Herzberg-Teller vibronic theory

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... 

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. 

Since vibronic coupling effects in the adiabatic approximation are generally small compared to energy differences between electronic levels a first order perturbation can be applied. The perturbation operator contains all terms depending on the nuclear coordinates Si in the Herzberg-Teller series of Eq. (1) acting on the system with fixed nuclei which is represented by the zero order term which in ligand field theory is... 

This leads to an explicit expression for the vibronically induced component of the transition moment according to Herzberg-Teller theory,... 

We finally comment on the vibrational selection rules for vibronically induced transitions. The intensity of a vibrational band which occurs through vibronic coupling in normal coordinate is proportional to both the Herzberg-Teller and Born-Oppenheimer theories. When mode k is nontotally symmetric, the symmetry selection rule in that mode will be Av = 1, 3,. .. if the equilibrium position is undisplaced along in the electronic transition. If mode k is also harmonic, with similar frequencies in both electronic states, the more restrictive selection rule Av— applies. In such a case, the band intensity becomes proportional to [1 , times a... 

Such an expansion is, for example, at the base of the Herzberg-Teller theory of vibronic coupling we will present in Section 8.3.1.1. Unfortunately, the convergence of the expansion given in Eq. 8.11 is very slow, making its use unpractical in many... 

For forbidden electronic transitions, intensity is stolen from other allowed electronic transitions and thus further terms have to be added in Equations [36] and [37] (Herzberg-Teller theory of vibronic coupling). 

The substance of this section is based on the classic article by Herzberg and Teller (6) on vibronic transitions in polyatomic molecules. Some more specific aspects of the general theory are excellently described in recent articles (7, 8, 9). In the present section we wish to examine how symmetry arguments enter into the description and prediction of vibronic states, yet to attain this end it will be necessary to give a brief account of the quantum theory of the interaction between electronic and nuclear motion in molecules. 

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