)

B. An La table has one less n+1 violation than an Lu table.

Rubbish, as demonstrated above. It's actually the Lu table that gets rid of the n+l violation a La table gives. Double sharp (talk) 14:38, 20 February 2020 (UTC)

In my draft, see "Table 2: Differentiating electron discrepancies in each periodic table block". Take your trash out after you've read it :) Sandbh (talk) 04:19, 21 February 2020 (UTC)

@Sandbh: I don't care about DE violations, as they're irrelevant locality heaped on locality. Insofar as everyone uses Madelung rule violations rather than DE violations, by that metric it's the Lu table that gets rid of the blatant n+l violation the La one makes when it proclaims La a d-element. Double sharp (talk) 14:21, 21 February 2020 (UTC)

C. An La table has one less d/e violation.

Irrelevant. DE's are locality heaped on locality: they're based on ground-state configurations (which are not the full story), and then go further. Double sharp (talk) 12:23, 21 February 2020 (UTC)

Scerri: "…for the purpose of selecting an optimal periodic table we prefer to consider block membership as a global property in which we focus on the predominant differentiating electron." (Yes, he is wrong, of course.) Sandbh (talk) 01:09, 21 February 2020 (UTC)

@Sandbh: Yes, I would agree that he's wrong here. The DE is purely local as it only compares to the previous element. It gives no sense about whether the "wrong" DE is making the trend away from Madelung worse or actually correcting it; the latter is the case for Mn and Zn, say. Meanwhile, Cr and Cu with the wrong configurations are magically turned by DE's into not being anomalous at all, at variance with the whole chemical community. Double sharp (talk) 12:23, 21 February 2020 (UTC)

D. An La table has one less term symbol anomaly.

Still an irrelevant local argument. Double sharp (talk) 14:38, 20 February 2020 (UTC)

An anomaly nevertheless. And when did term symbols become irrelevant? Sandbh (talk) 00:28, 21 February 2020 (UTC)

@Sandbh: They always were because they only care about the ground state. Double sharp (talk) 12:23, 21 February 2020 (UTC)

E. An La table has one extra isodiagonal relationship.

Not a fundamental criterion as most elements do not show this. Double sharp (talk) 14:38, 20 February 2020 (UTC)

Per Professor Rayner-Canham: "Isodiagonality is, in some ways, a general attribute of the properties of the chemical elements." He is wrong, of course.

@Sandbh: Notice that he says "in some ways". If you want to take a hard line, then yes, he is wrong because it is generally not the important thing ongoing. More pragmatically we can say that there are various relationships of secondary periodicity, some more important than others, and there is no reason to take isodiagonality and lift it up above all the others.

I get the picture: Lu authors are allowed by you to be wrong (e.g. Nelson, Landau and Lifschitz), but La authors are not. So much for critical analysis of the literature. Well, if you're just going to parrot the literature and not critically analyse it, why are you writing an article? Double sharp (talk) 13:00, 21 February 2020 (UTC)

I love the way you strive to use toothpicks in an attempt to leverage your arguments into seeming to be far more noteworthy than they really are, and failing spectacularly.

Rayner-Canham elaborates: "For example, the metal-nonmetal divide forms an "almost diagonal demarkation" (Edwards and Sienko 1983). Similarly, the elements often considered to be semimetals fall on a roughly diagonal border between the metals and nonmetals (Hawkes 2001). A related phenomenon, the change in bonding type across periods, similarly lies upon a diagonal (Mingos 1998)."

Mingos is wrong of course.

@Sandbh: No. As usual, the authors are right, or speaking broadly and you extend their words into something they never said. These diagonals appear where the diagonal relationship is relevant. They do not by any means cover the whole table. For example, Mingos is right as a generalisation, but strictly speaking what he says is not quite right for the d-block. There the diagonal appears going from period 4 to 5, but not from period 5 to 6 because the Ln contraction wipes it out, and turns it into "straight down". (Just analyse any compounds yourself, you'll see it.) As usual what is really going on is that the diagonal comes from two trends (horizontal and vertical) both working at rates that change throughout the periodic table continuously. Double sharp (talk) 23:13, 21 February 2020 (UTC)

Earlier: "Some 77 years later, French felt that the diagonal linkages were so significant that he proposed slanting ("warping") the periodic table (French 1937).

French too is wrong, of course. Sandbh (talk) 22:55, 21 February 2020 (UTC)

@Sandbh: Yes, he's indeed wrong here. Anyone can see that the vertical and horizontal relationships are far more direct periodicity than the diagonal ones. Double sharp (talk) 23:13, 21 February 2020 (UTC)

I'm developing the article to present a perspective on group 3 that has not been previously considered, as well as OR. Thanks to your indefatigable stress testing I've had to fine tune it quite a bit. As far as critical analysis is concerned you seem unable to grasp the logic of Jensen's hierarchy of classification criteria. This says that lower criteria do not have to be applied elsewhere if they did not come into play but for the application of higher criteria. I hope I've explained that OK. Let us not forget that I have to get the article past (1) the editor-in-chief, and (2) the peer reviewers, and that (3) it is the peer reviewers' recommendations to the editor-in-chief that are pivotal.

As you know Double sharp, both of us addressed Nelson, and L&L in our IUPAC submission. Nothing has changed since the time.

@Sandbh: Nothing has changed indeed about Nelson, his argument is still refuted by the s-block. What has changed is that you've decided that the modus tollens argument valid against him as a Lu supporter is invalid against you as a La supporter. That's not logic.

As for Landau and Lifschitz, our argument has been scuppered by you actually giving me the scans of what they wrote. It wasn't a periodic table, so the whole argument was invalid.

I am perfectly able to grasp the logic of a hierarchy of criteria. I've used it myself. The problem is that (1) you have no good justification for why your criteria are important and (2) you are either inconsistent in the ordering of your hierarchy, or you are artificially restricting their domains without any actual discontinuity in order to avoid making them fight each other (case study: thorium, everywhere in this page). Double sharp (talk) 23:13, 21 February 2020 (UTC)

I still owe you on the chemical significance v d/e argument, and I will get to that! Sandbh (talk) 22:55, 21 February 2020 (UTC)

@Sandbh: I am awaiting this one. Because for me this is one of the main killing blows that means I totally don't accept your chain of logic. Double sharp (talk) 23:13, 21 February 2020 (UTC)

F. An La table has one extra maximum oxidation number triad.

The biggest bastions of strong periodicity on the table (alkali metals and halogens) have no such thing, so it must be irrelevant. Double sharp (talk) 14:38, 20 February 2020 (UTC)

Bah! Humbug! You are the kind of person who says, "since it does not hold where I expect it should, it must mean nothing." I'm the kind of person who says, "since it does not hold where I expect it should, I wonder why?".

@Sandbh: You ought to apply that criticism to yourself. The only way you avoid the former problem with your own arguments is simply declaring by fiat that everything outside your scope is irrelevant. The scope is, of course, artificially selected, and there is never any real difference that explains why your argument cannot rather than should not be used outside it. By this logic, the most useful argument of all is the one explicitly declared to be only relevant for one element. Well, suppose I say La must be in the f-block / d-block because of something that only applies to La and doesn't apply to any other element at all, but I declare that the scope is for La only. Something is clearly wrong here regardless of whether it's arguing for the f or the d placement. Double sharp (talk) 12:23, 21 February 2020 (UTC)

Of course, that was why DIM used horizontal triads when he predicted the properties of the then undiscovered elements Al, Ga, and Ge, and to estimate the atomic weight of Se. And why Dias observed that "A periodic table is defined as a partially ordered [italics added] set forming a two-dimensional array which complies with the triad principle where any central element has some metric property that is the arithmetic mean of two flanking [i.e. horizontal] member elements."

@Sandbh: Has some metric property. It will, in general, not be the same one throughout. It's a statement "for any X there exists Y", not "there exists Y such that for any X". You'd better do some homework on logical quantifiers. This is a big difference, in mathematics among other things it is the difference between continuity and uniform continuity. ;) Double sharp (talk) 12:23, 21 February 2020 (UTC)

@Double sharp: Yes, I know the drill: Dias is wrong, of course. Distinguished Professor Emeritus of Chemistry, University of Missouri - Kansas, cited by 4,102. Sandbh (talk) 22:55, 21 February 2020 (UTC)

@Sandbh: I see you don't understand what I'm saying. I'm not saying he's wrong. I'm explaining what he's saying. When you use one criterion only like you do for maximum oxidation states, that extends it to something he did not say. And he did not say it for a good reason: that extension is wrong. Double sharp (talk) 23:32, 21 February 2020 (UTC)

Here's an expanded version of the pattern:

                       +1 +2 +3
                       Li Be B
N  5 O  2  F -1  Ne 0  Na Mg Al
P  5 S  6  Cl 7  Ar 0  K  Ca Sc
As 5 Se 6  Br 7  Kr 2  Rb Sr Y
Sb 5 Te 6  I  7  Xe 8  Cs Ba La
Bi 5 Po 6  At 7  Rn 6  Fr Ra Ac

Wow! Do I see some sort of pattern among the alkali metals? And maybe even among 80% of the chalcogens, and halogens? And what's going on with the noble gases?

@Sandbh: Yes! And amazingly enough, that pattern only exists when we stop looking at horizontal neighbours! Double sharp (talk) 12:23, 21 February 2020 (UTC)

@Double sharp: Yes, nothing to see in the +1 +2 +3 pattern! And check out the addition of the pnictogens. Nothing to see in the +5 +6 +7 pattern. Maximum oxidation state triads? Bah! Humbug! Figment of the imagination! Nothing to see! Move on! 22:55, 21 February 2020 (UTC)

@Sandbh: But there's no 0 +1 +2 or 6 7 8 or -2 -1 0 pattern for everyone's favourite poster children for great periodic trends. Which suggests strongly that the neighbours are the superfluous ballast and the important thing here is the group trend only, since without those neighbours it starts working more or less consistently apart from first-row and relativistic anomalies! Sanity check: if we happened to discover that Hg +4 someday, does it really mean anything for how good Tl is as a congener of In?

Not to mention that in many cases these "maximum oxidation states" that create the patterns DIM was looking at are uncharacteristic for the elements: Cr and Mn would really rather not be in their group oxidation states, although they can get there. But of course, for this argument predominance may be thrown out the window because it happens to support La. Double sharp (talk) 23:19, 21 February 2020 (UTC)

And lookie, a figure showing a similar pattern was used by Irving Langmuir in 1919 in one of the early papers about the octet rule.^[1] The periodicity of the oxidation states was one of the pieces of evidence that led Langmuir to adopt the rule.

Double "sharp: "Nothing to see here folks! Move on!" Sandbh (talk) 00:28, 21 February 2020 (UTC)

G. With La in group 3, the number of f electrons in the trivalent cations of the f-block metals corresponds perfectly with their position in that block.

Purely local argument, as only in 4f is there something like this sort of characteristic oxidation state. Double sharp (talk) 14:38, 20 February 2020 (UTC)

Yes, it therefore cannot possibly have any significance. Never mind that a similar effect is seen in the An. "With the exception of Th and Pa, the common oxidation state, and for the trans-americium elements the dominant oxidation state, is +3, and the behaviour is similar to the +3 lanthanides." Cotton et al. 1999, Advanced inorganic chemistry, 6th ed., p. 1135 (Yes, they are wrong, of course.)

@Sandbh: Since when is +3 all that common for U, Np, and Pu? U³⁺ even reduces water. And for the very late 5f elements the +2 state rises in importance till it becomes the dominant one at No. So already for almost half the series +3 is not dominant.

And somehow, the fact that there isn't such a thing for the s, p, and d block contractions is treated as irrelevant. What is so categorically different about the f block that justifies this? Double sharp (talk) 12:23, 21 February 2020 (UTC)

Time for you to write a letter to Nature Chemistry pointing out that Cotton et al. were wrong. You're going to be writing a lot of letters. Sandbh (talk) 22:04, 21 February 2020 (UTC)

@Sandbh: I don't have to when the specialised sources on actinides get it right, just check out The Chemistry of the Actinide and Transactinide Elements, or Cotton's own Lanthanide and Actinide Chemistry. Realistically speaking, the only actinides a chemist who isn't actually a radiochemist will encounter are thorium and uranium, so as long as those two are taught properly it doesn't really matter if a general text gets the others wrong. What chemist who doesn't work with superheavy elements cares about nobelium? When they are important, we see Cotton gets it right:

“

By the end of this chapter you should be able to ... recognize +4 and +6 as the main oxidation states for uranium, and +4 as the only important state for thorium. ...

”

(Imagine that! Multiple main oxidation states! Oh, that's also exactly what I've been saying, not the single one Sandbh insists on!)

“

Table 9.2 depicts the oxidation states of the actinides. For the early actinides, Ac-Np, the highest (though not necessarily the most stable) oxidation state reflects the total number of electrons (6d and 5f) that can be removed from the outer shell. This resemblance to the transition metals was noted for Ac-U nearly a century ago and initially made people think that the actinides were another block of transition metals. Later, starting round about Bk, most elements tend to exhibit one stable oxidation state, +3 in nearly all cases, thus resembling the lanthanides.

”

And the table only lists +3 as the common state for Ac, Am through Md, and Lr. So it's exactly like what I said: for 40% of the series +3 is not dominant! Double sharp (talk) 22:45, 21 February 2020 (UTC)

@Double sharp:@Droog Andrey: Here some extracts from Cotton’s Lanthanide and actinide chemistry (2006), re 4f participation, and the nature of the Ln contraction.

10-11. How f Orbitals affect Properties of the Lanthanides

"The 4f orbitals penetrate the xenon core appreciably. Because of this, they cannot overlap with ligand orbitals and therefore do not participate significantly in bonding. As a result of their isolation from the influence of the ligands, crystal-ﬁeld effects are very small (and can be regarded as a perturbation on the free-ion states) and thus electronic spectra and magnetic properties are essentially unaffected by environment. The ability to form π bonds is also absent, and thus there are none of the M=O or M≡N bonds found for transition metals (or, indeed, certain early actinides). The organometallic chemistry is appreciably different from that of transition metals, too."

Comment: The observation that the 4f orbitals "do not participate significantly in bonding" calls into question your reliance on the 4f character of La.

@Sandbh: So what alternate explanation is given for cubic complexes? Double sharp (talk) 07:51, 26 February 2020 (UTC)

12. The lanthanide contraction

"The lanthanide contraction is sometimes spoken of as if it were unique. It is not, at least in the way that the term is usually used. Not only does a similar phenomenon take place with the actinides (and here relativistic effects are much more responsible) but contractions are similarly noticed on crossing the ﬁrst and second long periods (Li—Ne; Na—Ar) not to mention the d-block transition series. However, as will be seen, because of a combination of circumstances, the lanthanides adopt primarily the (+3) oxidation state in their compounds, and therefore demonstrate the steady and subtle changes in properties in a way that is not observed in other blocks of elements."

Comment: I feel that Cotton’s observation that the Ln demonstrate steady and subtle changes in properties in a way that "is not observed in other blocks of elements", supports my arguments based on the Ln contraction. Sandbh (talk) 23:34, 25 February 2020 (UTC)

@Sandbh: It's not a block thing, as this is not seen consistently through the 5f row. It's simply one effect of primogenic repulsion as it affects the 4f subshell. The 5g subshell should have the same thing going on too, so it's something totally common in deeply buried subshells. For a block you must look at the whole column to be holistic, not the first row that is always weird. Double sharp (talk) 00:10, 26 February 2020 (UTC)

@Double sharp: On the An, G&E, say, "it is clear an 'actinide contraction' exists, especially for the +3 state, which is closely similar to the lanthanide contraction". (p. 1264) Sandbh (talk) 09:52, 26 February 2020 (UTC)

@Sandbh: They also, as I recall, make Cotton's observation that it is equally clear that other contractions exist everywhere. Note what you don't bold: especially for the +3 state. The actinides have nothing like the unison preference for +3 than the lanthanides do. Indeed the ones that the average chemist can encounter (Th and U) absolutely don't. Double sharp (talk) 19:40, 26 February 2020 (UTC)

@Double sharp: FYI This article lists CN6 ionic radii for the trivalent cations of La to Lu; and Ac to Lr. The Ln show a 17% contraction; the An = 20%. Sandbh (talk) 21:48, 17 March 2020 (UTC)

@Sandbh: I'm sure +2 cations of 3d, 4d, and 5d will show a contraction too per basic high-school chemistry. That will not make the +2 state any more relevant for most of those elements. Double sharp (talk) 16:54, 18 March 2020 (UTC)

H. The Ln contraction is congruent with the start and end of the f-block; the Lu table introduces an irregularity.

Scrooge McDouble sharp: "Ln contraction? Bah! Humbug! Couldn't possibly have any relevance to the rest of the periodic table. Nothing to see here! Move on!"

Purely local argument, as the way in which the Ln contraction is declared to start at Ce and end at Lu is based on a criterion that cannot be applied at all to the rest of the table. Double sharp (talk) 14:38, 20 February 2020 (UTC)

Yes, let's blame Goldschmidt, who discovered the contraction, and whose name is still cited:

"…his work on the relative abundances of the elements, atomic and ionic radii, interionic distances, the effect of radius ratio on coordination number in crystals, replacement of ions in minerals, and the lanthanide contraction is found in almost every textbook of general and inorganic chemistry and has provided the basis for modern crystal chemistry and the use of size relationships for interpreting properties of inorganic substances."

Of course, as this is a purely local arrangement we should not expect such a phenomenon elsewhere in the periodic table. All of those textbooks should be burnt. Sandbh (talk) 03:54, 21 February 2020 (UTC)

@Sandbh: As usual, you don't get it. The Ln contraction is perfectly fine as far as it goes. As Greenwood and Earnshaw noted, such contractions are common throughout the periodic table and the weird thing about the Ln one is that the +3 state is dominant throughout, which makes it obvious. Indeed Seaborg stated himself that it was somewhat accidental:

“

Thus, the characteristic tripositive oxidation state of the lanthanide elements is not related directly to the number of "valence electrons" outside the 4f subshell, but is the somewhat accidental result of a nearly constant small difference between large energy terms (ionization potentials on the one hand, and hydration and crystal energies on the other) which persists over an interval of fourteen atomic numbers.

”

— Glenn T. Seaborg, Origin of the Actinide Concept

It's not a matter of expecting it elsewhere, even. You don't see it anywhere else on the PT, at least till we discover 5g elements. And then we'll see that the whole point is just primogenic repulsion for deeply buried subshells with high l, so chemically active valence subshells win again. Double sharp (talk) 12:23, 21 February 2020 (UTC)

I. Each block starts with the appearance of the relevant electron; the Lu table introduces an irregularity.

No reason is given why this should be taken as the definition of a block in the first place, given its numerous difficulties with periodic trends and with delayed collapses. Double sharp (talk) 14:38, 20 February 2020 (UTC)

The n+l rule serves as the indicator of when a block starts i.e. with the appearance of the relevant electron. Sandbh (talk) 03:54, 21 February 2020 (UTC)

@Sandbh: No reason is given for the dogma that a block must start with the appearance of the relevant electron and that only the first row of the block matters. The chemistry and physics is at variance with this dogma. Double sharp (talk) 12:23, 21 February 2020 (UTC)

@Double sharp: I don't need to summarise the entire history of chemistry before each of my arguments. You know how science works. You start with an observation, and then test it and so how far it gets you. Wow, in an idealised n+l table, the first row of each block starts with the relevant electron. In the real world, despite the 20 variations from the n+l rule, the same thing happens. Hmm. We must be onto to something here. Sandbh (talk) 21:59, 21 February 2020 (UTC)

@Sandbh: The n+l rule as everyone has it leads naturally to a Lu table. In the real world what we see is that the 4f row in a Lu table doesn't start with the relevant electron in the ground state but the element in question (La) shows 4f involvement anyway. That clearly shows that (1) ground-state electron configurations are not the full story for chemistry and we must go further to reflect periodicity, and (2) in the real world, the real n+l pattern following Lu is still seen, even if the ground states show turbulence because of all those configurations so close to each other for d and f elements. Double sharp (talk) 22:47, 21 February 2020 (UTC)

P.S. Where did you get this "idealised n+l table" from, anyway? Why should it be about DEs rather than ground-state configurations like everyone uses it for? (You know, if we randomly had an extra 8s electron stuck in at boron or something, and then everybody else showed the correct DE, it would be one DE anomaly, but the Madelung rule would be obviously wrong for everybody in that scenario and it would urgently need a change to explain that miraculous 8s being held up!) Meanwhile, deriving n+l from scratch like D. Pan Wong's paper I linked for you did shows that it really predicts 3d starting at Z = 21 and 4f at Z = 57. True, at this level of derivation it doesn't quite determine the configuration correctly, but in the real world this can change anyway, and the fact that it identifies chemically active subshells so well is amazing. That's what we should be looking at. Double sharp (talk) 22:51, 21 February 2020 (UTC)

@Double sharp:

The idealisation of n+l started with Janet and his LST. He thought that the anomalous electron configuration must have been wrong so he "fixed" so that his LST matched the n+l rule perfectly. In this case he really was wrong; the anomalous configurations were correct. Philip Stewart, as I recall, covered this in his paper on Janet, as an unrecognised genius. DE's came into play as a result of the Scerri and Parsons 2018 paper. The boron example is too hypothetical to be meaningful for me. Sandbh (talk) 07:07, 22 February 2020 (UTC)

@Sandbh: So DE's are of extremely recent vintage. I wonder how they square with the crushing weight of history which either favours ground-state configurations at a basic level, or chemically active valence subshells when considering this seriously (witness all the quotes I gave about that). And both of those support Lu. Oh, but of course the crushing weight of history is only important when it is supporting La...

Meanwhile, if you consider chemically active valence subshells holistically, and not worry about the noise of which electron configuration happens to luck out and be the ground state among many that are very close to each other in energy, Janet was actually completely right outside the s-block. Double sharp (talk) 11:39, 22 February 2020 (UTC)

@Double sharp: Be careful with your assumptions. The concept of a d/e goes back to at least 1935. I can't remember if Bohr referred to the idea. Sandbh (talk) 12:20, 22 February 2020 (UTC)

@Sandbh: As something cool that appears as a common sideline? Yes, that is old. And that old article recognises that many times the DE is not really well-defined because there is no clear choice of what electron has been added, e.g. going from V d³s² to Cr d⁵s¹, and that's why it says "for most elements one of these valence electrons is the one added to the electronic configuration of the preceding element", since for most anomalous ones you cannot point to any such thing. As something that replaces Madelung anomalies as the foundation? That's certainly of recent vintage, and you admitted it yourself when saying that DE's came into play as the result of a paper from 2018. And they're also quite preposterous given that for most anomalous cases like Cr there is no well-defined DE at all! Double sharp (talk) 12:28, 22 February 2020 (UTC)

Argument 4

A. History ("Standing on the shoulders of giants") is what got us to where we are now.

Wrong. What got us to where we are now is taking what was correct from our predecessors, rejecting what was wrong, and adding things beyond what they did. I claim that the La table is wrong on the grounds of argument 1. Double sharp (talk) 14:31, 20 February 2020 (UTC)

Good example of using a toothpick to leverage the world. Sandbh (talk) 03:57, 21 February 2020 (UTC)

@Sandbh: I must be doing something right if all you can do is come up with the same tired old similes over and over again rather than use logic. Double sharp (talk) 19:53, 21 February 2020 (UTC)

B. Since it was first realised (in 1937!) that the 4f sub-shell was completed at Yb rather than Lu, nothing has changed with regard to the chemistry of Lu to warrant moving it out of its position at the end of the f-block.

Double sharp ignores the atomic weight gap between Ba and Lu, and jams it in under Y. Nothing to see here, folks! Regularity? What regularity? Move on!

Which just proves that Lu should not have been in the f-block in the first place. Double sharp (talk) 14:38, 20 February 2020 (UTC)

How inconvenient then that La was discovered first, and in terms of its properties, such as atomic weight, it fitted nicely after Ba. Of course, if Lu had been discovered earlier it would have been the prototype Ln instead, Lu being the most dense of the Ln, having the highest atomic weight, and being the least basic. Never mind the chasm in atomic weight i.e. Ba 137 and Lu 175. Brilliant! Sandbh (talk) 01:24, 21 February 2020 (UTC)

@Sandbh: Meanwhile, La has the lowest atomic weight and is the most basic, so the same argument applies. The chasm of atomic weight is absolutely no problem either, in your favourite La table there is one between La 139 and Hf 178.5. Since the chasm Ba-Lu fits the absolutely common thing that the chasm appears whenever a new block has been inserted, and that never happens jammed within another block anywhere else in the table, regularity absolutely supports the Lu table, as usual! Which is obvious when you just look at the two tables, but you have a marvellous ability to twist this obviousness round in ever more amazingly contorted ways to save your bad arguments. Double sharp (talk) 19:53, 21 February 2020 (UTC)

@Sandbh: Well, yes, as you know La was placed naturally after Ba given the small difference in AW. For DIM the issue was always the chasm in AW between La and, say whichever 5d metal as known at that time, and how to fit the then known rare earth asteroids, into that chasm. So your assertion that the same argument applies has no basis. There is no chasm between Ba and Lu, as you know, thanks to the footnoted Ln/An. Sandbh (talk) 21:52, 21 February 2020 (UTC)

Mendeleev's 1871 table

@Sandbh: Wrong. Here's a history lesson. For DIM the issue was the chasm in AW between Ce and Ta, because Ce had a maximum oxidation state of +4 and therefore fitted according to his theory into group IV. The main issue with the rare earths for DIM was that his idea of maximum oxidation state periodicity simply does not work in the 4f row. Oh, it works very well for Li through Mn, but then we get into a little problem with his transitional group VIII and the ambiguous status of the group IB elements in it. In much of the rest of the periodic table, he had great success correcting such problems where periodicity didn't seem to work just by correcting valences: Be was corrected to be divalent instead of trivalent (as there wasn't room for it otherwise), U was corrected to be hexavalent instead of trivalent, and so on. And he indeed tried this: he considered that maybe since Di and La both looked like they should go into the group III spot after Ba, perhaps one of them had the wrong oxidation state. And guess what, the one he picked to correct was La, which promptly went into group IV as a predicted tetrxavalent element (the heavier congener of Zr and Ce, so where he initially predicted an element that turned out to be Hf). So no, Mendeleev went in period 6 Cs, Ba, ?Di (= Pr+Nd), ?Ce, a lot of blanks, and then ?Er in group III, ?La in group IV, Ta in group V, W in group VI. Whatever this is, it seems to have as much to do with a Lu table as a La table.

After this we must part from Mendeleev, as he appears to have refused to leave the intraperiodic (though chemically nonsensical) accommodation of the elements that should appear there, even though by the time of his last table of 1906 all the rare earths but Pm were already known (Lu was discovered that year). Although even there his modern period 6 goes Cs, Ba, La, Ce, a lot of blanks, and then Yb in group III (not too far from being right; perhaps the news of the discovery of Lu had not yet reached Mendeleev; if he had known it, given the lower atomic weight gap to Ta he might well have gone for Lu = 175 rather than Yb = 173), a blank in group IV (returning to the old 1869 prediction), Ta in group V, W in group VI. Again, whatever this is, the point where we "go back to normal" is the group III element of the 5d metals, two spaces before Ta!

The source of the mistake is probably the old wrong idea of the asteroidal hypothesis, whence what appeared below Y was all the rare earths, which naturally became "La and succeeding elements" instead. The idea of a Sc-Y-La-Ac table where those are literally the only group 3 elements (without Ce through Lu also as degenerate group 3 elements) came later, no doubt as a result of this "placeholdering" of La just because it is the first of the period 6 rare earths, and because we didn't understand the 5f block had already started and therefore we just kept putting Ac in the wrong place.

Also, thank you for that slip at the end where you say "there is no chasm between Ba and Lu, as you know, thanks to the footnoted Ln/An". Precisely. Just like there isn't a chasm between La and Hf in a La table, there isn't one between Ba and Lu in a Lu table. So your counterargument against me is inconsistent. Double sharp (talk) 22:34, 21 February 2020 (UTC)

C. Regularity has a sound basis in the periodic law. In this context, and that of ceteris paribus, and condensed phase configurations, since La represents the first occurrence of a 5d electron, and Lu effectively the thirteenth, there is no case for skipping La in favour of Lu.

Double sharp: "Aieee! I can't refute Sandbh's arguments! Bring out the fog machine!"

A baseless argument as the first condensed-phase 2p electron appears in Be and the first gas-phase 5f electron appears in Th. Double sharp (talk) 14:38, 20 February 2020 (UTC)

Sigh. Be has an s-electron, it goes in the s-block. Th goes under Ce, in accordance with the periodic law, and aufbau, amongst other things. La and Lu represent the only issue, and require some further consideration. Regularity has a sound basis in the periodic law. In this context, and that of ceteris paribus, and condensed phase configurations [noting the cited presence of f character in Th; and a parallel f orbital collapse, like Ce; and the blue Th³⁺ (aq.) cation], since La represents the first occurrence of a 5d electron, and Lu effectively the thirteenth, there is no case for skipping La in favour of Lu. Sandbh (talk) 04:06, 21 February 2020 (UTC)

@Sandbh: Your caption suggesting that I'm desperately trying to find fog since I supposedly can't refute your argument is completely false. But I like having it here as it speaks volumes for the level of argument you have descended to. ;)

Meanwhile: in the condensed phase, Be has a p-electron. And much Be chemistry involves hybridisation with the p-orbitals. So in order to refute Be as a p-block element you have to explain why condensed phases have somehow become relevant for Th but not for Be. Which you can't do. Your "periodic law" is simply an assumption: no evidence is ever given why your concept of it is the right one. (Indeed, most chemists do not actually care about your concept of it, it is totally foreign to them.) It is hilarious that you can call Th a "parallel f orbital collapse, like Ce" and not realise that it is exactly the same situation in La and Ac. I rest my case: no logic is being applied here, and there so far has been no good argument against the Lu table from you. Double sharp (talk) 19:53, 21 February 2020 (UTC)

D. There is no basis for starting with symmetry; it is a consequence of the structure of the system and cannot at the same time be its cause.

The structure of the system, as evidenced by actual relevancies, produces exactly the symmetric n+l structure for the first 7 periods. There is nothing strong enough to disturb it there. Double sharp (talk) 14:38, 20 February 2020 (UTC)

As Eugen Schwarz (2019, pers. comm., 8 Dec) stated, “The real, rich pattern of elements’ chemistry does not fit into a clear-cut rectangular grid.” He is wrong, of course. Sandbh (talk) 04:11, 21 February 2020 (UTC)

@Sandbh: Of course there is no absolutely perfect fit. In that sense he is right. However there is a clear-cut rectangular grid for the first seven periods that fits extremely well as a first approximation. Not only that, but changing it away to a La table makes it worse as a first approximation. So in the pragmatic sense, what he is saying is true but not the full story. Double sharp (talk) 13:02, 21 February 2020 (UTC)

E. Symmetry breaking just means that if the interaction of the laws of physics governing the structure of the periodic table can be mathematically expressed in a symmetrical form, this nevertheless yields an asymmetrical outcome. Sandbh (talk) 04:54, 20 February 2020 (UTC)

But the outcome is not asymmetrical if you focus on relevancies. Double sharp (talk) 14:38, 20 February 2020 (UTC)

As per my prior response, re Schwarz. 04:11, 21 February 2020 (UTC)

@Sandbh: Focusing on relevancies gives a clear-cut large-scale symmetry fitting into a rectangular grid at the first order of approximation. That's what matters. Double sharp (talk) 13:02, 21 February 2020 (UTC)

@Double sharp: Schwarz must be wrong, of course. Time for another letter to Nature Chemistry. Sandbh (talk) 05:31, 24 February 2020 (UTC)

@Sandbh: Everyone who has ever drawn a periodic table agrees that the power of the rectangular grid far outweighs the exceptions to it. And I don't have to write any letters about this, because you say it's a personal communication, and so it isn't actually published. ;) Double sharp (talk) 11:53, 25 February 2020 (UTC)

Spectroscopy history

@Double sharp:@Droog Andrey:@R8R:

In his White Book (2020), Scerri noted Meggers discovered in 1937 that the 4f sub-shell closed at Yb, rather than Lu. He then said, "This fact renders it more puzzling that the relocation of Lu was not seriously considered in earlier times." (p. 394).

Frye (1949, p. 4) wrote:

"Lanthanum, the first member of the series, has no 4f electrons and is not considered a rare earth by some spectroscopists."

And from Collier's Encyclopedia (1958):

"Lanthanum, 57, is excluded by spectroscopists because it has no electron in the fourth shell and, therefore, has a markedly different spectrum from that shown by the other members of the group. Lutetium, 71, is sometimes excluded from the rare earth group because its fourth shell is filled completely. Elements 57 and 71 are, however, usually included by chemists because the chemical behavior of these elements makes them typical rare earths."

Earlier, I said:

"The interesting thing about the new configurations is that nothing changed for La and Lu in terms of their chemistry."

So there it is, there was no unanimity among the spectroscopists, and there was nothing new for the chemists.

In this context, given the physicists were content to leave the periodic table to the chemists, La and Lu stayed where they were, La under Y, and Lu at the end of the Ln. Sandbh (talk) 06:40, 20 February 2020 (UTC)

Integrity of the f-block

@Double sharp:@R8R:@Droog Andrey:

In our IUPAC submission, we wrote:

Shchukarev (1974, p. 118) [a well regarded Russian chemist, as I understand it] appears to support La-Ac on the grounds that the 4f shell does not start filling until Ce and that (effectively) the filling sequence—which runs from Ce to Lu—is periodic, with two periods. Thus, after the occurrence of a half-full 4f shell at Eu and Gd, the filling sequence repeats with the occurrence of a full shell at Yb and Lu (Rokhlin 2003, pp. 4–5). A similar, but weaker, periodicity (Wiberg 2001, p. 1643–1645) is seen in the actinides, with a half full 5f shell at Am and Cm, and a full shell at No and Lr. Placing Lu and Lr under Y obscures the start of the filling of the f block (it would appear to start at La) and visually truncates its double periodicity (it would be cut off at Yb whereas it would actually end in the d block). The reference is in Russian and is written in the style of Soviet scientific literature of the time, which makes it a little hard to follow. What we have written above is therefore our interpretation of what we understand the author appears to be saying. A translation of what Shchukarev wrote reads as follows:

"If we […] considered the latter [Lu and 103] not as 4f and 5f elements but rather as members of 5d and 6d series, the d-electron prevention† determining filling f vacancies as stable would be lost as well as the correctness of placing of imitators before Gd and Cm as well as Lu and 103. The exceptional uniqueness of Gd and Cm, akin to that of Mg and Ca, would also be unclear."

We do not understand the reference to Mg and Ca having a uniqueness akin to Gd and Cm.

†@R8R: translator's note: Probably you find that this word doesn't really fit in the context of English. It doesn't look any better in Russian.

References

Rokhlin LL 2003, Magnesium alloys containing rare earth metals: Structure and properties, Taylor & Francis, London

Shchukarev SA 1974, Neorganicheskaya khimiya, vol. 2 Vysshaya Shkola, Moscow (in *Russian)

Wiberg N 2001, Inorganic chemistry, Academic Press, San Diego

I see better now what Shchukarev was getting at. Shchukarev:

recognises the delayed start of filling of the f-block;
recognises the better regularity of the La option; and
sheds no tears over Th.

Here's what it looks like:

+4             +2    | +4             +2
Ce Pr Nd Pm Sm Eu Gd | Tb Dy Ho Er Tm Yb Lu
               ½f ½f |                f  f
                     |
+4             +2    | +4             +2      
Th Pa U  Np Pu Am Cm | Bk Cf Es Fm Md No Lr     
               ½f ½f                  f  f

The imitators are Eu²⁺ and Yb²⁺ which like to attain the Gd³⁺ and Lu³⁺ cores.
Then there is Ce⁴⁺, which likes to attain the core of its Ln prototype namely La³⁺; and Tb⁴⁺ attaining the same configuration as Gd³⁺.
Psycho-metal Eu is associated with the place of a halogen, and Gd is associated with place of a noble gas, although to a much lesser degree. See the Rare-earth metal long term air exposure test, here. Tb to Lu are much less reactive, so the group 17/18 analogy is not seen here.
The f-block contraction starts with Ce³⁺ and culminates in Lu³⁺

The Lu option is less regular:

   +4             +2 |    +4             +2
La Ce Pr Nd Pm Sm Eu | Gd Tb Dy Ho Er Tm Yb
                  ½f | ½f                 f
                     |
   +4             +2 |    +4             +2      
Ac Th Pa U  Np Pu Am | Cm Bk Cf Es Fm Md No     
                  ½f   ½f                 f

The ½-filled and filled f sub-shell regularity is lost.
The correspondence of Eu and Gd to group 17 and 18 metals is lost.
The f-block contraction starts with Ce³⁺ and finishes in the d-block.

Our analysis at the time was:

We agree with the basis of Shchukarev's support for -La-Ac, noting the most important periodic property of the Ln and An is their valency. Thus, in the Ln, we see the analogous +2 ions of Eu and Yb, and the +4 ions of Ce and Tb (Wiberg 2001, p. 1644–1645). The double periodicity of the Ln and An is further explored by Ternstrom (1976) and (for the Ln only) by Horovitz and Sârbu (2005, pp. 473, 483). The former treats the Ln as running from Ce–Lu; the latter refers to 15 Ln from La to Lu. For reasons previously explained we think the approach of Horovitz and Sârbu lacks rigour.

New references

Horovitz O & Sârbu C 2005, "Characterisation and classification of lanthanides by multivariate-analysis methods", Journal of Chemical Education, vol. 82 no. 3, pp. 473–483

Ternström T 1976, "Subclassification of lanthanides and actinides", Journal of Chemical Education, vol. 53, no. 10, pp. 629–631

Sandbh (talk) 10:45, 20 February 2020 (UTC)

@Sandbh: You draw an obviously more regular option and call it less regular. That's at least strange. Droog Andrey (talk)

@Droog Andrey: Could you please explain? I've listed 4 regularities observed in the La form. I've listed the 3 irregularities introduced in the Lu form. Shchukarev must have been wrong, of course. Sandbh (talk) 21:44, 21 February 2020 (UTC)

@Sandbh: The drop to +2 at the end of each half-block is more regular than +2 at the second last element and then again +3 at the last one. Droog Andrey (talk) 09:22, 24 February 2020 (UTC)

@Droog Andrey: Thanks for the focused response to my question. I don't understand your point. The start of each block with +4 is more regular than +4 at the second last element. When you say "again +3 at the last one" what are you referring to? This is not evident in the Lu form. Sandbh (talk) 00:09, 25 February 2020 (UTC)

@Sandbh: The stability of +2 gradually reaches maximum at Eu and then suddenly disappears for Gd. Then it gradually reaches maximim at Yb and suddenly disappears for Lu. The same situation between Am and Cm; between No and Lr. These are four places where the sharp boundaries should be lined. Droog Andrey (talk) 07:22, 25 February 2020 (UTC)

@Droog Andrey:@Double sharp: Well, yes, all 4 transitions fall within the f-block in the La table. In the Lu table the transition has to carry over into the d-block. As well, per Shchukarev, the pattern of Eu2+ and Yb2+ liking to attain the Gd3+ and Lu3+ cores is contained within the f-block in the La form, but spills over into the d-block in the Lu form. And so on. Sandbh (talk) 09:26, 26 February 2020 (UTC)

@Sandbh: With that logic, we should include Ga in d-block since Mn²⁺ and Zn²⁺ like to attain the Fe³⁺ and Ga³⁺ configurations, right? :) Droog Andrey (talk) 10:35, 26 February 2020 (UTC)

@Sandbh: Exactly this, look at the 3d row (drops to +2 at Mn and Zn). Or look at the 5f row, where the trend at the end is for 5f to fall into the core, and it's clear that the predominant +3 state of Lr is coming from a very different reason. Double sharp (talk) 19:21, 24 February 2020 (UTC)

@Droog Andrey:@Double sharp: In response to Droog Andrey's comments about Mn and Zn. No, since there is no delayed start to the 3d row. In response to Double sharp's comment, and pick me up here if I'm being inconsistent: No, there is no need for drilling down; I'm staying at the higher level of the pattern. Sandbh (talk) 04:47, 4 March 2020 (UTC)

@Sandbh: This is more or less exactly why this thread keeps running in circles. For you the delayed start of 4f is an absolute axiom. No matter how many times we refute its relevance, by pointing to 4f involvement in chemically relevant excited states of La (which is hilariously, given that 4f hasn't drowned fully yet, more direct than in, say, Gd), or pointing to how delayed collapses are totally normal for all heavy elements, your case for La always goes back to this falsehood. Either that or some false dichotomy or false composite trend or self-contradiction that gets adhered to despite careful correction. So I think this discussion has outstayed the point where it could be of any use, since for you no evidence seems to be able to overthrow the La form. Everything is either thrown away by either declaring it irrelevant or chucking out-of-context and sometimes mistaken statements from the literature at it. And masterful rationalisations of the self-contradictions involved in you collecting facts out of context as isolated baubles.

