Talk:Franck–Condon principle

Explanation of tau

please, somebody should explain what dtau means in the integral in the qm derivation —Preceding unsigned comment added by 164.54.94.95 (talk) 20:29, 11 November 2010 (UTC)

Also, tau should be a vector and be a vector and be in bold. Otherwise the probapility amplitude P would not be an scalar. —Preceding unsigned comment added by 164.54.94.95 (talk) 21:47, 11 November 2010 (UTC)

Where is the polarization of the photon in the qm formula? If it is a dipolar transition the polarization of the photon should be somewhere and it would be the vectorial quantity that multiplied by the vectorial quantity dipole moment would give the scalar quantity amplitude of probability P. Is it tau? or tau is something else? —Preceding unsigned comment added by 164.54.94.95 (talk) 22:23, 11 November 2010 (UTC)

Comments

I have added a major expansion to the existing stub in an attempt to bring the Franck-Condon Principle entry to full article standards. There are quite a few improvments that can be made and I will try to work on some in the comming weeks. In particular I think it would be nice to incorporate figures with real data, for example a real data version of figure 2. I someone has some nice data to incorporate please go ahead, otherwise I will try finding something in the literature that can be added under fair use. Somoza 10:51, 3 July 2006 (UTC)

Franck Condon approximation

Should "Franck-Condon approximation" redirect to here? I've made this redirect already... --HappyCamper 16:48, 19 July 2006 (UTC)

I think "approximation" is used instead of "principle" when the author wishes to emphasize the limitations of the assumptions that are used in the Franck-Condon principle.Somoza 09:23, 15 August 2006 (UTC)

Lemma

Why is the article buried under stuff which belongs to the harmonic oscillator ?Arnero 08:19, 20 September 2006 (UTC)

For example??Somoza 10:32, 20 September 2006 (UTC)

Next steps

What are the next steps for this article? Perhaps we should highlight some computational approaches for handling large FC systems? --HappyCamper 15:35, 25 January 2007 (UTC)

Go ahead HappyCamper, I now little about computational methods, but I would be interested in reading a sections on the topic.Somoza 12:11, 26 January 2007 (UTC)

Ratings

I changed the ratings because I don't think that Wikipedia articles on any of the sciences will get any better than this one. Further it is well-known that the Franck-Condon principle is of utmost importance in spectroscopy. I realize that these two sentences are highly subjective, but (i) at least I have read the article and (ii) I bothered to write this (short) motivation.--P.wormer 00:59, 11 April 2007 (UTC)

The next highest rating beyond B is GA (Good Article). See WP:GOOD for information about the nomination and review process. --Kkmurray 19:11, 1 September 2007 (UTC)

Reversal of edit by 212.192.238.23

The Russian anonymous 212.192.238.23 deleted half of van der Waals equation. Looking at what (s)he further did I saw that (s)he removed some didactic and nice LaTeX stuff from the present article. Again without a single word of motivation! That is why I reverted. Please anon 212.192.238.23 explain why you find it necessary to delete stuff. Remember Wiki is not paper, size is not an issue!--P.wormer 08:07, 8 June 2007 (UTC)

Reply from 212.192.238.23

I insist on the fact, that the section "quantum mecanical formulation" contained errors. Well, I'll explain.

Total wave function is expressed as a product of electronic, nuclear, and spin wavefunctions. That is true. But according to the commonly used Born-Oppenheimer (adiabatic) approximation, an electronic wavefunction depends not only electronic but nuclear degrees of freedos (as parameters) also. Accordingly, the integration of the dipole moment operator over electronic degrees of freedom leads to the quantity, which depends on nuclear degrees of freedom. This quantity is called transition dipole moment (TDM) between two electronic states. Thus, the integrand (over nuclear degrees of freedom) is not a simple product of two vibrational eigenfunctions but includes TDM. When I edited the page, I've corrected errorneous statements and deleted unnecessary information.

