Herzberg-Teller Vibronic Coupling

The transition moment f between the vibronic states where 

By expanding the electronic transition moment operator z(g) as a Taylor series in the nuclear normal coordinates about the equilibrium configuration go, one obtains  

Substitution of Eq. (6.3) into Eq. (6.2) leads to the following expression for the vibronic transition moment 

6 Electronic Structure and Energy Transfer in Solid a-Sexithienyl 

The room temperature Raman spectrum excited in pre-resonance conditions 

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The 10a,1 band, as well as many bands built on it, and also the 10a , band obtain their intensity by the Herzberg-Teller vibronic coupling mechanism discussed in Section 7.3.4.2(b). 

Bacon, A.R. and Hollas, J.M. (1985) Duschinsky effect caused by Herzberg-Teller vibronic coupling of two b2 vibrations in the Si-So systems of benzonitrile and phenylacetylene. Chem. Phys. Lett., 120, 477. 

Due to the relatively strong forbiddenness of the purely electronic transition 11) <-> 10), for example, displayed in the long emission lifetime at T = 1.2 K of Tj = 230 ps, vibronic coupling (Herzberg-Teller, HT, coupling) becomes an important mechanism of radiative deactivation. This mechanism provides intensity to specific vibrational satellites by vibrationally induced admixtures of... 

Fig. 26. Different mechanisms of vibronic coupling (Herzberg-Teller, HT, coupling) - symbolized by the matrix elements - open radiative deactivation paths from a triplet sublevel to a singlet ground state. This results in the occurrence of vibrational satellites Vq (HT). These mechanisms become particularly obvious, when the purely electronic transition JO) I) is strongly forbidden like in [Os(bpy)3] doped into [Ru(bpy)j](PFj)2...

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,... 

The vibronic theory of the RR effect distinguishes two major intensity enhancement mechanisms that play a dominant role in the RR spectra (i) Franck-Condon (FC) principle and (ii) Herzberg-Teller (FIT) vibronic coupling, which have quite different properties. The FC scattering mechanism involves displacement of the potential minima of the ground and excited electronic states along a vibrational normal... 

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...

This is called the Herzberg-Teller expansion. The fourth term in the last line describes a vibronic coupling. The electronic part of the vibronic operator is defined... 

Vibrational Contributions Contribution of vibrational modes has been described for TPA [5-9, 11-17, 19, 22, 23, 31, 37, 61, 235, 309, 343-345] and for other nonlinear optical processes [346]. One classical example is the 1A j -1 B2u TP transition of benzene, the so-called green band. This electronic transition is allowed due to a vibronic coupling mechanism [346]. Semiempirical [60, 61] as well as ab initio response theory calculations using the Herzberg-Teller expansion [344] demonstrate the role of vibronic coupling. Such contributions can either enhance an allowed transition or intensify a symmetry-forbidden transition. 

In those cases where the adiabatic approximation can be assumed to hold, the influence of vibronic coupling on the spectroscopic properties of a system can be treated within the Herzberg-Teller (perturbative) formalism (20) for vibronic interactions. This formalism is applicable when the vibronic interaction energies are small compared to the energy spacings between the... 

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