Vibronic Interactions. The Adiabatic Approximation

Abstract

A general treatment of vibronic interactions is given in terms of the adiabatic approximation. It is pointed out that the terms arising from the dependence of the electronic transition moment on nuclear configuration which are commonly used to discuss vibrational borrowing are also closely related to the terms involved in the coupling of the adiabatic wavefunctions. Formulas for spectral intensities and band strengths are given. An inequality is derived which states that if the excited state geometry closely approximates the ground state geometry, the emission band strength is less than the absorption band strength. The interplay between the coupling of the adiabatic wavefunctions and the dependence of the electronic transition moment on nuclear coordinates is illustrated by a simple model which complements that given by Fulton and Gouterman [J. Chem. Phys. 35, 1059 (1961)]. It is shown that in weak coupling spectral intensities due to vibrational borrowing can be understood qualitatively, but not quantitatively, by the Herzberg—Teller mechanism [Z. Physik. Chem. B21, 410 (1933)], while in the case of strong coupling both the coupling of the adiabatic wavefunctions and the dependence of the transition moment on nuclear configuration must be included to obtain a quantitative description of intensities. Comparisons are made with the previous model.