Talk:Vibronic spectroscopy

Band head

I'm having trouble with the expression

$m={\frac {B^{\prime }+B^{\prime \prime }}{2(B^{\prime }-B^{\prime \prime })}}$

for the quantum number corresponding to the band head, which is given (with a minus sign) in Banwell&McCash, p172. The right hand side is not an integer! This arises because in the expression for the wavenumber of a rotational line m is an integer, but the derivative with respect to m (which is equal to zero at the maximum) is calculated as though it were continuous. I'm not even sure that a "nearest integer" qualifier would be correct.

The line positions in the Fortrat diagram can be said to lie on a parabola, which is a continuous function of some variable x, so the formula for the x value at the maximum

$x={\frac {B^{\prime }+B^{\prime \prime }}{2(B^{\prime }-B^{\prime \prime })}}$

is correct for that parabola.

What to do? Remove reference to the position of the band head? Any other suggestions? Petergans (talk) 10:18, 21 March 2013 (UTC)

Strictly the maximum must be at one of the two nearest integers, one on each side. If the continuous function has a maximum between n and (n+1), the observed maximum (for integer m) must be at either n or (n+1).

Note that a similar difficulty arises for the statement at Rotational spectroscopy#Rotational line intensities about the maximum relative intensity. The square root obtained by setting the derivative of (2J+1) times the Boltzmann factor equal to zero is not in general an integer, and so does not correspond to a real line. Again the most intense observed line will be one of the two integer lines on either side. Dirac66 (talk) 13:37, 21 March 2013 (UTC)

Sign problems

The signs are still confused in the discussion which includes the above point.

1. First, the Fortrat diagram has an undefined J on the vertical axis. This suggests either J' or J", but these two values must be nonnegative. The vertical axis should in fact be labelled as m, which can take either sign as defined in the text.
2. For the band head position, there is no reason to suppress the minus sign given in Banwell and McCash (as well as Straughan and Walker, p74). In the usual case B' < B", the expression with the minus sign gives x > 0 as required for the R-branch.
3. If the above is corrected, then the maximum is at the integer part of x (or x+1), not of -x (or -(x+1)).

I can fix the problems in the text, but I cannot edit the Excel file with the Fortrat diagram since it is uploaded as a .png file. Dirac66 (talk) 20:21, 2 April 2013 (UTC)

Looking at the original spreadsheet I see that the y-axis variable is m. Diagram changed. Petergans (talk) 10:58, 3 April 2013 (UTC)

Term energies or transition energies?

I do not understand today's change of the description of the formula for G(J', J") from transition energies ... of the lines to term energies ... of the P- and R- branch states. I inserted the phrase transition energies on 17 March because this formula involves quantum numbers of both upper and lower states, so that it must refer to the transition between the two states. More precisely, it should be transition energies expressed in wavenumbers or transition energies divided by hc or just transition wavenumbers. But not term energies, since the word term refers to a single state and a transition energy is always the difference between two terms. Ref. Hollas p93.

Also I hope to contribute more to this article soon - today I took Hollas and Straughan-Walker out of the library again which will help. Dirac66 (talk) 20:59, 25 March 2013 (UTC)

Well spotted! What concerned me was that the formulae

$G(J^{\prime },J^{\prime \prime })={\bar {\nu }}_{v^{\prime }-v^{\prime \prime }}+B^{\prime }J^{\prime }(J^{\prime }+1)-B^{\prime \prime }J^{\prime \prime }(J^{\prime \prime }+1)$

and

${\bar {\nu }}_{P,R}={\bar {\nu }}_{v^{\prime },v^{\prime \prime }}+(B^{\prime }+B^{\prime \prime })m+(B^{\prime }-B^{\prime \prime })m^{2},\quad m=\pm 1,\pm 2\ etc.$

appear to be contradictory. In fact when I look again at Banwell and McCash I see that the first eqn. should be (B&McC, eqn. 6.19)

${\bar {\nu }}_{spect}={\bar {\nu }}_{v^{\prime }-v^{\prime \prime }}+B^{\prime }J^{\prime }(J^{\prime }+1)-B^{\prime \prime }(J^{\prime \prime }+1)$

This explains the discrepancy, so I'll return the text to its previous state, but with this correction. Petergans (talk) 08:39, 26 March 2013 (UTC)

