A Unified Model for the Electrochemical Rate Constant That Incorporates Solvent Dynamics

Abstract

A generalized Anderson−Newns Hamiltonian is employed to model electrochemical electron transfer kinetics via a potential energy surface approach. Important novel features of this treatment are inclusion of the electrode induced broadening of the reactant level and the effect of solvent dynamics on the pre-exponential factor, which is determined by a numerical integration of the Kramers’ diffusion controlled barrier crossing rate expression. An interpolation scheme is provided to treat nonadiabatic, transition state theory adiabatic, and solvent dynamical effects in the weak coupling (nonadiabatic) and strong coupling (adiabatic) limits in a unified manner. The derived rate expressions are valid for arbitrary values of the electrode−reactant coupling term V, solvent polarization mode frequency ωr, and longitudinal solvent dielectric relaxation time τL. A comparison of the results obtained here with the earlier treatments of electron transfer reactions is presented, and the relevance of the present formalism for experimental systems is provided. The density of states based approach for the heterogeneous electron transfer reaction is briefly discussed.