Exactly solvable models for vibronic coupling in molecular spectroscopy. I. Nontotally symmetric harmonic mode

Abstract

Molecular vibronic coupling is studied on a model consisting of two electronic states coupled by one vibrational mode. If adiabatic potentials corresponding to the two states are available (e.g., from experiment), the model can be solved exactly in terms of a coupling function defined implicitly and self-consistently by means of a chosen or calculated diabatic potential. Alternatively and equivalently, the model can be formulated and solved in terms of one adiabatic and two diabatic potentials. In the harmonic-oscillator approximation, the coupling function reduces to one parameter modulated by the electronic energy separation. Near the limit of weak vibronic coupling, the model reduces to the well-known linear Herzberg–Teller approximation. A formally equivalent but complementary linear perturbation approximation is developed for strong coupling. For intermediate coupling, where both of these perturbation schemes are shown to fail, the model is solved by two complementary numerical procedures of which at least one converges quickly for any given set of physically acceptable parameter values. Detailed results are presented for coupling through a nondegenerate, non-totally-symmetric normal mode. Energy level diagrams as well as absorption and emission spectra are calculated for the full range of coupling parameters and energy gaps compatible with the harmonic approximation. The results show anomalous level spacings, intensities, and isotope effects, especially under intermediate-coupling conditions. The anomalies can be qualitatively understood on the basis of avoided crossings in energy-level correlation diagrams. As an example, the model is used for a qualitative explanation of anomalous intensity variations of the 1Lb transition in aromatic hydrocarbons.