Green function theory of charge transfer processes in solution

By using a Green function Q to characterize the linear response of a dielectric body to electric charges, we obtain a theory for the solvent dielectric contribution to relaxation along the reaction coordinate RC(t) in an electron transfer process. For an electron transfer reaction model, in which the ions are embedded in a dielectric continuum, the theory gives, at t=0, the reorganization free energy derived by Marcus in 1956. For the same model the characteristic time τQ associated with RC(t) is evaluated in terms of the dielectric function εω of the medium. How the rate constant ket for an electron transfer process depends on τQ is illustrated for both high-barrier and low-barrier cases by approximating RC(t) as a Smoluchowski process on a potential surface. Applying the theory to a molecular model (charged hard sphere ions in a dipolar hard sphere solvent), treated in the mean spherical approximation for the response at any frequency (Wolynes, 1987), indicates that the effects of the molecular structure of the solvent on τQ are large even if the ion is several times larger than a solvent molecule.