Reversible electron transfer dynamics in non-Debye solvents

Abstract

The general solutions obtained earlier [J. Chem. Phys. 95, 3325 (1991)] for the coupled diffusion-reaction equations describing reversible electron transfer reactions in Debye solvents, governed by Sumi–Marcus free energy surfaces, are extended to non-Debye solvents. These solutions, which depend on the time correlation function of the reaction coordinate Δ(t), are exact in the narrow and wide window limits for Debye and non-Debye solvents and also in the slow reaction and non-diffusion limits for Debye solvents. The general solution also predicts the behavior between these limits and can be obtained as the solution to an integral equation. An iterative method of solving this equation using an effective relaxation time is discussed. The relationship between Δ(t) and the time correlation function S(t) of Born solvation energy of the reacting intermediates is elucidated.