The effect of the electron–electron interaction on the pre-exponential factor of the rate constant of the adiabatic electrochemical electron transfer reaction

It is shown within the simple model of the polar solvent and the classical multidimensional transition state method in the harmonic approximation that the pre-exponential factor of the rate constant of the adiabatic electrochemical electron transfer reaction depends on the energy of the Coulomb repulsion of electrons occupying the valence orbital of the reactant. The exact expressions for the effective frequency ωeff determining the pre-exponential factor are obtained using two exactly solvable limits of the Anderson–Newns model: the surface-molecule model and the wide-bands approximation for the electronic structure of an electrode. The list of expressions for ωeff for different particular cases is presented. It is shown that, due to the non-zero Coulomb repulsion, the transition state method in the harmonic approximation breaks down in some regions of values of physical parameters of the system. The stochastic approach permits the proper calculations of ωeff in this case. The results of calculations of ωeff are presented and the effect of the Coulomb repulsion on the dependencies of ωeff on the electronic matrix element and the overvoltage are studied. It is shown that this effect can be rather significant.