Vibrational progressions

We now proceed to some examples of this Fourier transfonn view of optical spectroscopy. Consider, for example, the UV absorption spectnun of CO2, shown in figure Al.6.11. The spectnuu is seen to have a long progression of vibrational features, each with fairly unifonu shape and width. Wliat is the physical interpretation of tliis vibrational progression and what is the origin of the width of the features The goal is to come up with a dynamical model that leads to a wavepacket autocorrelation fiinction whose Fourier transfonn... 

Figure Al.6.11. Idealized UV absorption spectrum of CO2. Note the regular progression of intemiediate resolution vibrational progression. In the frequency regime this structure is interpreted as a Franck-Condon...

The observation of a bend progression is particularly significant. In photoelectron spectroscopy, just as in electronic absorption or emission spectroscopy, the extent of vibrational progressions is governed by Franck-Condon factors between the initial and final states, i.e. the transition between the anion vibrational level u" and neutral level u is given by... 

Iff states. Sinee eaeh of these involves removing a bonding eleetron, the Franek-Conden integrals will be appreeiable for several vibrational levels, and thus a vibrational progression should be observed. 

Figure 7.1 8 Vibrational progressions and sequences in the electronic spectrum of a diatomic molecule...

Figure 7.22 Typical vibrational progression intensity distributions...

Question. Which low-lying states of NO would you expect to feature in the He I ultraviolet photoelectron spectrum of NO (Consider removal of an electron from only the three outermost orbitals of NO.) Indicate whether a long or short vibrational progression would be anticipated in each case. 

Figure 8.17 A short, barely resolved, vibrational progression in the v- vibration of CHj in the carbon Is X-ray photoelecton spectrum of methane obtained with a monochromatized X-ray source. (Reproduced, with permission, from Gelius, U., Svensson, S., Siegbahn, H., Basilier, E., Faxalv, A. and Siegbahn, K., Chem. Phys. Lett, 28, 1, 1974)...

To simulate the vibrational progression, we obtain the Franck—Condon factors using the two-dimensional array method in ref 64. We consider 1 vibrational quantum v = 0) from the EC stationary point and 21 vibrational quanta (z/ = 0, 1,. .., 20) from the GC stationary point. The Franck— Condon factors are then calculated for every permutation up to 21 quanta over the vibrational modes. It is necessary in order to get all Franck—Condon factors of the EC stationary point with respect to each three alg vibrational state (Figure 6) of the GC to sum to one. One obtains a qualitative agreement between the calculated and the experimental emission profiles (Figure... 

Schmidtke, H.-H. Vibrational Progressions in Electronic Spectra of Complex Compounds Indicating Stron Vibronic Coupling. 171,69-112 (1994). 

FIGURE 5. The lowest energy ionization bands of nitromethane. The vibrational progressions are labelled. The argon lines are shown to the right. Reproduced by permission of the American Institute of Physics from Ref. 31... 

Fig. 2.20. High resolution photoelectron spectrum of O2, showing overlapping vibrational progressions from transitions to different electronic states of the ion (range of IE not shown). Reproduced from Ref. [88] with permission. Royal Swedish Academy of Sciences, 1970.

A third analysis of the UV absorption spectrum of borazine reported by Bernstein and Reilly is not in reement with Kaldor s assignments. Bernstein interprets the first vibrational progression in the same manner as Kaldor. However, for the second progression he reports a band at 2011 nm (not observed by Kaldor) which he interprets as a Vi hot band of aa" symmetry. He identifies the 197.5 nm origin of this band as the location of the Aj state. 

Below 625 nm the reported absorption spectra consist of a series of intense LMCT excitations and their marked polarization dependence allows an unambiguous band assignment. In the red and near-IR region of the spectrum the highly structured d-d transitions are of low intensity. The vibrational progressions that are observed in the absorption and in the lumines-... 

Schmidtke H-H (1994) Vibrational Progressions in Electronic Spectra of Complex Compounds Indicating Stron Vibronic Coupling. J71 69-112 Schmittel M (1994) Umpolung of Ketones via Enol Radical Cations. 169 183-230 Schroder A, Mekelburger H-B, Vogtle F (1994) Belt-, Ball-, and Tube-shaped Molecules. 172 179-201... 

Figure 16 Electron energy-loss spectra with 14-eV electrons incident on (a) a 5-ML film of methanol condensed on an Ar spacer after exposition to small (lower curve) and large (higher curve) electron doses and (b) a 10-ML film of CO condensed on a platinum substrate. The a H excited state of CO is characterized by a vibrational progression having a spacing of about 0.21 eV. (From Ref. 37.)...

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