Meanwhile, the newcomer to this debate Dreigorich seems to have been convinced by some of it straight to the Lu side. And I bet the same will happen for everyone who reads all of it without having a preconceived opinion beforehand. ;) Double sharp (talk) 07:56, 4 March 2020 (UTC)

Just look at the actinides. In my preferred 5f row (Ac-No), the first few 5f elements start using more and more valence electrons like the start of a d-series (Ac +3, Th +4, Pa +5, U +6 as most common oxidation states), before doubling back (Np and Pu are OK in +6 but increasingly prefer +5 and +4 respectively), and then going for a more constant +3 state like the Ln for a while (Am +3, and then a firm return to Cm +3). Except that now +2 starts gaining dominance slowly until by Fm and Md it becomes stable in water, and at No +2 becomes the dominant state. This can all completely be explained by the increased valence-like character of 5f (radial node + relativistic destabilisation) in the first half of the series which gets drowned into the core later, so soon direct 5f involvement dwindles, and then so does promotion energy into 6d. And then Lr goes back to +3 right out of nowhere, which is a good sign that this is not 5f involvement at all but something else completely. And indeed this starts becoming like the totally normal start-of-block trend of adding more electrons and raising oxidation state past the +2 that the s-electrons give (Lr +3, Rf +4, Db +5, Sg +6, even Bh +7 before Hs decides it prefers lower oxidation states after all).

In your preferred 5f row (Th-Lr), not only does the end not make any sense (how does Lr fit into the late actinide trend at all?), but neither does the beginning (Ac is cut off despite continuing the trend perfectly backwards from Th, and at the expense of destroying the normal trends in the 6d row; Lr-Rf-Db-Sg is smooth and continuous, Ac-Rf-Db-Sg absolutely isn't). For the lanthanides it is the same problem, only a bit less obvious: the stability of the +2 state increases as we approach the end of each half (Sm, Eu; Tm, Yb), and it is in fact the +3 state of Gd and Lu that represent new beginnings over a stable 4f⁷ or 4f¹⁴ configuration. You need to look at where you get the really stable half-filled configuration by itself: Gd 4f⁷5d¹6s² is not exactly stable by itself before it gets rid of those outer subshells! The whole point is that the element doesn't have to work so hard: its inner orbitals should already be half- or fully-filled and it should just need to get rid of the outer s-orbitals. Just like Mn and Zn in the d-block. Asking for one 5d electron to "hang up" as the La table does destroys the meaning of the half- and fully-filled subshells.

@Double sharp: There is no need to drill down. Ac does not cut off the start since it is the prototype actinide, not an actinide in itself. Gd is quite stable by itself as you would've seen in the Ln exposure test. Sandbh (talk) 04:47, 4 March 2020 (UTC)

@Sandbh: Nope, Gd metal has delocalised three electrons. Appealing to Ac as not an actinide is so far from real chemistry rather than semantics that there is nothing to say about this argument anymore. Double sharp (talk) 07:56, 4 March 2020 (UTC)

Remember, it's only the s-orbitals that "hang up" and fill early, so the only reasonable baseline is +2 and every other block should start with +3 (boron and its group, scandium and its group, lanthanum and its group, certainly not cerium and its group) until the inert pair effect for the outer s-shells starts ruining it for the heavy 6p and 7p elements. Just compare with the d-block trends (data from Droog Andrey's table and any source you may care to check, only most common states included):

Sc Ti V  Cr Mn | Fe Co Ni Cu Zn    3d   [+2 starts gaining dominance near the end of the series, so clearly Ga +3 is something else]
            2    2  2  2  2  2
3        3       3
   4  4     4
      5

@Droog Andrey:@Double sharp: Unlike Droog Andrey, I agree with Double sharp that Ga⁺³ is something else. Sandbh (talk) 04:47, 4 March 2020 (UTC)

@Sandbh: Consistency would then demand that you recognise Lr³⁺ as something different, too. Double sharp (talk) 07:56, 4 March 2020 (UTC)

Y  Zr Nb Mo Tc | Ru Rh Pd Ag Cd    4d   [first we climb more with disappearing double periodicity, then fall more]
                          1
                       2     2
3                3  3
   4     4  4    4
      5
         6  6
            7

Lu Hf Ta W Re | Os Ir Pt Au Hg     5d   [6d looks exactly the same]
                      2     2
3                  3     3
   4            4  4  4
      5
         6      6
            7

Once again we see that the Lu table is much better at anchoring regularities from reality. The pattern is always "start going up from 3 and then start falling down slowly with much hovering, and lastly start favouring 2 at the end as your characteristic shell starts going quiet". ^_^ Double sharp (talk) 20:09, 26 February 2020 (UTC)

@Double sharp: Your explanation doesn't pass the principle of "the best education is found in gaining the utmost information from the simplest apparatus." The downwards drill of complexity is not required. Sandbh (talk) 04:47, 4 March 2020 (UTC)

@Sandbh: Everything should be made as simple as possible, but not simpler. The La table squeaks along only because you artificially limit all arguments to make it verboten to criticise its inherent double standard of picking only one effect of secondary periodicity and putting it on a pedestal. If you don't drill down, you're doomed to coming up with irrelevant arguments that are unrelated to and even contradict each other once you take off the artificial boundaries. This drilling down is the only way to get at the deeper truth. Double sharp (talk) 07:58, 4 March 2020 (UTC)

Schukarev, SA

Here.

Russian, Soviet chemist, hydrologist, teacher, historian of the methodology of science.

Check out that bibliography. Sandbh (talk) 04:37, 21 February 2020 (UTC)

@Sandbh: And would you like to know the credentials of Landau and Lifschitz with their Lu argument? Not to mention that argument from authority proves nothing? Double sharp (talk) 07:57, 21 February 2020 (UTC)

@Double sharp: You know from our IUPAC submission how we assessed them. If you have a look at what L&L wrote they are all over the place. Please check your e-mail re this.

Oh, I have no authority of my own so I have to rely on citations, the more so for the peer reviewers. Sandbh (talk) 11:35, 21 February 2020 (UTC)

@Sandbh: Landau and Lifschitz were not drawing a periodic table, as evidenced by how the electron configurations are scattered across lots of different tables. I have no problems with treating La as an "honorary group 3 element" for the purposes of comparative chemistry, just like is commonly done when considering the trends as we split into A and B subgroups, which is similar to what L & L do in their tables (La + Lu-Pt in a "platinum group"). I do have a problem with putting it in the d-block under Y in a PT, but L & L haven't drawn a PT in your screenshots.

Authority in science is not determined by credentials but by actually applying logic and the scientific method and having insights conforming to that. The credentials are usually a sufficient guarantee that the author with them can do this, but they are in principle not necessary. Double sharp (talk) 11:49, 21 February 2020 (UTC)

Cause and effect sequence: Element properties

@Double sharp:@Droog Andrey:

Starting with the nucleons and going upwards, I’ve tried to map the cause and effect sequence up to the assignment of a chemical element to a periodic table position:

1. Inter-nucleon interactions (protons and neutrons etc)

2. The nuclear charge increases as we move through the atoms and there is a complicated set of interactions between the electrons and the nucleus as well as between the electrons themselves. This is what ultimately produces an electron configuration.

3. With each increase in Z an electron is added (so to speak).

4. At this time DE, EN, IE, EA, CAS, and ECG and ECC, among other properties, are locked in.

DE = differentiating electron

EN = electronegativity

IE = ionisation energy

EA = electron affinity

CAS = chemically active subshell/s

ECG = electron configuration (gas phase)

ECC = electron configuration (condensed phase)

5. The chemical behaviour of the element, as mediated by one or more of these properties, can be observed.

6. The CAS, which refers to being able to participate in chemistry as a valence subshell, can then be gauged by looking holistically in many different but still chemically normal environments, and analysing the molecular orbitals involved in the bonding, with the caveat that:

(a) such involvement must be a significant; and

(b) in deeply buried cases like 4f and 5g, the subshell must at least act as a reserve area where electrons can easily go in and out of from bonding MO's.

How does this look?

One observation by me, at this stage, is that I think when there is a transition in DE from s to p (B, Al, Ga, In, Tl); s to d (Sc, Y, La, Ac); and p to s (Li, Na, K, Rb, Cs, Fr); there is an impact on physical properties, including IE—which implies an impact on EN. Sandbh (talk) 06:43, 22 February 2020 (UTC)

@Sandbh: Well, there's a concrete, testable statement. Let's see, Re isn't a DE anomaly, Tc is. Now, do Tc and Re look any different in their physical-property-trend positions in 4d and 5d respectively? Clearly not, so your statement is false. As we could have expected since DE anomalies are about the gas-phase and physical properties imply condensed-phase. Which are just single possibilities among the many chemically relevant configurations.

Whenever the DE change really correlates to those property changes, like your examples, there is also a CAS change (for Sc-Y-La-Ac, the first two are s-d and the last two are s-f, with the understanding that I mean the labels from my table above); and when the DE change means nothing like this example, there's no CAS change. Suggests that CAS is more correct for properties, doesn't it? Double sharp (talk) 10:11, 22 February 2020 (UTC)

@Double sharp: Good. Please note that #5 referred to "at least one or more of these properties", rather than all of them, so your example of Re and Tc is a non-example, in this case. More to follow. Sandbh (talk) 12:11, 22 February 2020 (UTC)

@Sandbh: It's still valid. Can you find any example at all in which Tc and Re look different in their trends passing to them from Mo and W (the preceding element, as DE's exhort us to look at)? Double sharp (talk) 12:15, 22 February 2020 (UTC)

@Double sharp: Yes, in passing from Mo-Tc there is an increase in IE of +0.188 eV. In passing from W-Re there is a marginal decrease in eV of 0.03 V. At face value, the 1st increase is caused by the closure of the 5s² sub-shell. In the second case of 5d⁴6s² to 5d⁵6s² the 5d sub-shell becomes half-full, but apart from that there must be something else going on. Sandbh (talk) 06:47, 24 February 2020 (UTC)

@Sandbh: Okay, this is a minor difference, I'll admit it. (Albeit this is again the same issue of making a big deal out of a change in sign when really both are close to zero in the first place, so the change of sign is not terribly significant when it comes to the trend.) A more plausible explanation would be that spin-orbit effects are getting mildly important, so we're really removing one electron above a stable 5d_3/2 configuration, and double periodicity therefore shifts from 5+5 to 4+6 this far down the d-block. Your first explanation for the first increase is clearly at least insignificant, since we have that increase anyway going from Y-Zr, Zr-Nb, Nb-Mo as well. The high-school explanation of increasing Z_eff on electrons in the same subshell is clearly more correct, and DE's are not involved there.

Now, can you find some way in which this causes any difference at all in their chemistries? Double sharp (talk) 11:51, 24 February 2020 (UTC)

@Double sharp: To my first list of examples can be added sub-shell closure DE's. For example, when the p sub-shells close at group 18. I'd also add sub-shell closure caused by a d DE at Cu, and Au; sub-shell opening due to an s DE at Ag; and sub-shell closure due to an s DE at group 12.

Here's a quote for the coinage metals:

"The outer electron conﬁguration of Cu, Ag, and Au is d¹⁰s¹. Following Hund's rule, one of the two s electrons has moved to the d sub-shell to achieve the lower energy of a completed d sub-shell. This electron structure suggests that Cu, Ag, and Au might have properties similar to the heavy alkali metals (K, Rb, and Cs), because they also have a single s electron in their p⁶s¹ outer electron conﬁguration. However, their physical properties and chemical compounds are drastically different. The filled p shell of an alkali metal shields the nucleus from the outer s electron much more effectively than do the filled d shells of Cu, Ag, and Au; this makes the alkali atom larger, more easily ionized, and more weakly bonded to neighboring atoms. Consequently, the alkali metals are less dense, much more reactive, and have lower melting and boiling temperatures than those of the group 11 metals. The high electronegativities of the group 11 metals (Sec. 1.6) give them inherently good corrosion resistance. The filled d sub-shell and free s electron of Cu, Ag, and Au contribute to their high electrical and thermal conductivity. Transition metals to the left of group 11 experience complex interactions between s electrons and the partially filled d sub-shell that lower electron mobility. In group 11 metals, the d sub-shell is filled, thereby improving the mobility of the s electrons and making the group 11 metals excellent electrical and thermal conductors. The conductivity, oxidation resistance, ductility, and color of these metals make them useful for a wide range of applications, including wire, plumbing pipe, jewelry, photographic ﬁlm, and batteries." -- Russell AM & Lee KL 2005, Structure-property relations in nonferrous metals, Wiley-Interscience, New York, p. 302

For group 12, each with an s sub-shell closure DE, we can observe an abrupt and significant reduction in physical metallic character from group 11 to group 12. Sandbh (talk) 22:26, 22 February 2020 (UTC)

@Sandbh: You're saying that Cu, Ag, Au have a completed d-subshell, which is true. I suppose you are claiming that this has an effect on their properties. But your quote says that the electron configuration suggests that Cu, Ag, and Au would behave like the alkali metals. And then it goes on to say that this is not so. In fairness, it also attributes the physical properties to the d¹⁰s¹ configuration. But at this stage you see already that there isn't a simple relationship between the ground-state electron configuration and the actual behaviour. In fact, sometimes it's correct (when the ground state happens to actually be the arrangement in that context), and sometimes it's wrong (when the arrangement is something else). Meanwhile, taking a step back to chemically active subshells, we resolve the contradiction just by noting that the important thing is just (dsp)¹¹ (i.e. dsp are all active and have a total of eleven valence electrons), and that the interplay between d⁹s² and d¹⁰s¹ is clearly somehow important and we shouldn't insist on all or nothing in favour of one. BTW, in terms of physical properties, you already see a significant drop in metallic character at group 11: just look at their low melting points.

Also: I was talking about Tc and Re in particular, and even mentioned them explicitly. By the standards you have been using, it seems to me that your statements that are totally not about those two elements are fogging because I have limited a scope for my rebuttal. While I don't agree with those standards in the first place, I think this illustrates the issue I have with your entire argumentation: simply put, it reeks to me of double standards everywhere to support La, and does not feel balanced. Double sharp (talk) 22:34, 22 February 2020 (UTC)

@Double sharp: Well, the situation is analogous to the n+1 rule. Sure, it has 20 exceptions but it still does quite well.

If I were to present the n+l rule as an argument you would focus on the 20 exceptions and say that my focus on n+1 represents fogging. Never mind your own reference to an Lu table as an n+l table.
Or you drill down to the "divalent Ln, Sm, Eu, and Yb pattern with the alkaline earths and not their Ln partners" and ignore the more general, higher level pattern that "Ln chemistry is predominately the chemistry of highly electropositive metals in the +3 oxidation state, just as the chemistry of the alkali metals and alkaline earth metals is the chemistry of the highly electropositive metals in the +1 and +2 states, respectively" (King 1995, p. 289). And that the divalent Ln, Sm, Eu, and Yb pattern with the alkaline earths therefore means my more general, higher level argument is invalid.

These two are simple examples of your attempted use of toothpicks to leverage the world. At which point I beat my head on my study desk… Sandbh (talk) 03:24, 24 February 2020 (UTC)

@Sandbh: Well, here's the little thing: you like to boast about how few exceptions you have, but chemically active subshells don't have any outside the s-block at all. Outside that they follow the n+l rule perfectly to period 7, and if you apply a little tweaking to common sense the pattern is still more or less right in period 8. And that little exception because a very important thing (subshell energy levels) differs from the s-block to the rest of the table, so the exception actually has chemical relevance. There's absolutely zero chemical relevance coming from weird exceptional DE's, ill-defined as they usually are for the exceptions.

My point is simply: if you change the conditions, keeping within chemically relevant bounds, chemically active subshells don't change. But ionicity changes, and ground-state configurations change. That says just about everything. Double sharp (talk) 19:25, 24 February 2020 (UTC)

Silberberg 2009

@Double sharp:@Droog Andrey:

Writing in Chemistry: The molecular nature of matter and change, 5th ed, Silberberg sheds some light on few things:

308: The section heading here is, The quantum-mechanical model and the periodic table

308: "QM provides the theoretical foundation for the experimentally based periodic table…Note especially the recurring pattern in electron configurations, which is the basis for the recurring pattern in chemical behaviour."

310: "Even at this early stage of filling the table, we can make an important correlation between chemical behaviour and electron configuration: elements in the same group have similar outer electron configurations."

312: "To summarise the major connection between QM and chemical periodicity: orbitals are filled in order of increasing energy, which leads to outer electron configurations that recur periodically, which leads to chemical properties that recur periodically."

315. The aufbau sub-level filling order picture appears on this page.

315-316: "In Period 6, the 6s sub level is filled in Cs and Ba, and than La , the first member of the 5d transition series, occurs. At this point, the first series of inner transition elements, those in which f orbitals are being filled, intervenes."

316: "Several irregularities in filling pattern occur in both the d and f blocks…Whenever our observations differ from our expectations, remember that the fact always takes precedence over the model."

317: "All physical and chemical behaviour of the elements is based ultimately on the electron configurations of their atoms. In this section, we focus on three properties of atoms that are directly influenced by electron configuration and, thus, effective nuclear charge: atomic size, IE, and EA."

This appears to be consistent with my article and the first row of each block starting with the first appearance of the relevant electron. Not to mention the link to QM and the connection between ECG, IE, EA, and, "ultimately" physical and chemical behaviour.

How does it look from your end of the paddock? Sandbh (talk) 11:47, 22 February 2020 (UTC)

@Sandbh: Making the usual mistakes. If it is really the aufbau sub-level filling pictured, then there is an inconsistency between it (which supports Lu) and the bald statement that La is the first 5d metal. Meanwhile, there is no analysis on why the ground-state configuration is the basis of physical and chemical behaviour. Since he doesn't use your artificial boundary not to be crossed, we even know it is false due to thorium, and the same argument works for La and Ac. Similarly, the numerous "wrong" configurations in the d- and f-blocks don't seem to correspond to any kinks in the atomic size and IE trends. Chemically active valence subshells get it right instead, as usual.

@Double sharp:. Yes, it's the usual vanilla aufbau wriggly snake graphic; what good do you think the 170 professors were? There is no inconsistency between it and La as the first actual 5d metal, as S explained at pp. 315-316, above. No it is not false due to Th, for the same reason. On GSC he says in part, "QM provides the theoretical foundation for the experimentally based PT…we will fill the table with elements and determine their EC—the distribution of electrons within their atoms's orbitals. Note especially, the recurring pattern in EC, which is the basis for the recurring pattern in chemical behaviour…we can make an important correlation between chemical behavior and EC: elements in the same group have similar EC." Of course correlation does not imply causation but we do know that there is indeed a cause and effect linkage here, as mediated by one or more of the 7 properties I listed earlier. Re the numerous "wrong" configurations in the d- and f-blocks, which I haven't looked closely at, yes, as noted in my hypothesized CAE sequence, "The chemical behaviour of the element, as mediated by one or more of these properties, can be observed." Sandbh (talk) 01:41, 23 February 2020 (UTC)

@Sandbh: So name me a single chemical property in which Nb differs from Ta that may be attributed to the difference in ground-state electron configurations. Double sharp (talk) 23:24, 23 February 2020 (UTC)

@Double sharp: Tricky, as there is a dearth of literature on Nb-Ta compared to V. I see there is a 2% increase in IE for the sequence Zr to Nb, compared to an 11% increase going from Hf to Ta. Nb is 4d⁴6s¹ and 6.75 V; Ta is 4f¹⁴5d³6s² and 7.55 V. I'd expect the single s electron in Nb would be relatively easy to ping. Ta is complicated by the presumably poor shielding from the 14 f electrons. Pinging one its 5d electrons is in fact 11% harder.

@Sandbh: Two things:

How then do you explain that this difference also appears going Y-Zr (6.7% increase) vs. Lu-Hf (25.8% increase), and is even more extreme there? There is absolutely no change in configuration now: Zr and Hf are both d²s², they both add a d-electron from their predecessor. In Hf we are pinging a 5d electron whereas in Zr we're pinging a 5s one, that's true. Is it not then possible that this is the major effect instead, rather than what DE we happen to have?
And what difference does this make for the chemistry of Nb vs Ta? Double sharp (talk) 11:49, 25 February 2020 (UTC)

It's one thing to say that the fact always takes precedence over the model. The little problem with saying it, of course, is that the facts that are at variance with the model have absolutely zero effect on the chemistry and physics involved, which mostly behaves as if the model was completely right. Double sharp (talk) 11:53, 22 February 2020 (UTC)

Placeholder. Sandbh (talk) 02:14, 23 February 2020 (UTC)

"All physical and chemical behaviour of the elements is based ultimately on the electron configurations of their atoms"

That's wrong. The behaviour is based on atomic number (and slightly on atomic mass) through the complex structure of electron cloud. Ground-state configuration, just a tiny reflex of that structure, is used for educational purposes focusing on main groups. Nowhere in real chemistry GSC are of big relevance. Droog Andrey (talk) 18:47, 22 February 2020 (UTC)

@Double sharp:@Droog Andrey: Yes, the complex structure of the electron cloud is modelled using orbitals, and their order of filling GSC energy sublevels with electrons, which are represented as electron configurations. Bohr used quantum theory to write GSC electron configurations for atoms and related these to the structure of the periodic table. Nothing to see here! As noted above, per S: "QM provides the theoretical foundation for the experimentally based PT…we will fill the table with elements and determine their EC—the distribution of electrons within their atoms's orbitals. Note especially, the recurring pattern in EC, which is the basis for the recurring pattern in chemical behaviour…we can make an important correlation between chemical behavior and EC: elements in the same group have similar EC." Sandbh (talk) 02:14, 23 February 2020 (UTC)

@Double sharp:@Droog Andrey: Droog Andrey, on your bold assertion, "Nowhere in real chemistry GSC are of big relevance":

"A rigorous description of the ground-state electron configuration is of crucial importance to treat the physical and chemical properties of actinide metals."

--- Here. Sandbh (talk) 02:36, 23 February 2020 (UTC)

@Sandbh: And it will get you nowhere for thorium, as you admit that 5f involvement is visible there despite not appearing in the ground state configuration. This statement is really clearly false due to all the hybridisation going on in these f-metals. Double sharp (talk) 09:48, 23 February 2020 (UTC)

@Double sharp:@Droog Andrey: Earlier, we had the following Q&A:

"Do gas phase electron configurations still have any relevance to the chemistry of the elements? Sandbh (talk) 10:24, 15 February 2020 (UTC)"
"No direct relevance. They have been simplified too much to be really useful. Double sharp (talk) 10:38, 15 February 2020 (UTC)"

I provided the above quote and citation: "A rigorous description of the ground-state electron configuration is of crucial importance to treat the physical and chemical properties of actinide metals."

Setting aside Th, how does this now sit with your assertion re gas phase electron configurations, namely, "No direct relevance. They have been simplified too much to be really useful."? Sandbh (talk) 11:40, 23 February 2020 (UTC)

@Sandbh: We already explained it. Your quote and citation is mistaken, as has been demonstrated over and over. Double sharp (talk) 11:42, 23 February 2020 (UTC)

@Double sharp:@Droog Andrey: I laughed when I read this. If all else fails, and you cannot come up with a reasoned rebuttal, then Sandbh's citation must be wrong. Ahh, how often have I heard that? Fortunately, this kind of thing speaks for itself. I'll have to make a list of all the citations that must, of course, be wrong, and post it here. Not forgetting the PT of predominately ionic or covalent chemistry, with citations. 05:27, 24 February 2020 (UTC)

@Sandbh: We've already come up with many reasoned rebuttals referring to chemical behaviour and other sources who are drilling deeper down into something than your elementary-level treatments. But you seem to be choosing not to hear them. Double sharp (talk) 11:54, 24 February 2020 (UTC)

@Double sharp:@Droog Andrey: Getting back to Droog Andrey's statement that "Ground-state configuration, just a tiny reflex of that structure, is used for educational purposes focusing on main groups. Nowhere in real chemistry GSC are of big relevance". And Double sharp, your follow-on comment that gas phase electron configurations have "No direct relevance."

Why then does Schwarz, here, say: "There are only a few special topics in chemistry that require the correct understanding of free atoms in vacuum (e.g., atom molecular gas-phase reactions) or of orbit-orbit and spin-orbit couplings of bonded open-shell atoms (e.g., the chemistry of the transition, lanthanoid, and actinoid metals; spin-flip enhanced reaction mechanisms; so-called spin-forbidden processes)? Sandbh (talk) 12:19, 24 February 2020 (UTC)

@Sandbh: He mentions exactly these few special topics in chemistry where GSC are somehow relevant. Droog Andrey (talk) 15:06, 24 February 2020 (UTC)

@Double sharp:@Droog Andrey: Thank you each for your interesting responses. A quick comment before I return and address them later today.

The extract from Silberberg is the standard chemistry paradigm which forms the background to my article. For the book he had a nine-professor Board of Advisors. The previous edition was subject to focus group discussion, content review and class-testing by another 181 professors. Sandbh (talk) 21:54, 22 February 2020 (UTC)

@Sandbh: As Droog Andrey says, "Ground-state configuration, just a tiny reflex of that structure, is used for educational purposes focusing on main groups" (bolding mine). This is just an example of the well-known phenomenon of lies to children for a better pedagogical experience. It's why we start teaching Arrhenius' theory of acids and bases even though we know better ones, for example. Or why we don't start teaching linear algebra over a general division ring instead of starting easy with vectors in R² and R³ and then graduating just to real and complex vector spaces (finite fields usually come later). Or why we don't start music classes with Schoenberg. Or why we don't start physics with Einstein instead of Newton. Double sharp (talk) 21:57, 22 February 2020 (UTC)

@Double sharp: Several things here:

As Stewart and Cohen noted, reality itself is viewed within the prism of human perspective: "Any description suitable for human minds to grasp must be some type of lie-to-children — real reality is always much too complicated for our limited minds."
University instructors often explain at the outset that the model they are about to present is incomplete; when that is done there is no lie-to-children subterfuge. This practice has been referred to as the 90% rule. It works this way:

"If something is true about 90% of the time or more, state the generalization as true and indicate that there are exceptions that will be dealt with later (perhaps even in another course); further indicate that even though the textbook may deal with these exceptions, you will not test students on them. Here is an application of the 90% rule: Oxygen has an oxidation number of -2 in the combined state. I indicate that because F is more electronegative than oxygen, fluorine-oxygen compounds are one exception; a second exception involves a class of compounds called peroxides. Are peroxides important? Sure they are, but they can wait. Oxygen-fluorine compounds and peroxides number significantly less than 1% of all substances containing oxygen. For me it is far more important that students are able to use this generalization confidently in determining the oxidation numbers of other elements in species where getting the right oxidation number is very important."

3. Some other relevant extracts from our WP article are:

In a contribution about evolution for the 2001 book Nonlinear Dynamics in the Life and Social Sciences, reproductive biologist Jack Cohen discussed the lie-to-children teaching technique and its use educating students on the concept of evolution and its complex facets including the notion that DNA is an architectural guide for life.[17] The author concluded: "Only the search for universal features, while treasuring all the exceptional specifics, offers some hope of sketching out the general shape of the evolutionary process so that we can explain it honestly as a Lie-to-Children."

"The authors conclude that the lie-to-children teaching technique: "allows the basic features to be understood without confusing things by considering exceptions and enhancements."

There is no getting way from the phenomenon. It's a question of where you pitch your explanation on the "lie-to-children" scale, and explaining at the outset what the limitations of your model is. The "lie-to-children" terminology is actually ethically corrupted; a better term would be the equivalent of "at our level of approximation and setting aside an exceptions" or something like that. Sandbh (talk) 01:41, 23 February 2020 (UTC)

@Sandbh: Absolutely none of this refutes my point that presenting ground-state electron configurations as the basis of chemistry is a lie to children. We already have many prominent chemists on record as noting that other things are more important in reality (Seaborg and Schwarz, for example). Differentiating electrons, being an ill-defined concept based on ground-state electron configurations (what exactly is the DE from vanadium d³s² to chromium d⁵s¹?), are even more of a lie to children, and one even easier for the children to see through on the grounds I've just brought up. So, do you want to draw a table based on lies to children that create an asymmetry with no effect on real chemistry, or a table based on something higher-level and closer to the truth that gets rid of that asymmetry? Given that the standard n+l rule supports Lu-Lr and is ubiquitous, I see no reason a Lu-Lr table would be a pedagogical harm. Indeed it would be even easier to teach: you'd say "the ground state configurations are blah blah blah, actually many configurations are important especially for d- and f-elements, so the anomalies at the trees level are levelled at the forest level". Lie to children averted, since the model is outright stated as incomplete the first time it is presented. Double sharp (talk) 23:16, 23 February 2020 (UTC)

@Double sharp: Far out. I explain my approach to avoiding lies to children and then you ignore it. Well done Double sharp. You say to the children that:

GSC are the most stable way to organise n electrons around a nucleus with a z⁺ charge noting this is for single atoms in the gas phase; optional cue for a brief intro to spectrometry.
this is a simplified model, and while it has some exceptions, which can sometimes be addressed by more in-depth models, that the GSC model works well enough for most purposes
they will not be tested on these exceptions or, if they are to be tested, only to the extent that a more detailed model has been explained
the aufbau mnemonic, does not mean atoms are actually put together one electron at a time (this is a model, remember) and that it is not absolutely correlated with orbital energy (though they are related)
the "Aufbau diagram" provides a way to predict, with some exceptions, electron configurations for neutral elements.

I'm sure the "children" will understand, and be provided with a firm foundation for drilling down, when they need to, and appreciate the absence of lies.

PS: The d/e for Cr is d, or if you want to drill down, d + one 4s1 promoted to 3d1.

PPS: The n+l rule does not support an Lu table. Rather, an Lu table has an external appearance that is closer to the n+l rule when the n+l rule is displayed, for example, as a LSPT. Sandbh (talk) 03:56, 24 February 2020 (UTC)

@Sandbh: My approach avoids lying to children at all. We simply tell them the truth from the start. This is how I'd see a lesson go once we finally manage to dump the historical relic that is the La table:

The most important thing to understand is the nature of the blocks and the subshells (I trust we already know what n and the shells are). We know of four now (s, p, d, and f), and almost certainly within the very near future we will open a fifth (g). These are distinguished by a certain quantity called l: s, p, d, f, and g correspond to l values of 0, 1, 2, 3, and 4 respectively. The names s, p, d, and f come from spectroscopy, before we really understood the regularity. Now that we do know it, future ones go alphabetically (whence g). [Well, OK, I guess by the time the La table really gets dumped we will probably have actually discovered g elements. But, one speculation at a time. Since meitnerium has been waiting since 1982, I guess it's still quite possible that by the time this happens there still won't have been actual experimental chemistry of g elements. ^_^]
We may look at their shapes, how many of each there are, how far they extend from the nucleus, and the important concept of radial nodes. You don't need to understand what these mean now, because there is some complicated mathematics here: the important thing is that the first subshell of any type is smaller than you'd expect and often acts rather exceptionally.
Most tables you encounter will show ground-state electron configurations in the gas phase, which are OK for the s and p elements as an understanding. Those are the elements where you begin.
In chemically bound environments, the d and f elements switch between many configurations of about equal energy level, and our best scientists have predicted the same for the g elements. The ground-state electron configurations for these elements do not really mean anything much for chemistry for this reason, and you will therefore not be tested on those exceptional configurations even when we do get to basic d block chemistry. Unless you do spectroscopy or molecular gas-phase reactions you'll hardly ever need to know them.
The important invariant is chemically active subshells and how many electrons are held within them, in which the PT displays an astonishingly perfect regularity. The better understanding here comes from "fuzzy configurations", e.g. La = [Xe] (4f5d6s6p)³, Lu = [Xe]4f¹⁴ (5d6s6p)³. What this means is that we write the core first (the electrons not participating), and then write how many electrons are participating and what subshells they happen to come from.
There are important heuristic ideas of what configurations are important for the d and f elements based on important motifs in the PT. For example, in the d elements of groups 3 through 10, it is best to assume a dⁿ configuration in compounds. Also for example, the important thing we see in the f elements is the "reserve area" nature of the deeply buried and small f orbitals, where electrons may be promoted from into bonding MOs: this is one way in which we see that La-Yb are real f block elements and Lu is something different. You don't need to know all of this now: if you go further into d and f block chemistry you will learn it then. And maybe when you grow up you will become the pioneers of g block chemistry! Now that you know something about what those orbitals are like, you may not be surprised to here that it is expected to be something like f block chemistry, but also starting an unprecedented situation that builds on it.
Blocks are delineated by which subshells are chemically active. For most elements, we will have many subshells active. The order of energy of subshells generally follows Madelung's n+l rule: orbitals fill in order of increasing n+l, and within each group of equal n+l, in order of increasing n. (Also consider Hund's rule here, which is important for light elements.) With the exception that the important gap comes before each s-orbital (not between values of n+l), which therefore fraternises with the "wrong" company. We will see more of this exception soon.
The Madelung rule is thus restored to perfection. It gives the characteristic "two rows at a time" structure of the periodic table, and something called "double periodicity" that you see across each group: "kinks" in the trend occur every time a block is inserted. Except for the s block; we'll get back to that in a moment.
We will test you on using the Madelung rule throughout the table, even for d and f elements. For those elements you may either write a "fuzzy configuration" or simply assume everything holds as the Madelung rule expects, e.g. La = [Xe] 4f¹6s². If you go for the second option, you are expected to include a disclaimer for those elements that you know that that might not be the ground state but that it will be close and it will be chemically relevant.
We notice that elements tend to use subsets of each group of orbitals: if we look across row 6, we see the s block (we'll come back to it in a moment). Then we see the f block, where 4f, 5d, 6s, and 6p are all being used: all four in one group. Then the d block, where 4f stops being used, and only the other three are left. Then the p block, where 5d stops being used, and only the last two are left. The characteristic subshell is the one of highest l that is active, and we use it to name the block. Each corresponds to filling its characteristic subshell from empty to full.
The weirdo is the s block. Nominally, like the others, it corresponds to filling its characteristic subshell. But it has no qualms about using ones of higher l than it. The only really pure s elements are H and He: everybody else has no problem using p or even d orbitals. Not only that, but we can see that due to peculiar gap movement in the Madelung rule (in a sense, a symmetry break from n+l), it can never show any double periodicity: H and He form a huge exception, then 1s shields perfectly, but after that there's never anything cutting in line between a p-subshell and the next s-subshell. We can see this straight from the pattern of the periodic table.
The duet, octet, 18-, and 32-electron rules (the last mostly unattainable because of buried f-electrons, except for early actinides) come from an element's drive to "fill up" all of these vacancies in its chemically active subshells.
We also see the important rule of subshell energy level (e.g. 4f < 5d < 6s < 6p) which goes in order of increasing n within each group, with the understanding that the s-block constitutes an important exception where the s subshell cuts the queue to fill first. In order to emphasise the different regions in which each of those rules are applicable, we draw the blocks absolutely distinct and separate, even with helium over beryllium.
Most people will not draw He over Be, but over Ne. This is because He is a noble gas in physical and chemical properties: its only shell is full, so it doesn't desire anything to change that status, which makes it quite like Ne and its congeners. However, the block difference makes a big impact for atomic properties. Moreover, H and He then stand as the first-row anomaly for the s block just like the other ones if we put them over Li and Be, which creates a deeper regularity. You will just have to remember that although H and He are all the way on the left side of our table, they are nonmetals. It will turn out that the position means something: H has many metal-like properties in its chemistry, and when our top theoreticians investigated what happens when He is forced into bonding, it seems to want to behave more like Be than Ne.
The Madelung rule allows one to predict these "fuzzy configurations" absolutely perfectly. If you wish, you may consider filling up the exact configuration according to it: while this will not always be right for the ground state, what you come up with will be chemically relevant, and you can often use it with some heuristics that you'll learn to predict how many electrons will be used for chemistry.
Some old tables put La and Ac into the d block instead of Lu and Lr. You will often see this if you read some old books (many of which are still quite good when it comes to describing the chemistry), but we will not use this classification. The historical reason for this is that we previously did not know about the f block: the 5f elements that we knew "pretended" to be d elements (we will explain why this happens at a much later date). Therefore we thought all fifteen lanthanides belonged below yttrium, and we misguidedly picked La as the prototype. This mistake obscures the point of blocks, and drags group 3 into the odd lack of double periodicity that should by rights only appear in the s block. It ruins many regularities in the periodic table's trends because they all, at length, lead to this block filling and Madelung rule. It does more harm than good and you shouldn't use it anymore. If you wish, you may do some research and presentations on old periodic tables. You will see really marvellous things from today's perspective, since we only had the chemical properties and we didn't yet know the physics and mathematics that was behind that. You may learn a bit from them about secondary periodicities, and we may even (when dealing with those groups) do a comparison with the secondary linkages; but we have picked the table that is the most consistent and goes for the most important linkages. We respect and honour our past, but we continue building on it, and don't stop there. [Hopefully one day this will be the situation, with Sc-Y-La relegated to the status of the equally plausible Be-Mg-Zn! In the meantime, you can read this as "some misguided tables" instead.]
When we get to really heavy elements, like for those g elements shrouded in mystery that maybe some of you will penetrate, but more at home for those elements from the sixth and seventh rows, Einstein's theory of relativity comes into effect. You see it every time you look at a beautiful golden ring, watch the mercury in your thermometer flow (do people see those much anymore?), and see a car running on a lead-acid battery. When you look at those elements later you will only need to understand for now the qualitative aspects, which are in fact mostly about the orbitals. The point is that in each part of the periodic table you must understand how the orbitals have become different, and what that means from the effect of the chemically active ones on chemistry and physics.

That concludes my tale. Not a single false word has been spoken, but I think it would do some good. And not a word has been spoken about ill-defined and irrelevant DE's. Double sharp (talk) 20:00, 24 February 2020 (UTC)

@Double sharp: WOW!! Nice work! I'll have to do me one of these too! Sandbh (talk) 04:44, 25 February 2020 (UTC)

Bond order

@Double sharp: One of the most important outcomes of GS electron configurations is the stable oxidation state or number of bonds that an atom can form to other atoms. For example Ni being 3d⁸4s² tells that it will probably be quite comfortable as Ni²⁺, which is in fact the case. With oxygen, Ni will form an oxide of composition NiO, with a bond order of two, which is in fact the case.

How do I tell this from your PT of significantly chemically active sub-shells? Sandbh (talk) 05:26, 23 February 2020 (UTC)

@Sandbh: I don't know, how do I tell from your PT that Fe is about equally happy in +2 and +3, whereas Os prefers higher states like +4 and +6, even though both are d⁶s²? Double sharp (talk) 09:44, 23 February 2020 (UTC)

@Double sharp: I start from the premise that about half the elements show some regularity between electron configuration and common oxidation states. For cases such as Fe and Os, I presume there must be other factors at work and I take it from there. Sandbh (talk) 12:20, 23 February 2020 (UTC)

@Sandbh: I get it, so if it happens to fit the ground-state electron configuration, that must be the reason, and if it doesn't happen to fit, there is another factor at work. What exactly makes you think then that ground-state electron configurations are relevant, and that it is not another factor working all the time instead even when the ground-state configuration coincidentally gives the right answer? Double sharp (talk) 12:31, 23 February 2020 (UTC)

@Sandbh: NiO is not molecular compound, but if you consider one molecule in gas phase, the bond order will be slightly larger than two because of O->Ni donation. As for oxidation states, Madelung-based electron configurations are better to predict the most stable states. For Ni we have 2 valence electrons in outer subshell and 8 more in inner subshell close to completion; that leads to the most stable +2 state (outer shell), possible +3 (one electron from inner subshell) and higher ones, and also 0 with 4s electrons displaced to 3d to complete it.

Another example is Cr: Madelung suggests 3d⁴4s², which corresponds to stable +2 (outer shell) and +3 (one d-electron), with higher states possible up to +6. The general trend of decreasing +3 stability from Cr to Ni is explained with 3d drowning, and the local stability of +2 for Mn is explained with symmetry of half-populated 3d. Real GSC 3d⁵4s¹ for Cr explains nothing but the highest oxidation state.

So it's better to use Madelung-based electron configurations for teaching, making a footnote that for single atoms in gas phase some of these configurations have not really the lowest energy, but are at least close to ground. Droog Andrey (talk) 05:05, 24 February 2020 (UTC)

Predominantly ionic

@Sandbh: That's not an argument at all. Predominant ionicity follows from low oxidation states and large radii. So all the elements to the left of Group 4 have predominantly ionic chemistry (except for H and Be due to their small radii), no matter where Sc and Y are located (either above La-Ac or above Lu-Lr). So stop this holy war please :) Droog Andrey (talk) 09:34, 24 February 2020 (UTC)

@Sandbh and Droog Andrey: Oh, but it's even worse, since the early 5f elements from Th to Pu don't want to be in low enough oxidation states to be ionic. ^_^ Yes, this is precisely the reason (see Fajans' rules which I have been referring to ad nauseum). There's nothing fundamental about it that makes it relevant to the group 3 position; just switch the conditions a little, and the line gets pushed one way or the other. You can't average this out to give anything very sensible for the chemistry of an element as a whole; the only sensible thing to do is to talk about how ionicity changes with oxidation states and atomic radius. Which is just Fajans' rules and comparing EN. Double sharp (talk) 19:16, 24 February 2020 (UTC)

@Droog Andrey:@Double sharp:

Droog Andrey, yes you get it. La or Lu then come into play. You know the rest:

1929	"…If Sc, Y, La and Ac are the only rare-earth elements, the series would have revealed the same gradual change in properties as the Ca, Sr, Ba and Ra series, and hence it would not have been of any special interest." (Hevesy 1929, cited in Trifonov 1970, p. 188).
1937	When it was learnt that the 4f sub-shell became filled at Yb, rather than Lu, nothing changed wrt to the chemistry of La and Lu, so La stayed where it was under Y and Lu stayed where it was at the end of the Ln.
1996	"The trends in properties in the family [Sc-Y-La-Ac]…are quite regular, and similar to the trends in Groups 1 and 2." (Lee 1996, p. 679)
2017	In our IUPAC submission, Double sharp and I wrote: ""Given, as previously examined, that Sc-Y-La-Ac matches better with group 1 and 2 trends, whereas Sc-Y-Lu has been shown several times (including by Jensen), to more closely parallel trends in groups 4 to 10, we contend that the choice of Sc-Y-La-Ac over Sc-Y-Lu-Lr is clear."
2020	Double sharp agreed that the really characteristic transition metal properties of coloured compounds, multiple oxidation states, and paramagnetism are first commonly seen in the first element of group 4 i.e. Ti as Ti³⁺.

