Exactly solvable models for vibronic coupling in molecular spectroscopy. III. The pseudo Jahn–Teller effect

Abstract

A model system consisting of two electronic manifolds coupled through a nontotally symmetric mode of vibration is solved exactly and self-consistently by the method described in Paper I [J. Chem. Phys. 65, 2071 (1976)]. As in I, the model is defined in terms of harmonic diabatic potentials, but the restriction to harmonic adiabatic potentials, applied in I, is lifted here. As a result, the adiabatic coupling operator which has the same analytical form as in I, can assume a much wider range of values. It leads to adiabatic potentials which in general are anharmonic and may exhibit a double minimum. The coupling is taken to be an odd function of the vibrational coordinate so that it describes the (pseudo-) Jahn–Teller effect. Absorption and emission spectra are calculated for selected combinations of four spectroscopic parameters: (1) the electronic energy gap; (2) the diabatic harmonic frequency difference; (3) a linear adiabatic coupling parameter; and (4) a nonlinear (quasiquadratic) adiabatic coupling parameter. In the appropriate limits, the results are shown to reduce to analytical weak- and strong-coupling results, but the model is shown to differ from the molecular dimer model which also permits exact numerical solution for arbitrary coupling. The calculated spectra are interpreted in terms of a number of basic characteristics. Recognition of these characteristic spectral patterns may be helpful in the analysis of vibronically contaminated spectra. For certain combinations of parameter values, the model predicts strong and possibly anomalous solvent and isotope effects. As an example, the vibrational structure of the lowest singlet absorption band of pyrazine is analyzed and shown to indicate evidence for nonlinear vibronic coupling.