On the role of solvent electronic polarization in charge transfer reactions

Abstract

The effect of a solvent’s electronic polarization on the rate of a charge transfer reaction is studied in both continuum and discrete solvent models. An effective system Hamiltonian that contains the equilibrium solvation from the solvent electronic polarization is obtained, and leads to an effective matrix element Veff coupling the charge transfer states that is smaller than the gas phase value. Both the effective Hamiltonian and Veff are dependent on the solvent’s instantaneous nuclear configuration, and liquid state theory is used to carry out the configuration average. The solvent electronic polarization reduces the transition rate for both adiabatic and nonadiabatic reactions. A standard relation between the equilibrium solvation energy of the reactants and the solvent reorganization energy is established that permits evaluation of the effect of a molecular solvent (using a Drude model for the electronic degrees of freedom) on the rate by evaluating a partition function. This permits use of a path integral formulation for the mixed quantum (electronic polarization) classical (slow nuclear configuration) solvent that leads to the information required for the rate constant. In a strong coupling regime, where the coupling between the charge-transfer species would be so large as to preclude reactant and product species, we show that a new mechanism for charge localization arising from the solvating effect of the electronic polarization may occur, and formulate a rate constant expression for this regime. It has the form of a quantum Kramers rate and shows that the solvent provides a friction effect that will reduce the rate relative to the no-friction rate.