Generalized Mobility Theory of Electron Transfer Reactions in Solution

Abstract

This paper reports a generalized theory of electron transfer reactions in solution; such reactions are typically termed oxidation-reduction reactions. The theory involves the use of the Kubo linear response analysis to examine the transport processes in an electrolyte system. In particular, we examine a system in which electron transfer between ions in the solution is possible. The substance of the theory is contained in an expression for the electron transfer rate constant. This rate constant is general, valid for all degrees of coupling between the electrons, ions, and surrounding dielectric medium. An expression of this type has not been reported previously. In deriving this general rate constant we find that there are new, hitherto unexpected processes which contribute to the electron transfer rate. Such processes are evident when, through the use of the Kubo theory, we examine the probability of electron transfer correlated with a simultaneous ionic diffusion step and a polarization displacement in the dielectric continuum. The degree to which these various transport processes contribute to the electron transfer rate is examined by means of a calculation on a model system. The system consists of two ionic species, one an electron donor and the other an acceptor, immersed in a dielectric continuum. The transfer electron is considered harmonically bound to the donor ion. The analysis is carried out without recourse to the Born-Oppenheimer separation approximation. We ignore the interaction between the transfer electron and the surrounding ions, but include a brief discussion of ways of handling this problem in the Appendix. This analysis of a model system points the way to future more detailed analyses of the problem.