From these few straightforward observations I conclude, noting your disagreement, that Group 3 is better placed next to Groups 1−2, with the result that elements of like chemistry are more closely grouped together. Sandbh (talk) 23:56, 24 February 2020 (UTC)

@Sandbh: You're being selective. I freely admit that I was mistaken in 2017: I think R8R may have mentioned the group 4 problem (Zr and Hf), but I think I did not appreciate its importance until Droog Andrey discussed this with us in 2018 (because group 3 is really not as skewing to groups 1 and 2 as we thought). Anyone can see that Ti is rather TM-like, yes. Anyone can also see that Zr, Hf, Rf, Nb, Ta, and Db are all rather main-group-like in the sense that they don't like to go below their group oxidation state (whence your "really characteristic TM properties" come from). The truth is that group 3 is intermediate, it's equally often close to groups 1 and 2 and close to groups 4 and 5, just look at various different properties spanning the whole of chemistry. So there's no reason to reject the arguments that group 3 trends with Lu are similar to groups 4-10, because group 3 is a d-block group, and it shouldn't show the completely unusual trend of the s-block that lacks double periodicity. That comes from the real symmetry break in n+l (that s-subshells join the next batch instead, not the La one that means nothing at the forest level): this means s-subshells fill preemptively, without double periodicity, and the s-block has a totally different energy level order from everybody else. And in fact we may relatively well understand what makes the similarity happen in each case. Whereas chemically active valence subshells are astonishingly constant and relevant across chemistry. But then the gap is between strict Madelung blocks, i.e. between Yb/No and Lu/Lr. ^_^

If Sc, Y, Lu had been the only REMs, the series would look just like Ti, Zr, and Hf, or V, Nb, and Ta, and no one would have raised an eyebrow either. I put it to you that an argument that may be symmetrically inverted to work just as well for the other side is completely inconclusive. Double sharp (talk) 00:17, 25 February 2020 (UTC)

@Double sharp: Sandbh (talk) 04:34, 25 February 2020 (UTC)

Yes, that's a rather good post. Yes, I'm being selective in that I'm nailing my colours to the flag post of the most important thing for a chemist, according to RC & O, which is the ionic-covalent tendency. Underneath that first order approximation, we can can indeed see that Zr, Hf, Rf, Nb, Ta, and Db are all rather main-group-like. That said, from a classification science point of view, effectively nobody makes anything of this. That is not to say it isn't accurate but rather, it's not pinging on the radar. I think the symmetry-based argument, which does work both ways, only effectively does so because it lacks temporal context. I will give this argument some more thought. Sandbh (talk) 01:07, 25 February 2020 (UTC)

@Sandbh: Well, so authors who were excluding group 3 from transition metals either overlooked or were unaware of the similar situation of group 4. Science marches on, after all. And I'll just note that excluding group 3 from transition metals in the first place seems to have become rare enough that IUPAC doesn't feel the need to allow it.

The ionic-covalent tendency is not fundamental. It comes from electronegativity differences, that's all; elements are more ionic in lower oxidation states and if they have lower atomic radii. The precise gap shifts completely predictably from this as we look at different chemically relevant environments. Yes, in chlorides the gap is between Sc and Ti; in oxides TiO₂ is clearly ionic; in organometallic compounds the gap is rather between Ca and Sc. Not the slightest problem, we know the real fundamental thing is EN. But that's a continuous trend across the table, so it's not a good La argument either. Double sharp (talk) 11:44, 25 February 2020 (UTC)

P.S. Helium in group 2 seems fine too, then. It has one of the smallest radii in the periodic table too, after all! ^_^ (P.S. This is not a reductio ad absurdum: I actually think helium in group 2 might be the "right" placement. Though chemically speaking you probably want He with the noble gases, He in group 2 anchors some regularities that are revealed in trends that exist in the real world.) Double sharp (talk) 14:34, 25 February 2020 (UTC)

I get it

@Double sharp:@Droog Andrey:

Double sharp, it seems to me that the nub of your argument goes as follows:

In their condensed states, La, Ac, Lu and Lr are d-metals.
Given a choice between La in group 3 and a split-d block, or Lu in group 3 and no split-d block, one presumably starts with an Lu table, which shows more regularity and symmetry.
It then becomes a matter of showing that there are or aren't other factors of sufficient import, that would merit switching to an asymmetric La table?

Sandbh (talk) 23:56, 24 February 2020 (UTC)

@Sandbh: No, my main argument is that in chemically relevant environments, La and Ac are f-metals because they use their f-subshells. Condensed-phase configurations are incomplete just as gas-phase ones were. Lu and Lr, on the other hand, are d-metals. The increased symmetry and regularity in the blocks and periodicity, combined with the fact that a Lu table has more explanatory power than a La one, are a confirmatory argument slamming it in. Ionicity vs covalency is simply not strong enough for this, given how much it depends on chemical environments in an extremely well-understood way, not strictly on block and group divides. The history is not relevant: we may improve on it, just like what we did ages ago against Be-Mg-Zn and the 8-column table. Double sharp (talk) 00:15, 25 February 2020 (UTC)

@Double sharp: How do you say that "Condensed-phase configurations are incomplete" and then refer to La and Ac as f-metals, and Lu and Lr as d-metals? Sandbh (talk) 01:48, 25 February 2020 (UTC)

@Double sharp: Possible f-involvement in La and Ac is quite marginal, and does not represent a robust basis for a main argument.

On symmetry and regularity Scerri commented that we should be aware of such arguments viz.:

"Too many proponents of alternative tables seem to argue about the regularity in their representation and forget that they may be talking about the representation and perhaps not the chemical world itself.

There is no basis for asserting that an Lu table has more explanatory power than an La table.

Ionicity v covalency works quite well in the case of Group 3.

You can dismiss the relevance of history but not its staggering momentum. Sandbh (talk) 03:16, 25 February 2020 (UTC)

@Sandbh: La and Ac aren't fs² in the condensed phase either. That's not a strike against them as f-elements, since Be is sp in the condensed phase. The important thing is that f-involvement in La and Ac, far from being "marginal", explains a great deal of their chemical and physical properties. It explains their huge coordination numbers, even some lower coordination numbers on symmetry grounds (cubic complexes), and it explains a lot about the thermodynamic properties of La (ref. Gschneidner). We can even see many cases where 4fⁿ5d and 4fⁿ⁺¹ states are both important for Ln compounds; here La patterns like a normal lanthanide, but for Lu one of these states doesn't exist.

What I mean about symmetry is that the chemical world itself is showing the symmetry in group 3, not breaking it, given the already often explained f-involvement in La and Ac. The real symmetry break comes in the s-block, which I've explained already. It's not symmetry for the sake of symmetry.

On these bases, along with the more consistent trends that are obtained across periods and down groups as a result, the Lu table clearly has more explanatory power than a La one.

Ionicity vs covalency changes depending on oxidation state and atomic radius in a very well-understood way. It's completely irrelevant to group 3 as by simply changing between many chemically relevant situations you can change this. Well, if you look at chlorides, then yes, the gap is between Sc and Ti. If you look at oxides, TiO₂ is pretty clearly ionic. If you look at organometallic compounds, then the gap is rather between Ca and Sc. The important thing here is electronegativity, but we all know that that is a continuous trend.

If we were having this conversation 80 years ago, the staggering momentum would be for Th, Pa, and U in groups 4, 5, and 6. This is science: tradition counts for nothing when we learn something that overthrows it. Double sharp (talk) 11:40, 25 February 2020 (UTC)

Something like an explanation for my current approach (He in group 2, with a Sc-Y-Lu group 3; no metalloids, but a 3-way nonmetal split) is on my userpage below the table I have there. So as not to spam this page again, you may read it at User:Double sharp/Idealised electron configurations (look under the first "fuzzy configurations" table).

@Droog Andrey: What are your comments on my current approach? Double sharp (talk) 23:07, 25 February 2020 (UTC)

@Doible sharp: your tale of 17 paragraphs is very close to what my students learn :) Droog Andrey (talk) 05:03, 26 February 2020 (UTC)

@Double sharp: As above :) Sandbh (talk) 09:27, 26 February 2020 (UTC)

Most important valence orbitals

@Double sharp:@Droog Andrey: Here's some nascent thinking, as influenced by our astonishing discussions, and reading more widely about the relevance of gas-phase- and condensed-phase-configurations.

A draft list of the most important valence orbitals, in the condensed phase:

main group elements = sp
transition metals:

groups 3-11 = d

group 12 = s

Ln, An:

Ce, U-Pu = d + f

Pr-Yb, Th, Pa, Am-No = d

This doesn't resolve group 3, so I have to look at other considerations.

My first thought is that for a chemist, rather than a spectroscopist, the 4f sub-shell closes at Lu. Here I’m referring to ion configurations, where Yb⁺³ is f¹³, and Lu⁺³ is f¹⁴. Many parts of the puzzle then fall naturally into place, such as:

the La table is based on the chemistry world, and the GSEC's of interest to chemists; whereas
the Lu table is based on e.g. the fact that—for a neutral, isolated, ground state atom—"the pth element in the f-block series, with the exception of Gd, has p f electrons." Sandbh (talk) 00:32, 26 February 2020 (UTC)

@Sandbh: the La table is not based on chemistry world. Droog Andrey (talk) 04:55, 26 February 2020 (UTC)

@Sandbh: Exactly what Droog Andrey said: a holistic examination of chemistry world supports the Lu table, as the two of us have previously demonstrated. Ground state electron configurations appear nowhere in my case for Lu. Double sharp (talk) 20:24, 26 February 2020 (UTC)

@Droog Andrey:@Double sharp: I feel that the La table, in a chemistry world context, does a better job in terms of:

Item	Notes
1. f-block regularity per Schukarev	Consistent with (a) Rokhlin (2003, pp. 4–5), Mg alloys containing REM: Structure and properties; (b) Ternstrom (1976); (c) Remy (1956); (d) Klemm (1929, 1930)
2. Horizontal triads (per DIM)	(a) Dias (1989–1991) refers to the PT as being characterised by horizontal triads; (b) no more than a local issue according to DS
3. The behaviour of the monocations of Sc, Y, La and Lu	(a) Per Elkind et al. 1989; (b) similar results were reported by Sunderlin & Armentrout (1989) for reactions with CH₄ and C₂H₆, inc. attributing the different behaviour of Lu to an indirect effect of the Lu f¹⁴ sub-shell
4. An ionic-covalent distinction	(a) Rayner-Canham and Overton (2006) say this is the most important consideration for chemists; (b) nonsense according to DS
5. The first appearance of characteristic TM behaviour in group 4, at Ti	As agreed with DS ^_^
6. Lining up the Ce³⁺-Lu³⁺ contraction with the f-block	(a) Per Cotton (2006), and Mingos, a key distinction is made between the direct contraction caused by the progressive filling of the 4f sub-shell from Ce³⁺ to Lu³⁺, and the indirect knock-on consequences starting at Hf whence 4f electrons are no longer being added; (b) nonsense according to DS
7. Isodiagonality (per DIM)	(a) As buttressed by a quasi knight’s move relationship between La and Ca; (b) Scerri refers to horizontal, vertical, and diagonal trends as characterising the periodic table; (c) Mingos refers to diagonal relationships as one of the essential periodic table trends; (d) no more than a local issue according to DS
8. A smooth gradation of properties going down group 3 before this is impacted in subsequent groups by the filling of the 4f sub-shell, in gaseous and condensed states	(a) While this impact is seen in all subsequent groups of the TM it is "never more pronounced" than in group 4 (Greenwood & Earnshaw 1998, pp. 957–958); (b) see also (Lawrance 2013, pp. 177–178), Introduction to coordination chemistry
9. Reflecting the delayed start of filling of the f shell as one goes down the table i.e at Ce for 4f (a); at Pa for 5f although there is some 5f chemistry seen with the Th³⁺ cation (b); and at E123-125(?) for 5g (c)	(a) Per Schukarev; (b) as brought to my attention by DS (^_^); (c) as agreed by everyone ^_^
10. Being congruent with condensed phase electron configurations, which are more relevant than gas-phase configurations	In an La table the number of f-electrons is congruent with the place of each f-block element in 12 of 14 cases; in an Lu table the situation is reversed, with congruency seen in only 2 of 14 places
11. Stoichiometry	(a) Per Restrepo (Max Planck Institute for Mathematics in the Sciences); (b) as disputed by DS; (c) subject to clarification with Restrepo
12. The most important condensed phase sub-shell	(a) For La this is the 5d subshell; (b) for the following lanthanoid series of 14 elements (Ce to Lu) this is the 4f subshell, which is their raison d'etre, per Cotton, and Mingos

PS: I've earlier responded to Double sharp's modus tollens objections. Sandbh (talk) 12:02, 27 February 2020 (UTC)

@Sandbh: 1 is refuted above; 2 is local (noting that you are misunderstanding Dias, who is carefully using a "there exists" quantifier rather than "for all"); 3 is irrelevant (Sc, Y, La, and Lu in real chemistry are scarcely monovalent, and besides we should expect Lu to be different as just as Hf++ are thanks to the 4f subshell that regularly should be added); 4 is nonsense out of context; 5 is true but there is no reason why this one property should be singled out over all others (particularly since that trend is pushed later and later in later periods); 6 is both local (because the motive for making Ce-Lu the contraction is only because +3 exists as a dominant oxidation state for the Ln contraction; by those standards there are no other contractions) and wrong (there is no difference between knock-on consequences for Lu and Hf, 4f is core in both); 7 is both local and wrong (as is hilariously demonstrated by you referring to a "knight's move" relationship instead of a diagonal one between Ca and La; indeed, the precise ratio between horizontal and vertical trends needed keeps changing through the table); 8 is based on false premises (the 4f subshell has already started at La, and the knock-on consequences going from Y-Lu make group 3 match group 4 as it should for a d-block group); 9 is irrelevant (this is not something special for the f and g blocks, but for heavy elements; noticeably you don't quote the 6d and 7d delays; and indeed, the lanthanides with the most active direct f involvement are La and Ce which come before or during the 4f collapse); 10 is irrelevant (condensed-phase configurations are just as incomplete as gas-phase ones); 11 is refuted above; 12 is misguided (since the most important holistically viewed chemically active subshells for La are 4f5d6s6p, just like for Ce-Yb, and unlike Lu where they are only 5d6s6p). Double sharp (talk) 20:22, 2 March 2020 (UTC)

@Double sharp: Very nice.

1, 4 I'm very comfortable with my supporting citations. Sandbh (talk) 05:09, 3 March 2020 (UTC)

@Sandbh: Which you don't critically analyse, when Droog Andrey and I point out the mistakes they make. Well, we can probably come up with loads of old citations for Be-Mg-Zn which speak chemical sense about their relationship, too. But it will not make the Be-Mg-Zn placement superior to the Be-Mg-Ca placement. Double sharp (talk) 15:29, 3 March 2020 (UTC)

@Double sharp: My last response addressed your concerns about f-block double periodicity etc. Forget your old citations for Be-Mg-Zn. They've been superseded by modern electronic periodic table theory, as you know. Sandbh (talk) 04:54, 4 March 2020 (UTC)

@Sandbh: And it's been refuted. Sooner or later we can supersede the old Sc-Y-La table with modern theory that doesn't rely only on gas-phase configurations, just like Seaborg and Schwarz noted. Double sharp (talk) 11:52, 4 March 2020 (UTC)

2. Here's the relevant extract from Dias:

"A periodic table is defined as a partially ordered [italics added] set forming a two-dimensional array which complies with the triad principle where any central element has some metric property that is the arithmetic mean of two flanking [i.e. horizontal] member elements." Sandbh (talk) 04:21, 3 March 2020 (UTC)

@Sandbh: "has some metric property" (my bold): that's a "there exists" quantifier, not a "for all" quantifier. So there will be at least one such metric property, but there is no guarantee that the same one will be the relevant one everywhere. Certainly maximum oxidation state triads don't cut it. Double sharp (talk) 15:29, 3 March 2020 (UTC)

@Double sharp: Indeed; no periodic table is capable of capturing all relationships among all elements; nor will all such relationships have universal relevance. You pick your properties of interest and take it from there.

Your focus is on restoring symmetry, which is fine for matching the idealised regularity of the aufbau process or n+l rule, and wonder-inducing tetrahedral symmetry (ADOMAH in a cube).

I choose to observe the congruity of the f-block; pattern density (e.g. horizontal and isodiagonal triads), the periodic law; and global considerations, including the most important orbital. The systemic aspect of this approach is that each one of my arguments reinforces the others, consistent with the facts and parts of the periodic table as an integrated, complex structure. Sandbh (talk) 04:23, 4 March 2020 (UTC)

Nope. I actually analyse the real chemistry and real patterns, noting what being in a block really means (i.e. involvement of that subshell), and the most fundamental patterns (horizontal and vertical triads), and real periodicity. Every single one appears in a hierarchy stemming from the chemically active valence subshells, whereas you take each one out one by one without bothering to figure out where they all come from. And, surprise, surprise, this approach leads to Lu. The only reason you manage to get some of it to lead to La is by taking it out of context. Not to mention that Lu authors are allowed by you to be wrong but La authors never are. ;) Double sharp (talk) 11:52, 4 March 2020 (UTC)

3. This argument deals with periodic trends in chemical reactivity, as observed in the reactions of Sc+, Y+, La+ and Lu+ with H₂, D₂, and HD, CH₄ and C₂H₆.

The first ionization energy of the elements is a key indicator of periodic trends. That is why the monocations of these metals, which are hardly representative of their general chemistry, are relevant. Hydrogen represents one of the two elements, the combining power of which Mendeleev based his periodic table of elements on, the other element being oxygen.

Under the experimental conditions set out in the article, the Lu⁺ system was found to be rather different from the other three systems in several respects, including electron configuration, reactivity onset, thermodynamic behaviour, and interactivity mechanism. Meanwhile, Sc, Y and La showed properties consistent with periodic trends. Sandbh (talk) 04:30, 3 March 2020 (UTC)

By such logic (based on the 4f¹⁴ addition for Lu), I bet Hf will be seen to be just as anomalous under Zr. The true regularity expected from periodic trends is that the addition of the 4f¹⁴ core affects every 5d element just as the addition of the 3d¹⁰ core affects every 4p element. And, lo and behold, that's what we see from chemically active valence subshells.

Meanwhile, the whole point of 1st IE is that the process of stripping the first electron is part of what often happens chemically speaking. Not all of it, obviously, because often the 2nd electron also goes. It doesn't somehow make the behaviour of the +1 oxidation state especially important when all four elements involved do not have major chemistry in that state. Double sharp (talk) 15:29, 3 March 2020 (UTC)

5. I don't single out that one property ahead of all others. It's just 1 of 12 that mutually reinforce one another. Sandbh (talk) 05:09, 3 March 2020 (UTC)

Picked out from many. Just look at the difference between when the ionic-covalent-metallic (yes, it's three-way) distinction appears for M-As, M-C, M-Cl, M-O.

Besides, this is a continuum, as usual. V shows more transition character than Ti shows more transition character than Sc shows more transition character than Ca shows more transition character than K. All five have some if you look hard enough (very strong for vanadium, extremely weak for potassium outside truly extreme conditions). OK, titanium is the one where you cannot treat it as the unusual thing anymore. Why does that force a separation between groups 3 and 4? Particularly when for 4d and 5d it's Mo and W in group 6 instead? Double sharp (talk) 15:29, 3 March 2020 (UTC)

There's nothing to say here as #5, as expressed, is a matter of fact. Sandbh (talk) 04:54, 4 March 2020 (UTC)

As demonstrated above, it is a fact that is taken out of the context of continuity of this trend, and it is a fact that is chosen among many other possible breakpoints for no particularly good reason. Therefore it means nothing for drawing the PT. Double sharp (talk) 11:46, 4 March 2020 (UTC)

6. Per Cotton (2006), and Mingos, there is no knock-on consequence for Lu, unlike Hf, since the filling of the 4f sub-shell is not completed until Lu³⁺. The knock on consequence of the filling of the 4f sub-shell therefore starts at Hf. Sandbh (talk) 04:34, 3 March 2020 (UTC)

Unfortunately for this argument, the filling of the 4f subshell has already been finished at Yb. The subshell getting filled is supposed to be the one that's getting ionised or at least contributing, and for Lu it is definitely a core subshell (at least 3d in Zn has a demonstrated valence contribution). If we look at ions in typical oxidation states, 6s starts filling in a major oxidation state at Hg₂²⁺. ;) Double sharp (talk) 15:29, 3 March 2020 (UTC)

@Double sharp: Yb³⁺ is [Xe]^f13 i.e. the filling of the 4f sub-shell is incomplete. Lu³⁺ is [Xe]f¹⁴, the 14th f electron concluding the mostly f-electron caused contraction. As you wrote above we should expect Lu to be different thanks to the 4f sub-shell.

@Sandbh: Yet again you're only considering the common +3 oxidation state, thus dooming your criterion to locality as only in 4f is that a thing. Well, Ba²⁺ is [Xe], 6s has not even started as it's always ionised away. So we have to wait for Hg₂²⁺ and Tl⁺ to start the s-block. The difference is simple: are the f-electrons actually participating in chemistry. As demonstrated above, yes for Yb, no for Lu, so off to the d-block Lu goes. Therefore the fact that Lu deviates from the "straight down" Sc-Y-La trend is exactly expected since we've already demonstrated that 4f¹⁴ is added, just like Hf deviates from the "straight down" Ti-Zr-Ce trend, and so Lu takes its natural place under Y just like Hf does under Zr. And the periodic trends argument 3 is blown out of the water again. The starting point is that 4f involvement is La-Yb (most direct at La and Ce; after that it is mostly indirect as a reserve area), and from there we see that the trends demand Lu in group 3 and that this placement causes regularity. Double sharp (talk) 11:45, 4 March 2020 (UTC)

7. There is no diagonal relationship between Ca and La; there is a quasi-knight's move relationship:

The ionic radius of Ca²⁺ is 114 pm; that of La³⁺ is 117 pm (cf. Lu 100).
The basicity of La₂0₃ is almost on par with CaO₂ whereas Lu₂O₃ is the least basic of the Ln oxides.
Freshly prepared La₂O₃ added to water reacts with such vigour that it can be quenched like burnt lime (CaO)—Lu₂O₃ is insoluble in water.
The similarity in sizes means La₃₊ will compete with Ca²⁺ in the human body, and usually win on account of having a higher valence for roughly the same hydrated radius.
The electronegativity of Ca is 1.0; that of La is 1.1 (cf. Lu 1.27). Sandbh (talk) 04:19, 3 March 2020 (UTC)

That's exactly why the argument is wrong. Isodiagonality is not so relevant as a knight's-move relationship here. And that's precisely because these are not basic relationships, but composed of horizontal and vertical trends, that in different parts of the table move at different rates. Sometimes you want a vertical knight's move (Ca-La), sometimes a diagonal (B-Si), sometimes a horizontal knight's move (Ag-Tl). Your argument appealing to Ca-La doesn't buttress your focus on isodiagonality but rather refutes it. Double sharp (talk) 15:29, 3 March 2020 (UTC)

@Double sharp: Here are the relationships involved:

+2	+3	+4
Ca	Sc	Ti
Sr	Y	Zr
Ba	La	(Ce)

There are:

three horizontal triads
one isodiagonal triad; and
two horizontal triads (not that I count these for much, but there you go).

So the Ca-La vertical knight's move buttresses the Ca-Y-Ce isodiagonal triad. Sandbh (talk) 00:58, 4 March 2020 (UTC)

@Sandbh: No, it rather reinforces my point. Depending on where you are in the table, the important interaction of horizontal and vertical trends might lead to going straight down (Zr-Hf), going in a horizontal knight's move (Ag-Tl), going down a diagonal (B-Si), or going down a vertical knight's move (Ca-La). There's no reason why isodiagonality should then be taken as fundamental, all those are just linear combinations of the actually existing horizontal and vertical trends which are the ones that are really fundamental. Oh, except they support Lu in group 3. Double sharp (talk) 11:45, 4 March 2020 (UTC)

8. The filling of the 4f shell has not started at La. This happens from Ce³⁺ to Lu³⁺. As G&E note the consequences are "never more pronounced" than in group 4. Sandbh (talk) 04:38, 3 March 2020 (UTC)

Wrong, the first element with pronounced 4f valence character is La as demonstrated ad nauseum here. Tripositive ions are irrelevantly local, you cannot use this criterion anywhere else, not even in the 5f row. In a Lu table the consequences start regularly at the beginning of the d-block with group 3 and are the strongest there, continuing the trend, just as the consequences of the scandide contraction begin logically in group 13 at the beginning of the p-block. Double sharp (talk) 15:29, 3 March 2020 (UTC)

Ho, ho, ho @Double sharp: La has "pronounced" 4f valence character. If you believe that I have a bridge to sell you. Sandbh (talk) 01:23, 4 March 2020 (UTC)

@Sandbh: Mock it all you like, it's true. Just look at significant overlap coming from La 4f in complexes. With Lu we don't see any such thing. Double sharp (talk) 11:45, 4 March 2020 (UTC)

9. What 6d delay are you referring to? In what sense does La have the most active direct f involvement among the Ln (along with Ce)? Sandbh (talk) 04:48, 3 March 2020 (UTC)

Just look at how the octahedral symmetry in the complexes I linked to is strong at La and Ce, and then is broken afterwards, which is totally consistent with decreasing 4f influence as the lanthanides from Pr onwards cannot (outside truly extreme conditions for Pr(V)) reach their "group oxidation state". The 6d delay is Lr 7s²7p¹ vs. Rf 7s²6d². Double sharp (talk) 15:29, 3 March 2020 (UTC)

That narrow example doesn't equate to the most active direct f involvement among the Ln. Thanks for the Lr clarification. Sandbh (talk) 01:19, 4 March 2020 (UTC)

@Sandbh: It does, because this behaviour is totally normal. The collapse of 4f is quick; already Pr and Nd start having significant trouble pulling out an extra 4f electron. The difference between La and Ce and the later lanthanides is the relative position of 4f: for later lanthanides it is strongly penetrating the Xe core, for Ce it is nearly degenerate with 5d, and for La it is even above it. That naturally implies that for La and Ce the 4f involvement can be direct, whereas for later lanthanides it will be more of a reserve area to pluck electrons out of. Same difference between the early 5f and late 5f elements. Double sharp (talk) 11:45, 4 March 2020 (UTC)

10. I'm very relaxed about the relevance of solid state configurations, per Schwarz's various writings in this area, and that old JChemEd article on why do we teach the eletron configurations that we do? Sandbh (talk) 05:09, 3 March 2020 (UTC)

Unfortunately Schwarz, as I quoted him, specifically mentions "dominant electronic valence configurations of the atoms embedded in a molecular or crystal environment". Not only solid-state configurations. Just because something is in the literature, or because you think something is in the literature, does not give you a free pass for a bad argument that contradicts the facts of chemistry. Double sharp (talk) 15:29, 3 March 2020 (UTC)

@Double sharp: Yes, that is included in the notion of solid-state configurations. Sandbh (talk) 01:19, 4 March 2020 (UTC)

@Sandbh: In that case La has well-established 4f involvement, and we get the Lu table without any fuss. Double sharp (talk) 11:37, 4 March 2020 (UTC)

11. I'm waiting for Restrepo's follow-on research using the entire Reaxys database. Sandbh (talk) 05:09, 3 March 2020 (UTC)

Will this follow-up consider relationships between elements with different characteristic valences, or will it still focus only on stoichiometry? Double sharp (talk) 17:25, 3 March 2020 (UTC)

@Double sharp: Don't know; I'll take that up with him, and advise. Sandbh (talk) 04:56, 4 March 2020 (UTC)

12. In terms of its impact on the properties of the metals, d is the most important for Sc, Y, La and Ac; f for Ce to Yb; and d+f for Lu. Sandbh (talk) 04:58, 3 March 2020 (UTC)

False. fdsp is important for the chemistry of La and Ac, but only dsp for Lu and Lr, as demonstrated above. Double sharp (talk) 15:29, 3 March 2020 (UTC)

@Double sharp: My source is Schwarz. As well, IMO, 4f involvement in La is peripheral or diffuse at best. For Lu³⁺ I note the impact of the f-electron caused f-block contraction starting at Ce³⁺ and concluding at Lu³⁺; and the impact that the 4f core has on Lu, as you agree, unlike Sc, Y, and La. Of course the impact of the 4f contraction is seen in Hf, but Hf is not a lanthanide whereas Lu is. I side with Cotton, and Mingos, on this one. Sandbh (talk) 00:42, 4 March 2020 (UTC)

@Sandbh: Real chemistry contradicts your opinion. Your consideration is, as usual, purely local, and claiming that Lu's lanthanide status gives it a special pass into the f-block despite a total lack of significant 4f involvement is nothing but semantics. In fact, looking at the late actinides and to a lesser extent the late lanthanides, oxidation states and the stability of +2 vs +3 strongly suggests that if we are going to remove one column from the Ln and An it ought to be Lu and Lr. Double sharp (talk) 11:54, 4 March 2020 (UTC)

@Double sharp: From a real chemistry perspective it seems to me that any 4f involvement is a peripheral part of La chemistry whereas the impact of Lu's 14 f electrons permeates 100% of its chemistry. This is also the case for Hf, but Hf is not a lanthanide (Ce to Lu), whereas Lu is. Sandbh (talk) 06:38, 5 March 2020 (UTC)

@Sandbh: Pure semantics. You can see that there is no real difference between the 4f involvements in Lu and Hf, both are core. Same for 5f in Lr and Rf. And there is also no difference between the 5f involvements in Ac and Th, neither is actually filled in the ground state, but both are contributing anyway. And 4f in La and Ce is also quite similar. Whereas, from Yb to Lu or No to Lr, f-involvement dives down to the core. If we hadn't had a definition of Ln and An already, these facts that translate to real chemistry (oxidation states) would strongly advocate for a La-Yb and Ac-No definition of the Ln and An respectively. Lu and Lr are really beginning something new. Double sharp (talk) 07:54, 5 March 2020 (UTC)

Carbonyls

A couple of articles:

"Octacarbonyl Anion Complexes of Group-3 Elements [TM(CO)₈]- (TM = Sc, Y, La) and the 18-Electron Rule", here.

"The adducts TM(CO)₈^- (TM = Sc, Y, La) fulfill the 18-electron rule when one considers only those valence electrons, which occupy metal-ligand bonding orbitals."

"One referee pointed out that the relative contribution of the a_2u orbital in La(CO)₈ is twice as high as in the lighter homologues, which might be due to some mixing of the 4f orbitals of lanthanum. We checked the AO composition of the HOMO-1 and found that there is a small contribution of the 4f AOs of La, which contribute 8.4% to the MO. However, this is partly due to the polarization of the orbitals rather than genuine 4f orbital contribution to the bonding. The f type polarization functions in Sc(CO)₈ and Y(CO)₈ have a contribution of 1.2% and 2.0% to the respective a_2u orbital. Note that the a_2u MO of the naked cage in La(CO)₈ is also more strongly stabilize than in the lighter systems. Thus it appears that the 4f orbitals have a negligible contribution to the metal-CO bonding in La(CO)₈."

Comment: 4f involvement in La is not genuine 4f orbital involvement. Sandbh (talk) 09:11, 26 February 2020 (UTC)

"Octacarbonyl Anion Complexes of the Late Lanthanides Ln(CO)8^- (Ln=Tm, Yb, Lu) and the 32-Electron Rule", here.

"The metal f orbitals play a very minor role in the bonding [3–4%]. The electronic structure of all three lanthanide complexes obeys the 32-electron rule if only those electrons that occupy the valence orbitals of the metal are considered."

"For An and Ln with the f orbitals being chemically accessible, the valence shell of the metals requires 32 electrons to obtain the s²p⁶d¹⁰f¹⁴ noble-gas configuration.[1] Although a series of intermetallic cluster compounds such as An@Pb₁₂ (An=Pu, Am⁺) and An or Ln encapsulated fullerene clusters have been classified as 32-electron systems,[8, 9] no An and Ln metal–carbonyl complexes have been reported that satisfy the 32-electron principle."

"The 4f orbitals of the Ln have a strongly contracted radial distribution and thus, their contribution to the bonding interactions appears negligibly small. Except for some oxides and fluorides of the light Ln, in which the 4f orbitals were suggested to engage in orbital interactions,[18] their effect on covalent bonding appears so small that the 4f functions of the heavier Ln can be considered as core orbitals."

"Is the 32-electron rule valid for the complexes Yb(CO)₈ and Lu(CO)₈, which possess 33 and 34 valence electrons, respectively? Inspection of the 2a_2u MO, which is occupied by the additional one and two electrons of Yb(CO)₈ and Lu(CO)₈ respectively, revealed that it is essentially a ligand-based orbital of the carbonyl cage, with negligible contributions from the 4f AOs of the metal. The situation is similar to the transition metal octacarbonyl anions TM(CO)₈ (TM=Sc, Y, La), which were recently reported by us.[24] The molecules formally possess 20 valence electrons, but two electrons occupy a molecular orbital of the carbonyl cage that does not have the correct symmetry to mix with the valence orbitals of the metal."

Comment: It is odd that La shows zero 4f bonding participation whereas Lu shows 3–4%. Sandbh (talk) 09:11, 26 February 2020 (UTC)

@Sandbh: I'm laughing out loud :) They use def2-TZVPPD basis for La which hasn't any valence f-functions, only polarization ones, and then conclude that there's no 4f contribution :) They should use at least Stuttgart basis set for Ln instead. Droog Andrey (talk) 09:51, 26 February 2020 (UTC)

@Droog Andrey: I'll add them to the list of authors who are wrong. That's going to be quite a list :) Sandbh (talk) 09:55, 26 February 2020 (UTC)

@Sandbh: You build a list of La arguments, a list of references, a list of authors who are wrong. But could you make a little analysis of what you have built? Do you understand how does a set of basis functions affect the results of computations? Droog Andrey (talk) 10:20, 26 February 2020 (UTC)

@Droog Andrey: I’ll email the authors and ask them about their apparent mistake. Sandbh (talk) 10:25, 26 February 2020 (UTC)

@Sandbh: That would be nice. However, the article is accepted already, so they will scarcely be interested to change anything. I'm running a quick computation to check their results for La(CO)₈⁻. Droog Andrey (talk) 10:49, 26 February 2020 (UTC)

So, there are MOs of La(CO)₈⁻ in order of energy increasing:

1 from La1s: a_1g

1 from La2s: a_1g

3 from La2p: t_1ut_1ut_1u

1 from La3s: a_1g

3 from La3p: t_1ut_1ut_1u

5 from La3d: t_2gt_2gt_2ge_ge_g

8 from O1s: a_2ut_2gt_2gt_2gt_1ut_1ut_1ua_1g

1 from La4s: a_1g

8 from C1s: t_2gt_2gt_2ga_2ua_1gt_1ut_1ut_1u

3 from La4p: t_1ut_1ut_1u

5 from La4d: t_2gt_2gt_2ge_ge_g

1 from La5s: a_1g

8 from O2s: a_1gt_1ut_1ut_1ut_2gt_2gt_2ga_2u

3 from La5p: t_1ut_1ut_1u

8 from C2s: a_1gt_2gt_2gt_2gt_1ut_1ut_1ua_2u

16 from COπ: e_ge_gt_2ut_2ut_2ut_2gt_2gt_2gt_1ut_1ut_1ut_1gt_1gt_1ge_ue_u

8 from COσ: a_1gt_2gt_2gt_2gt_1ut_1ut_1ua_2u

2 from La5d: e_ge_g

(HOMO-LUMO gap)

6 from COπ*: t_2ut_2ut_2ut_1ut_1ut_1u (with La4f contribution)

3 from COπ*: t_2gt_2gt_2g (with La5d contribution)

1 from La6s: a_1g

5 from COπ*: t_1gt_1gt_1ge_ue_u

7 from La4f: t_1ut_1ut_1ut_2ut_2ut_2ua_2u

2 from COπ*: e_ge_g (with La5d contribution)

3 from La5d: t_2gt_2gt_2g

8 from COσ*: t_1ut_1ut_1ua_1gt_2gt_2gt_2ga_2u

3 from La6p: t_1ut_1ut_1u

1 from La7s: a_1g

a2u orbital for La complex

Two bolded a_2u orbitals come from interaction between La4f and COσ. The first of them (see the picture) has less 4f involvement than the second, but both obviously have.

Droog Andrey (talk) 13:38, 26 February 2020 (UTC)

a2u orbital for Y complex

Here is the same orbital for Y complex, look at the difference. Droog Andrey (talk) 05:56, 27 February 2020 (UTC)

@Droog Andrey: Thank you. Are you able to run the same computation for Lu(CO)₈⁻? Sandbh (talk) 12:00, 27 February 2020 (UTC)

@Sandbh: here we are:

a2u orbital for Lu complex

No overlap, no bonding. Droog Andrey (talk) 15:54, 28 February 2020 (UTC)

4f and 5f involvement

@Droog Andrew:@Double sharp: Here's Mingos (1998, pp. 374-375) on this topic. No joy here:

"The participation of the 4f orbitals (for the lanthanides) and the 5f orbitals for the actinides in covalent bond formation is clearly an important issue and it remains a topic which is actively investigated. The previous discussion of transition metals suggested that the 3d orbitals are far more contracted than the 4s and 4p orbitals and consequently they behave in a semi-core-like manner and participate only strongly in covalent bonding when the metallic bond distances are short. The 4f and 5f orbitals, and particularly the former, are even more contracted and are even less available for bonding. The corelike behaviour of the 4f orbitals in lanthanide complexes is supported by the following circumstantial evidence:

1. The lanthanides form extensive series of isostoichiometric compounds and complexes with closely related structural and chemical properties, particularly in the +3 oxidation state.

2. The splittings of the 4f orbitals induced by the ligand field environment are an order of magnitude smaller than those observed for the 3d orbitals in transition metal complexes. The f-f transitions observed in complexes are related to the emission spectra of the corresponding free ions in the gas phase, but are red-shifted indicating a somewhat smaller positive charge in the complex. The f-f transitions in complexes are very weak and sharp indicating only weak d-f orbital mixings occurring during the vibrations of the complex.

3. The lanthanides do not form stable complexes with pi-acceptor and pi donor ligands which indicate that f[pi]-p[pi] multiple bonding is weak.

4. The rates of nucleophilic substitution of the aqua-ions in solution do not show any significant discontinuities as a function of the number of f electrons, i.e. there is no lanthanide equivalent of d3 and d6 (low spin) and d8 inert complexes.

5. The complexes are generally stereochemically non-rigid and there is no equivalent to the EAN (18 electron) rule governing their stoichiometry. This suggests the absence of strongly directional covalent bonds. The increased principal quantum number makes the 5f orbitals less contracted in actinide complexes and their participation in covalent bonding is greater. Specifically, the actinides do form stable complexes with pi-donor ligands and particularly with O2-, and provide some examples of pi-acceptor complexes. Although the role of the 5f orbitals remains energetically ill-defined it is convenient to invoke it to account for some anomalous observations, e.g. the occurrence of cubic coordination in [UF8]3- and the sandwich structures based on cyclooctatetraene ligands."

The same as what I've read elsewhere. Still no smoking 4f gun. Sandbh (talk) 04:41, 27 February 2020 (UTC)

@Sandbh: That's mainly about f-splitting, not about f-involvement. You continue to ignore facts and collect citations without analyzing them :) Droog Andrey (talk) 05:22, 27 February 2020 (UTC)

@Sandbh: I love how he admits that it is at least convenient (recte: necessary, as how else do you explain it?) to invoke f-orbitals to explain cubic complexes. Which lanthanum forms. ;) Double sharp (talk) 07:49, 27 February 2020 (UTC)

@Droog Andrew:@Double sharp: Both of you missed the point. In his 115 page chapter on Transition elements (d block), lanthanides, and actinides (f block elements) this is his only discussion on the question of 4f involvement in the lanthanides. I'd expect that since he took such care to address the question of 4f involvement in covalent bond formation, he would've said something about any other significant kind of 4f involvement in bonding. The fact that he didn't says a lot. Double sharp, your comment is particularly egregious since Mingos' reference to cubic complexes occurred only in the context of 5f orbitals. Sandbh (talk) 21:42, 27 February 2020 (UTC)

@Sandbh: There's nothing egregious about it at all. Mingos is moved to invoke f-participation for cubic complexes of uranium, for good reason since such a shape on symmetry grounds requires the involvement of f-orbitals. Well, lanthanum forms such cubic complexes too, and I linked the paper earlier in the thread. The same argument applies and it doesn't matter that the orbitals are 4f instead of 5f. Double sharp (talk) 21:53, 27 February 2020 (UTC)

@Double sharp: Which paper was that? AFAIK we still only have Parish ruling it out and unconfirmed speculation by MacKay et al. I'd expect it would matter that the orbitals are 4f instead of 5f given the differences in spatial extension. Sandbh (talk) 22:13, 27 February 2020 (UTC)

@Sandbh: La complex with almost perfect cubic structure: you can hardly explain that without 4f orbitals. BTW, as we pass through the Ln series the shape distorts away from that until it gets to a slightly distorted square antiprism for Lu, which clearly requires no 4f involvement as Ta and Xe show it too. ^_^ Double sharp (talk) 22:22, 27 February 2020 (UTC)

@Double sharp: In that article, the key passage is, "These structural studies are of special interest, since, to date, only a very small number of crystallographic data describing monomeric lanthanide complexes with coordination number 8 in which the coordination polyhedron is a cube have appeared in the literature." For any possible 4f participation we need a CN of 9+.

