Abstract
Abstract A generalization of a previous theory of non-radiative processes (based on a one-frequency oscillator model) is developed by considering a system of harmonic oscillators with an arbitrary number of vibration frequencies. Part I is devoted to the dynamics of these processes. The first step is an investigation of the geometric properties of the ‘diabatic’ potential energy hypersurfaces which govern the nuclear vibrations in two different electronic states and their relation to the ‘adiabatic’ electronic hypersurfaces. The cases of both strong and weak electon-phonon interaction are considered. The second step is the calculation of the non-radiative transition probabilities from one electronic state to another, making use of both classical and quantum mechanics to describe the nuclear motion in the high and low energy ranges, respectively. The expressions derived apply to the whole range between the limits of adiabatic and non-adiabatic transitions.
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