Resonance effects in the semiclassical theory of electronically nonadiabatic collision processes

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Abstract
Significant advances in the theory of electronically nonadiabatic collision processes have been made in recent years by the advent of models that treat all the ’’heavy particle’’ degrees of freedom—i.e., translation, vibration, and rotation—by classical mechanics; only electronic degrees of freedom are treated quantum mechanically. The ’’surface hopping’’ model of Tully and Preston and the generalized Stuckelberg model of Miller and George are examples of this type of approach. There have, however, been questions as to whether or not such models are capable of describing resonance effects in electronic–vibrational energy transfer, e.g., A*+BC(v=0) →A+BC(v=1), with ΔEA?h/ωBC. This paper shows that these resonance effects are the result of interference of amplitudes for different classical trajectories that contribute to the transition. The Miller–George model, which incorporates interference and tunneling within the framework of classical S‐matrix theory, thus describes resonance behavior, while the Tully–Preston model, which adds probabilities (rather than amplitudes) for the various trajectories, does not.