This passage was interesting too, "It is worth noting that the cube is a rare coordination polyhedron for lanthanide ions. It has been observed mainly for complexes with unidentate ligands such as in La(pyridine-N-oxide)8(ClO4)3.[12]" Ref 12 adds nothing. Sandbh (talk) 23:22, 27 February 2020 (UTC)

@Sandbh: That's wrong, 4f participation must be invoked for the cube even with CN = 8 on symmetry grounds. Parish in what you quote him as saying understood this: "to obtain eight bonding orbitals directed towards the corners of a cube (as in C602) requires at least one f-orbital". Note that the almost perfect cubic complexes mentioned are for La and Ce, as expected since these are the ones with the highest-energy 4f orbitals that are more than just a "reserve area". So it seems that La actually has one of the biggest direct 4f involvements of all the Ln. ^_^ Double sharp (talk) 23:59, 27 February 2020 (UTC)

@Double sharp:

"It has been well-established that the 4f electrons of the lanthanides are localized and not chemically active in molecular bonding.[4][9]" From here (2003). Rather emphatic! Sandbh (talk) 04:41, 28 February 2020 (UTC)

@Double sharp:@Droog Andrey: This is a 2016 lanthanide paper Gschneidner was working on just before his death. It's surprising that he spends quite a bit of time on 4f hybridization, yet he limits himself to physical properties i.e. crystal structure sequence; melting points; and solid-solution behavior; and has nothing to say about chemical properties. Most curious. Sandbh (talk) 23:23, 28 February 2020 (UTC)

La 4f orbital involvement

@Double sharp:@Droog Andrey: Here's what looks to be quite a good semi-smoking La gun candidate:

"The 4f orbitals are marginally populated—except for the quartet La(N₂)₈, where the spatial arrangement of the N₂ ligands may require a pronounced hybridisation."

"The La valence orbital populations indicate considerable non-bonding 6s populations in La(N₂), which is decreased in the larger complexes. Parallel, the 5d populations increase somewhat in the larger complexes, though they remain below the end-on ones mostly by ca. 0.4 e. On the other hand, the 4f orbitals are more populated (up to 0.2 e) in the side-on complexes than in the end-on ones. This implies a slight hybridisation between the La 5d and 4f orbitals in the side-on structures."

Kovács A 2018, "Coordination of N₂ ligands to lanthanum: the complexes La(N₂)_1–8. Struct Chem 29, 1825–1837

Sandbh (talk) 00:54, 1 March 2020 (UTC)

The above comes with one caveat: "In general, coordinatively unsaturated metal dinitrogen complexes of metals have low stability and thus can be synthesised, isolated and studied only under extreme conditions." Sandbh (talk) 00:57, 1 March 2020 (UTC)

@Sandbh: So, just like Pr(V), then, which you've been accepting as relevant for this thread in the past. Consistency demands a Lu table. ;) Double sharp (talk) 10:50, 1 March 2020 (UTC)

La2(SO4)3.9H2O

@Double sharp: This article records a hexagonal, rather than cubic structure (p. 602).

@Sandbh: So? No one is saying that La only forms cubic complexes. Just that it does form some. Double sharp (talk) 00:00, 28 February 2020 (UTC)

@Double sharp: I was thinking of MacKay's reference to "a regular cube". AFAIK all of the "cubic" examples we've talked about have been distorted. Sandbh (talk) 03:23, 28 February 2020 (UTC)

@Sandbh: The one I mentioned above for La and Ce is almost perfectly cubical. Double sharp (talk) 11:49, 28 February 2020 (UTC)

@Double sharp: The space group involved is orthorhombic rather than cubic. The authors say, "It is worth noting that the cube is a rare coordination polyhedron for lanthanide ions. It has been observed mainly for complexes with unidentate ligands such as in La(pyridine-Noxide)₈(ClO₄)₃.[12] That citation says, "The co-ordination polyhedron in the eight-co-ordinate complex cation La(C₅H₅NO)₈³⁺ closely approximates D4 symmetry and exhibits large deviations from the geometry of the square antiprism, towards that of the cube." i.e. still not a regular cube. The article itself says, in part, "It now appears that the cube might be a common stereochemistry for discrete eight-co-ordinate complexes of the actinide elements, in contrast to the transition elements where the square antiprism (D4d) and the dodecahedron (D2d) 3 (or their intermediates) are judged to be the preferred polyhedra." Sandbh (talk) 23:42, 28 February 2020 (UTC)

@Sandbh: As this is a one-liner, I will answer: here's what you don't quote on La(bpyO2)4(ClO4)3. "The distortion of angles transforms a cube to a dodecahedron and a square antiprism. This corresponds to a point symmetry change from Oh [emphasis and link mine] → D2d → D4d. A pathway from the Dod to the SAP exists through an intermediate structure with D2 symmetry.23 For the largest ion, i.e. La3+, the steric crowding is less than that for the other lanthanides. The lanthanum ion is located on a two-fold axis and crystallizes in the Pbcn space group.11 In this structure, the angles between the planes of the rings are almost identical for the four ligands (mean value equals 61.4°), and the La–O distances are also very similar (2.495–2.512 Å). These factors make possible the creation of a coordination polyhedron with high symmetry (slightly distorted cube) with a mean value of θ equal to 56.1°.". Double sharp (talk) 23:56, 28 February 2020 (UTC)

Broken symmetry

@Double sharp:@Droog Andrey: Here’s a beautiful and illustrative quote:

'…nothing makes me more optimistic than the discovery of broken symmetries. In the seventh book of the Republic, Plato describes prisoners who are chained in a cave and can see only shadows that things outside cast on the cave wall. When released from the cave at ﬁrst their eyes hurt, and for a while they think that the shadows they saw in the cave are more real than the objects they now see. But eventually their vision clears, and they can understand how beautiful the real world is. We are in such a cave, imprisoned by the limitations on the sorts of experiments we can do. In particular, we can study matter only at relatively low temperatures, where symmetries are likely to be spontaneously broken, so that nature does not appear very simple or uniﬁed. We have not been able to get out of this cave, but by looking long and hard at the shadows on the cave wall, we can at least make out the shapes of symmetries, which though broken, are exact principles governing all phenomena, expressions of the beauty of the world outside.
— Steven Weinberg, ‘Conceptual foundations of the unified theory of weak and electromagnetic interactions’, Nobel Lecture, December 8th, 1979

The La table represents the broken symmetry version of the idealised form of periodicity seen in, for example, the n+l rule, Janet's left-step periodic table, and ADOMAH.

@Sandbh: The only little problem is that the symmetry break only appears when you don't look at the full story. Looking holistically at the whole chemistry world the symmetry is restored with 4f valence involvement in La. And smooth trends from group 1 to group 2 to group 3 to group 4 to group 5. And smooth transitions between bonds with more ionic, more covalent, and more metallic character all according to Fajans' rules. Not a single one of the catastrophes you cite in favour of splitting group 3 from group 4 persists across the whole of chemistry. Double sharp (talk) 21:31, 3 March 2020 (UTC)

@Double sharp: Chemistry is not about restoring symmetry. The peripheral involvement of 4f in La is like using a toothpick to leverage the world. Sandbh (talk) 01:11, 4 March 2020 (UTC)

@Sandbh: Unfortunately for your argument, the chemistry shows the symmetry that the ground-state configurations lack. Just look at the trends down Sc-Y-Lu (more congruent with the rest of the d-block, and avoiding an asymmetric d-block split that never exists anywhere else). Or the trends down Lu-Hf-Ta-W-Re-Os-Ir-Pt-Au-Hg, much more congruent than with La. And all that thanks to noting the 4f involvement of La, which with Ce is more direct than any other lanthanide's 4f involvement. Especially Lu which lacks any significant 4f involvement at all. ;) Double sharp (talk) 11:49, 4 March 2020 (UTC)

@Double sharp: Here’s a nice Soviet era quote about the delayed start of filling of the 4f and 5f sub-shells:

"In La, the usual order of filling of the electron shell occurs, and a 5d electron is added in the fifth shell. Beginning with Ce, the analogy with the 4th and 5th period is disturbed; the electrons begin to fill the deeper-lying 4th shell." [Italics by me]

— Savitskii et al. 1962, Rare earth alloys. Academy of Sciences, Moscow, p. 12

This description is congruent with a transition from the idealised Platonic Lu form to the broken symmetry of the La form. Sandbh (talk) 05:29, 10 March 2020 (UTC) Sandbh (talk) 05:29, 10 March 2020 (UTC)

@Sandbh: Calling La a manifestation of the "usual order" is a misunderstanding. A true analogy with the earlier periods would be for a new subshell to enter after an even-numbered s subshell: 1s; 2s 2p; 3s 3p; 4s 3d 4p; 5s 4d 5p; 6s 4f 5d 6p; 7s 5f 6d 7p; 8s 5g 6f 7d 8p, just as the Madelung rule ordered. So it is actually the La table that is a disturbance (one 5d, fourteen 4f, nine 5d) from the usual pattern of the Lu table. Not to mention a disturbance for no reason, given significant 4f involvement in La as has been demonstrated here ad nauseum, a total lack of valence 4f character in Lu, and trends across blocks, groups, and periods that are universally more regular and more logical from the table if Lu and Lr are placed in group 3. Double sharp (talk) 12:11, 10 March 2020 (UTC)

The transition from 4f to 5d elements

@Double sharp:@Droog Andrey:@R8R: New article, here:

"This paper analyzes the trends in atomic size, coordination number, and relative abundance of metal–oxygen bonds throughout the 6th row of the periodic table, as deduced from the structural data in the CSD. Special emphasis is given to the transition from Ba to the lanthanide series, and from these to the 5d metals. All the data indicate that Lu is closer than La to the behaviour shown by the 5d metals. Besides, a Lu-containing group 3 gives trends down the group that are similar to those of neighboring transition metal groups." Sandbh (talk) 05:16, 28 February 2020 (UTC)

+1 Double sharp (talk) 11:48, 28 February 2020 (UTC)

Triple triad

I happened to notice that with La in group 3, Y forms the central element of a unique triple triad:

Vertical = 21 +57 = 78/2 = 39 Y

Horizontal maximum oxidation state (MOS) = Ca(+2)...Y(+3)...Ti(+4)

Isodiagonal = Ca-Y-Ce

Not forgetting the trifurcate form of the Y symbol for yttrium!

@Sandbh: Exactly how is this science? Double sharp (talk) 15:13, 3 March 2020 (UTC)

Li-Mg-Sc and Si-As-Te also form triple triads, but only Y forms a MOS triad of the form seen consistently up to at least Z = 100.

Very cool. Sandbh (talk) 04:03, 3 March 2020 (UTC)

@Sandbh: Exactly what does the first one have to do with real chemistry? The second and third have been critiqued already. And exactly why would this be decisive when, as you point out, this would never occur anywhere else in the table anyway? (Whereas a Lu table, of course, anchors deep-seated regularities that actually mean something for real chemistry and actually permeate the rest of the table.) Double sharp (talk) 15:13, 3 March 2020 (UTC)

@Double sharp: It's not decisive. It's one of many factors. As you know, DIM used horizontal and vertical triads, too. If regularity has any relevance then we can see that:

An Lu table has:

34 vertical triads
7 horizontal +2+3+4 maximum oxidation state (MOS) triads, up to at least Z = 100
2 isodiagonal triads

43 total triads of interest (TTI)

An La table has:

the same number of vertical triads
9 such horizontal +2+3+4 MOS triads
3 isodiagonal triads

46 TTI.

In this context then, an La table is more regular than an Lu table. Sandbh (talk) 05:21, 5 March 2020 (UTC)

@Sandbh: Neither the MOS nor the isodiagonal triads are actually fundamental. Looking only at the really fundamental vertical and horizontal triads, naturally both the La and Lu tables look equally good, as Sc-Y-La is still a good piece of secondary periodicity. You need to go further to global rather than local 3-element-only regularities to see why Sc-Y-La breaks regularity if elevated to more than that. Double sharp (talk) 07:58, 5 March 2020 (UTC)

In fact: you are collecting peripheral factors like the Modern Major-General, and not analysing how they fit together, what is driving them, and if they are even true. See my earlier analysis of your 12 points. Double sharp (talk) 09:58, 14 March 2020 (UTC)

Group 2 as TM, not?

@Double sharp: We've spoken about this. My search fu not withstanding I haven't been able to track down how this concluded. Specifically, you refer to La as an f metal on the basis of its 4f sub-shell involvement; by this standard, why then are the heavier congeners of Ca not counted as d-metals? Sandbh (talk) 06:03, 5 March 2020 (UTC)

@Sandbh: Because I recognise that the s-block is a special exception because of the preemptive filling of its characteristic orbital. Otherwise there are no s-elements outside H and He, because already Li and Be are using the 2p orbital as well. It is all explained at my page. Whereas, we can see from the facts of chemistry that we are not in this situation at La and Ac. Double sharp (talk) 07:49, 5 March 2020 (UTC)

Most important orbitals in a chemical sense

@Double sharp: This table, as inspired by your table of chemically active subshells, sets out my thinking:

  ----------------Group -----------------               
P 1-2 | 3 | f-block | 4-11 |  12  | 13-18
1  s  |   |         |      |      |  
2  s  |   |         |      |      |   p
3  s  |   |         |      |      |   p
4  s  | d |         |  d   | s    |  p(d)
5  s  | d |         |  d   | s    |   p
6  s  | d |   fd    | d(f) | s(f) |  p(f)
7  s  | d |   fd    |  d   | s    |   p

(d) = knock-on impact of scandide contraction
(f) = knock-on impact of lanthanide contraction

One difference is that I focus on the most important orbitals, whereas you focus on all chemically active sub-shells.

At this high level of classification the most important orbital in a chemical sense is more important than all chemically active sub-shells. Sandbh (talk) 00:24, 7 March 2020 (UTC)

@Sandbh: Except that that's far too simple to be simple, since everyone knows that both s and p are both very important for the p-elements (whence the octet rule). Hybridisation is a common thing everywhere! Not to mention that Lu and Lr don't have any significant f involvement, so that if this was done somewhat more properly it would still support La in the f-block as having more valence f involvement than Lu. So once again we are in Arlou's imaginary country where there is one of everything, never mind "vague rumours circulating to the effect that not everything had always been quite so perfect in the country". These vague rumours being, of course, the facts of chemistry everywhere on the table.

And I guess I should also note that getting rid of the non-characteristic subshells destroys the ability to pull out the duet, octet, 18-, and 32-electron rules from it and significantly weakens the predictive power of the theory. ;) Double sharp (talk) 00:58, 7 March 2020 (UTC)

@Double sharp: Well, here's the short version. (1) The primary ordering principle is Z. (2) The secondary ordering principle is the most important orbital in a chemical sense.

It can be elaborated along any of the lines you have suggested or the 10–12 primary arguments I set out before.

I'm astonished the whole thing can be set out in just 20 words. Philosophically, for a chemical table, this is the cat's pyjamas. Sandbh (talk) 03:11, 7 March 2020 (UTC)

@Sandbh: You haven't addressed the problem I raised that (1) there is almost always not a single one, which is why the p-elements form sp octets instead of p sextets; and (2) Lu and Lr do not have f as a chemically important orbital. Double sharp (talk) 12:42, 7 March 2020 (UTC)

@Double sharp:

For (1) I feel this doesn't matter since the criterion is the "most important orbital in a chemical sense". If required, one can always elaborate the details, as you've done.

@Sandbh: It matters exactly because it reveals that the criterion you picked is chemically not sensible. There is no single most important orbital in a chemical sense, multiple ones are always active and happily hybridising with each other for everybody but H and He. Double sharp (talk) 13:26, 8 March 2020 (UTC)

@Double sharp: I'm unable to reconcile what you're saying here with the observation that, for example, the d orbitals are the most important for groups 4-11. Sandbh (talk) 23:30, 8 March 2020 (UTC)

@Sandbh: It's common knowledge that sd hybridisation is important for the transition metals, that's how the molecular geometries come about (see VSEPR theory#Transition metal molecules), and how we have an 18-electron rule rather than a 10-electron rule. OK, some people think the p-orbital contribution is weak enough to make it a 12-electron rule, but even then everyone agrees s orbitals are just as important as d orbitals in the transition metals. So there's no need to reconcile the two statements: mine is correct, yours is simply not. Double sharp (talk) 14:55, 9 March 2020 (UTC)

@Double sharp: sd hybridisation wouldn't occur in the first place but for the d orbitals. And, as you know, it is the d electrons that give rise to the characteristic transition metals properties of groups 4-11. Further, as you convinced me, irregularities in electron configurations among the transition metals don't matter hardly anything; the transition metals proper are largely more effectively treated as having as many d electrons as their group number (according to my reading of the subject matter). Sandbh (talk) 23:42, 9 March 2020 (UTC)

@Sandbh: You should rather consider them as at least (ds)ⁿ and probably even (dsp)ⁿ like I do, where n is the group number to allow for sd hybridisation. Yes, sometimes dⁿs⁰ is the important configuration, other times it might be some weird fractional hybridisation or linear combination of configurations. (And I wonder where group 11 is in your approach?) The important thing is when some d electrons are left to show transition properties, but they can shift around, it is no problem. Double sharp (talk) 23:53, 9 March 2020 (UTC)

@Double sharp: I don't feel I need to since I already know from reading the literature that the d contribution is predominant. For group 11, Ag may warrant a footnote re the importance of the s orbital. Nice call. Sandbh (talk) 05:40, 10 March 2020 (UTC)

@Sandbh: The only reason the d contribution is predominant is because the d subshell can hold more electrons. sd hybridisation is absolutely normal and reveals the need to consider the s electrons on an equal footing, just the same as sp hybridisation in the p elements. This is totally standard in the literature, which why the d-element rule is always stated as an 18-electron rule and not a 10-electron rule. Meanwhile, you misunderstand my point about group 11: you can hardly consider that to be pure dⁿs⁰ as a d subshell cannot fit eleven electrons. Double sharp (talk) 12:13, 10 March 2020 (UTC)

On (2) I'd say the chemical properties of Lu and Lr don't arise in the first place, but for the progressive occupation of the 4f and 5d sub-shells seen in the condensed ionic forms of the Ln and An. The causa est existentium in other words, for the Ln and An. In the case of the Ln, while 4f electrons rarely participate in bonding interactions they are the main cause of the f-block contraction running from the Ce to Lu, and give rise to a uniform and characteristic +3 oxidation state. The knock-on impact of the contraction is such that the following period 6 d(f) metals have sizes and properties very much similar to their period 5 counterparts.

@Sandbh: This is irrelevant. The important thing is whether the orbitals are being used in chemically normal environments, not just condensed-phase configurations. Not to mention that the divalent-trivalent change will as usual be possible for Yb but not Lu. What we see instead is:

La: direct valence 4f involvement in compounds, clearly start of f block
Ce: same as La
Pr-Yb: at least, 4f is mostly being used as a reserve area with electrons coming in and out of it to be ionised
Lu: 4f is a core subshell. Only 5d and 6s are doing anything chemically. The 4f addition does make Lu more similar to Y, but this is exactly like every other 5d element and eliminates a glaring anomaly.
Hf-Hg: same as Lu

Therefore we see that progressive occupation of 4f coincides with the fourteen elements La through Yb that do something for the chemistry, and it is quite an accident that properties conspire to create a uniform +3 oxidation state. Indeed, just like in the An, as we approach a fully filled configuration, 4f becomes more reluctant to ionise and +2 becomes more important, showing again that Lu is different from Yb. There is, in fact, no qualitative difference between Lu and Hf-Hg here. All ten are d elements whose only f involvement is a knock-on impact of the 4f contraction from La to Yb. The only argument you have is that Lu is traditionally termed a lanthanide, but this if anything is an excellent argument that it shouldn't be as it chemically starts the next series. With Lr it is even clearer. Double sharp (talk) 13:26, 8 March 2020 (UTC)

@Double sharp: As I wrote, I was referring to the "condensed ionic forms" of the Ln and An i.e. in chemically bonded environments. As you know:

4f involvement in La is peripheral, at best, and could hardly be considered to represent the most important orbital, which is d;
the 4f contraction described by Goldschmidt runs from Ce³⁺ to Lu³⁺;
the knock-on impact starts at Hf(IV).

@Sandbh: Wrong. In chemically bonded environments we can clearly see that 4f is active in La in many complexes, whereas it is not at all for Lu. A criterion that got rid of that would presumably ignore f involvement totally in Pr through Yb as well, since there it is more or less a "reserve area", so apparently there is only one 4f element. Not to mention that even if you want to discount 4f involvement in La, your table is still wrong when it attributes 4f involvement to Lu, and you should instead be concluding that at the very least your criterion cannot conclude this because you have not drilled down deep enough. Lu is not part of the 4f contraction any more than Ga is part of the 3d one; it is part of the knock-on impact, as demonstrated on this page ad nauseum. But no matter what we bring out to demonstrate the truth of this, you never take it into consideration. Instead all we hear is a repetition of this wrong statement from which we will never get anything useful out of. Double sharp (talk) 14:55, 9 March 2020 (UTC)

Simply put:

Lu = [Xe] 4f¹⁴ 5d¹ 6s², has three electrons outside a stable [Xe] 4f¹⁴ core, almost always uses all three to form a stable Lu^III oxidation state, with similar radius and position on the acidic-basic continuum to its lighter congener Y^III due to poor shielding by the 4f¹⁴ core electrons. The two (Y and Lu) are almost invariably found together.
Hf = [Xe] 4f¹⁴ 5d² 6s², has four electrons outside a stable [Xe] 4f¹⁴ core, almost always uses all four to form a stable Hf^IV oxidation state, with similar radius and position on the acidic-basic continuum to its lighter congener Zr^IV due to poor shielding by the 4f¹⁴ core electrons. The two (Zr and Hf) are almost invariably found together.
Ta = [Xe] 4f¹⁴ 5d³ 6s², has five electrons outside a stable [Xe] 4f¹⁴ core, almost always uses all five to form a stable Ta^V oxidation state, with similar radius and position on the acidic-basic continuum to its lighter congener Nb^V due to poor shielding by the 4f¹⁴ core electrons. The two (Nb and Ta) are almost invariably found together.

Compare:

La = [Xe] 5d¹ 6s², has three electrons outside a stable [Xe] core, almost always uses all three to form a stable La^III oxidation state, but due to the hard noble gas core is very much larger and more basic than its purported lighter congener Y^III. Indeed they are often not so closely associated as Lu and Y, because the early and late lanthanides separate from each other, and Y patterns as a late lanthanide due to its size. Not to mention that it often uses its 4f orbitals to bond in complexes, which the other 5d elements never do.

So, who is creating a great anomaly within 5d?

Yb = [Xe] 4f¹⁴ 6s², has 4f as a valence orbital, and the core is only [Xe]. Sometimes uses only the 6s electrons, sometimes throws in a 4f one, and is close to the border between divalence and trivalence in the metallic state (but on the divalent side). No clear lighter congener.
Tm = [Xe] 4f¹³ 6s², has 4f as a valence orbital, and the core is only [Xe]. Sometimes uses only the 6s electrons, sometimes throws in a 4f one, and is close to the border between divalence and trivalence in the metallic state (but on the trivalent side). No clear lighter congener.

See the graph for divalent and trivalent metallic states.

So, isn't it absolutely clear that the trend in the Ln is really ending at Yb, and that Lu is something different that patterns totally with Hf through Hg? Double sharp (talk) 15:13, 9 March 2020 (UTC)

@Double sharp: Your assertion that "the early and late lanthanides separate from each other, and Y patterns as a late lanthanide due to its size" is contradicted by the literature (as cited by me) which shows the ambivalent nature of Y.

@Sandbh: The "characteristic behaviour" (a phrase you use a lot) for Y is self-evidently closer to the late lanthanides than the early ones. That is basic chemistry, it's the separation groups that were discovered very early. The exceptions were noted later. Double sharp (talk) 23:50, 9 March 2020 (UTC)

Your assertion that "Lu is not part of the 4f contraction any more than Ga is part of the 3d one; it is part of the knock-on impact, as demonstrated on this page ad nauseum" is incomprehensible. As you know, the 4f contraction starts at Ce³⁺ 4f¹ and concludes at La³⁺ f4¹⁴. As you know, Ga is irrelevant, since it is subject to the knock-on impact of the scandide contraction, rather then being a driver of it.

Your references to Tm and Yb are not relevant. As you know, in their characteristic trivalent forms, Tm is [Xe] 4f¹² and Yb is [Xe]4f¹³. As you know, the lighter congeners of Tm and Yb are Sm [Xe] 4f⁵ and Eu [Xe] 4f⁶.

@Sandbh: That is a completely different way to be a congener. Not to mention that we are at the end of the half- or full-series and therefore, as we see clearly, Sm, Eu, Tm, and Yb show increasing tendencies towards divalence, just look at their compounds and the metals themselves. This interplay is totally expected for the end of a block, tendencies towards +2 happen just as well for 3d, 4d, 5d, and 5f (double periodicity is strongest for the first row, so only for 3d is it also strong for the middle just like 4f). So what I'm saying is the relevant thing, and you are artificially not noticing the elephant in the room: that this interplay does not exist for Lu, which is getting its +3 from somewhere else rather than plucking electrons out of 4f and promoting them. Which is exactly like Ga, which is no longer using 3d electrons. Double sharp (talk) 23:57, 9 March 2020 (UTC)

Loggerheads: contraction per se v knock-on impact

Rather then being at loggerheads about this, why do you believe that Lu is subject to the knock-on impact of the Ln contraction, rather than being the last contributor to the impact? We can see this in the configurations of the trivalent cations, Yb 4f¹³, Lu 4f¹⁴. Here the contraction culminates in Lu with +1 f electron. At Hf the extra electron is +1 d, so rather than continuing the f-block contraction, Hf is instead subject to its influence. An f-block contraction knock-on recipient so to speak. Why is this so hard for you to understand? Sandbh (talk) 23:42, 9 March 2020 (UTC)

@Sandbh: Because, respectfully, it is simply plain wrong according to what I can see from the facts of chemistry. That's why we continue to be at loggerheads over it.

For the umpteenth time: for La, there is clear 4f involvement as demonstrated here over and over. You can't insist on ions because that will never work for delineating anything across the rest of the table. All authorities agree that contractions exist everywhere on it, but if you insist on ions you will never find them because outside 4f there's no characteristic constant oxidation state for everybody. So what you say is totally irrelevant for finding when a contraction starts and ends.

Now: for Lu, the 4f electrons are emphatically not valence electrons, but core electrons. The situation for Lu is exactly the same as that for Ga coming after the end of the 3d block. What we see is that as we reach the end of the series, the characteristic subshell is drowned deeper into the core, so that increasingly we prefer to withdraw only the s-electrons. That's why Tm and Yb start preferring +2, and the actinides are even more up front about it. Just like how Co-Zn prefer +2, same as Pd and Cd, with Ag even more up front and preferring +1 (reminds Md with the possibility). Only when we start the next series do we get up to +3 again. For Ga and In, just like it is for Lu and Lr.

The fact that La begins 4f involvement as valence electrons and Yb ends it is exactly why the Ln contraction must be La-Yb, not La-Lu, not Ce-Lu. Just like the scandide contraction is Sc-Zn. Ions never get into it because with them you can never find the start and end of the scandide contraction. Just like Ga-Kr is the knock-on impact for the 3d contraction, it is Lu-Rn that is the knock-on impact for the 4f one. There's nothing difficult to understand about this. Double sharp (talk) 23:50, 9 March 2020 (UTC)

@Double sharp: La has no 4f valence electrons, as you know. In what possible way can La, with zero 4f electrons, contribute to the Ln contraction? Sc, in contrast, at least has one d valence electron. Sandbh (talk) 06:09, 10 March 2020 (UTC)

@Sandbh: In the exact same way Ac and Th (the latter of which you agree is an f element), with zero 5f electrons in the ground state, contribute to the An contraction: by showing valence f involvement in compounds and in the condensed phase. (I do not have a cite for Ac 5f involvement in the condensed phase being experimentally determined, but Wittig cited below at least predicts it to be like La, which he agrees is an f band metal.) Lu and Lr can do neither and are thus definitely not part of the 4f and 5f contractions respectively. Double sharp (talk) 12:14, 10 March 2020 (UTC)

@Double sharp: Neither La nor Ac show valence f involvement in their trivalent compounds in the sense of having f valence electrons of their own. Lu and Lr each have fourteen f electrons in their trivalent forms, the poor shielding of which contracts the ionic radii; ditto Yb and No which have thirteen f electrons, all the way back to trivalent Ce with 1 f electron; and trivalent Th with 1 f electron. Sandbh (talk) 03:40, 11 March 2020 (UTC)

@Sandbh: Your first statement is simply false: we have already shown that 4f often contributes to the bonding and has a low but real occupation in the condensed phase for La. You again make a fallacious comparison of Lu to Yb, forgetting ths salient difference that for Lu the 4f electrons are core electrons and never participate chemically other than providing incomplete shielding effects. This is nothing like La-Yb and everything like Hf-Hg.

Your criterion also doesn't work at all for the 3d contraction that you admit exists, because there is no constant oxidation state to go for there. So what makes you think it starts at Sc and ends at Zn? Double sharp (talk) 08:00, 11 March 2020 (UTC)

@Double sharp: Well, setting aside (a) the La 0.17 4f hybridisation, and (b) peripheral 4f involvement due to ligand contribution, La has no 4f valence electron of its own; and the 4f contraction is not seen in La³⁺. Perhaps we are at cross- purposes as to the meaning of the term "valence electron"? I can't recall saying the scandide contraction starts at Sc (did I?). The scandide contraction is usually referred to as the contraction seen in Ga onwards, due to having ten 3d electrons, and the difficulty of being able to see it in a constant oxidation state across Sc to Zn. The Ln contraction is unique in that regard.

@Sandbh: Yes, you all but said it. From Archive 42:

“

Another irregularity arises wrt to the boride, scandide, and lanthanide contractions. Each contraction starts with the first appearance of a p, d or f electron at the start of the applicable block. This regularity is not observed in an Lu table.

”

— Sandbh

This statement about the La and Lu tables only makes sense if you consider only ground-state gas-phase configurations (or else, of course, La already has 4f involvement and is the first to have gotten out of the two-element s-block that we know should behave weirdly).

Notice also the double standard. When determining the start of the Ln contraction you want to discuss ions. But you can't do that for the boride and scandide contractions as there is no such thing as a characteristic oxidation state all the elements involved show. If we go by individual characteristic oxidation states, then the scandide contraction cannot start at Sc either, because it is usually Sc³⁺ which is just an [Ar] core, no d electrons in sight. The real trend that you should be looking for is of course something different: when we start the block, at first the newly filling electron shell is above or at least at about the same energy as that of ns, and they all hybridise together happily and we want the group oxidation state. Then later this becomes less favourable and preferred oxidation states go down. But that implies that each block ought to start with preferred +3, which it only does in a Lu table.

@Double sharp: I see, so I did say it. Thank you. So, the knock-on impact (KOI) of the 1s contraction is seen two s electrons later in Li⁺; the KOI of the boride contraction is seen six p electrons later in Na⁺, with its p⁶ core. For the scandide contraction it is seen ten d electrons later in Ga³⁺ and its d¹⁰ core. For the Ln contraction, the KOI is seen fourteen electrons later in Hf (IV). Sandbh (talk) 05:58, 14 March 2020 (UTC)

@Sandbh: And what makes you think so? Because for you it seems to be axiomatic that La and Ac cannot be allowed in the f block despite being in the same boat as Th qualitatively, with no f electron in the ground state but clear f involvement in real chemistry? I see that if you do it the Sc-Y-Lu way, the first element after a contraction is always the first one where the orbital is really inactive (of course 1s He and 2p Ne are active, or else what is populating the antibonding orbitals that keeps them inert, and what is providing IMFs in their liquids and solids?). If you do it your way, f is an anomaly: it's already inactive in Lu and Lr, but your table puts them as f elements. There's nothing different between Lu/Lr and Hf/Rf, so if the latter group is part of a knock-on effect, so is the former. Double sharp (talk) 06:44, 14 March 2020 (UTC)

Referring to the scandide contraction as the smaller size of Ga-Kr relative to Al-Ar is in fact an error. This is a knock-on consequence of the scandide contraction, not the scandide contraction itself. Just like the decrease in radius along the 4f row is the Ln contraction, and the consequence is the 4d-5d similarity (which is, as usual, more regular if Lu is in group 3; then everything is harmonised, because Lu is not filling 4f anymore, and now all ten of the 5d elements show the minuscule radius increase from the corresponding 4d congener). There's absolutely nothing special about the fact that a Ln contraction exists (a contraction exists in every period in every block). Its special status due to the constant +3 oxidation state is in fact a higher-order effect due to many other factors, as Seaborg explicitly said:

“

...the characteristic tripositive oxidation state of the lanthanide elements is not related directly to the number of "valence electrons" outside the 4f subshell, but is the somewhat accidental result of a nearly constant small difference between large energy terms (ionization potentials on the one hand, and hydration and crystal energies on the other) which persists over an interval of fourteen atomic numbers.

”

— Glenn T. Seaborg

@Double sharp: Eh? A "somewhat accidental" result persisting over an interval of not two, not three, not four, but fourteen atomic numbers? Excuse me if I show some scepticism. Sandbh (talk) 05:18, 14 March 2020 (UTC)

@Sandbh: Ah, so authors are allowed to be wrong even if they show a La table, provided they say something you disagree with? ^_-☆

Seriously, there is really one key thing controlling this accident, which is that the slopes of the IE and hydration/crystal energy trends almost coincide over this period. Considering that the almost constant difference is in fact present for fifteen elements (La to Lu), we see that actually it's not so terribly conclusive about the start and end of the f block after all. Double sharp (talk) 06:44, 14 March 2020 (UTC)

So, it seems to be me taking the important and regular table-wide view towards chemically active subshells that exposes the similarities of 4f with other subshells, and you drill down and look at one special coincidence that makes it different. And then you're forced to plead regularity (or rather, symmetry) in order to force 5f into compliance. Meanwhile, I can not only take the big-picture view, but also note the deeper regularity in that such a phenomenon seems to happen when you have a deeply buried subshell lacking radial nodes (thus the closest comparison to 4f seems to be 5g that is knocking on our doorstep three elements from what we now know). Double sharp (talk) 17:17, 13 March 2020 (UTC)

My comparison of Yb and Lu is simply an extract from the series Ce [Xe]4f¹; Pr [Xe]4f²; Nd [Xe]4f³…Yb[Xe]4^f13; Lu [Xe]4^f14. Nothing fallacious there.

@Sandbh: In fact, this is exactly where the fallacies creep in. Your use of ions is a double standard because you cannot apply it anywhere else. And you neglect the vast difference between the valence activity of the 4f shell in Yb vs that in Lu which implies that you are not comparing like with like. And you neglect that such a difference does not exist for La vs Ce, choosing instead to harp on the chemically irrelevant anomalous ground state configuration of La and Ac, and then backpedalling for Th only to make sure your criterion doesn't force it out of the f block as well. Where is the consistency? When is an anomalous ground state configuration irrelevant (Th, Lr) and when is it decisive (La, Ac)? Well, I have consistency: it is always irrelevant, and you have to look holistically instead. And real chemistry as demonstrated here ad nauseum is decisive in favour of Lu under Y. Double sharp (talk) 09:50, 14 March 2020 (UTC)

I further note the mainly 4f-induced Ln contraction largely gives rise to the similarity in the chemistry of the lanthanoids, including Yb and Lu.

The addition of a d electron to Hf results in it having a common oxidation state of +4, unlike the +3 common oxidation state of La and the lanthanoids.

It is not that simple. You have to look at other factors (e.g. ionisation energies, lattice energies) to determine what the stable oxidation states will be. Even for group 2 it is not enough to say that the s² configuration must necessarily mean the +2 state is favoured: you must also draw the energy cycle at least to see that +1 compounds should disproportionate. Otherwise, how come V and Ta are both adding a d-electron from the previous element, but Ta is dominated by +5 and V has a much richer chemistry in lower oxidation states with +4 and +5 about equally common? Double sharp (talk) 17:25, 13 March 2020 (UTC)

In Hf a continuation of the 4f contraction per se is not seen, as the last increase in 4f occupancy is seen in Lu ³⁺. That said the knock-on impact of the contraction is certainly seen in Hf as you have rightly pointed out.

Consider the 4th IE's of the lanthanoids, which show a smooth progression from Ce 3547 to Gd 4250 kJ/mol; and from Tb 3839 to Lu 4370, and here we are mostly discussing breaking into the 4f sub-shell. Meanwhile La stands out as the anomaly at 4819, since it has no 4f sub-shell to break into, and instead has to break into the underlying [Xe] core. The difference in 4th and 3rd IE for the Ln averages 1850, whereas La is nearly 2700, a 45% premium.

Why the fourth IE? Most lanthanides don't go that far unless you force them. The ones that are happy to do it are, guess what, two electrons away from (or at least close to that, Pr gets horseshoes-and-kisses benefits as 4f is still collapsing) a stable configuration with s² and then possibly a happy half- or fully-filled configuration inside, which should by regularity appear just before the block (viz. Ca), at the halfway element (viz. Mn), and at he last element (viz. Zn). This makes perfect sense if you think the 4f analogues for those three are Ba, Eu, and Yb, and doesn't make any sense if you think they are La, Gd, and Lu. Double sharp (talk) 17:25, 13 March 2020 (UTC)

@Double sharp: I was reading an item about Ln and there was some discussion about tetravalency, which prompted me to look at the 4th IE trend. We know about Ce, Pr, Nd, and Tb, Dy; Pm and Sm have 4th IE's <= Dy so they may do it too. Anyway, the trend line rises smoothly from Ce to Gd and from Tb to Lu. La does not fit the trend, nor does Hf. Sandbh (talk) 05:13, 14 March 2020 (UTC)

@Sandbh: It's still shifting the boundaries artificially. Just look at the 2nd IE trend across the table and you'll equally well come to the conclusion that we have to draw the period break between group 1 and group 2. Double sharp (talk) 06:10, 14 March 2020 (UTC)

I think it is reasonable to say that the filled 4f sub-shell impacts every aspect of Lu chemistry given that e.g. it is the least basic of the Ln on account of this, whereas 4f involvement on this scale is not evident in La. Sandbh (talk) 07:21, 12 March 2020 (UTC)

@Sandbh: By any reasonable definition of "valence electron", the 4f electrons of Lu are not valence electrons because they do not contribute to chemical bonding. They only contribute by causing incomplete shielding effects, which is no different from 3d in Ga-Kr or 4f in Hf-Rn, which you agree are core electrons. Whereas we have by now already shown lots and lots of examples of 4f valence involvement of La because hybridisation promotes electrons into there in compounds and in the condensed phase, but you insist on setting them aside. Therefore all comparisons of Yb to Lu are fallacious because they miss the key point that 4f is chemically active in Yb and absolutely not so in Lu. The mere fact that we seem to have added a 4f electron in the +3 state means nothing. If we insist on characteristic ions fallaciously, we can equally well conclude that group 1 are not s elements as they characteristically form ions where the s electrons are lost and therefore cannot have started significant s involvement.

