MICROSCOPIC FORMULATION OF MARCUS THEORY OF ELECTRON-TRANSFER

A microscopic theory for the rate of nonadiabatic electron transfer is developed and its relation to classical Marcus theory is analyzed. Th e focus is on how the nonlinear response of a molecular solvent to a c hange in the charge distribution of the donor-acceptor pair influences the rate; quantum mechanical and solvent dynamical effects are ignore d. Under these restrictions, the rate is determined by the probability density of the energy gap, which is defined as the instantaneous chan ge in solvation energy upon moving an electron from the donor to the a cceptor. It is shown how this probability density can be obtained from the free energies of transferring varying amounts of charge between t he donor and acceptor (as specified by a charging parameter). A simple algorithm is proposed for calculating these free-energy changes (and hence the energy gap probability density) from computer simulations on just three states: the reactant, the product, and an ''anti''-product formed by transferring a positive unit charge from the donor to the a cceptor. Microscopic generalizations of the Marcus nonequilibrium free -energy surfaces for the reactant and the product, constructed as func tions of the charging parameter, are presented. Their relation to surf aces constructed as functions of the energy gap is also established. T he Marcus relation (i.e., the activation energy as a parabolic functio n of the free-energy change of reaction) is derived in a way that clea rly shows that it is a good approximation in the normal region even wh en the solvent response is significantly nonlinear. A simple generaliz ation of this relation, in which the activation energy is given by par abolic functions with different curvatures in the normal and inverted regions, is proposed. These curvatures are inversely proportional to t he reorganization energies of the product and the antiproduct, respect ively. Computer simulations of a simple model system are performed to illustrate and test these results and procedures.