Curve crossing problem with dissipation: Uniform rate expression in diabatic representation

Abstract

The approach based on identification of the quasi-ballistic collective mode using the variational transition state theory (VTST) is applied to evaluation of the radiationless transition rate in the diabatic representation. The results for the rate match smoothly with the corresponding results derived in the adiabatic representation. This implies that the uniform expression for the rate constitutes a good approximation to the exact result. Analytic expression for the renormalized barrier frequency for Ohmic dissipation in the high barrier limit is derived. The result for the adiabaticity parameter in the strong damping regime reduces to Zusman’s result. The effect of non-Ohmic dissipation on the electron transfer kinetics in polar solvents is explored. A new procedure for the determination of the quasi-ballistic mode, based on variation of the total flux, is suggested. The procedure reduces to the VTST procedure in the adiabatic limit. In the nonadiabatic limit the quasi-ballistic mode coincides with the original reaction coordinate independently of the dissipation strength.