On the role of medium electrons in the outer-sphere electron transfer reactions

Abstract

We consider the nonlinear Schrödinger equation arising when an explicit separation of the medium electron polarization is performed in the Hamiltonian describing the outer-sphere electron transfer (ET) reaction. The corresponding classical activation energy is determined by the point of intersection of two diabatic energy curves rather than by the stationary saddle point of the free energy functional, in agreement with the earlier treatment of Kim and Hynes. Analytical expressions for the free energy terms as functions of the ET coordinate are derived. The relative energy of this cross point is the same as the traditional activation energy of the Et process as given by the Marcus formula. In order to find the interaction matrix elements which promote the nonadiabatic transition and avoided crossing, an alternative quantum-mechanical description of the two-level ET model is given in terms of the wavefunction which allows independent reorganization of electrons belonging to the medium and to the chemical substrate. Explicit expression for matrix elements are presented and different kinetic regimes generated by this refined model are discussed.