Theory of electron transfer in the presence of dissipation

摘要

An analytic study of the density matrix and Wigner representation equations for dissipative electron transfer is presentd.An explicit expression is derived for the off-diagonal Green's function,which shows avery fastrelaxation in time if the barrier to reaction is greater than the thermal energy.Thisfastrelaxationinvalidates previous attempts t derive coupled equations for the density in the large friction limit.The fast off-diagonal relaxation disallows an adiabatic elimination of the momentum even in the large friction limit.We hten show,with the aid of the boundary layer method,how one can use the same analysis to derive a set of two coupled equations for the diagonal densities.These equations are a generalization to phase space o fthe large friction Zusman equations[Chem.Phys.49,295(1980))].Adiabatic elimination of the momentum from these generalizedZusman equations solution of the generalized Zusman equations is presented for symmetric electron transfer for weak and stong electronic coupling,moderate and high barriers,and a large range f damping.the numericla results provide new insight into the friction dependence of th erate in the weak damping regime and show that previous analytic expresisons for the rate onlyqualitative in nature.