• In principle you are right: the matrix element (integration over electronic coordinates) of the dipole operator is still a function of nuclear coordinates (it is a so-called transition dipole surface). However, part of the Franck-Condon approximation is to replace the integral over this transition dipole surface by the overlap integral between the two nuclear wavefunctions (times an average dipole). This is indeed an approximation, but it is an inherent part of the F-C approximation. --P.wormer 10:26, 9 June 2007 (UTC)

212.192.238.23 14:12, 9 June 2007 (UTC) The formulation given in the Article is not clear, so I tried to clarify the situation. As far as I know, the Frank-Condon approximation implies the expansion of TDM in a Taylor series over nuclear degrees of freedom (at the equlibrium geometry of the ground state). Only with that approximation one may talk about the infuence of the overlap between two vibrational eigenstates aka Frank-Condon factors on the total transition probabilities.

• As I understand it (but I'm no expert), one simply approximates the Taylor series of the transition dipole moment surface by the constant (first) term. Clearly, the Franck-Condon approximation is very simple-minded. It sounds to me that you have an improved version in mind. Do you have a source for this?--P.wormer 16:19, 9 June 2007 (UTC)

212.192.238.23 17:20, 9 June 2007 (UTC) No, I did not claim to posess any "extension" to Frank-Condon approximation. I would like to draw one's attention to the fact that the derivation of this approximation is not completely correct and provide better suited set of the equations.

• I read the subsection somewhat more carefully and I agree with you that the text is misleading. Maybe we can insert something like the following:

The factorization

$\int \int {\psi _{v}'^{*}}{\psi _{e}'^{*}}{\boldsymbol {\mu }}_{e}\psi _{e}\psi _{v}d\tau _{e}d\tau _{n}=\int {\psi _{v}'^{*}}\psi _{v}d\tau _{n}\int {\psi _{e}'^{*}}{\boldsymbol {\mu }}_{e}\psi _{e}d\tau _{e}$

involves the extra approximation that the integral $\int {\psi _{e}'^{*}}{\boldsymbol {\mu }}_{e}\psi _{e}d\tau _{e}$ is assumed to be independent of the nuclear coordinates, although in the Born-Oppenheimer approximation $\psi _{e}\,$ depends (parametrically) on the nuclear coordinates.

Does this cover your objection?

--P.wormer 13:49, 10 June 2007 (UTC)

212.192.238.23 08:02, 15 June 2007 (UTC) I'm sorry for the long silence. Yes, you are right, but it is a little bit unclear at what geometry integral $\int {\psi _{e}'^{*}}{\boldsymbol {\mu }}_{e}\psi _{e}d\tau _{e}$ should be evaluated, sinse it may vanish in particular configuration, e.g. at equilibrium geometry, while the transition itself is not forbidden.

• Hmm... Usually one takes the equilibrium (or vibrationally averaged) structure of the ground electronic state and considers transitions that are not electronically forbidden, so that the vertical electronic transition (from this ground equilibrium state) matrix element is non-zero. But, I have no first-hand experience in applying the F-C principle, so maybe I'm naive (which is why I don't yet fiddle around with the text of the article).--P.wormer 09:33, 15 June 2007 (UTC)

212.192.238.23 15:19, 16 June 2007 (UTC) You may find an extensive discussions of the electronic transitions in "Molecular Symmetry and Spectroscopy" by Philip R. Bunker and Per Jensen. Authors discriminate two distinct cases:

• TDM is nonzero at equlibrium geometry. They call that case electronically allowed transition,
• TDM=0 at equlibrium, but its first derivative(s) with respect to the nuclear coordinates is large. This case is called vibronically allowed.

For the details you may consult the beginning of Chapter 14 of the cited book.