Possible source for permanganate spectrum

The discussion on permanganate needs a published source. With the help of Google I have found a paper by P.A. Cox, D.J. Robbins and P. Day, Molec. Phys. 30, 405-411 (1975) [1]. It mentions a progression in the ν₁(a₁) Mn-O stretching mode, but I am uncertain whether it should be cited here because the method used was magnetic circular dichroism which is not in this article. Dirac66 (talk) 21:21, 27 April 2013 (UTC)

Uranium complex

I am confused about the relation between the two source papers re UCl₆^2-? Do both papers consider the same band? Does the first paper fail to explain certain peaks which are explained by the second paper? Or does the second paper provide an alternate explanation for the peaks (or bands) explained in the first paper? Or ...? Please clarify. Dirac66 (talk) 01:38, 29 April 2013 (UTC)

I took these references from work I did a long time ago (Spectrochim. Acta, 1965, 21,1589-1595), so its ages since I looked at the papers. They are definitely about the same electronic transition. As I recollect, the second paper reveals also lattice vibrations, which occur at much lower frequencies than the U-Cl stretching and bending vibrations, but I don't remember the details. The second citation was included in order to instance a case involving lattice vibrations. Are we ready to go for DYK? Petergans (talk) 07:58, 29 April 2013 (UTC)

OK, I have made the last 2 changes which I wanted to make now. I restored the reference to Housecroft + Sharpe but in the right place this time, as I had previously confused you by placing it after the sentence saying there is a vibronic progression in the band from MnO₄^-. Actually it was a source for the statement that this band is an LMCT. And for UCl₆^2- I added a few words to clarify what we are talking about.

So go ahead now and submit the article as a DYK if you wish. I note from your user page that you are experienced at getting scientific articles accepted there. Dirac66 (talk) 20:27, 29 April 2013 (UTC)

Good news- the article has been entered for DYK. Many thanks, Dirac66, for all your help which has resulted in a great improvement from my first draft. Bad news - I've just posted another new article, spectroscopic line shape, which you might like to look at. Petergans (talk) 09:57, 30 April 2013 (UTC)

Pure vibronic? Band origin?

Still on the UCl₆^2- complex, I am not sure what "pure vibronic" means. My guess is that it means that all observed intensity for the electronic transition in question involves vibrational excitation as well. If so this should be explained, as it is a more complex concept than "pure rotational" or "pure vibrational" which only involve one type of molecular motion each. Also, the next sentence says that "At ... 4K, the vibronic structure was completely resolved, with no intensity at the band origin, ..." Does "band origin" here mean the vibrationless transition excluded from "pure vibronic", or does it mean the rotationless transition analogous to the "band origin" in the Diatomic molecules section? Dirac66 (talk) 20:58, 3 May 2013 (UTC)

The wording is not quite right. Band origin here refers to the electronic transition, which is forbidden (f-f transition, symmetry u×u=g). The spectra show zero intensity there (dipole moment operator has u symmetry), with 3 side-lines due to 3 distinct vibrations of u symmetry. No progression, as I rememeber it. Rotations don't come into it, these are solid state spectra. Petergans (talk) 22:01, 3 May 2013 (UTC)

This seems clearer but then why do d-d transitions in octahedral TM complexes have only "some" vibronic character, whereas f-f in the uranium complex is "pure" vibronic? The Laporte rule argument would seem to apply to both.

Also, would you object to replacing "pure vibronic" by "entirely vibronic" or "exclusively vibronic"? It seems to me that "vibronic" implies a combination (of vibrational and electronic character), and that a "pure" combination is contradictory. Dirac66 (talk) 22:18, 4 May 2013 (UTC)

Orgel, p 92, outlines the "classical explanation" of the break-down of the Laporte rule for d-d transitions in octahedral complexes, in terms of d-p mixing in a vibrationally excited state in which the molecule is not centrosymmetric. I guess that's why I used the term "pure" for the f-f case. Petergans (talk) 23:23, 4 May 2013 (UTC)

OK, thanks. I have reworded "pure vibronic" and "band origin", the latter to avoid a term having two meanings in different parts of the article. As for the explanation of why f-f is pure vibronic but not d-d, I judge that it is too complex to include here as it would require lots of supplementary explanation (of d-p mixing for example, etc. etc.) Dirac66 (talk) 19:07, 5 May 2013 (UTC)