Nonadiabatic processes involving quantum-like and classical-like coordinates with applications to nonadiabatic electron transfers

Nonadiabatic processes may involve both classical-like and quantum-like coordinates. A semiclassical analysis is used to treat the contribution of the former to the Franck-Condon factor in the reaction rate expression, thereby avoiding the usual harmonic oscillator approximation. Microcanonical and canonical rate constants are calculated, yielding an expression which includes contributions from both types of coordinates. The results are applied to nonadiabatic electron transfer reactions in solution, and show how Ll G 0 enters the final rate expression, even though LlE 0 is present in the initial Golden Rule nonadiabatic formula. This result avoids an approximation which has arisen in the nonadiabatic electron transfer literature.