You don't seem to understand that since the circumstances of the 4f contraction are very special, it is illogical to use it as a basis for how we are drawing the table. With such logic we will never be able to find the start of any other block. And that applies to all your arguments based on the +3 state because it is purely thanks to this coincidence that it becomes common. Preferred oxidation states don't just come from ionisation energies but also from lattice energies of the resulting compounds, which is why the alkaline earth metals don't form a +1 state (draw the energy cycle, you'll see +1 salts would disproportionate exothermically). So it seems to be you trying to drill down and make a mountain over a very special coincidence that arises due to a combination of many factors when the problem is already resolved at a higher level: 4f activity is significant in La and totally insignificant in Lu, for which it is a core subshell no different from 4f in Hf through Rn. Double sharp (talk) 08:05, 12 March 2020 (UTC)

@Double sharp: Sandbh (talk) 04:32, 14 March 2020 (UTC)

The start of a block in simply found according to the appearance of the first atomic valence electron, in bold:

Table 1
  s    d   fds  d    (s)   p
  ---------------------------
1 H*   
2 Li                       B†
3 Na                       Al‡
4 K    Sc       Ti   (Zn)  Ga
5 Rb   Y        Zr§  (Cd)  In
6 Cs   La  Ce=  Hf   (Hg)  Tl
7 Fr¶  Ac  Th^  Rf   (Cn)  Nh

*	The 1s sub-shell becomes inaccessible at He
†	The 2s sub-shell becomes inaccessible at O; the 2p sub-shell further becomes inaccessible at Ne
‡	The 3s and 3p sub-shells are inaccessible at Ar
§	While the 5s sub-shell is empty in Pd the 4d sub-shell is accessible
=	The 4f sub-shell is inaccessible at Lu
¶	The 5p sub-shell in Fr may still be accessible
^	The f¹ electron in Th is seen only in the rare (deep blue) trivalent cation; the 5f sub-shell in Lr is inaccessible

Sandbh (talk) 04:30, 14 March 2020 (UTC)

@Sandbh: Notice the same old double standard with thorium, the only element where chemically relevant non-ground-state configurations are permitted to save the theory. Funnily enough, it's not allowed for La and Ac which can equally have f involvement in their compounds. Double sharp (talk) 06:14, 14 March 2020 (UTC)

@Double sharp: The model doesn’t need saving; it works according to its parameters. Sandbh (talk) 10:03, 14 March 2020 (UTC)

@Sandbh: Parameters which are chosen inconsistently. Because the 4f and 5f ground-state collapses occur over slightly different times, a consistent criterion can only produce an f-block starting at La-Ac or one where 4f starts at Ce and 5f at Pa. Neither produces the La table. Double sharp (talk) 12:19, 14 March 2020 (UTC)

* * *

I subscribe to what Double sharp says. I've really been wondering ever since, well, I learned noticed that most periodic tables had La under Y despite this being such an uncharacteristic shift from period 5 to 6 for a transition metal in terms of atomic number, why that is the/a reason if this principle does not apply elsewhere in the periodic table. La has zero 5d electrons in its most common oxidation state; if it is to be put in the d block, then where exactly, based on that? Same question for Hf, which also has zero 5d electrons in its most common oxidation state; same question for Cs and Ba with zero 6s electrons in theirs. Makes little sense to me to say that this finding is of any consequence for block placement in the periodic table to me.

This is not to say that there are no possible valid arguments for putting La and Y, but this one is not one of them.--R8R (talk) 08:04, 13 March 2020 (UTC)

@R8R: Bohr did not find anything uncharacteristic about the shift from period 5 to 6 for a TM. He said the 5d and 6d rows would be interrupted by the filling of the 4f and 5f sub-shells. And nobody worried about it. La with d¹s², representing the first appearance of the 5d¹ electron evidently goes in group 3. Hf with d²s², representing the 4th appearance of a 5d electron, evidently goes in group 4. Cs and Ba with s¹ and s² evidently go in groups 1 and 2. Sandbh (talk) 04:12, 14 March 2020 (UTC)

@Sandbh: Of course he didn't, as he was writing almost a century ago when Ac-U were thought to be d elements based on their preference for higher oxidation states. So it looked like there was already a precedent. At that point I guess it was also probably not well understood that there is more to chemistry than ground state configurations. Now that we know what is really going in the aufbau and the sequence of valence orbitals we can see that there is something very wrong with Sc-Y-La-Ac because the latter two show distinct f involvement and the former two don't. Every other time we pass from 4d to 5d we add a full f shell, and therefore we should do that in group 3 as well and put Lu below Y. It also harmonises better with trends. You have to look at the sequence holistically instead of harping on the ground state anomaly that matters very little for real chemistry. Otherwise thorium is a d element that belongs below Hf by the exact same logic that you use to put La erroneously under Y. Double sharp (talk) 09:35, 14 March 2020 (UTC)

@Double sharp: I encountered this fine passage by Rich (Inorganic reactions in water, 2017):

"In the 5f series some of the distinctively f-subshell chemical behavior arises later, with U, leading to the term “uranoid”, especially for elements 92–95, which, unlike the other “actinoids” in the same period, have six (VI) as an important oxidation state in water. We may refer to the higher-Z actinoids, with III as the more characteristic oxidation state, as “post-uranoids”. Nature is clever in complicating our task by precluding full consistency and simplicity in any periodic chart."

The last sentence is priceless.

There is nothing very wrong with Sc-Y-La-Ac in the sense you are concerned about. What f involvement there is in La-Ac is peripheral, and of no significance to be concerned about. f significance in Lu, OTOH, is a matter of a different order. In the context of Rich, there is no intrinsic basis for arguing that "every other time we pass from 4d to 5d we add a full f shell, and therefore we should do that in group 3 as well and put Lu below Y". OTOH, as you said however, Lu under Y [may] harmonise better with trends. That said, there is more to Th than its ground state anomaly; there is also the question of where the contraction in each block ends, and hence where the next block starts. I'll expand on this in a subsequent post. Sandbh (talk) 02:20, 18 March 2020 (UTC)

@Sandbh: So if Rich claims that uranium is the first element with distinct 5f behaviour, and you believe him, why don't you start the 5f row at U instead of Th? And by those standards, isn't the f-involvement of Th about as "peripheral" as that of La and Ac? And why exactly does Lu still get a free pass from you to allow core f-involvement unlike any other element, just because we humans decided to call it a lanthanide? We made that up, you know. Yttrium displays totally lanthanide-like behaviour as well, so are we going to allow it to magically appear in the f block too despite an equally total lack of 4f involvement? Double sharp (talk) 15:55, 18 March 2020 (UTC)

Nine DS arguments for Lu

@Sandbh: There are two things in your reply I want to reply to.

1) Double sharp is right, and I would say the same if I were to respond to that first, that Bohr also thought that the 5f series begins sometime after uranium. Can we drop the "Bohr thought" argument at that? I also don't know the exact chronology here, but I know that for much of the first half of the 20th century it was considered that most lanthanides were [Xe] 4f^n-1 5d¹ 6s². We know now they are not, maybe that wrong premise also influenced Bohr (but again, I don't know the exact chronology here).

2) I find it rather curious that I disagreed with a certain argument A (on whether or not you can decide on elements' placement in the periodic table based on the electron configurations of their ions in the most characteristic oxidation state), to which you responded that it was okay because the outcome you prefer is supported by a certain argument B (that you can decide on elements' placement in the periodic table based on a certain interpretation of the electron configurations of neutral atoms). My point, however, was that the original argument A was bad, not whether argument B was right or not (that is up for discussion if you want). So can we drop the original argument A, as I suggested?

We could, generally, isolate each argument and try to assess it critically. I have been watching this discussion myself and I think that you sometimes lacked that when it came to your arguments. One example was when you said that it was okay to arrive to a conclusion based on a wrong premise (of electron configurations of the lanthanides) and when the error was pointed out, it was okay because chemistry did not change with that observation. Chemistry indeed did not change, but the conclusion was corrupted by wrong premises, and you have to either drop the notion that there is a conclusion or arrive at a conclusion via different means. Either way, the corrupted argument should not be a part of the story but you make it just that. DS tried to analyze your arguments himself, but I think he didn't get through to you because of his lack of impartiality in a certain sense, because, it appears to me, he is to a certain extent emotionally invested into staying at his conclusion, and that does not exactly help him discuss things when he thinks he's right and you're not. Getting through to someone also requires the ability to be heard, something I really want to train myself. We could also critically assess DS's arguments if you want that. I'm aware of my own biases but I try to have them influence my judgment as little as possible. Generally, I'm more interested that this issue is resolved via proper discussion rather than to the result I'd like to see.--R8R (talk) 13:02, 14 March 2020 (UTC)

@R8R:@Double sharp: The conclusion was that nothing changed about the chemistry Lu. In what sense was this conclusion corrupted? It stands by itself. There is nothing about it that needs to be dropped. What did change was that the f sub-shell was in fact completed at gas phase Yb rather than gas phase Lu. Sandbh (talk) 02:34, 18 March 2020 (UTC)

@Sandbh: Exactly what I say below: if the original placement of Lu and Lr was based on some premises, that we now know to be false, then the demolishing of those premises requires the placement to be reassessed. At the very least you must find a new reason to support Lu and Lr in the f-block, not the old one that has already been demolished. And in fact, correcting those old ones to the truth strongly suggests Lu and Lr in the d-block. Double sharp (talk) 16:36, 18 March 2020 (UTC)

@Sandbh: The conclusion that group 3 is -La-Ac based on the electronic configurations, since the lanthanides mostly had a d electron, that was the conclusion that was corrupted. That argument is not correct and the conclusion is not correct by default. This does not exclude the possibility that you can obtain the same outcome in a different manner, but you must obtain it in a different manner.

I think I understand your logic here: we got a conclusion, got stuck with it for a while, and even though we know that that premise does not hold, it's still a good conclusion, and it's the default now anyway. (To put this in perspective, JINR did not get to rename element 102 because the priority of discovery was originally assigned to a Swedish institute based on wrong results. It was later assigned to JINR but the name nobelium had become entrenched in the literature, so they didn't get to name it even though they were the discoverers. And we're not even in a position like that, since there is hardly enough evidence for -Lu-Lr anyway. Is that a correct description?) However, what I'm saying is that these are separate things: announcing group 3 based on tradition and based on properties. In the very end, the two meet anyway, but not before then, and I don't find myself agreeing with the way you put that story. If you had said instead that by 1950 (?) that form had become the norm without any emphasis to the incorrect argument, the appeal to popular usage would be much more sound as it does not conflate those two different assessments so easily. However, a story that essentially says, "we had a properties-based argument for -La-Ac; yes, it was later shown incorrect but it did not matter because the popular usage got ahold of it even if that once-defining property didn't anymore" seems like an overly wide brushstroke, not very fit for a detailed discussion like the one here. (I imagine here a cowboy that shoots from a pistol, runs out of ammo, drops the pistol, takes out another pistol, and keeps shooting as if nothing had happened. However, a whole lot has changed between those two lines of argumentation.)

(If you ask me, that was a mistake. We had already deleted entrenched names like masurium for technetium per Paneth's criteria, and it doesn't make sense to me that someone who made a mistaken discovery should be allowed to name the element. A transfermium series of mendelevium, joliotium, lawrencium, rutherfordium, hahnium, seaborgium, nielsbohrium, hassium, meitnerium would mean that (0) priority was respected, acknowledging JINR as getting E102, and noting LBNL's rather convincing argumentation to this non-expert for E104 and E105; (1) as much as possible, scientists would be prioritised over locations – if you like, we could reinterpret hassium for Germain Henri Hess of Hess' law instead, as the surname indeed means "from Hesse"; (2) all JINR and LBNL names after scientists would appear somewhere, except for controversial Kurchatov; and (3) we would no longer have this silly problem of borate vs. bohrate. As well, we should have reinstated cassiopeium instead of lutetium, too. But this is purely a matter of nomenclature and is not as serious as the composition of group 3.) Double sharp (talk) 04:36, 20 March 2020 (UTC)

What do you want from this discussion and what do you find most important: do you want to show that first and foremost, properties of the elements point that group 3 should be -La-Ac? do you want to say that there is an established version and there is not enough argumentation to put it down? Please consider the two closely and then consider that those are two different things in nature, and then it is only natural that an attempt to play down the difference between the two that does not find understanding (rather than either of the two, both of which merit a separate discussion).--R8R (talk) 19:54, 18 March 2020 (UTC)

@R8R:@Double sharp: Re: “The conclusion that group 3 is -La-Ac based on the electronic configurations, since the Ln mostly had a d electron, that was the conclusion that was corrupted.” La in group 3 goes back to DIM. The problem then was where to fit in the rare earths. That was sorted out by at least the 1920s. It was subsequently appreciated that group 3 opened the d series in each row. There was no corrupt decision that group 3 had to be La-Ac since they all had d electrons. Rather, the fact they did all have the first d electron at the start of each period appeared to be consistent with the chemistry involved. That’s all. Sandbh (talk) 06:18, 22 March 2020 (UTC)

@Sandbh: But DIM's conclusion is also corrupted because he did not accept that the rare earths could not be accommodated intraperiodically as he would have liked to: it is chemical nonsense to put Pr in group V, Nd in group VI, etc. That is why, even in 1906 when all but Pm and Lu were already known, Mendeleev doggedly continued to put blank after blank between Ce and Yb. There were certainly elements known with intermediate atomic weights by that time between 140.2 and 173, but Mendeleev did not include them because they did not fit his theory! (Which is, showing him the greatest respect, already rather questionable scientifically.) Besides, since he puts not only La but also Yb in group 3 (presumably the news of the discovery of Lu had not reached him; if he knew about it, he may even have put it there because Lu 175 creates a smaller gap to Ta 183), his idea (as corrupted as it is from our perspective) is as close to the Lu table as it is to the La table and is not even conclusive for either.

Another corruption came later when the whole bad idea that the f block are really degenerate members of the d block came around, i.e. all the Ln belonged under Y and therefore La was plucked out as the prototype (fitting in the rare earths). Maybe that was influenced by the idea that all the Ln should be fⁿds², or maybe by how chemistry seemed to imply that Ac through U were simple group IIIB through VIB elements. Now we know better: the f block elements are not degenerate members of the d block (because the f electrons really are involved in chemistry), the Ln are not fⁿds² for the most part, Ac through U are not d elements. Every single one of the premises that could plausibly at that time have led to that conclusion is wrong! And now that we understand better how configurations affect chemistry, it is now also clear that an assertion that Lu and Lr are f elements is totally inconsistent with the chemistry involved (cf. the trend of increased stability of the +2 state reaching f¹⁴, which is nonsense with Lu and Lr in the f block but makes perfect sense if the f block ends at Yb and No!). Therefore the original conclusion must be reexamined, and such a reexamination clearly shows that a Lu table is consistent with the chemistry observed and a La table is not. Double sharp (talk) 06:30, 22 March 2020 (UTC)

@Double sharp: Re: “the Ln are not fⁿds² for the most part.” As we noted in our IUPAC submission they are just that in the condensed form, which is more chemically relevant. Sandbh (talk) 06:47, 22 March 2020 (UTC)

@Sandbh: That's both irrelevant and false. It's irrelevant because it's only one among many chemically relevant configurations. And it's false because actually every single Ln in the condensed phase has p involvement in its condensed-phase configuration, too. The d and p occupancies are usually non-integers, as you would expect from large hybridisation. You can also see there the very different configurations of gas-phase Ln₂ dimers, so at this point one should absolutely expect that Ln atoms in chemical environments will switch between many different possible configurations and you cannot harp on just one and produce anything sensible. Double sharp (talk) 06:50, 22 March 2020 (UTC)

@Double sharp: Does this mean the two sources we included in our IUPAC submission—Johansson and Rosengren (1975, p. 1367); Greenwood and Earnshaw (2002, pp. 1232, 1234)—are wrong? The reference you provided is for the metallic phase in equilibrium with the liquid i.e. an average of 1200°C. Cleary not SATP. Sandbh (talk) 10:09, 22 March 2020 (UTC)

@Sandbh: Greenwood and Earnshaw did not refer to fⁿds² in what you quote them as saying in User:Sandbh/Group 3, but rather referred to "3 electrons in the 5d/6s conduction band", without prejudice to how many are in 5d and how many are in 6s. Yes, it is true that 6p is wrongly neglected here, but at least that is not the major point: the important thing is the shift between configurations that implies plucking electrons out of the f shell. Clearly, Johansson and Rosengren also understood this, because they refer to a "6d7s state" for the actinides. Gschneider in his 1971 paper agrees that all four subshells (4f, 5d, 6s, 6p) "are involved in the metallic bonding of all of the trivalent lanthanides except Lu". Of course it is quite conceivable that the relative occupancy changes with temperature, and therefore one should absolutely expect (as really exists) even bigger changes with the chemical environment; but what will not change is that for La-Yb all of those four will be somehow involved, and for Lu only the last three (just like Hf-Hg). This consistent lack of use of 4f by Lu, coupled with the consistent use of 4f by La, is exactly why placing La in group 3 should be considered a mistake. Double sharp (talk) 12:17, 22 March 2020 (UTC)

P.S. Why are you trying to refer to condensed-phase configurations to save the argument here, when they suggest that Be and Mg are p elements? Double sharp (talk) 07:22, 23 March 2020 (UTC)

@R8R: Thank you for providing the voice of calmness in this discussion! ^_^

Yes, I admit I'm biased. I may not think it, but probably I am to some extent being coloured by the fact that this chemically-active-subshell theory of mine has been formulated originally last year and been thrashed out into something more complete this year. But I like to think that I have some good points that are not being addressed properly. So, here are my Lu arguments simply put forward, hopefully for the kind of critical discussion R8R has in mind:

1. La and Ac have f involvement in the metals and their compounds, whereas and Lu and Lr don't. Therefore it is more chemically and physically natural to put La and Ac in the f block. The s block is the only consistent exception that uses the higher-l subshells across the table, and there doesn't seem to be any special reason why group 3 should follow them. More on this later.

The extent of f involvement in La and Ac is quite marginal, physically and chemically. For La, it is its 2.5 d electrons that give rise to its dhcp crystalline structure. Just like in Th it is its 0.57 f electrons that give rise to its fcc structure. The chemistry of group 3 is predominately that of its group 2 and 1 neighbours. That is a strong reason to place group 3 next to them. Sandbh (talk) 06:29, 18 March 2020 (UTC)

So why exactly are the dhcp lanthanides the ones early in the series up to Pm with the most f involvement, then? Your statement about the chemistry of group 3 has been refuted many times over on this page and in archive 42; in reality there is a smooth continuum from group 2 to 3 to 4 and there is no smoking gun for group 3 skewing only to group 2. Double sharp (talk) 16:36, 18 March 2020 (UTC)

2. The trend across 5d, as well as going from 4d to 5d, is more consistent with Lu and Lr in group 3. These horizontal and vertical ones are the basic trends, everything else is secondary as just a linear combination of them.

The 5d trend is interrupted by the filling of the 4f sub-shell. In this sense, Lu in the f block can be regarded as an incipient d metal. The trend going down group 3, is as expected for the notion of the 4f sub-shell interrupting the filling of the 5d sub-shell. Sandbh (talk) 06:29, 18 March 2020 (UTC)

But how do you know a priori that the 5d trend should be interrupted? La has clear 4f involvement that is only second to Ce among the lanthanides, so in fact it is clearly not interrupted. Double sharp (talk) 16:36, 18 March 2020 (UTC)

3. In fact the similarity of Lu to the lanthanides is a bit suspect from the electronic perspective, because for Lu there isn't any more interplay between 4fⁿ⁺¹ and 4fⁿ configurations. The 4f electrons in Lu are much more like those in Hf through Rn, giving only incomplete shielding effects.

Agree, except that Lu has Ln properties whereas Hf does not. Further, interplay between 4fⁿ⁺¹ and 4fⁿ configurations is not so important as the successive occupancy of the 4f sub-shell in the Ln trivalent cations. Sandbh (talk) 06:29, 18 March 2020 (UTC)

Scandium and yttrium have tons of Ln-like properties, are we going to claim them for the f-block too? Speaking in terms of what electrons are being used for chemistry, Sc, Y, Lu, and Lr form a natural quartet, and La-Yb and Ac-No form a different cluster. Trivalent cations cannot be generalised to the rest of the periodic table and cannot be admitted as evidence for the placement of La. Double sharp (talk) 16:36, 18 March 2020 (UTC)

4. Because of this, the trend in 4f and 5f makes more sense with an f block beginning at La and Ac. Then we naturally drop down to +2 when we reach more stable half-full (Eu) and full (Yb, No) configurations. In a table with the f block beginning at Ce and Th, it doesn't really make sense that Lr as the latest actinide reverses utterly the trend of the late actinides that prefer +2 over +3 increasingly. That should be a warning sign that Lr +3 comes from something else, just like Ga +3 after the 3d elements.

The +3 oxidation states are the more natural in Eu and Yb, being more stable than +2. There is only one late An that prefers +2. There is no +2 trend. For the late An, Cm to Bk, 6 out of 7 prefer +3. There is no warning sign. Sandbh (talk) 06:29, 18 March 2020 (UTC)

You're missing the point, which is that as we reach the end of the block +2 becomes more stable. Tm²⁺ is already significant, Yb²⁺ is even more significant. Starting from Fm²⁺ the An already have aqueous +2 chemistry (they have solid-state +2 chemistry earlier), and indeed, by No²⁺ it is preferred. A trend may be continuous and that the stability of the +2 state may gradually increase; it is not all or nothing. If you plot that, it becomes totally clear that Lu and Lr are not part of the f-block trend. Double sharp (talk) 16:36, 18 March 2020 (UTC)

5. Group 3 naturally is intermediate in all significant trends between groups 2 and 4, and not skewing all one way or the other. Therefore it ought to have a trend that follows group 4 as that one is in the same block. And indeed, the transition tendencies are incipient in both groups: they start later each period, so Nb and Ta in group 5 are in a similar position to Sc in group 3. Splitting group 3 from 4 creates the illusion that the break is bigger than it really is.

Since the trends don't skew, we can take a step back and recall that blocks are characterised by the similarity of their chemistry. We can further see that the chemistry of group 3, in its ionic tendencies, is more like that of groups 2 and 1, than groups 4+. There is no split in the popular 18-column form. Which would've been a major factor in effectively nobody being fussed. Sandbh (talk) 06:29, 18 March 2020 (UTC)

Which is totally false. Ionic vs. covalent has been demolished many times over here, and we have already shown so many examples in which group 3 chemistry is absolutely intermediate between groups 2 and 4. Just look at how Zr and Hf are in a similar position to Sc. Also, the split is right there in the 18-column form in the asterisks between La/Hf and Ac/Rf.

Moreover, blocks are not characterised by similarity of chemistry, but by what subshells the electrons being used for chemistry come from. There is no f-like similarity of chemistry in the p-block, which includes a huge range of electronegativity from moscovium (well, thallium if you insist on elements relevant to the typical chemist only) to neon. And hydrogen and helium, universally acknowledged as s elements even if He is often drawn elsewhere, are extremely different compared to Li-Fr and Be-Ra exactly as first-row anomaly considerations would have us predict. How similar the elements in a block really are to each other is a function of the more fundamental question of what the characteristic subshells are, and is not the fundamental basis for placing elements in the periodic table, which is instead to ask what block is the element in (which we determine from what subshells are being used as valence subshells), and what group is it in within that block (which we determine from how many valence electrons there are). Such a criterion leads immediately to Sc-Y-Lu-Lr, as well as He over Be. Double sharp (talk) 16:36, 18 March 2020 (UTC)

6. If you insist that ground state electrons only are decisive for La and Ac, then Th is put in a difficult position. You cannot consistently say that other configurations are relevant for Th but not for La and Ac. Lr has about the same issue. It's more important to look at all possibly relevant configurations, but then La and Ac are in the same position as Th. Whereas, Lu and Lr never show any chemically significant f involvement and are totally different from Yb and No in this respect, but perfectly similar to Hf-Hg and Rf-Cn.

Pending. Sandbh (talk) 06:29, 18 March 2020 (UTC)

7. In fact, Lu and Lr are not analogous at all to group 12, because the Zn group actually does use its d electrons to strengthen the bonding in some compounds, and the Lu group does not.

d electron involvement in Zn is marginal. The analogy between Lu and Zn is that their gas phase configurations are an outcome of the 3d and 4f races to get to the filled sub-shell configuration. Looking at the ionic configurations shows a good analogy: Zn⁺² d10; Lu +3; f¹⁴. In a similar manner the impact of the scandide contraction starts at Ga; and the impact of the Ln contraction starts at Hf, with its well known nearly-impossible-to-separate resemblance to Hf. Sandbh (talk) 06:29, 18 March 2020 (UTC)

And why are we plucking out different oxidation states for 3d and 4f? You're not comparing like with like. In the Ln you can pluck out a characteristic oxidation state. You can do that exactly nowhere else. And Lu is equally hard to separate from Y as Hf is from Zr, even setting aside the fact that we have even more chemical twins of Lu over there. Double sharp (talk) 16:36, 18 March 2020 (UTC)

8. Equally, it's dangerous to refer to the special constant +3 state of the Ln contraction. This is actually something that is explained at a higher order from lattice energies etc, and is not fundamental enough to base our PT drawing on. Especially since it is literally a one-off phenomenon within the bounds of our current experimental knowledge: no other contraction but the predicted 5g shows this.

There is nothing dangerous about it; in the same way that DIM based his PT on oxidation number patterns, and that valence patterns are still regarded as an important aspect of periodicity. The An contraction is similar to the Ln contraction; the An have a common oxidation state of +3, although this is not the most stable oxidation state for all of them. Sandbh (talk) 06:29, 18 March 2020 (UTC)

But they are not the driving factor. Preferred oxidation states are rather a tertiary outcome of many secondary factors (ionisation energy, lattice energy, etc.), not just electronic structure, which is the real driving factor that is informing how we draw our modern PT. When they differ, of course, it can be a symptom of some primary factor as it is for a clear-cut case such as Fm-Md-No-Lr. Meanwhile, your preferred ionicity/covalency is even a quaternary factor that itself depends on preferred oxidation states per Fajans' rules...

I could equally well note that according to oxidation state every element (except for noble gases) from H to Ba has a +1 oxidation state. The fact that for most of them it has about zero chemical relevance can be swept under the rug just like you do whenever you parade Th³⁺ as a shining example of 5f involvement. Never mind that reports of aqueous Th³⁺ were already debunked in 2006 by Wickleder et al., see compounds of thorium: "In 1997, reports of amber Th³⁺ (aq) being generated from thorium tetrachloride and ammonia were published: the ion was supposedly stable for about an hour before it was oxidised by water. However, the reaction was shown the next year to be thermodynamically impossible and the more likely explanation for the signals was azido-chloro complexes of thorium(IV)." Don't get me wrong, thorium definitely has 5f involvement, but pointing to the +3 state is not a good argument for it as it is so rare and unstable. Analogously, pointing to Ir(IX) is not a good argument for changing all the chemistry textbooks to note that the rise in maximum oxidation state in the 5d row lasts longer than in the 4d one, because it is literally a one-off that no one has ever seen in a solid-phase compound. Double sharp (talk) 16:36, 18 March 2020 (UTC)

9. The fact that Sc-Y-La is historically the more common form does not mean it is right. Some decades ago the same could have been said about Be-Mg-Zn. In both cases the chemistry has not changed but we have learnt a more effective and consistent way to organise it. Double sharp (talk) 13:55, 14 March 2020 (UTC)

I agree. That said, if you're going to upturn the establishment you have to have pretty convincing and compelling evidence. The challenge involved becomes massively exacerbated by the multiple chemistry-based arguments that can be made in support of La under Y. Sandbh (talk) 06:29, 18 March 2020 (UTC)

Every single one of those chemistry-based arguments is based on wrong assumptions about the behaviour of group 3. The most compelling evidence comes from clear valence f-involvement in La and Ac, which is of the same kind as that of the universally acknowledged f element Th, and the concomitant improvement in trend regularity that results from a Sc-Y-Lu-Lr group 3 and La and Ac in the f block. Not to mention how it is the only way the oxidation state trend at the end of the 4f and 5f series is ever going to make any sense. Double sharp (talk) 16:36, 18 March 2020 (UTC)

@R8R: If you have the time, since I have given my nine arguments, Sandbh has responded to eight of them, and I have given rebuttals, your appearance as a calm referee would be much appreciated! ^_^ Double sharp (talk) 16:40, 18 March 2020 (UTC)

@Double sharp: well, you see, I have my doubts about whether I could be a referee. I think all three of us could agree that I am less proficient in chemistry than either of you two :) I could hope, however, that it is my judgment of the existing arguments and the argumentation behind the said judgment that could make a difference but then again, for an arbitration you need both parties to agree to hand the issue over to someone else (even if in this case, any judgment can only be advisory and have no real consequences). I have not seen Sandbh want me to be a referee over him, and I wouldn't want to do that without him asking me to do so; I even joined the discussion originally in response to his call for more opinions on his article, rather than anything else. That being said, if Sandbh does want me to be anything like a referee or even at least a third opinion in this debate, I'll try my best to be cold-minded and unbiased here. However, I could see why he would not, and that would be fine by me (my luck of authority is notable; it could also not have escaped his attention that generally I've questioned his position more often than yours here, even though the reason here is that I originally came here in response to his call for more opinions and I was concerned about his article). To sum it up, I will not press the issue myself, though I'll be ready to help if asked to.--R8R (talk) 20:31, 18 March 2020 (UTC)

Bohr

@Sandbh: BTW, I realise R8R would like us to drop the argument of referring to Bohr, but I realise I forgot to say one little thing. If you think Bohr is a good argument here, why then do you depart from gas-phase configurations once specially for Th to make sure each block starts symmetrically in a vertical column? Bohr had no problem allowing the possibility that 4f and 5f did not start together. Neither did Victor Goldschmidt, for that matter. This is why I keep feeling that thorium is one of those cases that exposes an inconsistency in your logic. Double sharp (talk) 15:22, 14 March 2020 (UTC)

@Sandbh: I simply referred to Bohr in the context of R8R saying, "I learned noticed that most periodic tables had La under Y despite this being such an uncharacteristic shift from period 5 to 6 for a transition metal in terms of atomic number, why that is the/a reason if this principle does not apply elsewhere in the periodic table?". In response I said, "Bohr did not find anything uncharacteristic about the shift from period 5 to 6 for a TM." Nor was, effectively, anybody else fussed about it. That's all. Bohr was guessing about 5f, in the same way that we've been guessing about 5g. I don't place any special significance on that guess, given what was known at that time. Where did Goldschmidt consider 6f to start? Pa?

@Sandbh: That's exactly the problem. OK, so Bohr thought that 4f started at Ce. I haven't read his original article, but there are some plausible reasons why he might have done so. He might have looked at the general trivalence of the Ln and assumed they must have been 4f^n-15d¹6s² mostly, since at that time probably the ground-state configuration was given more importance than we now know it really has. He might certainly also have been swayed by the fact that Ac-U seemed to be filling a d subshell based on their higher oxidation states (well, if you only know the 4f row, it makes sense because you'd think that such deeply buried orbitals must always be essentially doing nothing!). (Though this is equivocal since he also seems to have posited 5f electrons for uranium at some point. We know from Seaborg that Bohr at one point suggested that 5f should begin at element 94, so evidently he changed his guess several times.) So he may have been led to his conclusion that way. Then now we know that actually the trivalence of the Ln has almost nothing to do with their ground-state configuration, that the ground-state configuration of the Ln is mostly instead 4fⁿ6s², that Ac-U are not filling a d subshell, so that every single one of those plausible premises is wrong. Therefore we have to reexamine the conclusion that they originally led to. Maybe something else justifies it. Maybe those were the only good arguments for it, in which case we should abandon that conclusion. But only for you does none of this corrupt the original conclusion. If the original placement of Lu and Lr was based on those arguments, then the demolishing of those arguments requires the placement to be reassessed, and the newly discovered true statements point towards Lu and Lr as group 3 elements, certainly not La and Ac.

As for Goldschmidt, according to Seaborg he originally suggested 5f to begin after element 96 (1924), but later changed his mind to suggest Pa on crystallographic grounds (1937), although he noted that Th, U, and transuranium elements were also possible starting points for 5f (presumably his data was only suggestive, then, if he didn't feel very sure). The original discoverers of Np thought that its uranium-like chemistry signified that 5f began there only with a uranide series (1940)! So while Goldschmidt suggested (though was not sure about) the correct starting point of 5f at Pa in the ground state, we have to temper this success by noting that he also predicted a concomitant thoride series. Which is not what we see: after the initial craziness, the characteristic oxidation state drops down to +3 (Am-Es) before gravitating towards +2 (Fm-No), whereas a thoride series would be expected to have imitators of Th which is basically always +4. (And yet again the break of Lr from this trend is exactly why it is clearly not a 5f element, but one thing at a time.) This is much more like the lanthanide series and suggests that 5f forms an actinide series. Seaborg's insight was to realise the following: even if in the ground state Th lacks an f electron, it doesn't matter, because looking at oxidation states of the elements later in the series strongly suggests where the f contribution begins. So ground state electron configurations are not everything. Bravo! Today we can go even further and actually computationally model the 5f elements in compounds, and see that Ac and Th both show clear 5f valence involvement in compounds, just like Pa-No, and totally unlike Lr. The case for Lu-Lr is clear-cut on this basis. Double sharp (talk) 16:15, 18 March 2020 (UTC)

On Th, it's treatment is related to where a block ends:

A block finishes when the relevant chemistry-based contraction ends and just before there is a knock-on impact to ionic radii:

                Preceding
    block  end  cation     First "knock-on" impact
    1s     He   H+   0s2   1s2 in Li+	
    s      Be   Li+  1s2   2s2 in B3+
    p      Ne   O2+1 2p3   2p6 in Na+, K+, Rb+ etc
    d      Zn   Cu+2 3d9   3d10 in Ga3
    f      Lu   Yb+3 4f13  4f14 in Hf(IV)

I now think that trying to define the start or end of a block is not a case of using either the earlier start table or the above end table. Instead it's a "start table" AND an "end table" situation. You have to keep both definitions in your head at the same time in order to appreciate what’s going on.

The start table may be easier to hang one’s hat on, as long as one remembers that Zn in group 12 is also a d metal in the sense that e.g. the source of the scandide contraction ends with it. A lesser contraction occurs across the 4d metals. And there is a small but perceptible contraction across the 5d metals.

I'll see if I can add some more notes to the start table to make all this clearer. Sandbh (talk) 03:32, 18 March 2020 (UTC)

@Sandbh: And exactly how are you choosing your cations, since there is no such thing as a characteristic oxidation state outside 4f? What exactly is a knock-on impact, and how do you know that Lu³⁺ vs. Y³⁺ is not also one? (Using the chemically sensible definition that a "knock-on" impact should be done by core electrons, we see that actually it is, just like Hf⁴⁺ vs. Zr⁴⁺.) Double sharp (talk) 16:15, 18 March 2020 (UTC)

P.S. You keep looking at such chemically outlandish processes as "add a proton and an electron, there's the next element", which is implicit in examining contractions like Ce³⁺ to Pr³⁺ to Nd³⁺ etc. Why don't you look at the chemically absolutely relevant process of what subshells are being used as valence subshells in a single element, which outside of nuclear processes that will make the majority of its current chemical bonding moot is not going to change its identity? Double sharp (talk) 06:41, 22 March 2020 (UTC)

Bringing an element to the f-block

@Sandbh: Neither presense of the 4f core nor its influence on the chemistry bring an element to the f-block. That's true for Lu as well as for Hf. Droog Andrey (talk) 07:32, 13 March 2020 (UTC)

@Droog Andrey: What brings an element to the f-block? Sandbh (talk) 04:04, 14 March 2020 (UTC)

@Sandbh: Very simple. You need the element to (1) show valence f involvement, (2) not show valence g involvement, and (3) not be in the s block (i.e. it's at least two elements away from the last noble gas). We have it for La and Ac and not for Lu and Lr, so the case is resolved immediately. Double sharp (talk) 06:07, 14 March 2020 (UTC)

Group 4+ higher valence compounds more stable

On a side-note I see group 4 is the first to show the phenomenon whereby compounds of higher valence become increasingly more stable in any group with increasing Z, whereas the contrary trend is observed in the p-block. Sandbh (talk) 03:54, 8 March 2020 (UTC)

That is because of different subshells, d is relativistically destabilised while p_1/2 is stabilised. Which immediately implies that group 3 as a d-block group should follow the group 4 trend. And indeed it does: Sc has the most developed +2 chemistry among Sc, Y, Lu, and Lr. With Y and Lu this is more limited although known: with Lr lower oxidation states should be even more strongly unstable than the already unstable ones of Rf, Db, and Sg according to predictions. Though this is not terribly conclusive since Sc, Y, La, Ac, contrary to your statement, also shows such a pattern. The more conclusive argument is what the orbitals are doing, as that underpins how the PT is constructed. Plucking out properties you like without that will never resolve Be and Mg, so why would anyone think it would resolve Sc and Y? You need to go deeper, and then not pluck out only the things you like out of the depths. Double sharp (talk) 13:28, 8 March 2020 (UTC)

@Double sharp: Since I'm observing characteristic properties there is no need to go deeper. As you know:

variable valence, along with compounds of higher valence showing increasing stability with Z, is a characteristic property of groups 4-11;
+2 is not a characteristic valence of group 3 i.e. variable valence is not a characteristic property of Group 3. Sandbh (talk) 23:30, 8 March 2020 (UTC)

@Sandbh: You artificially shift the boundaries. +2 is just as characteristic of group 3 as +3 is of group 4; well-defined, but rare, and favoured most of all for the lightest element in the group. There is a totally normal trend of how common and stable the lower oxidation state is going on from Sc to Ti to V to Cr (by which time the lower states are the main states).

Plucking out characteristic properties without any understanding of where they come from will never resolve anything conclusively. For one thing, it would never resolve the placement of Be and Mg. Well, shall they go over Ca, or over Zn? Without proper understanding of the aufbau, you'll never know. Once you understand that, though, it quickly becomes apparent that there is no really good reason to artificially shove the f-block awkwardly in between groups 3 and 4 rather than normally between groups 2 and 3. Double sharp (talk) 14:55, 9 March 2020 (UTC)

@Double sharp: I don't need to shift the boundaries. I rely on variable valence being a characteristic property of groups 4-11. As you know, variable valence is is not characteristic of group 3. Sandbh (talk) 23:42, 9 March 2020 (UTC)

@Sandbh: You indeed don't need to, but you do it anyway. This property is about as characteristic as it is for group 4, just a little bit less as expected from the trend going from group 3 to 4 to 5. The first element shows it the most, later elements increasingly don't want to show it. That's true of Sc-Y-Lu-Lr just as it is for Ti-Zr-Hf-Rf, V-Nb-Ta-Db, Cr-Mo-W-Sg, and Mn-Tc-Re-Bh. You force a cleft between groups 3 and 4 when the trend continues. Double sharp (talk) 23:50, 9 March 2020 (UTC)

PS: Use La force, Double sharp; use La force. Don't Luccumb to the dark side :) Sandbh (talk) 03:57, 8 March 2020 (UTC)

It's rather the La table that is pushing the weird dark side trend of the s-block into the rest of the table where it doesn't belong. Double sharp (talk) 13:26, 8 March 2020 (UTC)

La has ~0.6 d electrons > Lu

@Double sharp: In this article, the authors note that "La has approximately 0.6 d electrons more than Lu". There is a reduction in d-band occupancy from La to Lu, of about 2.5 to 1.5 electrons, and this is reckoned to account for lanthanum's anomalous double-hcp (dhcp) structure. Its funny to think that, on this basis, La is the most d-like of the Ln. Sandbh (talk) 22:16, 9 March 2020 (UTC)

@Sandbh: Gschneidner (1971) already wrote an article about 4f in La five years before the one you quote, based on how introduction of f orbitals depresses melting point (compare La with Lu). What we see instead is, as usual, a corroboration of my approach of chemically active subshells, involving everything in one range (4f5d6s6p for La through Yb, 5d6s6p for Lu through Hg, 6s6p for Tl through Rn). Choice quote:

"On the basis of these facts it is quite likely that all four kinds of electrons, 4f, 5d, 6s and 6p, are involved in the metallic bonding of all of the trivalent lanthanides except Lu." (For which, surprise, surprise, 4f involvement need not be invoked: "The lanthanide metals, other than Lu and perhaps Er and Tm, have two kinds of 4f electrons, the atomic 4f and the band or bond 4f electrons." For Er and Tm it is sinking into the core (almost zero but not quite on the graph) but we can still see chemical involvement due to the interplay between divalent and trivalent configurations, already chemically normal for Tm.
"The fact that the observed melting points [of the Ln] lie in most instances [actually all but Lu] well below the expected curve (dashed line) was interpreted by Matthias et al. as due to a difference in the valence electron configuration of the lanthanides La through Yb, as compared to those of Sc, Y and Lu. Their explanation was that the melting point lowering was due to 4f electrons in the valence band." Gschneidner agrees that this is an important factor, although he notes that the contribution of p and the relative proportion of s vs. d is a serious alternative explanation that must be addressed. Which he does, finally noting that there is no way to explain the properties of the lanthanides up to at least Ho without significant 4f involvement.
"The important point regarding Fig. 8 is the trend in the number of the various kinds of electrons. The 4f electrons show, as might be expected, a general decrease with increasing atomic number, while the 5d electrons exhibit the opposite behavior. The 6p electrons show a general rise across the series, but with minima when the atomic 4f level empty, half-filled and completely full."

As shown in that figure, 4f involvement weakens in the heavy lanthanides as it gets drowned into the core (reaching zero at Lu), whereas 5d involvement strengthens. 4f involvement is in fact highest in La and Ce, exactly as I have been saying. Ce is the most f-like of the Ln, but La takes a respectable close second, as they are the only two coming before the delayed collapse! As I said, though it seems paradoxical, when a delayed collapse like 4f (and probably 5g) happens, it's the elements with "pre-f" or probably "pre-g" involvement, where there aren't yet any such electrons in the ground-state configurations, that most strongly show involvement of the characteristic subshell!

And indeed, for La we have to include 4f6s² among configurations to reproduce the correct melting point and heat of sublimation. "Pseudo-La" with hypothetical zero f character simply has wrong properties (it should melt at 1450°C, whereas real La melts at 920°C).

