Rigorous calculation of electric field effects on the free energy change of the electron transfer reaction

Abstract

We theoretically investigate the effect of an external electric field on the free energy change of electron transfer reaction in polar solvents. The external electric field produces polarization both on the solutes and in the solvent. Since the polarization produced on the solute differs from that in the solvent, apparent surface charge is created on the surface of the solutes. The polarization charge on the surface of the solutes interacts with the charge associated with the electron transfer. The free energy change of the reaction including such effect is calculated rigorously. A simple formula is derived and compared to the exact result in the case of spherical solutes in the dielectric continuum media. Only slight deviations are observed for any values of the solvent polarity and of the ratio between the radii of the donor and the acceptor molecules. In addition, we also applied the same method to evaluate the reorganization energy rigorously: The Marcus expression for the reorganization energy is an approximate one. The accuracy of the Marcus expression is assessed by comparing it with the exact result.