• I know that book very well, and as far as I can see it, everything that I wrote so far in this discussion is in complete agreement with that book. The authors state that the case, which you call TDM=0, is only of interest for transitions within one electronic state. This case is not covered by the classical Franck-Condon principle. In the Franck-Condon principle one talks about two different electronic states $\psi '_{e}\,$ and $\psi _{e}\,$, with corresponding (large) electronic excitation energy. The F-C principle accounts for vibrational structure on top of this electronic transition. It is assumed that both factors (electronic dipole and vibrational overlap) of the TDM integral are non-zero. Different magnitudes of the vibrational overlap integral give different intensities of the vibrational lines superimposed on one and the same electronic transition--P.wormer 13:39, 17 June 2007 (UTC)

212.192.238.23 11:26, 18 June 2007 (UTC) I cannot agree with you. I've looked at the text a few days ago, Russian translation, so I cannot supply page numbers. You may look the discussion of Herzberg-Teller effect and the pages around it. Bunker&Jensen discuss the electronicaly allowed transitions opposite to vibronically allowed. Please, look at the text once more.

• I like to end this discussion (unless I made an error in my editing of the main article, then you can point this out of course). The Herzberg-Teller theory goes way beyond the Franck-Condon theory (and is of much later date). It treats indeed the case of electronically forbidden transitions where intensity is borrowed from vibrational transitions. However, it is not desirable (or possible) to extend the F-C article to cover that case. If you insist that Wikipedia has it then advise I you to start a new article entitled Herzberg-Teller effect. (I started the Renner-Teller article, you can refer to it if you start a new article).--P.wormer 14:33, 18 June 2007 (UTC)

orbital v. spatial

In the section quantum mechanical formulation the term "orbital" is used several times in contexts where I would use "spatial". Both terms are in contrast to "spin". However, for me "orbital" often implies a one-electron picture, which is here not necessarily the case. So I changed orbital to spatial or electronic in some places. But not everywhere, because for instance the term "spin-orbit coupling" does not necessarily imply a one-electron picture. Thinking about it, it occurs to me that QM terminology is not really unambiguous about the terms "space", "orbit" and "orbital" (to distinguish from spin). Further I assumed that everywhere in the article spin relates to electronic spin and not to nuclear spin.--P.wormer --P.wormer 15:34, 17 June 2007 (UTC)

Absorption/emission of energy packet

In the introduction, it is stated that "Vibronic transitions are the simultaneous changes in electronic and vibrational energy levels of a molecule due to the absorption or emission of a photon of the appropriate energy." However, a photon is not the only energy packet that can cause these transitions. Is it better to change the word "photon" to "energy packet"? Erwin (talk) 09:55, 29 July 2008 (UTC)

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Spin function

I do not think it is correct to write the electronic wavefunction as a product of spin and spatial parts: $\psi _{e}\psi _{s}$ For general many-electron wavefunctions this is not possible. Spin is constructed as a linear combination of different Slater determinants not as a product with a spin-function.

An important consequence of this is the following: If we want to look at absorption into Triplet states or at phosphorescence, we can't just look at the spin and spatial parts separately. Computing the intensities for such "spin-forbidden" processes is significantly more involved. One has to to a summation over all the individual Slater determinants involved. Felixp84 (talk) 14:06, 12 November 2018 (UTC)

You are thinking of an approximate wavefunction, ultimately derived from an independent particle model. Here the starting point is an exact eigenfunction $\psi _{\rm {ev}}\psi _{\rm {s}}$ of a spin-free, N-electron, K-nucleus Hamiltonian. --P.wormer (talk) 23:13, 12 November 2018 (UTC)

Thanks for the clarification. But I think it would make sense to explain where this really comes from. The separation of electrons and nuclei derives from the Born-Oppenheimer approximation. Is there an analogous approximation or even an exact statement that says that one can separate the spatial and spin electronic coordinates in the same way? It would be good to mention this -- Felixp84 (talk) 12:40, 13 November 2018 (UTC)

Because the Hamiltonian does not contain electronic- or nuclear-spin interactions the exact wavefunction can be factorized in a spatial factor—containing electronic and nuclear spatial coordinates—, an electronic-spin factor, and a nuclear-spin factor. And you're exactly right, further factorization of the first part requires the BO approximation. If I had written this article, I would have left out the electronic spin function $\psi _{\rm {s}}$, in the same way as as the nuclear spin function is left out. --P.wormer (talk) 14:56, 13 November 2018 (UTC)