Though I am not an expert in this sort of thing, I wonder: if d participation is really the factor, then how come it's the early Ln with the highest f participation (La-Pm) that are the ones with the dhcp structure? Meanwhile Lu is hcp, exactly like Y and following how Hf-Au all have the same structures as their lighter congeners, instead of forcing La dhcp in there to break the 5d trend. Oh wait, that's exactly what shoving La into 5d always does: break a trend that could have remained intact with Lu there. Double sharp (talk) 23:28, 9 March 2020 (UTC)

@Double sharp: The thing about Gschneidner's article (115 citations) and 4f involvement in La is that I've never found anyone that has confirmed his theory. Duthie and Pettifor (399 citations), writing five years later, don't cite him, which is astonishing! At the end of their paper they write, "We are at present investigating the effect of the large core in La on other apparently anomalous properties such as the large value of the superconducting transition temperature, the low melting point, and the negative coefficient of thermal expansion." That's nice but I haven't yet found any of their work about this. The plot is still cooking. Sandbh (talk) 11:19, 10 March 2020 (UTC)

@Sandbh: 4f band involvement in La (about 0.17 f electrons per atom) was confirmed by Glotzel in 1978. Wittig also pointed out in 1973 (p. 385) that 4f involvement is needed to explain the anomalously high critical temperature of La, and notes that Cs and Ba under pressure should have 4f involvement as well, corroborating exactly my prediction of "all higher" for Cs and Ba in the s-block with 4f involvement as well as 5d! So chemically active subshells win again. ^_^

I should like to know if the follow-up experiments on K and Rb to confirm they don't behave like Cs were done. Nota bene, he even uses the "fuzzy configuration" notation I use, discussing (6s5d)³ and (6s5d)^3-e4f^e as configurations for La.

And on p. 387, Wittig weighs in on the composition of group 3:

“

At the end of this section, we are able to give probably the final answer to the important question whether La or Lu is the proper element below Y in a periodic table tailored for the practical needs of a solid state physicist. Ten years ago, Hamilton [38] suggested removing La from its hereditary position and replacing it by Lu which matches better with Y and Sc than La does. We are convinced that La is a 4f-band metal. It belongs, therefore, to the rare earth group. The pressure induced superconductivity of Lu [35], revealing a T_c which fits very well into the general pattern of the transition temperatures of the d-period metals, now strengthens appreciably our confidence that Lu is the proper element below Y in the periodic table. There is apparently no interference by the closed 4f shell, which proves to be without influence on the metallic properties. Consequently, Lu should now be removed from the rare earth group and accommodated below Y in the 5d transition period in just the same way as one is used placing the next elements to the right (Hf, Ta ...) below the corresponding 4d-period metals.

”

Bravo! Though he also goes too far in my opinion by suggesting Ca-Sr-Yb at the end. His table shows Be-Mg-Zn, which I guess still had some legs then: so I think what is being missed here is the s-block exception; He is (s)², Be and Mg are (sp)², Ca and Sr are (dsp)², and Ba and Ra are (fdsp)²; note that for Yb, 4f is drowned deeper than for Ba and even Eu, so it makes sense that it should be closer to Ca and Sr in this respect than Ba. Confirmation of the properties of Ra and Ac (dare I suggest Fr?) would be an incredible thing to have (and is suggested for Ra and Ac on p. 393), but I doubt we'll get it. T_T Double sharp (talk) 14:46, 10 March 2020 (UTC)

@Double sharp: I found it interesting to see that the f contribution in Th and Ce seems to be more important than for La, judging from this passage:

The f bands in La and Th are essentially unoccupied, but through hybridisation the number of f electrons at the observed volume amounts to 0.17 (0.56) per atom for La (Th), whereas in Ce the f band is partially occupied and the number of f electrons is 1.2 per atom. For all three metals the number of f electrons increases slightly under compression. The bonding f contribution to the pressure is essential in determining the equilibrium radii as well as the bulk moduli in all three metals and, in Ce and Th, it is of the same order of magnitude as the bonding d contribution.

That said, his Fig 1. is hard to interpret. How do you read it? Sandbh (talk) 01:24, 11 March 2020 (UTC)

@Sandbh: I agree that Ce has more 4f involvement than La. The only trouble is that both have oodles more 4f involvement than Lu, and so your table claiming 4f as a most important orbital for Lu and not La is misguided. As demonstrated ad nauseum, Lu 4f orbitals are contributing in a way that is totally unlike the valence ones of La-Yb and totally like the core ones of Hf-Rn. Double sharp (talk) 08:00, 11 March 2020 (UTC)

Wittig's table

@Double sharp: On Wittig's table: This is a really nice example of table towards the physics end of the continuum-like series of periodic tables. Check out the spectacular triple split s-block, and with Y under Ca-Sr, to boot! The lack of symmetry is astonishing.

Wonderful! A periodic table tailored for the practical needs of a solid state physicist! Brilliant! Just so! Sandbh (talk) 02:42, 11 March 2020 (UTC)

@Sandbh: Given that he lets Be-Mg-Zn pass without comment, and focuses on the start of period 6, I consider this simply to be coming from the old misunderstanding of the s block even though he hit the nail on the head for the d block. Presumably Be-Mg-Zn was still standard enough that he didn't feel the need to comment on it, even though it is clearly seen to be wrong once you understand the aufbau (as Paneth correctly argued back in 1923, since the Zn group has the extra d¹⁰ added). The problem is resolved by noting the special status of the s block that uses all higher orbitals, so that f orbital usage for Ba does not have the same significance for its block placement as it does for La. This is not a double standard because the different status of the s block (it fraternising with the "wrong" n+l value) is acknowledged from the very beginning. Otherwise, his arguments about f band involvement in Cs should consistently imply shifting K and Rb to go over Tm.

The real thing to be astonished over is that when the aufbau is understood properly, we see that its symmetry is actually preserved chemically and physically for the most part, and that the real symmetry break is the s block jumping ship to the "wrong" n+l family. That symmetry break is why my preferred table is not an LSPT, but has the s-block shifted over to the front to recreate the alkali metal to noble gas pattern (noting period 1 as a tremendous first-row anomaly, and that Og is not really a noble gas, but the latter is a relativistic second-order correction that goes away for E172). Nothing to do with delayed collapses, which have a total lack of chemical and physical relevance. Double sharp (talk) 08:00, 11 March 2020 (UTC)

P.S. Lack of symmetry is nothing to be astonished about, as almost any random arrangement of the elements would show that. What would be astonishing is symmetry; without it there is no sense in talking about a periodic law. Even when symmetry is broken, it must have been there clearly to begin with, and there ought to be some deeper regularity controlling why it breaks. The s-block jumping ship is a reasonable symmetry break by that standard, but certainly not showing secondary periodicity that is Sc-Y-La without also including all the other equally important secondary periodicities. Double sharp (talk) 16:58, 13 March 2020 (UTC)

@Double sharp: I should add a footnote wrt the most important orbital for Th. It's crystalline structure is attributable to the presence of ~0.5 of an f electron in the condensed state; and there is evidence for the presence of a valence electron in a relatively minor part of its chemistry; and the f orbital collapse is thought to occur in Th, which is a bigger deal. This can be contrasted with La where the d electrons account for its DHCP structure; and the absence of a 4d collapse. The d orbital is the most important here, noting the absence of any 4f valence electron of its own. Sandbh (talk) 03:00, 11 March 2020 (UTC)

@Sandbh: The delayed collapse matters 0%, or else we have to raise questions about Lr 6d even though it's clearly nothing like Tl. It's really absolutely normal for heavy elements and it also really doesn't make any difference for the chemistry at least up to the early 5g elements: the subshell still goes into the core at the right time (last 4f element is Yb, last 5f element is No, last 6d element is Cn) even if its collapse takes a while. What matters is that 5f can be occupied and contributing for Th, but that should also be true for Ac according to Wittig. Meanwhile, the d electron explanation of La's dhcp structure is highly suspect when you realise that the Ln with that structure are La-Pm, the early Ln with the most f involvement. Double sharp (talk) 08:00, 11 March 2020 (UTC)

SECOND RELOCATION NOTICE

In order to avoid destroying everyone's browsers, the second batch of material has gone to Archive 42. Double sharp (talk) 05:19, 3 April 2020 (UTC)

Falsifiability

@Sandbh: One essential component of the scientific method is falsifiability.

I consider that my approach of chemically active valence subshells could be falsified by an element showing an inappropriate chemically active subshell for its block position in my table. This would imply something like the use of valence f orbitals by Lu and Lr that would have to be on the order of f involvement of Yb and No, or the use of valence d orbitals by group 13 that would have to be on the order of that of group 12, since I am claiming that the big gaps happen where you would expect from the Madelung rule. Neither of these, nor any analogous one within the first 114 elements, has so far been demonstrated, and current understanding makes both seem extremely unlikely; but in principle, the theory could be falsified this way. For elements 115+, relativistic effects demand a slight improvement to the theory that I have now incorporated due to the subshell splitting now being too big to ignore, but qualitatively the idea is the same.

What would be enough to falsify your Sc-Y-La stance, in your opinion? Double sharp (talk) 14:25, 22 March 2020 (UTC)

@Double sharp: I don't know. Recent RL obligations, and COVID-19 considerations, have gotten in the way of me being able to spend much time on such questions. I've been thinking about the group 3 question in my downtime and I hope to post something about this. Off the top of my head what could falsify my stance is a case of an element which has a mismatch between its block and its most chemically important orbital. Sandbh (talk) 04:42, 25 March 2020 (UTC)

@Sandbh: Leaving aside that "most chemically important orbital" is hardly well-defined (there are almost always several such, whence hybridisation), making the falsifiability of your stance a bit iffy already, the counterexamples are already clear: Lu and Lr are placed by you in the f-block, but the f orbital is not the most chemically important for them, being a core orbital.

Looking forward to your next post on the group 3 issue when you have enough time! Double sharp (talk) 05:17, 25 March 2020 (UTC)

@Double sharp: Yes, I placed Lu in the f-block since the Ln contraction culminates in Lu and permeates the entirety of its chemistry, and the contraction is caused by the progressive occupation of the 4f sub-shell in the trivalent cations from Ce to Lu. Now, the knock-on consequences of the contraction are seen in the 5d metals from Hf on, but nobody regards Hf or any of the other 5d metals as being f-block. Sandbh (talk) 02:16, 2 April 2020 (UTC)

@Sandbh: Well, we're back to the issue where we're at loggerheads. First of all, for the purposes of finding what the periodic table is supposed to look like, what people regard is not the issue. It can be illuminating, but we must apply logic and consistency: the Be-Mg-Zn table did not stop being ideal because most people abandoned it. Rather it was never ideal even when it was being used. I claim the same is true for the Sc-Y-La table: it is being used, but it's internally inconsistent.

Now, again: we cannot look at trivalent cations because it leads to an internal inconsistency. You cannot apply such to any other contraction, so it becomes a double standard which the f block is held to and no other block is. Rather, we should look at why we are so sure that the 2p contraction runs B-Ne, and the 3d contraction runs Sc-Zn, and the answer is clear: that's where the shells are being filled, and as confirmation the next element has that shell as a core orbital where it is just causing incomplete shielding knock-on effects. That's true of 2p in Na just as it's true for 3d in Ga. And we can confirm it for oxidation states. By the time we get to Ne, it's clear that 2s and 2p are controlling the difficulty of getting the element into chemistry (as they would enter antibonding orbitals and cancel the bond order out to zero), and that Na +1 is coming from something else, the 3s orbital, not the beleaguered 2p one again.. By the time we get to Zn, it's clear that the trend towards core-like functioning of the 3d orbitals is going quite strongly (whence how Co, Ni, and Cu increasingly sway more towards the +2 state), and now we've reached the point where states beyond +2 are impossible and 3d is just helping the bonding, not going so far as to allow higher oxidation states. So it's clear that Ga +3 is coming from something else, the 4p orbital, not the beleaguered 3d one again. For confirmation we can look at the higher congeners, and it's the same story for 3p, 4p, 5p, and 6p, just as it is for 4d, 5d, and 6d.

So, applying consistency, what is going on at the end of the lanthanide series? Well, we can see that for the last few lanthanides the +2 state becomes more stable (just look at the standard reduction potentials), even if of course it's not predominating (you need to look at the actinides to see that). Except that that trend ends at Yb and No: Lu and Lr both favour +3. That's clearly exactly the situation we would expect for what happens after the contraction has finished: Lu and Lr +3 must be coming from somewhere else, just like Ga and In +3. For confirmation we can equally well see that the block start appears correctly: La and Ac show the "delayed collapse" effect in the ground state, common for heavy elements (just look at Lr or E121; indeed, the 6p¹ state for Lu is also quite low), but it doesn't stop them from showing 4f/5f involvement in chemistry just like it doesn't stop Th, which is famously [Rn] 5f⁰ 6d² 7s², but an f block element according to almost everybody.

And applying consistency, we also see that there really isn't any difference between core 4f involvement in Lu and in Hf. They both permeate all of their chemistry, but only through incomplete shielding effects, so we shouldn't treat them differently.

Applying consistent criteria leads to a simpler situation. Gone is the need to say "we apply criterion A for this bit of the table and criterion B for that bit". Instead we say "we apply criterion A everywhere". That matches the desire to make our theory as simple as possible. But not simpler. Double sharp (talk) 03:55, 2 April 2020 (UTC)

@Double sharp: This is largely old ground which I won't visit. Could you please desist from repeating the idea that +2 state predominates in the late An? This only happens for No. Regarding the delayed collapse I no longer now where you are coming from. In one case you bag its relevance, now you cite it again. Ditto Th as an f metal. Sandbh (talk) 05:15, 2 April 2020 (UTC)

@Sandbh: Well, if we're not going to revisit the old ground, then this isn't going to do much good because that old ground is precisely where our disagreement stems from.

You are misunderstanding what I'm saying, which is that the +2 state becomes more stable, and reaches a predominant level by No. That is easily seen from the standard reduction potentials:

Dy³⁺ + e⁻ ⇌ Dy²⁺	−2.6 V	Cf³⁺ + e⁻ ⇌ Cf²⁺	−1.6 V
Ho³⁺ + e⁻ ⇌ Ho²⁺	−2.8 V	Es³⁺ + e⁻ ⇌ Es²⁺	−1.3 V
Er³⁺ + e⁻ ⇌ Er²⁺	−3.0 V	Fm³⁺ + e⁻ ⇌ Fm²⁺	−1.1 V
Tm³⁺ + e⁻ ⇌ Tm²⁺	−2.2 V	Md³⁺ + e⁻ ⇌ Md²⁺	−0.1 V
Yb³⁺ + e⁻ ⇌ Yb²⁺	−1.05 V	No³⁺ + e⁻ ⇌ No²⁺	+1.4 V

Nobelium +2 did not come out of thin air, even though it appears like it did if you only look at one oxidation state. Rather, it came as part of a trend, that crosses the surface there. A trend that, incidentally, absolutely does not extend to Lu and Lr, looking at their strong preference for the +3 state. It even more absolutely looks like a good trend if you observe the late 3d transition metals:

Fe³⁺ + e⁻ ⇌ Fe²⁺	+0.771 V
Co³⁺ + e⁻ ⇌ Co²⁺	+1.92 V
Ni³⁺ + e⁻ ⇌ Ni²⁺	+2.3 V
Cu³⁺ + e⁻ ⇌ Cu²⁺	+2.4 V

And for Zn, it'd no doubt be even higher. Clearly Ga with its preferred +3 state is not a part of this trend.

As for delayed collapses, I stated that it exists and is irrelevant. Meaning, La and Ac show a delayed collapse that doesn't stop them from showing 4f/5f involvement anyway. You can take that as my stand, that has been consistent since the start of the discussion. Double sharp (talk) 05:46, 2 April 2020 (UTC)

Block paradigm revisited

I think our focus on formal or theoretical blocks is misguided.

From a chemistry perspective each block has its misfits. For example, He is s-block but we treat it as being p-block. The other known misfits are:

Sc, Y, La, Lu, Ac, Th, and Lr. They are d-block but their chemistry is like that of f-block metals, with Sc as the outlier. Lu and Lr are more like the following d-metals.
Ag, Zn, Cd, Hg are d-block but their chemistry is largely like that of sp metals, with Ag as the outlier
Al is p-block but its chemistry is more like that of an s-block metal, especially Be.

All the misfits are found near the boundaries between blocks.

Focusing then on the actual chemistry gives the following empirical blocks:

Block	Members	Literature examples
s	groups 1-2, and Al	Deming (1940), in his book Fundamental chemistry calls them the light metals.
f	rare earths, and An	Parish (1977), in his book The metallic elements calls them (i.e. Sc, Y, La, Ac + Ln + An) the 4f- and 5f-elements; Cotton and Wilkinson et al. (1999), in their book Advanced inorganic chemistry, treat group 3 and the Ln together in one chapter.
d	groups 4-10; Cu and Au	Rayner-Canham and Overton (2006), in their book Descriptive inorganic chemistry count the TM as groups 4-10; Rayner-Canham later excludes Ag from the TM in his 2018 article "Organizing the transition metals".
p	Ag, and groups 12 to 18 (excl. Al)	King (1995) and Massey (2000), in their books Inorganic chemistry of main group elements and Main group chemistry, count group 12 as main group.

Block homogeneity is optimised in the empirical blocks.

That being said, the formal or theoretical blocks won't go away. As a first order model it's good enough to say a block is subtended by the first appearance of the applicable electron, as long as the phenomenon of boundary misfits is borne in mind.

In the context of the empirical blocks I’m showing group 3 as Sc-Y-La since:

the interpolation of the 4f series occurs between La and Hf for the more chemically relevant ionic phase electron configurations;
while Sc, Y, La, Ac, Th, Lu and Lr are all f-elements in chemical terms, Lu and Lr are closer to the following d-block elements;
f-element chemistry (less so for some early An) resembles that of the s-elements; and
Sc-Y-La follows a group 1 and 2-like trend whereas Sc-Y-Lu a group 4-to-8-like trend.

Harking back to earlier discussions, King (1995, p. 291) writes that "A consequence [italics added] of the Ln contraction is the nearly same size of the element immediately following the Ln, namely Hf…" i.e. he distinguishes between the contraction itself as opposed to its consequences. Sandbh (talk) 03:53, 26 March 2020 (UTC)

@Sandbh: First of all, Th is definitely an f block metal despite its [Rn] 5f⁰ 6d² 7s² ground state configuration, and you have even said so yourself by perpetually pointing to condensed-phase Th and the Th³⁺ cation. Now you say it is d block. Sandbh vs the world, I suppose, since I think you'll find absolutely nobody agreeing to that ever since the actinide concept was discovered. As Scerri and Parsons wrote in Mendeleev to Oganesson: "Similarly, we draw attention to the fact that there are anomalous cases such as the thorium atom, which features no f-orbital electrons—nobody disputes that this element belongs in the f-block of the periodic table". Also, it is AFAIK universally acknowledge that helium is an s block element. Blocks are defined by what orbitals are being used for chemistry, you know, not where we happen to draw an element!

Plucking out group 3 from the d block, and the other shufflings you suggest here, is basically phantastical. OK, sure, its chemistry has some similarities to the s and f blocks, and as you've noticed that's totally normal for groups at the end of each block: they show some similarities to the block next door, because all the trends are continuous (except once you cross the period divide). So you shift the boundaries and fail to notice the equally relevant similarities to the group on the other side that matches the block. Group 3 has TM-like physical properties that are exactly like group 4; it has poor coordination ability that is exactly like group 4; it favours the group oxidation state but its lightest member has a significant amount of low-oxidation state chemistry, that is exactly like group 4. The trend from group 2 to group 3 makes sense and is continuous, just like the one from group 3 to group 4, and they are both equally strong trends. Every group is about equally close to its two neighbours, excluding neighbours "wrapping" around the table (which is why the real symmetry break should be considered between a noble gas and the next alkali metal). And no one can deny that the (dsp)³ valence configuration plays a huge rôle in determining their chemistry. You simply draw some circles around chemically similar elements, but only end up making artificial cuts at slightly unusual places while ignoring the continuities there (if you can find any criterion that consistently excludes group 3 from the TM while not also throwing out some of Zr, Hf, Rf, Nb, Ta, Db, Sg, and Bh, I should like to see it). Far better to work with theoretical blocks that at least mean something, and point exactly to the types of orbitals being used for chemistry and therefore have explanatory power—and I hope we agree that the valence orbitals being used for chemistry are important, or we have to throw all the literature pointing to molecular orbitals out the window—rather than this totally subjective division elevating some categories at the expense of others that are chemically equally plausible. And of course empirically surveying what orbitals are really being used gives exactly the theoretical blocks and point to Sc-Y-Lu extremely clearly because Lu is not using its f orbitals for chemistry and is therefore categorically different from the 4f elements. Both the orbitals and descriptive-chemistry categories are important, so let's not conflate the two.

P.S. Repeatedly referring to ion configurations will not stop being a double standard no matter how many times you say it, because you cannot apply it anywhere outside the Ln and therefore cannot use it to find where any other contraction starts and ends. Y vs. Lu should be correctly viewed as a knock-on effect of the 4f contraction as the 4f electrons are core electrons there, exactly analogous to Zr vs. Hf, Al vs. Ga, and Si vs. Ge among others. Just like the important thing for the other primogenic contractions is the ending of the 2p and 3d rows (1s is kind of degenerate), the important thing here is the ending of the 4f row, and not the slightly different ending of rare earth chemistry. Double sharp (talk) 04:06, 26 March 2020 (UTC)

@Double sharp:

Thorium: "Now you say it is d block. Sandbh vs the world, I suppose, since I think you'll find absolutely nobody agreeing to that ever since the actinide concept was discovered."

I was inspired by Schwarz, who has written extensively on these matters: "Two elements (La and Lu) in row 6, and three ones (Ac, Th and Lr) in row 7 are rather typical d elements". This might seem odd but you need to read the rest of the paper to see where he's coming from.

@Sandbh: This article is basically getting towards chemically active subshells (they even use the phrase "chemically inactive" and the notation (sp)⁸ like I do) but missing the essential fact that La and Ac actually have chemically active f subshells (we may see the howler at the top of p. 1982). And again we are seeing a focus on delayed collapses (p. 1989), while forgetting that that doesn't stop the subshells involved from participating in chemistry. Meanwhile, the structure of thorium metal totally does not match what you would expect for a d-band metal like hafnium...

Chemically speaking, we may claim uranium as a typical eka-tungsten-like d element too. Doesn't change the fact that electronically speaking it is not. We have to use electronic bases for the periodic table, or else we have no way to decide between Be-Mg-Ca and Be-Mg-Zn after all this time. Double sharp (talk) 06:12, 28 March 2020 (UTC)

Helium: "…is an s block element." Yes, of course. It's highlighted since it's an s-element in the p-block.

It's not in the p-block. It's positioned above the p-block, sure, but no one will agree that it is a p-block element. Double sharp (talk) 06:12, 28 March 2020 (UTC)

Group 3: "…if you can find any criterion that consistently excludes group 3 from the TM while not also throwing out some of Zr, Hf, Rf, Nb, Ta, Db, Sg, and Bh, I should like to see it."

We've discussed this at length to no avail. Group 3 tends to have an ionic chemistry; groups 4–5+ don't. I provided citations supporting this.

It's still total nonsense based on citations being brought out of context. The simple fact of the matter is that ionic character depends on EN difference, there is not any such thing as a group predominantly displaying ionic character. Just switch the counteranion from F⁻ to O²⁻ to Cl⁻ to As³⁻ and tell me where the ionic-covalent or ionic-metallic divide happens. Usually it is not between groups 3 and 4. Double sharp (talk) 06:12, 28 March 2020 (UTC)

Blocks: "Far better to work with theoretical blocks…." Better to work with both, I think.

Better to work with one thing that is well-defined and relevant to chemistry, than combine it with a conflation of two ideas (chemically active valence subshells and patterns in the resulting descriptive chemistry a few levels up) that serves neither well. Double sharp (talk) 06:13, 28 March 2020 (UTC)

Lu: "…is therefore categorically different from the 4f elements." Lu is universally treated as a lanthanoid, along with the other 4f elements.

Yttrium is also universally brought in for comparison with the 4f elements by anyone with chemical sense. And it's nearly universally treated as a rare earth. That doesn't make it a 4f element either. Double sharp (talk) 06:12, 28 March 2020 (UTC)

4f contraction: "Lu should be correctly viewed as a knock-on effect of the 4f contraction…" The literature, as per my citation, begs to differ. Sandbh (talk) 06:02, 28 March 2020 (UTC)

The literature that actually thinks about and considers the group 3 question in detail mostly supports Sc-Y-Lu, and surely they must outweigh the sources that display a Sc-Y-La table and never show any sign that they thought about the question or that it was their focus. And the wider literature supports that 4f is an inactive core orbital by Lu, so my position is definitely supported. Double sharp (talk) 06:12, 28 March 2020 (UTC)

PT with chemistry- and electron-based blocks

Here's a table inspired by our thread. It’s nice that the number of "leaders and laggards"—the misfits as I used to call them—is coincidentally the same as the number of Madelung rule anomalies (20). I’ve informally called group 18 octogens rather than noble gases since Og is likely to be neither.

Comments to follow. Sandbh (talk) 05:14, 28 March 2020 (UTC)

@Sandbh: Again: chemistry-based categorisation is not based on the same principle as block-based ones, so conflating the two is not useful. Blocks ask "what kinds of electrons are used for chemistry" and explain the chemistry from the bottom up; categorisation by descriptive chemistry instead searches for patterns among the results, e.g. metalloids, alkaline earths, lanthanides, etc. You say that chemically helium is p-block: now, what exactly does that mean? Helium is like neon chemically, sure. What about the majority of the p elements that are not noble gases? Exactly how chemically homogeneous is a p-block that includes both thallium and neon? How can such a thing be a useful category for chemical behaviour? Of course it's not, that's not what it's meant for. The blocks tell you what orbitals the valence electrons are in; to go further to chemistry you also have to look at how many valence electrons there are, how close they are to the nucleus, ionisation energies, lattice energies, and a myriad of other things.

P.S. For me group names are also an example of this conflation. Noble gas can very well mean He (group 2) + Ne-Rn (group 18), it doesn't have to be a synonym of group 18. Similarly to how the superheavy Ts should not be considered a halogen (and in fact At is already ambiguous); it's a chemical category, no one said the whole group must be involved. Indeed, apart from alkaline earth metals, it usually is not (and that is a mistake chemically as Be and Mg are not alkaline). Sure, in terms of periodicity oxygen and polonium are in the same group; they are (sp)⁶. Just try to write a chapter on group 16 that covers their descriptive chemistry together. The blocks and valencies are only the starting point for periodicity: chemically relevant, but there are myriads of intermediate steps between them and chemistry even as they stand at close to the foot of the staircase. Double sharp (talk) 05:31, 28 March 2020 (UTC)

@Double sharp:

You wrote: "Again: chemistry-based categorisation is not based on the same principle as block-based ones, so conflating the two is not useful."

I draw on support from the literature:

"The division into blocks is justified by their distinctive nature: s is characterized, except in H and He, by highly electropositive metals; p by a range of very distinctive metals and non-metals, many of them essential to life; d by metals with multiple oxidation states; f by metals so similar that their separation is problematic. Useful statements about the elements can be made on the basis of the block they belong to and their position in it, for example highest oxidation state, density, melting point…Electronegativity is rather systematically distributed across and between blocks." --- Philip Stewart, p. 118, here.

What are you drawing on? Sandbh (talk) 06:15, 28 March 2020 (UTC)

@Sandbh: I'm laughing out loud. This quote from the literature is justifying, not defining, the division into blocks, by noting chemical similarities inside. Notice how it is difficult to note them between thallium and neon, hence why the p block gets characterised by having a wide and very distinctive range. The d block is correctly noted to have metals with multiple oxidation states in it, but that can hardly be a definition, as that there are oodles of metals with multiple oxidation states well outside the d block (Eu +2 and +3, Pb +2 and +4, just to give two really obvious examples). In actuality division into blocks is far more often defined by the outermost electrons' subshells. Maybe by the ill-defined differentiating electron, maybe by the Aufbau order, maybe by which electrons are the valence electrons. Common sense, in fact, dictates that that must be so, as those subshells are in the very names of the blocks. And we have Jensen to spell it out, straight from the literature: "Assignment of [an] element to a major block [is] based on the kinds of available valence electrons and/or valence vacancies (i.e., s, p, d, f, etc.)." Double sharp (talk) 06:20, 28 March 2020 (UTC)

If you want a categorisation based on chemical properties and the properties of the simple substances, let's make it that rather than force the blocks into doing that. Something like what I have on my page, maybe:

Strong metal

Doubly inner transition metal

Inner transition metal

Transition metal

Weak metal

Weak nonmetal

Strong nonmetal

Noble gas

Just splitting the s and p blocks into chemically more logical categories, and leaving the more homogeneous already d, f, and g blocks alone, already gives something that makes a whole lot more sense. Double sharp (talk) 11:39, 28 March 2020 (UTC)

Periodic table article: corrections

Since many of the falsehoods I recall hearing from this discussion appeared on the periodic table article, I have made some cited revisions (using the sources that have appeared earlier in this discussion), in particular busting the following myths:

The "similarity to the s block" is not confined to group 3 and the Ln. Heavy group 4 and 5 show it just as well, being hard cations stuck in the group oxidation state for the most part.
@Double sharp: Good luck finding a source saying heavy group 4 and 5 are similar to the s-block. What heavy group 4 (IV) or 5 (V) mono-cations (aq) did you have in mind? Sandbh (talk) 12:34, 28 March 2020 (UTC)
@Sandbh: Zr⁴⁺, Hf⁴⁺, Rf⁴⁺ are totally known in water. Sure, they are usually heavily hydrolysed, but so are all +4 cations, even Th⁴⁺: "hydrated Zr⁴⁺ and Hf⁴⁺ are reported to be stable in solutions with a pH below 0 and a concentration smaller than 10⁻⁴ mol dm⁻³" (10.1039/C0CP01330G). The whole point is the group 4 and 5 are usually stuck in their group oxidation states, in which they show pre-transition properties. Greenwood and Earnshaw even says so; so much for "good luck". Double sharp (talk) 12:39, 28 March 2020 (UTC)
@Double sharp: I think this is an unreasonable example. I had in mind normal conditions in aqueous solution rather than the many things that may become possible in extreme conditions. There is no comparison with the ionic chemistry that characterises group 3. I had a look at G&E and was not able to find any mention of group 4 and 5 being similar to the s-block. They do say that:
group 3 precedes the transition metals proper (p. 946);

in the main the chemistry of group 3 concerns the formation of the predominately ionic +3 oxidation state giving a well defined cationic chemistry (p. 948);

for Ti, Zr and Hf the group oxidation state of +4 is too high to be ionic (p. 958);

there is no doubt Ti is a transition metal (p. 958);

the elements of group 5 are in many ways similar to their predecessors in group 4 (p. 979);

the term "lanthanide" is used to refer to Ce to Lu (p. 1227);

the great bulk of Ln chemistry is predominantly ionic in character (p. 1236):

the term "actinide" refers to Th-Lr (p. 1250); and

it is clear that an actinide contraction exists, especially for the +3 oxidation state, which is closely similar to the lanthanide contraction (p. 1264).

Sandbh (talk) 06:41, 29 March 2020 (UTC)
@Sandbh: Such a measure excluding strongly acidic conditions is going to bar U⁴⁺ and Pu⁴⁺ as well. All highly charged cations are strongly hydrolysed in water unless acidity is high (even the huge Th⁴⁺ needs pH < 3 to predominate), but that doesn't make them chemically irrelevant. Meanwhile, ZrO₂ and HfO₂ are refractory oxides, certainly suggesting ionic character with those EN differences (I remind that Zr and Hf have Pauling EN similar to Mg and Sc, showing a diagonal relationship Mg-Sc-Zr that then as usual goes straight down to Hf instead of continuing the diagonal, which probably resumes going down from Hf to Db). So much for "too high to be ionic" (in this case the gap is from group 4 to group 5, as evidenced by the drop in mp when we pass from HfO₂ to Ta₂O₅). As stated ad nauseum here citing Fajans, ionic character is simply electronegativity and oxidation states, there is no such thing as predominantly ionic or covalent chemistry. Just switch the counter-anion to make the electronegativity difference greater or lesser. For example, observe just how ionic organometallic group 3 chemistry will possibly be (hint: not very) when RLi and RMg are already strongly polar covalent. Or just switch the cation, maybe even to change its oxidation state, as that changes EN just as well. You get the same trend from ionic to polymeric to molecular covalent species as you raise oxidation state to increase EN in the same element, it's exactly the same process. Just look at UF₃ vs. UF₄ vs. UF₅ vs. UF₆.

Meanwhile, let's hear what Greenwood and Earnshaw says about group 4 and 5: "Lower oxidation states are rather sparsely represented for Zr and Hf" (p. 958); "most of the chemistries of niobium and tantalum are confined to the group oxidation state +5" (p. 979). In other words, these metals are mostly stuck in their group oxidation states where they are d⁰ and hence show no major transition metal properties like coloured compounds or paramagnetism. So they fail on the exact criteria used to throw group 3 out of the transition metals. The idea that La is not a lanthanide and Ac is not an actinide is too chemically silly for words. Double sharp (talk) 06:57, 29 March 2020 (UTC)
Group 12 certainly shows d electron involvement in the bonding, and judging from predictions for copernicium it follows the trend just as well that higher oxidation states become more stable as the group is descended.
Trends are continuous. There is no such thing as a hard break between groups 3 and 4. Or between any other pair of groups except 18 and 1, actually.
Sc-Y-La does not display a more consistent set of electron configurations in the ground state. In fact, this neglects intraperiod analogies, as Jensen noted.
In chemical environments atoms are usually not in the ground state configurations, so constantly focusing on these will never give a complete picture.

Also added was some mention of authors who would like to move helium to group 2. Double sharp (talk) 14:10, 27 March 2020 (UTC)

Corrections have also been made to the block (periodic table) article, in particular disputing (see the talk page) the notion that a block is defined by differentiating electrons. In fact, it seems distressingly plausible that the term "block" is not often defined; when it is defined, it often does not involve the ill-defined notion of DE's (one would like to question once more what the DE between ground-state vanadium [Ar]3d³4s² and chromium [Ar]3d⁵4s¹ could possibly mean, since there is more than one). Double sharp (talk) 14:14, 27 March 2020 (UTC)

Since some prominent authors have of late started using a Lu table (not only the good old Wulfsberg; now Rayner-Canham and Overton use it, as does Clayden et al.), I have half the mind to heed the calls of Dreigorich and AnthonyDu0122 and start a new RFC requesting a change back to the Sc-Y-Lu form, on the grounds that:

The scientific arguments from the previous RFC are flawed; here are some reputable sources noting that.
The Lu table has been adopted by some serious authorities (Clayden et al.'s book is famous);
@Double sharp: Clayden et al.'s book is about organic chemistry. You have to be kidding me if, in the context of group 3, you're going to rely on an organic chemistry textbook for support. Sandbh (talk) 12:34, 28 March 2020 (UTC)
@Sandbh: It shows that the correct Lu table has disseminated throughout the chemical community and has gotten uptake. Not only does the vast majority of sources seriously considering the group 3 question support Lu in group 3, but we can now see increasing adoption of this form by chemists whose subfield has no big stake in the issue. Double sharp (talk) 12:39, 28 March 2020 (UTC)

@Double sharp: Good old Wulfsberg did no more than rely on Jensen's arguments which you and I discredited and Scerri politely referred to as being "too selective". I'll bet Clayden at al. did nothing better. I further note Wulfsberg relies on the electron configurations of the ions, a practice your have derided. Sandbh (talk) 05:16, 29 March 2020 (UTC)
@Sandbh: With Droog Andrey's help, I then proceeded to rehabilitate Jensen's arguments, as reflected in this section. So everything is all right. As for good old Wulfsberg, we can see on page 7 that he is considering idealised valence electron configurations (perfectly following Madelung) of single atoms, which is exactly the practice I have been recommending here. Double sharp (talk) 06:14, 29 March 2020 (UTC)

Could you please list the vast majority of sources seriously considering the group 3 question support Lu in group 3? Sandbh (talk) 05:16, 29 March 2020 (UTC)
@Sandbh: Straight from User:Sandbh/Group 3: Jensen (1982, 2009, 2015); Wittig (1973); Chistyakov (1968); Trifonov (1970); Landau and Lifschitz (1958); Horovitz and Sârbu (2015); Settouti and Aouragi (2014); Scerri and Parsons (2019); Alvarez (2020), the last two from this thread. Contra Lavelle (2008, with Jensen soundly rebutting him), Shchukarev (1974), Restrepo (2017, not to mention that Jensen's 1982 comment about neglecting intraperiod analogies applies just as well to his article), Cao et al. (2020). The majority of people who seriously think about what elements should go in group 3 plump for Lu. Those supporting La are decidedly in the minority. Double sharp (talk) 06:21, 29 March 2020 (UTC)

@Double sharp:

Jensen: as you know, was (too) selective in his data
- That's just because the chemically active subshells take some twists and turns before they translate to real chemistry. Yes, it is true that comparing structural similarities is not the most relevant thing in the world, just look at NaCl vs. CsCl, or even better CO₂ vs. SiO₂. But Jensen's exhortation to look at intraperiod analogies is decisive. All the 5d metals add a filled f core – only true with Lu in group 3. The 5d metal is in each case (up to about group 10) similar to the 4d metal, while the 3d metal stands apart – only true with Lu in group 3. And as I tabulated above: in no case relevant to real chemistry does a Lu table perform worse than a La table. First three ionisation potentials, as Scerri and Parsons point to as a counterexample, are not relevant because the +3 state is not common for most of the metals involved. In the absence of such a common state the only rational starting point is ionising the two s electrons, which generally go first, and is what Droog Andrey has plotted. Double sharp (talk) 06:22, 2 April 2020 (UTC)
Wittig: while interesting is very far from a chemical table e.g. he shows Cs and Ba as f-block. This may be so at temperatures close to absolute zero, but we are talking about a PT at ambient conditions
- His arguments about Cs and Ba aside, which mostly step from acceptance of Be-Mg-Zn and therefore a misunderstanding of the rôle of the s-block, his argument for the Lu table comes from the fact that La is an f band metal and is right on target. Double sharp (talk) 06:22, 2 April 2020 (UTC)
Chistyakov: as per Jensen
Trifonov: five main arguments, with four being inconsistent. For his strongest argument he committed an own goal i.e. "…in the spectrum of La the configuration levels containing 4f-electrons are extremely deep—already there is a tendency to strengthen the bonds of 4f-electrons" but that [and here comes the own goal] "this can hardly serve as a sufficient basis for considering La as the first element of 4f-family."[!] He also conveniently overlooked the precedents set by H and He.
- Own goal aside, he's right, and in fact this should be the basis for putting La into the f block. It has f-involvement credentials of the same order as that of Th, which is universally regarded as an f element. It is in fact more or less what Jensen notes about low-lying f-orbitals for La and Ac. Double sharp (talk) 06:22, 2 April 2020 (UTC)
  - Although I notice that on User:Sandbh/Group 3 Trifonov is listed both as supporting Lu and La in group 3, although he is under the La section, which is confusing. Double sharp (talk) 08:18, 5 April 2020 (UTC)
Landau and Lifschitz: inconsistent with group 12 as part of d block
- Not so because the d orbitals of group 12 have a cohesive effect on strengthening the bonds, which is absent for the f orbitals of Lu and Lr. Double sharp (talk) 06:22, 2 April 2020 (UTC)
Horovitz and Sârbu: seized on Lu—based solely on its outlier status—as their preferred homologue of Y absent of any consideration or comparison of the merits of La, which was also identified by them as an outlier lanthanide, albeit not quite as peripherally
- That's already a good Lu argument: La and Lu would be expected to be outliers anyway, because they are the last members of the series. Probably the most typical Ln is Gd. The fact that Lu is more of an outlier than La strongly suggests that it is the one that should be taken out of the Ln series. Double sharp (talk) 06:22, 2 April 2020 (UTC)
Settouti and Aouragi: looked at only one side of the equation
- That's irrelevant because the whole point is to compare to the 5d metals. The correct other side of the equation is to see how well La blends in as a transition metal, and it does so quite badly. Double sharp (talk) 06:23, 2 April 2020 (UTC)
Scerri and Parsons: Scerri has said this argument does not in fact work
- I would argue that it does, but I'll drop this because one of the authors has rejected it. Double sharp (talk) 06:22, 2 April 2020 (UTC)
Alvarez: I’ve seen arguments of this kind before. Whether Lu is placed after Yb or under Y doesn’t matter; it blends just as well into the the 5d row from either position. It’s silly to say La doesn’t look as good, without taking account of the 13 lanthanides falling between La and Lu.
- But La doesn't blend into the 5d row at all. One must ask: should the lanthanide intervention be considered to occur as Ce-Lu, or La-Yb? Given that one of the things that is most common about Ln chemistry is the use of f orbitals, chemically relevant configurations strongly suggest the latter.
- Might I also add: if we are simply tallying sources, then the point is to count them not so much as evaluate them ourselves. I can easily demolish the La arguments of the other papers, and have done so elsewhere on this page, but this is not the place to do it. Double sharp (talk) 06:22, 2 April 2020 (UTC)

Sandbh (talk) 10:30, 1 April 2020 (UTC)

New arguments have arisen about the Lu table (e.g. the one by Scerri and Parsons).
@Double sharp: As mentioned, Scerri has acknowledged that this argument doesn't work (Scerri ER 2020, pers. comm., 14 Feb). Sandbh (talk) 12:34, 28 March 2020 (UTC)
@Sandbh: He should take back his acknowledgement then, because it clearly does work as I demonstrated above. The "additional requirement" is in fact a totally standard part of the Madelung rule, so it is not setting up the La form to fail; it fails on its own merits. In any case, the argument is published and we can cite it. Double sharp (talk) 12:39, 28 March 2020 (UTC)

@Double sharp: I recommend not citing his argument, on ethical grounds. Sandbh (talk) 05:16, 29 March 2020 (UTC)

@Sandbh: What does Parsons think of the argument, then? If he still thinks it is OK, there is no reason it should be gotten rid of. And his is not even the only recent strong argument for Sc-Y-Lu anyway. Double sharp (talk) 06:14, 29 March 2020 (UTC)

@Double sharp: I don't know. Parsons was a student of Scerri, so I presume Scerri wouldn't have told me (and others) that their argument doesn't work unless he knew Parsons would go along on with it. I remember when Scerri set you and I some homework associated with this argument, and even then you were sceptical. Note the table that goes with their argument has two errors: (1) La is listed as a 5d d/e (right), Th is listed as a 5f d/e (wrong); (2) n+l, n for La is shown as 7, 5 (right); n+1, n for Th is show as 8, 5 (wrong). The d/e for Th is 5d; n+l, n = 8, 6. Sandbh (talk) 23:34, 29 March 2020 (UTC)

@Sandbh: The idea of the argument as I see it now is about the idealised differentiating electron following the Madelung rule, which is why it's perfectly correct to say that Th is 5f on the basis that it shows 5f chemistry. It is in the f block, and until recently you agreed with that. A Lu table follows the n+l rule; the La table doesn't, instead implying its own "one 5d, fourteen 4f, nine 5d" rule. That's not something I made up, Silberberg says the exact same thing on page 316: he presents on page 314 what looks most like a La table, and then says "In Period 6, the 6s sublevel is filled in cesium (Cs) and barium (Ba), and then lanthanum (La; Z = 57),the first member of the 5d transition series, occurs. At this point, the first series of inner transition elements, those in which f orbitals are being filled, intervenes (Figure 8.12)." That's the logical statement the La table is making. The reason this is important is because the pattern of subshells being used for chemistry follows the n+l rule perfectly (with the s-block exemption, but that still becomes active at the right time according to the n+l rule) until flerovium. And then with very little changes to allow for relativistic effects on the s and p_1/2 orbitals until element 172 and maybe even beyond. However, in deference to your statement, I have removed mention of it from periodic table (there are plenty more Lu arguments anyway, and this one requires referring back to the idealised configuration that settles the matter already). Double sharp (talk) 01:56, 30 March 2020 (UTC)

Perhaps within a few days, to let some comments to my last postings here and changes there come in.

