Talk:Symmetry of diatomic molecules

Plan about this page

Hi every one. I am Sudip. I have recently created this page. My plan about this page is as following:My plan about the page is as following:

• I will start with an introduction, I will give a brief overview of why we want to look into molecular symmetry (because it gives us insights about the properties such as structure and spectra without doing the actual rigorous calculation).
• This will be followed by a section on how symmetry is related to group theory and the idea of point groups.
• Then I will state and describe the 5 kinds of geometrical symmetries (symmetry axis, plane of symmetry, inversion center, rotation-reflection axis, identity) and the corresponding operations (I will also introduce Schoenflies notation).

• Then I will enlist the different kinds of point groups associated with molecular symmetry. I specific, I will discuss in detail the most prominent symmetry groups in diatomic molecules, namely C_∞v(linear) and D_∞h(linear with inversion center). In case of a Homonuclear diatomic molecule, we see both the symmetries and in case of Heteronuclear diatomic molecule, we see only the former one.
• Then I am planning to give a brief description of group representation and irreps (I am not sure about whether this will be relevant for my current reading or not, so there is a possibility that I will not include it).
• Then I would like to include a section on how the symmetry and the corresponding commuting operators differ in diatomic molecules from the atomic case. Here, Hamiltonian does not commute with L² and thus 'l' is no longer a good quantum number. The CSCO in this case is {H, J_z,L_z,S²,S_z,A, Π} (A inverts only one of the spatial co-ordinates).
• Then I would like to discuss about the most general Hamiltonian of a diatomic molecule and Born-Oppenheimer approximation and the 'electronic ket' (or electronic wave function, or the word 'electronic term' used by Landau-Lifshitz).
• Then I would like to probe into the role of symmetry in this electronic structure, and would introduce the molecular term symbol and discuss about Λ-doubling, gerade and ungerade states.
• Now I would like to explore the observable consequence of symmetry in physical observations, i. e., the difference in spectral lines of homonuclear and heteronuclear molecules.

Here, I would like to state the selection rules for the purely vibrational, purely rotational and vibration-rotation (or vibronic) transition for the two kinds of diatomic molecules. It will turn out that in order to show a purely vibrational spectrum, a diatomic molecule must have dipole moment that varies with distance. So, homonuclear molecules don't undergo electric dipole vibrational transitions; it shows, however, vibronic transition spectrum. A heteronuclear molecule shows both the spectra, although it needs to abide by the corresponding selection rules. It turns out that both the vibrational and rotational quantum numbers must change in the transition. So, the so called 'Q' (Δv=(+/-)1, ΔJ=0) branch of rotational spectra is forbidden.

• In the last section, I will discuss the intersection of potential curves for a diatomic molecules and the role of symmetry in it. Here, I would also like to discuss the von Neumann- Wigner non-crossing rule.

- This is my detailed plan till now. It can change depending on my further studies and discussions. You can ask any question regarding the page or any edit here. Your valuable suggestions are also appreciated. Feel free to discuss! --Sudip1993 (talk) 18:01, 15 October 2014 (UTC)

There seems to be nothing new here. Jut a bunch of things pulled in from other pages: group theory, symmetry in quantum mechanics, molecular symmetry,Schoenflies notation, etc. Either condense this page or delete it. I'll wait a day or two for your answer. --Bambaiah

Are you sure that there is nothing new in this page? I mean, in all the pages you mentioned, no explicit reference to the symmetry of a most general diatomic molecule has been made whatsoever,e.g. in the page of Rotational-vibrational spectroscopy, the implication of the symmetry on the rotational or vibration has not been dealt with (except in the case for the vibronic spectra), the implication of no-crossing rule to the diatomic case has not been mentioned at all in the respective page and so on. Nonetheless, this page can surely be condensed, making some part from the group theory short and adding new materials. I'm looking forward to some editor to take up that task. Cheers!

Conserved Quatities

Please explain which physical quantities are conserved due to various symmetry operations.Subhadip Roy (talk) 17:36, 14 November 2014 (UTC)

Some Suggestions

1)I think that the commutative property of a group should be emphasized separately, instead of bundling it together with the four necessary properties for the definition of a group. 2)Also the phrase "often called multiplication" which has been used for emphasizing a generalized binary operation appears inappropriate to me.Subhadip Roy (talk) 17:55, 14 November 2014 (UTC)

Hi, Subhadip! Thank you for your suggestions. Now, to answer your queries:

1. About the relation between symmetries and conservation laws: I have added this part and explained it in as much detail as I could in the respective section. Thank you for pointing it out. I hope that you find the section satisfying.
2. About the commutative property: Yes, I categorized them in one place, but I mentioned the phrase 'in addition to the above properties'. Well, I have edited that part and added it as a separate criteria. Thanks again!
3. About the 'often called multiplication': The group binary operation is indeed loosely called 'multiplication', and the corresponding binary operation table is called 'group multiplication table'. That apart, the groups we are dealing with can be represented as square matrices, and the corresponding binary operation can be replaced by the usual matrix multiplication. That's why I felt like mentioning it.

Thanks again for sharing your views. Cheers! --Sudip1993 (talk) 12:28, 26 November 2014 (UTC)