Dynamic solvent effects on outer-sphere electron transfer

Abstract

In this paper we present the results of a theoretical study of outer-sphere electron transfer (ET) in a polar solvent, with the modification of the nuclear states by the change in the charge distribution originating solely from the response of the exterior medium. The model Hamiltonian for the system corresponds to two parabolic diabatic potential surfaces with adiabatic coupling between them. The real-time path integral formalism is utilized to derive the general expressions for the influence functional of the medium in the Gaussian approximation and for the ET rate. The ET rate is explicitly evaluated for the particular case of a medium characterized by the Debye dielectric relaxation function. We explore the relation between the dynamics of the reaction coordinate and the character of the ET process, deriving an expression for the ET rate, which bridges between the nonadiabatic and the solvent-controlled adiabatic limits. We establish simple criteria for the validity range of various descriptions of ET dynamics, i.e., the transition state theory, the solvent-controlled ET as well as the adiabatic and nonadiabatic limits. The results are applied to intramolecular ET in alkanols, establishing the adiabatic nature of these processes, whose dynamics is dominated by the (slow) longitudinal dielectric relaxation rate of the solvent.