Fear not. I shall not be advocating helium over beryllium, as I know there is not yet enough support for that in the literature. Watch out for that next decade, maybe. ^_^ Double sharp (talk) 14:18, 27 March 2020 (UTC)

All fine, but since this is touching our published PT's, I'd like to read a separate boil-down section that expresses this consensus. A new ==-one I suggest. -DePiep (talk) 00:32, 28 March 2020 (UTC)

@DePiep: To clarify (since I seem to have expressed this a bit badly): I have not changed anything about the PT presentation yet, only the commentary text in the article. It still does not take a side between Sc-Y-La and Sc-Y-Lu: it only corrects factual errors, and the reason I mention this here is that it was this discussion that drew my attention to (and made me find the sources for) these errors. I intend to start a new RFC within the near future to propose the change back to Sc-Y-Lu; once the RFC runs, then we will either have a consensus to change it, not to change it, or no consensus at all (which would default to "keep the status quo for now"). Until then, I do not propose any changes; even though I guess you could say this discussion has something like 4-1 siding Lu in group 3 over La, it is strictly a Project-internal one, and since the previous change was done via an RFC, I think this proposed one should be done that way too. Double sharp (talk) 02:33, 28 March 2020 (UTC)

All clear. Yes that would be a good process. (Getting couclusions out of this long discussion would be hard for me; summaries would be welcome too but alas). -DePiep (talk) 12:01, 28 March 2020 (UTC)

@Double sharp: Such an RFC will effectively be a waste of time given we are here to reflect the literature, in which there is a 4:1 margin in favour of Sc-Y-La-Ac. Not to mention the IUPAC project is looking at the same question. Sandbh (talk) 12:34, 28 March 2020 (UTC)

@Sandbh: The literature that considers the question must be weighted above literature that simply presents a periodic table baldly and does no analysis of what table is right; therefore the margin is in fact in favour of Sc-Y-Lu-Lr among the relevant sources. Otherwise we would have to consider Sc-Y-*-** as a legitimate option, that is quite possibly about as common as the Sc-Y-La-Ac form. Double sharp (talk) 12:36, 28 March 2020 (UTC)

@Double sharp: I can't fault your HUGE ambition! The distribution is 4 in 6 = La; 1 = Lu; 1 = *. Sandbh (talk) 05:16, 29 March 2020 (UTC)

@Sandbh: Are you sure you are counting them correctly? As I'm sure DePiep would come along to tell you, any table with a cell below Y reading "La*", and not an asterisk between groups 3 and 4, or making any implication that the Ln and An also belong in those cells aligned with group 3, is really a Sc-Y-*-** table and not a Sc-Y-La-Ac table. Double sharp (talk) 06:14, 29 March 2020 (UTC)

@Double sharp: Yes, I had found more or less the same result. Scerri then did another survey, and found the same distribution. Sandbh (talk) 23:38, 29 March 2020 (UTC)

@Sandbh: I'd expect that if you counted group 3's looking like my illustration below, with the asterisks in the same cells as La and Ac, as Sc-Y-*-** as they literally mean, that the distribution would swing sharply towards Sc-Y-*-** instead. Or at least to a significant fraction of authors being inconsistent, e.g. by discussing group 3 as Sc-Y-La-Ac and then giving a Sc-Y-*-** table. That is already nothing new; we surely have countless authors who display the usual Aufbau graphic and then proceed to inconsistently not use the Lu table to go along with it. Double sharp (talk) 02:02, 30 March 2020 (UTC)

@Double sharp: They incorporated my research, and I knew what I was doing, into theirs. Wishful thinking is fine but you're on a (very) long shot here. Sandbh (talk) 09:54, 1 April 2020 (UTC)

@Sandbh: Well, if you saw a table with a group 3 looking like

3
Sc
Y
La*
Ac**

would you have classified it as Sc-Y-La-Ac or Sc-Y-*-**? If the latter, I can't argue with your 4-1-1 distribution. If the former, then DePiep and I are in disagreement with you. In any case, though, it certainly seems to me that the majority of authors who are explicitly focusing on the group 3 issue are writing articles in favour of Sc-Y-Lu. Double sharp (talk) 13:12, 1 April 2020 (UTC)

@Double sharp: It depends on what the footnote looked like. If 15 wide then it's counted as Sc-Y-*-**. If 14-wide, as in Ce-Lu, then it's Sc-Y-La-Ac. Yes, I agree about most of those authors. The rest who say naught are Lavelle's silent majority. Sandbh (talk) 01:06, 2 April 2020 (UTC)

@Sandbh: I object (strange talkpage flow, btw). The meaning does *not* depend on the content of the "footnote".

For starters: here the * does not mean "footnote" (like a note) as we undestand in academic literature. The * here, in the PT, is a placeholder for a part that is placed elsewhere. As such, they are just a replacement for a displaced part, they do not refer to some additional clarifying note. They are part of the graphic. There is no "meaning" in there. The modern word for this may be 'proxy' (for "100% resentative").

Simply, here: when it is below columnheader "3", it is a "3". Even when there by replacement placeholder.

A pity this clarification must come back again and again. But if needed, so be it. -DePiep (talk) 02:02, 2 April 2020 (UTC)

@Sandbh: But are they a silent majority? Or just a majority who never went out of their way to look at the issue? We don't know, because they mostly wrote nothing to justify it. And "nothing" is hardly a strong argument in the face of the authors who look at the issue! Double sharp (talk) 03:58, 2 April 2020 (UTC)

@Double sharp: Most likely. They never went out of their way since there was nothing perceived to be in it. Jensen gave it perhaps the best shot, and went nowhere. That is quite an achievement given the "nothing" in support of La. Sandbh (talk) 05:31, 2 April 2020 (UTC)

@Sandbh: Or more likely because they never even realised there was a dispute in the first place. I quote Jensen's 1982 paper (with my italics): "Indeed, in talking with his fellow chemists, the author discovered that none of them was aware of the evidence favoring the reassignment of lutetium and lawrencium or indeed that there ever was any question about their placements (a category in which the author must include himself until very recently). As chemists, the periodic table is presumed to be our special province; surely its about time we pay attention to what the physicists have to tell us about its arrangement." And the majority of chemists who have done such an analysis of their special province have plumped for Lu.

Meanwhile, DePiep and I agree that there are evidently some tables that you classified as Sc-Y-La that literally mean Sc-Y-*. If we reclassify them as Sc-Y-*, I bet the majority for Sc-Y-La will shrink drastically. Double sharp (talk) 06:26, 2 April 2020 (UTC)

@Double sharp: Yes, there was never dispute for them to take any notice of. Jensen is not a good example, for reasons I've previous discussed. As you know, the work of the rest of chemists who have done such an analysis in favour of Lu have been far too narrow in their scope, to come up with their findings and, consequently, to generate a dispute on the radar of the chemistry establishment. Sandbh (talk) 05:05, 4 April 2020 (UTC)

@Sandbh: And, yet, IUPAC sees fit to address the dispute. So much for the radar of the chemistry establishment. There is nothing narrow about the scope of Lu arguments: they are based on universal patterns and trends through the table, not just plucking everything out of context like La arguments tend to do. Double sharp (talk) 08:15, 5 April 2020 (UTC)

I agree our leading literature should be literature about this issue, their group presentations equally critically checked (I volunteer). A bit like our metalloids? And then, just tallying is a bit primitive, it could be that in 50 papers there are only two or five deciding principles used.

Even IUPAC has a 32-element group 3 presented [1] (2018), while OTOH having a taskfoce looking into this without that option [2] (2015). To me, a forked group 3 Sc-Y-La-Ac-Lu-Lr is imaginable too. hth. -DePiep (talk) 08:52, 29 March 2020 (UTC)

@DePiep: I don't feel we have to consider the forked group 3 significantly since it is an extreme minority view in the first place. (I personally sympathise with the idea of bringing in La and Ac as additional elements when describing general chemistry of group 3 for comparison. But I would also support bringing in Al. That doesn't change group assignments, which are from idealised electronic configuration just as I propose and Wulfsberg mentions.) In fact, I think it should be excised from the main periodic table article in the first place since apart from the mention of Silberberg there is no mention of anyone ever arguing for or adopting it. Sc-Y-Lu by contrast has been the persistent viewpoint that has slowly gained a lot of ground over the decades as newer and newer findings come in its favour. And it is even the majority viewpoint among those who seriously consider the group 3 situation; such sources, we agree, should be weighted higher. ^_^ Double sharp (talk) 11:39, 29 March 2020 (UTC)

P.S. Not to mention that Silberberg himself also gives a Sc-Y-La-Ac (sort of) table on page 58 (and again on page 314). Well, there is a gap drawn between La/Hf and Ac/Rf, that actually stretches across groups 3 and 4, so the literal reading is maybe that all the Ln and An are somehow not only group 3 but also group 4 elements. But at the very least, this table is either Sc-Y-La-Ac or Sc-Y-*-**, and is hardly a sign of consistency with the page 315 table which has the bifurcated group 3. So, since the one author we've seen using this option actually isn't even consistently using it, I think it should be deleted from the periodic table article as a fringe view. Double sharp (talk) 12:49, 29 March 2020 (UTC)

...and done. Double sharp (talk) 12:54, 29 March 2020 (UTC)

I am not advocating for any form, I just tried to say I am open to anything. And for me, I better not divert/"help" in this subthread, out of my league. Hope I can follow the condensed reasoning for whichever results, later on. (Or is there an other learning route?). -DePiep (talk) 12:10, 29 March 2020 (UTC)

@DePiep: I understand. I summoned you via the ping earlier to check with you: if a table shows a group 3 column that looks something like

3
Sc
Y
La*
Ac**

then it is really a Sc-Y-*-** table (asterisks in one cell) rather than a Sc-Y-La-Ac table, isn't it? For the latter, you would need the asterisks to be positioned between La/Hf and Ac/Rf like we currently do. Double sharp (talk) 12:51, 29 March 2020 (UTC)

Yes. (I added the "3"): everything in a column headed 3 = in group 3. That is not my interpretation. That is reading the table, any table, that is what "columnheader" means. The asterisks are placeholders, so simple substitution will clarify that. If someone wants to convey an other situation/claim/statement, then use a different graphic solution (or add descriptive footnotes for exceptions; may be elaborate an less intuitiuve, but at least it is a correct statement of what one wants to say). OTOH, omitting the '3' altogether introduces unclearness (or irresponsible ambivalence). Unfortunately, even Scerri did this [3]. -DePiep (talk) 15:55, 29 March 2020 (UTC)

re Pyykkö. Since Double sharp mentions Pyykkö in the es [4], I want to add this. Seeing Pyykkö's extended PTs (2011), I get the impression that PP is only extrapolating the old existing group 3 notion (Sc-Y-*-*) without reassessing its constitutional details (as this thread does, with new evidence btw). Looks like PP is more concerned with the extension build up itself, esp regular filling and irregularities in Z: 139, 140 (!). Without me having digested PP's paper, these drawings by themselves to me suggest that PP is not making any re-defining, explicit claims wrt group 3. -DePiep (talk) 13:58, 31 March 2020 (UTC)

@DePiep: Xu and Pyykkö do talk about group 3 in section 4 of this paper, preferring to have 15-element f-block rows (so Sc-Y-*-**). OTOH, I notice they call La f⁰ and Lu f¹⁴ (by that logic, what group is d¹?). Double sharp (talk) 14:02, 31 March 2020 (UTC)

thx. From 2016 I see, again triggered by the Lr ionisation energy (=recent data). lol @ "... and currently Wikipedia": example of WP:CIRCULARSOURCING ;-). I hope "chosen [by IUPAC and] by us" has its arguments in the paper, though "our conclusion" would sound better. I think I must leave this, out of my league. -DePiep (talk) 14:12, 31 March 2020 (UTC)

Science is the ability to admit mistakes

Double sharp's position

Abridged from my talk page:

I have not so long ago been on the other side of this debate. You may remember that in 2016 I was arguing profusely for Sc-Y-La, which based on the chemical knowledge I then had was a logical consequence. The only problem is that now with our current knowledge it is not. The fact that I am now vociferously arguing on the other side at least shows that I am not trying to protect my result first of all.

I see part of where Sandbh is coming from, because I used to use those arguments too. Well, one of the main arguments we were pushing then was that group 3 (all of the possible members) more strongly skewed towards s-block behaviour than d-block behaviour, so it should follow the s-block trend. And I agree that this would still be a good argument for La if the premise was true. The only problem is that, as Droog Andrey explained to us back in 2018 and now, it is not:

In fact, this s-block-ish behaviour is totally normal for many early transition metals: just look at Zr, Hf, and Rf (which even form +4 aqueous cations, what more could you ask for?), and to a slightly smaller extent Nb, Ta, and Db. They all much prefer the group oxidation state. It's not special to group 3.
In fact, group 3 equally often shows behaviour similar to group 4. Just look at the contribution of the d electrons to its physical properties, and the poor coordination power of both groups. Or the trend in oxidation states (the first member has the biggest lower oxidation state chemistry of all four).

And the delayed collapse of 4f and 5f would be a good argument if it mattered for the chemistry, as I thought it did then. But, as Droog Andrey explained to us back in 2018 and now, it is not:

Lanthanum has no problem displaying 4f involvement in chemistry. Many examples have already been brought out for the discussion;
The exact same thing is true for thorium. You cannot consistently say that the delayed collapse is relevant for La and Ac but not for Th. If the chemistry of Th was categorically different by the presence of 5f involvement from that of Ac, that would be one thing, but that is false.
In general, ground-state electron configuration anomalies have about zero effect on real chemistry.

And the analogy of Zn to Lu and concomitant double periodicity would be a good argument, except for the fact that as Droog Andrey explained to us back in 2018 and now, it is not:

Zn 3d is chemically active, and the activity of the d subshell increases down the Zn group. Lu 4f is totally chemically inactive, and the activity of the f subshell decreases down the Lu group.
In fact, the real similarity is Eu to Mn and Yb to Zn, as we expect that across the series 4f collapses into the core similarly to 3d. The increased favouring of +2 done by the late actinides, contra Lr +3 off the trend, is exactly like the favouring of +2 done by Fe through Zn, contra Ga +3 off the trend.

It's the fact that despite all these refutations of the premises of the La arguments, Sandbh keeps trotting the same ones out over and over (e.g. predominant ionicity or covalency, and differentiating electrons, neither of which are well-defined), that makes me frustrated about the whole thing. I started out from the same arguments as he did that formed the backbone of the IUPAC submission, which was mostly based on the prongs:

Group 3 is more similar to the groups to the left than those to the right;
Delayed collapses are important for chemistry;
Double periodicity is better with a Ce-Lu f block.

The arguments would all be valid if these premises were true! But all three, I have now learned, are false. Therefore the conclusion cannot stand, and I changed my mind.

Not to mention the following Lu arguments that have instead been substantiated:

Lu cannot be an f element because it totally lacks f involvement.
La on the other hand does have distinct valence f involvement similar to Th.
Trends are superior, having better analogies across the table, with the Lu table.

And that's why I think it is still correct to start an RFC. Real science consists of admitting our mistakes. Double sharp (talk) 07:00, 29 March 2020 (UTC)

Sandbh's view

Pre 2016 I supported Sc-Y-Lu.

In 2016 I was in the same camp as Double sharp, arguing instead for Sc-Y-La.

I haven't changed my opinion since that time, although I did briefly explore Sc-Y=, where = denotes a bifurcation into an La tranche and an Lu tranche.

That is the first time I've had to use something else then an = to explain what = meant. Otherwise it would've gone, "…where = = a bifurcation…".

I read Droog Andrey's arguments. I was particularly stumped by one of these (Mar 7th, 2018) and left it there for a while. I eventually (Jan 21st, 2020) addressed it, to my satisfaction.

I think DA's arguments look good on the surface and with further digging don't stand up. In my view Double sharp has been hasty in accepting DA's arguments.

I trot out general chemical behaviour rather than marginal, peripheral, extreme or exaggerated chemical behaviour.

Yet your reliance on monocations to debunk DA's argument depends on such extreme behaviour. Double sharp (talk) 05:59, 2 April 2020 (UTC)

For the most part, group 3 behaves like groups 1-2, showing a tendency to ionic chemistry. Their oxides are basic (exception: Be). Their halides are characterised by ionic bonding.

Group 4, for the most part, shows a tendency to covalent behaviour. Their oxides show amphoterism. Their halides (aside from the fluorides) are characterised by covalent bonding. The +4 aqueous cations of Zr and Hf are formed only in extreme circumstances.

Sc₂O₃ also shows amphoterism, and as I've demonstrated this is purely a matter of oxidation state difference and electronegativity. The +4 aqueous cations of the actinides also need strongly acidic conditions to persist. And we've already debunked the idea of predominant covalency or ionicity. Not to mention that calling the circumstances for Zr⁴⁺ and Hf⁴⁺ "extreme" leaves U⁴⁺ in doubt already. Far better to consider cations for all elements, real or notional, and just use periodicity to guess how far they will be hydrolysed under normal conditions. There's not really a difference between Ti⁴⁺ and Zr⁴⁺, that's just solvent levelling for acids in water: water cannot support an acid stronger than H₃O⁺, because it will protonate water to form H₃O⁺ and that's all you'll be left with. Just look at other solvents, you'll see lots of nonmetal(!) simple cations there. Double sharp (talk) 05:57, 2 April 2020 (UTC)

The d-electrons in group 3 mainly play a part in the physical properties and have little to do with chemical behaviour.

Same is true for the d electrons in heavy group 4 and 5, which are mostly d⁰ in chemistry. Double sharp (talk) 05:57, 2 April 2020 (UTC)

4f involvement in La is marginal. In the trivalent Ce to Lu cations the 4f sub-shell electrons cause the Ln contraction. This is not seen in La.

We can't use such a criterion anywhere else on the table, so its use makes our criteria more complicated and internally inconsistent. Double sharp (talk) 05:57, 2 April 2020 (UTC)

Th has no 4f valence electron, but its chemistry is effectively universally regarded as being like that of an actinide.

Same for La and Ac. Double sharp (talk) 05:57, 2 April 2020 (UTC)

3d involvement in Zn is marginal.

It's near the top of the valence region of ZnF₂, hardly marginal. And just like you'd expect for a chemically active orbital (cf. s in He-Be-Mg-Ca-Sr-Ba-Ra, or p in Ne-Ar-Kr-Xe-Rn-Og), it goes up in energy as the Zn group is descended, whereas the f orbitals are drowned deeper as the Lu group is descended. Double sharp (talk) 05:57, 2 April 2020 (UTC)

The double periodicity seen in Sc-Y-La is more regular than that seen in Sc-Y-Lu. The former does not line up with Mn and Zn due to the delayed start of filling of the 4f sub-shell; the latter does not recognise the delayed start.

In chemical environments there is no such delayed start: La shows 4f occupation already. Therefore it is reasonable to neglect it as chemically irrelevant just as we neglect the anomalous p electron in the ground state of Lr. Double sharp (talk) 06:01, 2 April 2020 (UTC)

There is no "favouring" of +2 done by the late actinides, as can be seen here. This is only the case for No.

There absolutely is an increased tendency towards the +2 state, as shown by the electrode potentials. Es²⁺ is less stable than Fm²⁺ is less stable than Md²⁺ is less stable than No²⁺ which is much more stable than Lr²⁺. Same story for Tm²⁺ being less stable than Yb²⁺ being more stable than Lu²⁺, or Fe²⁺ being less stable than Co²⁺ being less stable than Ni²⁺ being less stable than Cu²⁺ being less stable than Zn²⁺ being more stable than Ga²⁺. Chemistry is continuous trends; clearly Lr, Lu, and Ga are falling off them here and are really starting something else. Double sharp (talk) 05:57, 2 April 2020 (UTC)

Dy³⁺ + e⁻ ⇌ Dy²⁺	−2.6 V	Cf³⁺ + e⁻ ⇌ Cf²⁺	−1.6 V
Ho³⁺ + e⁻ ⇌ Ho²⁺	−2.8 V	Es³⁺ + e⁻ ⇌ Es²⁺	−1.3 V
Er³⁺ + e⁻ ⇌ Er²⁺	−3.0 V	Fm³⁺ + e⁻ ⇌ Fm²⁺	−1.1 V
Tm³⁺ + e⁻ ⇌ Tm²⁺	−2.2 V	Md³⁺ + e⁻ ⇌ Md²⁺	−0.1 V
Yb³⁺ + e⁻ ⇌ Yb²⁺	−1.05 V	No³⁺ + e⁻ ⇌ No²⁺	+1.4 V

Fe³⁺ + e⁻ ⇌ Fe²⁺	+0.771 V
Co³⁺ + e⁻ ⇌ Co²⁺	+1.92 V
Ni³⁺ + e⁻ ⇌ Ni²⁺	+2.3 V
Cu³⁺ + e⁻ ⇌ Cu²⁺	+2.4 V

Both cases show trends where the stability of +2 relative to +3 increases gradually. They don't extend to Lu, Lr, and Ga, which are all equally clearly starting something else. Double sharp (talk) 12:07, 2 April 2020 (UTC)

The trends going down Sc-Y-La are like those seen in groups 1-2. Those going down Sc-Y-Lu are like those seen in groups 4-5.

Correct, and inconclusive. Double sharp (talk) 05:57, 2 April 2020 (UTC)

The literature is dominated by Sc-Y-La. That does not make it right. There has been no demonstration that it is egregiously wrong, despite isolated spasmodic arguments for Sc-Y-Lu appearing in the literature over the past six or so decades. Sandbh (talk) 04:49, 2 April 2020 (UTC)

That demonstration comes from 4f involvement in La, the oxidation states' double periodicity which is nonsensical with a Sc-Y-La table, and the more consistent trends in the 5d and 6d rows that result with a Sc-Y-Lu table. The fact that these important points have had no serious effect is likely a case of inertia, not a case of the Lu arguments being seriously debunked. Double sharp (talk) 05:57, 2 April 2020 (UTC)

Aqueous chemistry

This table shows the solubility of a range of compounds from groups 1 to 5:

         1-3  4-5
bromide   s    d
chloride  s    d
fluoride  s/i  d
iodide    s*   d
nitrate   s    d
sulfate   s/i  d^

s soluble
d decomposes
i insoluble
* Cs slightly soluble; Be decomp
^ Zr-Hf only

Note the rather distinct difference between groups 1–3 and groups 4–5.

My source is Schweitzer GK and Pesterfield LL 2010, The aqueous chemistry of the elements, OUP, Oxford

@Sandbh: This is a matter of oxidation state only. +4 cations in the d block are usually strong acids even for the ones that exist (Zr⁴⁺, Hf⁴⁺, Rf⁴⁺; Ce⁴⁺ and some An⁴⁺), whereas +3 cations in the d block are usually just moderately acidic. When the salt goes into aqueous solution, +1 through +3 cations can stay mostly as they are, water doesn't hydrolyse them so badly, and the important thing is the interaction between cations and anions that will determine solubility. +4 and notional +5 cations will be strongly to very strongly acidic, just look at the pKa table. Of course there will be substantial reaction with the water molecules instead, the salt hydrolyses and decomposes. It's the same as why dissolving Li₂O in water results in violent reaction to form LiOH: here the Li⁺ cation is no problem, it's the O²⁻ anion that is too basic for water. But it's not a relevant way to determine where a block starts and ends, because that comes from electronic structure, not this higher level of descriptive chemistry (which, depending on what we focus on, can show big differences starting not only at group 4, but also at just about any one; for example, look at the structures and states of the oxides, specifically at the melting point trends, where the gap may be at group 3 or 5 but never group 4). Unless you would like to propose cutting group 13 from group 14 in the p-block, because it has the exact same +3 vs. +4 cation problem? SnX₄ halides hydrolyse readily in water (Greenwood and Earnshaw, p. 381), but according to our article on InCl₃ that has no problem dissolving in water. I also remind that the filled d shell impacts all of Ga³⁺, In³⁺, and Tl³⁺ chemistry and does not exist for Sc³⁺, Y³⁺, La³⁺ and Lu³⁺, echoing your argument for keeping Lu in the f block. So by this logic pushing group 13 into the d block and group 3 out of it is not a far stretch either... Double sharp (talk) 14:26, 30 March 2020 (UTC)

(For group 14: CCl₄ is an exception because C⁴⁺ is so small and there is no room for water to attack it. SiCl₄ behaves like you would expect.) Double sharp (talk) 10:20, 2 April 2020 (UTC)

@Double sharp: I'm not looking at where a block starts and ends. What happens in the p-block has never and will never be a consideration of mine. I have no desire to take on the chemical establishment in this regard.

Yes, the pKa table is illuminating:

1         2        3       |4…          | 5        6       7        8       9
Li 13.6   Be  6.2          |            |
Na 14.2   Mg 11.4          |            |
K  14.5   Ca 12.8  Sc 4.3  | Ti -2.1?*  | V  3.5?^ Cr 4.0  Mn 10.6  Fe 2.2  Co 9.6
          Sr 13.3  Y  7.7  | Zr -0.3    |
          Ba 13.5  La 8.5  | Hf  0.2    |
                   Lu 7.6  |            |

* here; ^ here

The seeming group 4 valley is interesting.

The same sort of thing is seen with the oxides and their crystalline structures:

            1-3  4-5
cubic        ✔
hexagonal    ✔
tetragonal        ✔
monoclinic        ✔
orthorhombic      ✔
complex           ✔

Here the less symmetrical structures appear after group 3.

In this vein, Porter (1993, pp. 99-100) writes:

"Although there are many MO₂ oxides, the +4 oxidation state requires such a large energy input to ionize the cation that few such oxides can be thought of as strongly ionic in their binding. The obvious candidates are the group-IVb metals Ti, Zr, and Hf…It should be clear that the bonding…in the MO₂ oxides [TiO₂ and ZrO₂ listed as examples]…is at most partly ionic, with covalent bonding being significant in determining lattice geometry and energy relationships. This combination of energy factors can lead to very complex structures and superstructures."

Source: Porterfield WW 1993, Inorganic chemistry: A unified approach, Academic Press, San Diego, p. 336

My conclusion is that the solubility table, the pKa table, and the oxide crystalline structure table point to a natural rough divide between groups 3 and 4. The sky will not fall down as a result. Sandbh (talk)

@Sandbh: Again: what is the oxidation state? That is the important question. Of course the pKa of a +1 cation will be higher than that of a +2 cation, which will be higher than that of a +3 cation, and so forth. Ti⁴⁺ has a pKa of about −4.0, contrast Ti³⁺ with 2.2 (cite: Wulfsberg).

Oxides tend to be more acidic and covalent as the countercation increases in oxidation state, it's true throughout the periodic table. First I look at acidity. For chromium, contrast CrO (basic) with Cr₂O₃ (amphoteric) and CrO₃ (acidic). For nitrogen, contrast N₂O₃ (which dissolves in water to give the extremely weak nitrous acid) with N₂O₅ (which gives strong nitric acid instead). Then I look at covalency. RuO₂ has the rutile structure of TiO₂ (so, partly ionic, partly covalent), whereas RuO₄ forms discrete molecules. It's the same story absolutely everywhere. There's not a natural distinction between groups 3 and 4 at all, it's between oxidation states.

Of course the difference moves around throughout the periodic table as a bigger cation is better at handling high oxidation states: it is less polarising, exactly by Fajans' rules. That's why CO₂ and SiO₂ have such different structures. As for covalent character in oxides, we can guess when it starts becoming significant by basic high-school chemistry: it should be when the melting point goes down even though the charge of the notional cation went up. That happens between MgO and Al₂O₃, CaO and Sc₂O₃, and SrO and Y₂O₃, so here the gap is group 2 to group 3. Except that in period 6 the point where the melting point first dips jumps to between HfO₂ and Ta₂O₅, completely bypassing any stage when it is group 3 to group 4. That is true regardless of whether you put La or Lu in group 3, BTW. ^_^

For confirmation, just look at what happens in the group 4 and 5 lower oxides. Ti₂O₃ has the regular corundum structure, so does V₂O₃. Same thing happens with the solubility table: TiCl₄ and VCl₄ hydrolyse in water, TiCl₃ and VCl₃ dissolve readily without reaction. So, it's definitely not a difference between group 3 and group 4, but between the +3 and +4 oxidation states. Double sharp (talk) 07:37, 1 April 2020 (UTC)

@Double sharp: The most stable oxidation state in all cases i.e. the most representative. Sandbh (talk) 09:24, 1 April 2020 (UTC)

@Sandbh: Most elements do not have a single most stable oxidation state. Rather they have multiple chemically important ones. If you insist on only including the most stable, without taking into account things like Ti³⁺ (which, I should note, is the sole reason why Ti satisfies the typical transition metal properties, so without it we even more so have a gap between groups 4 and 5 and not 3 and 4), you are going to overlook that it is exactly the same process going on that controls the difference between Ti³⁺ and Ti⁴⁺ just as it does between Sc³⁺ and Ti⁴⁺. Double sharp (talk) 10:08, 1 April 2020 (UTC)

@Double sharp: That's news to me, that most elements don't have a single most stable oxidation state. Looking at our own list I count 81 out of 109 with one most stable oxidation state. I don't insist on including only the most stable. There would be no point in saying the most oxidation state of Ti is +4 and therefore concluding it's not a TM chemically when clearly it is. Like you said, many elements have more than one oxidation state, although most won't be that chemically important. Sandbh (talk) 11:02, 1 April 2020 (UTC)

@Sandbh: Just look at any set of Pourbaix diagrams; you'll see a lot of different predominating species in different oxidation states, depending on pH and E₀. To clarify what I meant, you can't have a single most stable oxidation state that will keep that status over most chemically relevant conditions. Rather there's a bunch of states that can be stable (you just need to choose the conditions correctly), and also a bunch that are not really stable under any conditions but persist because of kinetic hindrance or something like that. And then you'll have the really unstable ones that basically need cryogenic anaesthesia and to be locked away far away from everybody else to even exist like Ir(IX). But even restricting to the first group, there will usually be more than one. Should we pick Sn +2 or +4? We should always consider both, as they can both be relevant depending on conditions. Double sharp (talk) 12:05, 1 April 2020 (UTC)

@Double sharp: That's not quite right. I remember reading, when I was trying to work out the most stable state for N, that the most stable oxidation state is the one closest to the x-axis, or something like that, either in a Pourbaix diagram or something close to that. I'll see if I can find that reference.

Yes, found it. "The most stable oxidation state of an element corresponds to the species that lies lowest in its Frost diagram." Sandbh (talk) 02:06, 2 April 2020 (UTC)

@Sandbh: No, it depends on the conditions. You have to take into account whether the conditions are oxidising or reducing, because in real life there will be lots of species present and they can perform redox reactions with each other. Depending on such conditions, the predominant oxidation state for iron might be 0, +2, +3, or +6. Nothing wrong with that. Fe²⁺ is stable in water, so is Fe³⁺, and so is FeO₄²⁻: you can put all those ions in aqueous solution, and they won't reduce or oxidise the solvent. We must consider them all, or else our approach becomes too simple to be simple. And we must even include species that should disproportionate but are kinetically hindered from doing so: for chlorine, only Cl⁻, Cl₂, and ClO₄⁻ appear on the Pourbaix diagram, but the disproportionation of ClO₃⁻ is slow and so that species can persist in aqueous solution for some time. This is absolutely standard chemistry: the most stable state depends on the chemical environment. Just look at how fluorides often are in higher oxidation states than iodides. Double sharp (talk) 03:41, 2 April 2020 (UTC)

@Sandbh: As long as the conditions are specified and consistently applied in comparing elements, it's valid. Sandbh (talk) 05:08, 2 April 2020 (UTC)

@Sandbh: No, it obscures the important factor just as talking about "predominantly ionic" and "predominantly covalent" does. The important factor being that acidity clearly correlates with ionic radius and charge, and that varies between oxidation states of the same element just as it does between different elements. Double sharp (talk) 05:52, 2 April 2020 (UTC)

And let's see what happens for really small cations:

HCl soluble	(He)
LiCl soluble	BeCl₂ hydrolyses	BCl₃ hydrolyses	CCl₄ insoluble	NCl₃ hydrolyses slowly	(OCl₂) hydrolyses slowly	(F)	(Ne)
NaCl soluble	MgCl₂ soluble	AlCl₃ hydrolyses	SiCl₄ hydrolyses	PCl₅ hydrolyses PCl₃ hydrolyses	SCl₂ hydrolyses S₂Cl₂ hydrolyses	(Cl)	(Ar)

So much for the supposed gap between groups 3 and 4. Note also that some weak hydrolysis happens for cases like MgCl₂ (the resulting solution is weakly acidic). I say again as I have been saying for the past few months: everything here is a continuum, and there are no fundamental divides between groups even from the large-scale viewpoint! The only exception to that blanket statement is when you pass a noble gas to the next period! Double sharp (talk) 13:58, 2 April 2020 (UTC)

The group 3 to 4 "divide"

@Double sharp: We’ve been discussing whether or not this exists.

We’ve argued about predominately ionic v predominately covalent. You’ll recall the extract from Rayner-Canham and Overton:

"For chemists…the most important feature of an element is its pattern of chemical behaviour, in particular, its tendency toward covalent bond formation (or its preference for cation formation)." (p. 29)

They add some nuance:

"The Ionic-Covalent Boundary
Unfortunately, there is no firm predictable boundary between ionic and covalent behaviour for solid compounds of metals and nonmetals. As predicted from Fajans’ first rule, increasing theoretical cation charge results in increasing charge density, which will favour covalent behaviour. However, as predicted by Fajans’ second rule, the anion also plays a role: thus as the metal oxidation state increases, the iodide is first likely to exhibit a low melting point, then the bromide, then the chloride, and finally the fluoride and oxide." (p. 99)

"…inorganic chemists see not a rigid ionic-covalent divide but a bonding continuum. Figure 5.11 shows electron density profiles for four points on this continuum: the pure covalent, a polar covalent bond, a polarised ionic bond, and a pure ionic bond. The ratio of ionic to covalent character can be defined as the difference in electronegativities…between the pairs of atoms. Thus, pairs of atoms with…[a difference] close to zero will possess essentially pure covalent bonds with equally shared electrons, whereas those…> 3.0 are regarded as purely ionic… (p. 109)"

They go on to refer to the Van Arkel-Ketelaar bond triangle with its "rough" division into metallic, ionic, and covalent “zones” and Laing’s extension of the triangle into a tetrahedron.

These kinds of divisions, while rough, are nevertheless valuable. As expressed by Nelson (2011):

"…care needs to be taken to remember that…[this classification scheme] is only an approximation, and can only be used as a rough guide to the properties of the elements. Provided that this is done, however, it constitutes a very useful classification, and although purists often despise it because of its approximate nature, the fact is that practising chemists make a great deal of use of it, if only subconsciously, in thinking of the chemistry of different elements.

@Sandbh: Using those four categories is so much better than "predominantly ionic" or "predominantly covalent", so I'm glad we have come to some agreement on this. They are in fact the reason why I find "predominantly ionic" and "predominantly covalent" not useful: using those terms sweeps under the rug the very trend that is so clearly controlling it, that of electronegativity difference as Rayner-Canham and Overton are saying. Double sharp (talk) 13:09, 1 April 2020 (UTC)

@Double sharp: Quite so. Sandbh (talk) 01:08, 2 April 2020 (UTC)

@Sandbh: Well, I have been saying exactly that since January:

“

Look, there is no such thing as a complete volte-face from ionic to covalent. It depends on what the counter-anion is. We go from ionic to metallic (which you're overlooking completely) across the series NaCl, Na₂O, Na₂S, Na₃P, Na₃As, Na₃Sb, Na₃Bi, Na. And that's in group 1, with an example taken straight from Greenwood & Earnshaw p. 81. Ionic vs. covalent is (1) gradual, from covalent to polar covalent to mildly ionic to strongly ionic, depending on the difference of electronegativity between the two elements; (2) not a complete dichotomy, because you overlook metallic bonding; and (3) not split by elements, but rather by electronegativity differences, which have a lot to do with oxidation state (just compare uranium chemistry as we jack the oxidation state up from +3 to +4 to +5 to +6). So I'm astonished to see you put so much weight on "ionic vs. covalent" as a false dichotomy. (And as I keep saying, the general thing across the periodic table is continuity, and the sharp dichotomies you like to point to have a distinct tendency to not exist.) ... Double sharp (talk) 23:41, 26 January 2020 (UTC)

”

But it looks like it's only admissible when Rayner-Canham and Overton say it, not when I say it, even if it is absolutely normal high school chemistry material (which I learnt too). Now, the same thing is going on for the supposed volte-face between group 3 and group 4 on the basis of aqueous chemistry: it doesn't exist, all you have is oxidation states, atomic radius, and electronegativity too, exactly like I remember from high school chemistry. Or do I have to quote Wulfsberg explicitly? ;) Here's a quote from p. 94 of his Principles Of Descriptive Inorganic Chemistry:

“

Because the acidity of a cation rises rapidly with its charge, there are several d-block elements possessing several oxidation states (such as chromium) that have one or more oxides that show only basic properties (e.g. chromium(II) oxide, CrO), one or more oxides that are amphoteric (e.g. chromium(III) oxide, Cr₂O₃), and one or more oxides that possess only acidic properties (e.g. chromium(VI) oxide, CrO₃). Clearly, the higher the oxidation number of a given element, the more acidic the corresponding oxide will be.

”

Zero mention of group divides in his whole section on periodic trends in acid-base and solubility properties of oxides. Which is because there is no such thing. Double sharp (talk) 14:04, 2 April 2020 (UTC)

In this context, while there’s no sharp dividing line between groups 3 and 4, the substantial differences are clear enough to permit a collective demarcation.

I recently added the section on aqueous chemistry, now including kPa’s of metal cations and the crystalline structures of oxides.

Here are some more references supporting the 3/4 demarcation.

Hydroxides

This is a table of calculated pH₀ values for some hydroxides:

2         3        4…        6        8       9        10       11       12
Be  1.1
Mg  8.8
Ca 11.38  Sc 4.10  Ti 0.46…  Cr 3.54  Fe 1.5  Co 6.56  Ni 6.56  Cu 4.06  Zn 5.3
Sr 12.24  Y  5.84  Zr 0.99…                            Pd 2.5   Ag 6.27
Ba 12.85  La 6.77                                    
          Lu 5.00

Note the low values of group 4 compared to groups 2−3, and 6+

Source: Aksel’rud NV 1963, "Hydroxide chlorides and hydroxides of elements of the scandium subgroup and of the lanthanides", Russian Chemical Reviews, vol. 32, no. 7, (in Russian), pp 800−822 (813), viewed 31 March 2020.

NB: I don’t read Russian. I have the English version of the article in hard copy. I could only find an e-copy in Russian.

