Time dependent solution of generalized Zusman model of outersphere electron transfer reactions: applications to various experimental situations

Abstract

The Zusman model of the environmental effects on the outersphere electron transfer reaction has been widely used to study solvent effects on various important electron transfer reactions. We present here a generalized treatment of the Zusman model using a powerful Green's function technique. This generalization enables us to obtain the time dependent solution of the model for various complicated situations often encountered in experiments. In addition, the present formulation allows for a unified description of the barrierless and the high barrier reactions for both the nonadiabatic and the weakly adiabatic limits of electron transfer reactions. A merit of the present description is that one need not assume an initial equilibrium population of the reactants and therefore, this method is particularly suitable for the treatment of photoelectron transfer reactions. The following four model situations have been studied. (a) Ground state, symmetric, and asymmetric electron transfer reactions. The reactant surface population exhibits a markedly nonexponential decay. (b) A low barrier, photoelectron transfer reaction where an additional photochemical reaction occurs from the charge transfer state. In this case, the decay of the reactant population is largely exponential when the funnel is efficient. (c) A high barrier photoelectron transfer reaction with a radiative decay from either or both of the reactant and product surfaces. In specific situations, the radiative decay can even compete with the electron transfer to give rise to a fractional dependence of the fluorescence quantum yield (of the locally excited state) on the average solvation time. (d) A multichannel nonradiative decay of population from an excited state surface having multiple sinks. Here an interesting nonlinear interaction between the sinks is observed. In all these cases, it is found that the average rate of electron transfer can be considerably different from the long time rate. The generality of the present formulation has been demonstrated by deriving the rate expressions of the theory of outersphere electron transfer reaction due to Zusman, that due to Rips and Jortner and also that due to Sumi, Nadler, and Marcus.