Diffusion in a potential field under the Gaussian-Sink action: Analytical solution of the problem

Abstract

A method for analytical solution of a base model, which reduces to a diffusion equation with a Gaussian-sink term in the electron transfer theory, is described. The method is constructed as a generalization of the Kramers approach to the problems on the high barrier crossing and is applicable to situations where the reaching of the reaction zone is of activation nature. The derived formulas span a very broad range of variations in the solvent adjustment rate, provided certain conditions as to the sink's width and center position are satisfied. In this range the kinetics is single-exponential and the rate constant is perceptibly smaller than the equilibrium estimate and steadily decreases if the adjustment slows down.