@Sandbh: As usual, this is just the oxidation state difference all over again. Everybody but group 4 here is in a lower oxidation state, so of course the pH₀ value is higher. Double sharp (talk) 10:10, 1 April 2020 (UTC)

Acidity parameter for basic oxides

This is a table of giving acidity parameter values for binary oxides:

1           2          3           4         5
Li₂O  -9.2  BeO  -2.2
Na₂O -12.5  MgO  -4.5
K₂O  -14.6  CaO  -7.5  Sc₂O₃   ?   TiO₂ 0.7  V₂O₅ 3.0
Rb₂O -15.0  SrO  -9.4  Y₂O₃  -6.5  ZrO₂ 0.1
Cs₂0 -15.2  BaO -10.8  La₂O₃ -6.1
                       Lu₂O₃ -3.3

Note the close resemblance to the preceding table.

Source: Smith DW 1990, Inorganic chemistry: A prelude to the study of descriptive chemistry, Cambridge University Press, New York, p. 326

@Sandbh: Oxidation state difference all over again, which is why V₂O₅ is so high. I wonder how high Ti₂O₃ and V₂O₃ are? Definitely not very because those are basic oxides. Or compare CrO with Cr₂O₃ with CrO₃. Double sharp (talk) 10:11, 1 April 2020 (UTC)

Acid-base properties of oxides

This is a table rating the acid-base properties of binary oxides:

1         2          3            4          5           6
Li₂O  SB  BeO  VWVW 
Na₂O  SB  MgO  WB
K₂O   SB  CaO  SB    Sc₂O₃  M/WB  TiO₂ VWVW  V₂O₅  VWVW  Cr₂O₃  VWVW
Rb₂O  SB  SrO  SB    Y₂O₃   MB    ZrO₂ VWVW  Nb₂O₅ VWVW  MoO₃   MA
Cs₂0  SB  BaO  SB    La₂O₃  SB    HfO₂ VWVW  Ta₂O₅ VWVW  WO₃    WB
                     Lu₂O3  MB

A = acid; B = base; M = medium; M/W = medium or weak; S = strong; W = weak; VWVW = very weak base and very weak acid; italics = favoured

Note the close resemblance to the preceding tables.

Source: Sanderson RT 1967, Inorganic chemistry, Reinhold Publishing, New York, p. 172

@Sandbh: Oxidation state difference all over again. TiO and Ti₂O₃ are basic, for example. Double sharp (talk) 10:13, 1 April 2020 (UTC)

Amphoterism

Like it says

This is another table showing the acid-base properties of binary oxides:

Note the appearance of amphoterism in groups 4-6; and the nuanced definition of "amphoteric".

Source: Porterfield WW 1993, Inorganic chemistry: A unified approach, Academic Press, San Diego, p. 336

@Sandbh: Nope. Sc₂O₃ is amphoteric, and the nuanced definition hides the trend of increasing acidity as the oxidation state goes up (compare: CrO basic, Cr₂O₃ amphoteric, CrO₃ acidic). How are you selecting oxidation states? In the more common +2 and +4 states manganese forms basic and amphoteric oxides respectively, for example. Double sharp (talk) 10:14, 1 April 2020 (UTC)

Halides

This is a short extract from a table delineating between the properties of ionic, partly ionic, and covalent halides MXn:

Property	Ionic halides	Partly ionic halides	Covalent molecular halides
Formed by	Most metals from groups 1, 2, 3, and TM fluorides	TM and group 13 and 14 metals	Nonmetals and all MXn, where n is >3
EN difference between M and X	Generally ≥ 2.0 but as low as ~1.2 for iodides	Generally between 1.0 and 2.0, but as low as 0.5 for iodides	Generally between 0 and 1.0
Bonding description	Electrostatic lattice model; ordered 3-D lattices with high CN for all atoms; lattice energies very well reproduced by Madelung-constant expression	Electrostatic model or band theory; halide in unsymmetrical environment in lattice, usually chain or layer structures, low CN frequent, lattice energies from Madelung constant deviate from experimental by 5-20%	Shared-electron bonds (valence-bond or MO models); symmetry of molecules predictable from VSEPR; very weak bonding in solid lattice due to van der Waals forces

The table has another seven rows of properties.

The authors note:

"Notwithstanding the substantial differences between the individual halogens, chlorides, bromides and iodides are sufficiently similar to permit a collective classification, although it must be appreciated that there are no clear lines of demarcation between the different classes. Rather there is uniform gradation from halides which are for all practical purposes ionic, through those of intermediate character, to those which are essentially molecular." (Downs & Adams 1973, p. 1245) "…most binary halides other than those of transition metals in oxidation states > +3 are most profitably discussed in terms of the simple ionic model and of deviations from this model." (p. 1248)

Note the demarcation between groups 1−3 and 4+.

Sources: Downs AJ and Adams CJ, "Chlorine, bromine, iodine, and astatine" 1973, in JC Bailar JC et al. (eds), Comprehensive inorganic chemistry, vol. 2, ch. 26, Pergamon Press, Oxford, pp. 1107-1595 (1246−1247); Porterfield WW 1993, Inorganic chemistry: A unified approach, Academic Press, San Diego, pp. 122−123

@Sandbh: Again, that's because of the oxidation state difference, and then electronegativity differences (EN goes up as you go through each row of the d block). Note the last column where you mention all MX_n where n > 3. It's not entirely true for the heaviest and lightest elements though, see below: UCl₄ isn't molecular. In fact, just compare molecular TiCl₄ to polymeric ZrCl₄ and HfCl₄, to the lattice structures of ThCl₄ and UCl₄. Similarly we have a 1D polymer BeCl₂ vs a 3D polymer BeF₂. Again, we must look at the cation and the likely ionic character from Fajans' rules. It's a continuum all over again. Double sharp (talk) 12:58, 1 April 2020 (UTC)

Conclusion

Cake time as Double sharp and I reach some kind of agreement ^_^

IMO, there are multiple sources recognising and supporting a rough 3–4 boundary as a useful divide of simplest sufficient complexity. Sandbh (talk) 09:46, 1 April 2020 (UTC)

@Sandbh: All of this supports a boundary between +3 and +4 oxidation states indeed, but not a 3-4 boundary, as evidenced by what happens when the elements from group 4 onwards are in low oxidation states (+3 and down): they act more like their group 1-3 counterparts. Double sharp (talk) 10:15, 1 April 2020 (UTC)

@Double sharp: That's why it's a rough boundary. Sandbh (talk) 11:05, 1 April 2020 (UTC)

Providing more cake, since this agreement happens so rarely on this topic. ^_^ Double sharp (talk) 15:01, 1 April 2020 (UTC)

Oxidation states

Follows on from "Conclusion" section

@Sandbh: But the better conclusion, looking at data across multiple oxidation states, shows that the rough boundary is more usefully applied to oxidation states than groups or single elements.

Here is a chart of oxidation states that have well-defined basic, amphoteric, or acidic properties in water (usual source):

OS	Basic	Amphoteric	Acidic
+1	Li⁺, Na⁺, K⁺, Cu⁺, Rb⁺, Ag⁺, In⁺, Cs⁺, Hg⁺, Tl⁺, Fr⁺, Mc⁺	H⁺, I⁺, At⁺, Nh⁺	Cl⁺, Br⁺
+2	Mg²⁺, Ca²⁺, Ti²⁺, V²⁺, Cr²⁺, Mn²⁺, Fe²⁺, Co²⁺, Ni²⁺, Cu²⁺, Sr²⁺, Mo²⁺, Tc²⁺, Ru²⁺, Rh²⁺, Pd²⁺, Ag²⁺, Cd²⁺, Ba²⁺, Sm²⁺, Eu²⁺, Yb²⁺, Pt²⁺, Hg²⁺, Po²⁺, Ra²⁺, Fm²⁺, Md²⁺, No²⁺, Ds²⁺, Cn²⁺, Lv²⁺	Be²⁺, Zn²⁺, Ge²⁺, Sn²⁺, Pb²⁺, Fl²⁺, Og²⁺
+3	Ti³⁺, V³⁺, Mn³⁺, Y³⁺, Mo³⁺, Ru³⁺, La³⁺, Ce³⁺, Pr³⁺, Nd³⁺, Pm³⁺, Sm³⁺, Eu³⁺, Gd³⁺, Tb³⁺, Dy³⁺, Ho³⁺, Er³⁺, Tm³⁺, Yb³⁺, Lu³⁺, Re³⁺, Ac³⁺, U³⁺, Np³⁺, Pu³⁺, Am³⁺, Cm³⁺, Bk³⁺, Cf³⁺, Es³⁺, Fm³⁺, Md³⁺, No³⁺, Lr³⁺, Mt³⁺	Al³⁺, Sc³⁺, Cr³⁺, Fe³⁺, Co³⁺, Ni³⁺, Cu³⁺, Ga³⁺, Rh³⁺, Ag³⁺, In³⁺, Sb³⁺, Ir³⁺, Au³⁺, Tl³⁺, Bi³⁺, At³⁺, Rg³⁺, Mc³⁺, Ts³⁺	B³⁺, C³⁺, N³⁺, P³⁺, S³⁺, Cl³⁺, As³⁺, Br³⁺
+4	Th⁴⁺, Pa⁴⁺, U⁴⁺, Np⁴⁺, Pu⁴⁺, Am⁴⁺, Rf⁴⁺	Ti⁴⁺, V⁴⁺, Cr⁴⁺, Mn⁴⁺, Fe⁴⁺, Co⁴⁺, Zr⁴⁺, Nb⁴⁺, Mo⁴⁺, Tc⁴⁺, Ru⁴⁺, Rh⁴⁺, Pd⁴⁺, Sn⁴⁺, Ce⁴⁺, Pr⁴⁺, Tb⁴⁺, Hf⁴⁺, Ta⁴⁺, W⁴⁺, Re⁴⁺, Os⁴⁺, Ir⁴⁺, Pt⁴⁺, Pb⁴⁺, Po⁴⁺, Cm⁴⁺, Bk⁴⁺, Hs⁴⁺, Mt⁴⁺, Ds⁴⁺, Lv⁴⁺, Og⁴⁺	C⁴⁺, N⁴⁺, Si⁴⁺, S⁴⁺, Cl⁴⁺, Ge⁴⁺, Se⁴⁺, Te⁴⁺
+5	Pa⁵⁺, U⁵⁺	V⁵⁺, Nb⁵⁺, Ta⁵⁺, Np⁵⁺, Pu⁵⁺, Am⁵⁺, Db⁵⁺	N⁵⁺, P⁵⁺, S⁵⁺, Cl⁵⁺, Cr⁵⁺, Mn⁵⁺, Fe⁵⁺, Co⁵⁺, As⁵⁺, Br⁵⁺, Mo⁵⁺, Tc⁵⁺, Ru⁵⁺, Sb⁵⁺, I⁵⁺, W⁵⁺, Bi⁵⁺, At⁵⁺
+6		U⁶⁺, Np⁶⁺, Pu⁶⁺, Am⁶⁺, Cm⁶⁺, Sg⁶⁺	S⁶⁺, Cr⁶⁺, Mn⁶⁺, Fe⁶⁺, Se⁶⁺, Mo⁶⁺, Tc⁶⁺, Ru⁶⁺, Te⁶⁺, Xe⁶⁺, W⁶⁺, Re⁶⁺, Os⁶⁺, Po⁶⁺, Rn⁶⁺, Bh⁶⁺, Hs⁶⁺
+7		Np⁷⁺, Pu⁷⁺	Cl⁷⁺, Mn⁷⁺, Br⁷⁺, Tc⁷⁺, Ru⁷⁺, I⁷⁺, Re⁷⁺, Os⁷⁺, At⁷⁺, Bh⁷⁺
+8			Ru⁸⁺, Xe⁸⁺, Os⁸⁺, Hs⁸⁺

Seems pretty clear, looking at all stable enough oxidation states like that, that the biggest trend that jumps out to the eye is that as the oxidation state rises it gets harder and harder for the cation to still be basic, until at the end it's only the very largest and most electropositive ions that can do it. The gap appears between oxidation states +3 and +4, though you can see how for the lightest elements it comes early and for the heaviest elements it comes late.

I would also like to ask: why should a total categorical difference between groups 3 and 4, even if it existed (which it doesn't), be definitive for positioning it in the table? We have a similar order of difference between groups 13 and 14 (it's the oxidation state thing again), and you're not using that to claim anything about the p-block. Why should a group 3 vs. 4 difference then have anything to do with the positioning and composition of those d-block groups? The block assignments still come from the electronic configuration, that's why we know Al is not in group 3, and Be and Mg are not in group 12. So, it still comes back to two of my usual arguments about why it should be Sc-Y-Lu:

Any chemical criterion that separates group 3 from group 4 and argues for Sc-Y-La is pretty much always also enough to force Be-Mg-Zn, B-Al-Sc, or some other thing that we know we don't want, and is hence inadmissible. Therefore we must use electronic criteria, because that's the only reason we know that we don't want those other arrangements.
La and Ac have f involvement in their compounds, Lu and Lr don't. Therefore relevant electronic criteria point to Sc-Y-Lu immediately. Double sharp (talk) 12:55, 1 April 2020 (UTC)

(Cannot help but notice that Sandbh is sure more generous when it comes to sharing cake--R8R (talk) 15:49, 1 April 2020 (UTC))

@R8R: (I have a small appetite, the large piece in the background is his. ^_^) Double sharp (talk) 16:08, 1 April 2020 (UTC)

@Double sharp and R8R: This: "…the better conclusion, looking at data across multiple oxidation states, shows that the rough boundary is more usefully applied to oxidation states than groups or single elements" is nice, but as a supplement, not a replacement for parsing the periodic table, which represents the central organising framework of chemistry. In my terms, your table exceeds the simplest sufficient complexity (SSC) criterion.

I think the rough 3-4 boundary is supportive or convenient for positioning purposes rather than definitive. On group 13-14 I noted I never have and don't wish to take on the chemical establishment about this. In any event there is indeed a 13−14 "divide" called the Zintl border. That's good enough.

I disagree with your first point about unwanted consequences; classification science in chemistry doesn't work like that. From my reading of the literature, the periodic table is parsed for convenience not necessarily for purist logic.

I disagree with your second point.

Electronic tables are usually organised according to idealised configurations (in which case you have an Lu table) or actual configurations (in which case you have an La table). In both cases the correlation with chemical behaviour is irregular. That's why I posted the table showing the chemical block castes as well as the electronic blocks. So, for example, in the electronic d-block thee are f-, d-, and p- chemical behaviour castes. Sandbh (talk) 00:54, 2 April 2020 (UTC)

Simplest sufficient complexity (SSC)

Note to self: "simplest sufficient complexity (SSC)" looks like important meta-argument. Need to figure out some time. -DePiep (talk) 01:44, 2 April 2020 (UTC)

@DePiep: It comes from here:

"Nature always takes the path of "simplest sufficient complexity"; matter is complex only because it cannot be made any simpler and still come into existence through symmetry-breaking."

Some related quotes:

"The best education is found in gaining the utmost information from the simplest apparatus."

— Whitehead AN 1929, The aims of education and other essays, The Free Press, New York, p. 37

"Everything should be made as simple as possible, but not simpler." — Albert Einstein

Sandbh (talk) 02:56, 2 April 2020 (UTC)

@Sandbh: Well, here is where we start to disagree. Although I agree with Einstein's quote, I find your approach simpler than possible. Just look at the big table: most elements appear more than once because they show multiple important oxidation states. And whenever an element appears more than once, it nearly always appears in different columns depending on its oxidation state. Cr²⁺ appears as basic; Cr³⁺ as amphoteric; Cr⁶⁺ as acidic. You don't see group differences, only oxidation state differences, because most groups have their representatives appearing all over the place.

Regarding taking on the chemical establishment: this pretty much ties in with my first point. If we want to classify with criteria, I insist that the criteria must be applied consistently. If we say that group 3's preference for +3, and group 4's preference for +4, is important because of the consequences of the +3 vs. +4 divide, then it must be equally important that group 13 prefers +3 and group 14 prefers +4. Otherwise we don't end up with a holistic view that generalises everywhere, but a bundle of disconnected facts. To me, that is not a theory. If we were writing in 1920, the chemical establishment would be in favour of Be-Mg-Zn, because after all chemically Be and Mg are more like Zn than like Ca (the major gap this early in the table is between +2 and +3), and so I guess I would probably get a similar reception if I was advocating for electron configurations like Paneth was. Now, of course, the situation is different because the chemical establishment is in favour of Be-Mg-Ca. That seems to suggest that the correct table shifted along with what the majority of chemists thought, which seems rather absurd.

As I wrote above: applying consistent criteria leads to a simpler situation. Gone is the need to say "we apply criterion A for this bit of the table and criterion B for that bit". Instead we say "we apply criterion A everywhere". That matches the desire to make our theory as simple as possible. But not simpler. And we ensure that it's not too simple to be simple by checking to see if the criterion actually means anything at all chemically.

And that brings me to my second point. The relationship between electron configuration and chemistry is of course not simple. But the periodic table is based on the former, which is simpler than the latter, and at least still means something chemically sensible. If you just look at descriptive chemistry, there is not a lot in common between N and Bi. What one does, the other almost certainly won't do! But they share an (sp)⁵ outer shell, and that's why they go in the same group. And even though they are so different from each other, each step N-P, P-As, As-Sb, Sb-Bi shows similarities, and we can see where the trend is leading us, and we can see that this placement on the grounds of the electron configuration makes chemical sense.

As for the descriptive chemistry itself, there are so many factors here that depending on what you want to show you can go for almost anything and there will be some reason for it. Well, to some extent Al patterns as a pre-transition metal and you may wish to include it for comparative purposes, OK. To some extent also, Be and Mg pattern like the Zn group and we may wish to include it with post-transition metals, along with the similar Al! And maybe you want to focus on other categories like electronegativity lower than such-and-such, or favouring formation of cluster compounds, or something else entirely. So no, I reject chemical block castes: there are too many possible ones, and they are not a good basis for the periodic table because there is simply no chemical caste that plausibly includes both nitrogen and bismuth which are in the very same group according to absolutely everybody. Double sharp (talk) 03:35, 2 April 2020 (UTC)

@Double sharp: I won't address old ground. When it comes to descriptive chemistry I focus on the key ideas, which might cover 80% of what is good to know; there is no issue about "so many factors". N and Bi are in the p-electronic block and behave chemically like p-block elements. Sandbh (talk) 05:00, 2 April 2020 (UTC)

@Sandbh: I don't accept a key idea that is at variance with the fact that the divide clearly correlates with oxidation state and atomic radius and absolutely not with groups. Most groups have their members appearing in different columns in the above chart: what matters is what oxidation state they are in. Just look at what good old Wulfsberg says on p. 94 of Principles Of Descriptive Inorganic Chemistry:

“

Because the acidity of a cation rises rapidly with its charge, there are several d-block elements possessing several oxidation states (such as chromium) that have one or more oxides that show only basic properties (e.g. chromium(II) oxide, CrO), one or more oxides that are amphoteric (e.g. chromium(III) oxide, Cr₂O₃), and one or more oxides that possess only acidic properties (e.g. chromium(VI) oxide, CrO₃). Clearly, the higher the oxidation number of a given element, the more acidic the corresponding oxide will be.

”

I note that no mention is made of group divides in this whole section on periodic trends in acid-base and solubility properties of oxides. Which is because there is no such thing. The important thing is the acidity of the cation, which may be predicted from atomic number, charge, and electronegativity. And the gap is not even always between +3 and +4. It's around there for periods 4, 5, and 6, true. For period 3, you should look for it between +2 and +3. And for period 2, even between +1 and +2.

Not to mention that the chemical behaviour of p-block elements pretty much runs all over the place stretching from thallium to neon. Such a category is, speaking in terms of descriptive chemistry, effectively meaningless without subdivision.

And if we don't address old ground, we will never resolve our disagreement, because the old ground is where it starts. Double sharp (talk) 05:50, 2 April 2020 (UTC)

A key difference between Sandbh and DS

@Double sharp: That is a key difference between us. I attempt to derive a collective classification, based on the most common or important data points, that matches up with periodic table boundaries. You respond by looking at the entirety of the data points involved (oxidation states in this case) and attempting to draw boundaries among that. I've previously (unkindly) called this the downwards drill of complexity, or fogging, because in its detail it obscures the broad contours of the situation. Two variations of fogging are the indivisibility of a continuum and non-generalisability. The first variation is to assert that everything lies on a continuum and that it would therefore not be possible to draw rough lines of demarcation, never mind how useful these could be. The second variation is to attempt to bury (so to speak) my classification as non-generalisable, notwithstanding its validity and relevance within its boundaries.

You then criticise my classification/s on this basis. The unfortunate irony—as I see it—is that your attempts, in the enormity of their scope, lose the rough but easy connections to the groups that chemists use as a mental framework. Your approach is not wrong, but I think it exceeds the principle of simplest sufficient complexity. Speaking personally, this also explains why it takes me so long to respond to some of your posts (not that I am complaining).

All that said, your approach is invaluable in testing and sharpening my thinking. Sandbh (talk) 04:57, 4 April 2020 (UTC)

PS: I think it's more useful to speak of "continuum-like" properties, since that's more like what's going on, and there are, in my view, useful lines of demarcation that can be drawn among such, even if roughly so.

Fajans' rules and group divides

Oxidation state vs. ionic radius; plot from Greenwood and Earnshaw, p. 52

@Sandbh: So how come Fajans' rules are totally common to refer to in introductory chemistry, and group divides are not? These generalisations are not only Wulfsberg's, you know, even though I like to quote him because his approach has amazing generality. Greenwood and Earnshaw too understand the effect of oxidation state and ionic radius on the acidity of cations, and thought it useful enough to include in their famous book. (Of course, bismuth still appears in the wrong place, and Tl⁺ and Ag⁺ much higher than they should be, because they don't include electronegativity.) Whatever chemists are using as a mental framework seems from this evidence to be far closer to what I'm saying than what you're saying. Because your approach is too simple to be simple, ignoring as it is all the secondary but still important data points. If you insist on only one oxidation state per element, the whole point of the transition metal category is lost. I repeat in the face of your criticism of it as fogging: everything is a continuum, there are multiple factors, and even though you will be able to find some significant differences (whose boundaries are also fuzzy), you have to take into account all those factors: atomic radius, ionic charge, and electronegativity. Otherwise you won't get a general understanding, only a misunderstanding of the pattern which breaks totally outside its boundary (just look where the differences appear in periods 2 and 3). Anyone can see from extending Greenwood and Earnshaw's chart to plot all oxidation states that are stable in water that any idea of a group divide in the real pattern is simply contrary to the facts, not a broad-contour understanding. Double sharp (talk) 05:19, 4 April 2020 (UTC)

@Double sharp: You can reach for all those door-stop books (1,340 pp in the case of G&E) with the myriad tables of drill-down details anytime you like. In the first instance, what chemists carry around in their heads is the periodic table, and its trends and patterns, per the 80/20 rule. Then, as required or desired, you can take into account all the other factors that may or may not make up the 20% difference. That is how it works: you start with the broad contours, not the fine details. "Alice: Oh my, is that a bear approaching our picnic? Bob: I don't know, I can't see it for the fine the details of the taxonomical lineage of whatever creature it is. Once I have that worked out I can determine its threat profile."

G&E's table is an excellent example. Of the 50[?] elements listed I can seen only 5[?] dual entries. Note, in particular, the lines of demarcation (rough no doubt). Very good!

See here for a JChemEd article that deals with this issue of generalisation.

@Sandbh: Only problem with calling it "drill-down" is that the detailed analysis gives a totally easily carried around principle, which I bet is in fact what is carried around in chemists' heads, not supposed nonexistent group divides:

Acidity increases as electronegativity and oxidation state increase, and as atomic radius decreases.

That's even totally analogous to Fajans' rules, which are carried around so easily in heads, and which I remember even from the first year of chemistry as a standalone subject in school. And it's totally obvious from the obligatory high-school discussion of periodic trends, just look at periods 2 and 3 which every beginning chemistry student is at least familiar with at the broad-strokes level. And every bit of it is easily determined: well, oxidation state is obvious from the compound itself, we can roughly predict EN from the periodic table, and the same goes for atomic radius. And it's even better than 80% accurate; it's 100% accurate as far as we know. In the rare occasions when it seems to predict something wrong (e.g. why CCl₄ doesn't react explosively with water if C⁴⁺ is so small and highly charged and electronegative), it is because we have forgotten another effect (in this case, atomic radii causing steric hindrance).

So, making an analogy for the bear example, let's say I have to guess something about an element I don't remember much about. OK, rhodium will do, since it's a 4d element and therefore we barely touched on that in school. Let's see what the principles of general inorganic chemistry that I carry around in my head tell me. OK, rhodium is ideally [Kr]4d⁷5s², maybe it's not so in the ground state, but I don't care. So, a +2 state is reasonable using just s electrons, and higher states also reasonable bringing in d electrons. I know cobalt prefers +2 with a very easily reduced +3, I also know that 4d has radial nodes which 3d doesn't have. So I bet +3 will be preferred over +2 here, and we should expect significant chemistry in higher oxidation states. How high? The 3d drop in maximum oxidation state happens at Fe, so I expect it to happen at Rh one column later for 4d. So: the group oxidation state for Ru is +8, Rh must show something lower, I know Ag prefers +1 but fluoride can push it to +2. Therefore I will interpolate and guess Rh +6 as an effective maximum, thus guessing an expected approximately linear drowning of 4d that should take place more rapidly than the drowning of 3d after an initial high activity. The atomic radius increase won't make the EN go below about 1.4 since Co is already pretty high, so I'm going to guess Rh³⁺ as a plausible amphoteric aqua cation (because so is Cr³⁺), and I guess Rh⁶⁺ should hydrolyse completely and result in oxoanions with some medium coordination number befitting a fifth-period element, we haven't reached the range of really low ones late in the d block like Ag or Hg yet. Although I also know that the heavier elements going down the d block show more chemical affinity to P and S than for N and O, so I'd guess that water should be easily displaced from the coordination sphere by other ligands, and that we'll need weakly coordinating anions like perchlorate to see Rh³⁺ (aq). And I guess oxidation states above +3 should be acidic, whereas Rh²⁺ is the best chance for basicity because so is Hg²⁺.

Behold, that's all absolutely correct and I haven't even done any quantitative calculations. If I let myself look at quantitative data, I could say even more: Oh, look, the ionisation energies of Rh rise about linearly, so I expect most oxidation states in the +2 to +6 range to be about equally stable (I don't expect significant disproportionation if they're left alone), stability should depend on the ligands, and of course higher states should be stronger oxidisers. And that's also absolutely correct, now that I've looked it up.

We could even use this approach to predict stuff about superheavy elements. An off-the-top-of-our-heads guess based on cancellation of relativistic effects would work fairly well for the area around the "second island" centred on E164; for increased accuracy we'd just need to calculate Allred-Rochow electronegativity, see how it deviates typically from chemical electronegativity, and use periodicity and knowledge of qualitative results of relativistic effects to do it.

Can you do anything like that with your approach? That's an important question because the ability to make predictions like this is the litmus test for periodicity.

I am all for simple, general approaches. But only if they work. This is simple and generalises totally: group divides don't, because nothing of the sort exists in real chemistry, except between group 18 and group 1.

P.S. Greenwood and Earnshaw's rough lines of demarcation pay no heed to groups. They separate Sc from the rest of group 3, for instance. Double sharp (talk) 06:42, 4 April 2020 (UTC)

@Double sharp: I think you have just spent 735 words of fogging and its two variations of the indivisibility of a continuum, and non-generalisability, and in so doing have ignored my salient points:

(1) The periodic table, as the central organising framework of chemistry, is the starting point. Useful dividing lines can be drawn between the main-group metals, transition metals, inner transition metals. Most chemists will know that, for the TM, group 3 and group 12 are atypical. Here are some more or less rough divides:

the dividing line between metals and non-metals
the line between group 3 and 4+ halides
the oxo-wall between groups 8 and 9
the Zintl line between 13 and 14.

The context for above is your blusterous assertion that, "group divides don't [work], because nothing of the sort exists in real chemistry, except between group 18 and group 1."

(2) In addition to whatever other models chemists' carry around in their heads, Fajans' rules will be there, should they need to draw on them. The context for this one is your erroneous assertion that, "[my] approach is too simple to be simple, ignoring as it is all the secondary but still important data points." My approach is based on simplest sufficient complexity, not "more complexity that is warranted for a high order derivation".

(3) I repeat: There is no bonding continuum. There is a semi-continuum upon which rough but useful dividing lines can be, and are drawn. Even G&E draw such lines as per the image you posted.

(4) Boundaries between classes will rarely be sharp; that doesn't jeopardise their utility.

I don't like referring to your responses using terms like "fogging" etc. There does't seem to be any other way of getting you to appreciate what you are doing, and what you are ignoring. A polite way of saying this it that in looking at a forest you appear to focus on the leaves or needles on the supporting branches of each tree, and you can't see or choose to ignore, the trunks of each tree, and the topography of the forest.

I don't claim to infallible in my approach to classification science. Sandbh (talk) 03:40, 5 April 2020 (UTC)

@Sandbh: Just addressing your first two examples, as I don't have time for the other two right now, and probably this is the last megapost I have time for here:

(1a) The dividing line between metals and nonmetals is absolutely not a group divide. Not to mention that depending on the situation we may pragmatically move it in one direction or another in order to better illustrate a trend. Sb and Bi are around the borderline, there is a case for considering them either way.

(1b) The idea of just looking at halides alone lacks generality. In fact one can see a continuum, anywhere on the periodic table, not just in halides, that goes

discrete molecules (e.g. SO₂) – 1D polymers (e.g. SeO₂) – 2D polymers (e.g. TeO₂) – 3D polymers (e.g. PoO₂)

as EN difference rises. As usual, my approach is more general, instead of plucking out only particular types of compounds. Of course, near the boundaries we have structural deformation.

So let's apply the general theory to what happens in the early period 5 chlorides (EN_KK(Cl) = 3.06):

Rb (EN_KK = 0.77)	Sr (EN_KK = 1.05)	Y (EN_KK = 1.28)	Zr (EN_KK = 1.35)	Nb (EN_KK = 1.44)	Mo (EN_KK = 1.53)
RbCl	SrCl₂	YCl₃	ZrCl₄	NbCl₅	MoCl₆
3D ionic lattice, regular	3D ionic lattice, deformed rutile structure (undistorted rutile structure pictured, as I can't find a picture for the SrCl₂ structure)	layered 2D polymers like AlCl₃	linear 1D polymers	dimeric molecule	monomeric molecule
			ZrCl₃	NbCl₄	MoCl₅
			3D polymers	1D polymers	dimeric molecule
					MoCl₄
					1D polymers (diagram)
					MoCl₃
					layered 2D polymers like AlCl₃
					MoCl₂
					metal cluster structure

Seems to be passing with flying colours, looking at that continuous trend and change as electronegativity difference drops and oxidation state rises. The real topography of the forest is based on electronegativity differences like I have always been saying. What group gap is there? I'm sure every other supposed group divide will vanish when analysed properly this way into a real continuum. Call it fogging if you like: I just see that my approach allows for what seems more and more to be total generality, whereas yours fixates on a few compounds where the trend seems to line up (never mind that it quickly moves away once you get into the wrong place, e.g. look where the gap ends up in period 2 or period 7). Let me quote User:Droog Andrey from archive 42:

“

@Sandbh: Chemistry is not a heap of distinct conceptions standing apart alone, but rather interconnected system of conceptions based on experimental facts.

When Double sharp shows that your argument produces bullshit, you'd better learn what's wrong with the argument instead of continuously building artificial borderlines for its applicability. Droog Andrey (talk) 07:03, 20 February 2020 (UTC)

”

And while I personally wouldn't use the word BS for your arguments, I stand by the notion that outside the artificial boundaries you usually end up erecting, they never work.

Be wise: generalise!

You yourself admitted regarding the "ionic vs covalent" dichotomy:

“

@Sandbh: Using those four categories is so much better than "predominantly ionic" or "predominantly covalent", so I'm glad we have come to some agreement on this. They are in fact the reason why I find "predominantly ionic" and "predominantly covalent" not useful: using those terms sweeps under the rug the very trend that is so clearly controlling it, that of electronegativity difference as Rayner-Canham and Overton are saying. Double sharp (talk) 13:09, 1 April 2020 (UTC)

@Double sharp: Quite so. Sandbh (talk) 01:08, 2 April 2020 (UTC)

”

So how is this any different?

I don't have time for this detailed rebuttal anymore. So let me give you some homework instead, like Scerri did: read Wulfsberg's Principles of Descriptive Inorganic Chemistry, and see what generalisations chemists really use. Then we may resume this when I am back in July, hopefully without it needing to take months for you to realise the problem with your arguments like it did for your focus on "predominantly ionic" or "predominantly covalent". Double sharp (talk) 04:16, 5 April 2020 (UTC)

@Double sharp: Could you please read my posts carefully. I did not say the dividing line between metals and nonmetals is a group divide. It's a divide. People have been drawing lines on the periodic table at least since the time of Hinrichs (1869)…

"…elements of like properties or their compounds of like properties, form groups bounded by simple lines. Thus a line drawn through C, As, Te, separates the elements, having metallic lustre from those not having such lustre. The gaseous elements form a small group by themselves, the condensible [sic] chlorine forming the boundary… So also the boundary lines for other properties may be drawn."

…and will continue to do so.

Second, you continue to look at the leaves, needles, and supporting branches, and ignore or are incapable of seeing the supporting trunks and the topography of the forest.

On the halides, even the authors concerned acknowledged there are no sharp boundaries. They nevertheless, and this is the key point, recognised there were enough commonalities to warrant a rough demarcation and that doing so would be profitable endeavour in bringing order to a vast amount of information.

I don't believe you're incapable of understanding what I'm saying, nor its relevance in high order classification science. As the author of the JChemEd article said:

"…if something is true about 90% of the time or more, state the generalization as true and indicate that there are exceptions that will be dealt with later
(perhaps even in another course); further indicate that even though the textbook may deal with these exceptions, you will not test students on them."

I personally think the 80/20 rule will do most of time. Sandbh (talk) 04:53, 5 April 2020 (UTC)

@Sandbh: I recognise a real rough demarcation that really works, not group divides that don't work. That rough demarcation is drawn from ionic charge, electronegativity, and atomic radius. Exactly like Fajans' rules with a little extension. I have no objection to going for a large-scale broad-strokes classification if it fits the facts, like this generalised form of Fajans' rules. But not when it simply doesn't fit the facts, like supposed group divides.

And depending on what authors might be focusing on at any given moment, the boundaries may be shifted since it was a continuum anyway, no problem. Just look at the wide variety in exactly where the metalloid line is drawn. Which I know you're aware of.

That's all I have to say on this matter. Anything else would just be a repetition of what I've already been saying for the past few months. Double sharp (talk) 04:55, 5 April 2020 (UTC)

Unwanted consequences

P.S. Regarding unwanted consequences, let me quote you from above:

“

@Sandbh: So why can we not exercise some pragmatism with our treatment of La and Ac, noting that they obviously have low-lying f-subshells that can be involved chemically, and treat the accident of chemically irrelevant wrong DE's for them as just that: an accident? Double sharp (talk) 00:09, 14 February 2020 (UTC)

@Double sharp: I don't think it's that easy. You have to follow your core principles first i.e. periodic law, aufbau, d/e etc. Sandbh (talk) 04:50, 14 February 2020 (UTC)

@Sandbh: Well, I do: chemically active valence subshells. And they support Lu 100%. Those are a theoretical sound basis for periodicity (as it really is, not as you oversimplify it) and faithfully recreate the Aufbau motif all the way up to period 8 (and even then it still holds with very minor changes; the idea of "s, then g, then f, then d, then p" is still correct"). DE's are an oversimplification that we have progressed from. ... Double sharp (talk) 11:49, 14 February 2020 (UTC)

”

Why is consistently sticking to core principles necessary for rebutting a Lu table, but not for rebutting a La table? Not to mention that in archive 38 you were praising DE's, among other reasons, because they apply "to the whole of the table", and asked DA if he could generalise his dications suggestion (to which I replaced, yes, of course you can). Why's that not relevant now when your current criteria would give unwanted consequences if generalised and applied to the whole of the table? Double sharp (talk) 06:36, 2 April 2020 (UTC)

Supplement

I was looking for something else when I unexpectedly stumbled upon reference #1. It seemed odd and after further searching I found a confirmation in reference #2.

Literature extract #1:

"All the elements listed above [d- and f-metals] are metals with relatively high melting points (900-l000°C or higher) and crystallise in relatively simple structures [fcc, bcc, hcp, or sequences thereof (La—Sm)] except Mn and most elements of the actinide series. They show in general a wide range of solid solutions and form numerous intermetallic compounds and complex phases^[2][3] (except group III with groups IV, V, VI).
[2] Pearson WB 1967, Handbook of lattice spacings and structure of metals and alloys, vol. 2. Pergamon, New York
[3] Hansen M (ed.) 1958, Constitution of binary alloys, vol. 1. McGraw-Hill, New York; Elliot RP (ed.) 1965, Constitution of binary alloys, suppl. 1, McGraw-Hill, New York; Shunk FA (ed.) 1970, Constitution of binary alloys, suppl. 2. McGraw-Hill, New York"

Source: Bucher E 1983, ’Transition elements’, in Concise encylopedia of solid state physics, G Rita and GL Trigg (eds), Addison Wesley, Reading, MA, pp. 290--29

Literature extract #2:

"Compound Formation. The rare earth metals [Sc, Y and the Ln] form compounds with the elements to the right of the group VIA elements in the periodic table, except the rare gases, but not with the elements to the left of the group VIIA elements, except hydrogen, beryllium, and magnesium."

Source: Gschneidner KA Jr, Beaudry BJ and Capellen J 1990, "Rare earth metals", in ASM Handbook, vol 2, Properties and selection: Nonferrous alloys and special-purpose materials, ASM Handbook Committee, p 720-732

There you go. One more fruit in my basket, as Droog Andrey would say. That said, I don't know why this "divisive" behaviour occurs. Sandbh (talk) 06:24, 3 April 2020 (UTC)

@Sandbh: If we were to figure out why it occurs, I bet it will come down to valency, electronegativity, and atomic radius again, just glancing at the Hume-Rothery rules (which include those three and crystal structure). (Or play around with the Miedema calculator.) That would support my (based on Wulfsberg's) generalist approach. Double sharp (talk) 07:06, 4 April 2020 (UTC)

@Droog Andrey: Pinging you for this one, since this is not a branch of chemistry I am very familiar with. Double sharp (talk) 07:14, 4 April 2020 (UTC)

Simplicity: a look at DS' approach for the Lu table

@Sandbh: You talk about the simplest apparatus, so I think it should be hard to beat my single main reason why Lu must go in group 3:

An f block element must have valence f involvement. Which La and Ac have and Lu and Lr lack.

Simple as that.

Or, rephrased as something for the entire table that is totally generalised:

An element is placed in a block according to its number of valence electrons and the chemically active subshells they can go into.

To put it explicitly: if you have 1 or 2 valence electrons, you go in the s block, as they must be s electrons and those are the ones filled up front that will survive the whole row (other subshells may be active). And if you have more (n where n > 2), you go into the block corresponding to your valence orbital of highest angular momentum, and in the (n − 2)nd column of that block.

Job done, no fuss about ambiguous chemistry which can always go multiple ways because there are so many important factors acting. Looking at trends and seeing how much nicer they are is a great bonus showing that this gives a sound classification. Double sharp (talk) 14:31, 2 April 2020 (UTC)

Time commitments

Due to a sudden increase in current time commitments I will not be able to respond very actively to this thread from now, and since we are often going in circles here, I will step back and let the rest of us rise up with critiques. ^_^ Double sharp (talk) 18:17, 28 February 2020 (UTC)

Since time commitments are going to rise again from this weekend I would like to request a pause to the discussion unless something ongoing needs to be addressed quickly before this week is over. (The fact that it is now browser-crushingly huge is also a factor.) I plan to resume it with the RFC around July.

A summary of the situations where we disagree can be found below in #Group 3 StateOfMatter please, and a summary exposé of my current approach to the PT at User:Double sharp/Idealised electron configurations. Double sharp (talk) 05:29, 3 April 2020 (UTC)

@Double sharp:. All good. I'm behind on my responses any way. I'll post these; respond when you are able. Sandbh (talk)

References

^ Langmuir, Irving (1919). "The arrangement of electrons in atoms and molecules". J. Am. Chem. Soc. 41 (6): 868–934. doi:10.1021/ja02227a002.

Informal cessation of critique

@Double sharp:@Droog Andrey:@R8R: I cannot think of a better way to test the mettle of an article such as what has led to this point.

I submitted a revised manuscript, today, to Foundations of Chemistry.

The acknowledgements section currently reads, in part, "I thank members of Wikipedia’s WikiProject Elements for their indefatigable stress testing of an early draft of this article."

What happens next is initial consideration by the Editor-in-Chief; if it gets past him it goes through peer review; their comments go back to and inform the EiC, who passes them to me, with his decision on where to from there e.g. accept; accept with requested amendments; reject etc.

I'll keep you informed. Thanks again. 06:16, 9 March 2020 (UTC)

[1] Langmuir, Irving (1919). "The arrangement of electrons in atoms and molecules". J. Am. Chem. Soc. 41 (6): 868–934. doi:10.1021/ja02227a002.

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