Herzberg-Teller coupling

Figure 2.11 combines the Herzberg-Teller coupling scheme of Figure 2.9 with the level patterns and symmetries expected for the double minimum potential of Figure 2.10 and presents an overall view of the inversion levels, their vibronic symmetries, and the rotational band types. For the lower So state, the equispaced V4" manifold of levels (0o, 4i, 42,. ..) bear the vibronic symmetries A], Bi, A],. .. whereas the corresponding levels in the Si state (0°, 41, 42,. ..) are A2, B2, A2,. The transitions between the ground state zero point level, 00,... 

Fig. 17. Vibronic coupling mechanisms (Herzberg-Teller couplings). The purely electronic transition between the excited state I (triplet substate) and the ground state 0 (Sq) is spin and symmetry forbidden, i.e. no intensity is found at the electronic origin I. Two mechanism are proposed. Coupling route (a) is probably more important for vibrations of metal-ligand character, while mechanism (b) preferentially induces satellite intensities by internal ligand vibrations. The electronic state S is a singlet, for which an electronic transition is dipole forbidden to the electronic ground state Sq. On the other hand, the state S , represents a singlet that carries sufficient transition probability. For detailed explanations see the text...

Excitation into electronic absorption results in intensity enhancement of normal modes of vibration which are coupled to electronic transition by either Franck-Condon or Herzberg-Teller coupling allows for study of chromophoric active sites in biological molecules at low concentrations allows assignment of CT (and in some cases LF) transitions based on nature of excited state distortion can provide information on metal-ligand bonding as described above for vibrational spectroscopy... 

FIG. 1. Energy levels, transition dipoles, and electron-vibration (Herzberg-Teller) couplings in the symmetric Peierls-Hubbard dimer. 

Let us shortly digress by commenting on the fact that also the transition 3) 2) is dipole-allowed and exhibits Herzberg-Teller coupling with the anti-phase... 

Fig. 6. Similar plot as Fig. 3 for a nontotally symmetric (and hence undisplaced, B = 0) harmonic oscillator involved in weak vibronic (i.e., Herzberg-Teller) coupling (K = , = 20) between states with perpendicular, unit transition moments. The upper half of the graph depicts the depolarization ratio, which shows dispersion in this case. The u = 1 (fundamental) excitation profile shows a pair of bands corresponding to the 0-0 and 0 1 absorption bands and the depolarization ratio peaks sharply between them, a pattern referred to as a Mortensen doublet.

Figure 9 (Henneker et al., 1978a) shows an example of Raman scattering by a non totally symmetric mode involved in (linear) Herzberg-Teller coupling of two excited states, d> and <1> . It is an elaboration of Fig. 7 in that the result of resonance with both excited states is shown. For convenience, we have assumed that both transitions -> and <5, -> are allowed and have the same transition moment, but different polarization. This assumption makes the Rayleigh profile symmetric relative to the two states, but has no effect on the structure of the fundamental REP since its matrix elements are proportional to the product of the two transition moments. The difference in intensity of the overtones in the and <1> band region reflects the frequency differences cOg — co and cOg — co . Figure 9 is based...

The set of equations (121) can be diagonalized exactly by numerical methods. All results displayed in the figures of this and the next subsection are obtained in this way. For qualitative purposes, one can approximate these results by using perturbation expansions. For weak pseudo-Jahn-Teller (i.e., Herzberg-Teller) coupling and vanishing Renner-Jahn-Teller coupling, we have... 

Fig. 34. Similar plot as Fig. 24 showing the effect of interference between Jahn-Teller E X e coupling + = 0.1) and Herzberg-Teller coupling = 0.5, o = 5). The lower front panel depicts the absorption spectrum and its corresponding line spectrum in the latter, solid and broken lines indicate vibronic levels of different symmetry and arrows identify weak lines.

Whereas the activity of the 02 modes is due to Herzberg-Teller coupling between different electronic states, the activity of h, and 62 modes in addition involves Jahn-Teller coupling within a degenerate state (Shelnutt et al., 1976, 1977 Nishimura et at., 1977). As shown in Section VI,C, the Jahn-Teller effect in molecules turns the Jahn-Teller active bi and 62 modes into displaced oscillators. The Herzberg-Teller coupling, on the other hand, would by itself lead to a 0-0 0-1 doublet without polarization dispersion. The observed REPs represent a balance between these two effects. Their interference leads to a redistribution of intensity over the vibrational bands of the REP as discussed in Section VII,D. 

---