Abstract
We discuss the generalized moments of the nonadiabatic transition reaction by using the stochastic Liouville equation for the study of outer-sphere electron transfer in polar solvents characterized by Debye dielectric relaxation. We obtain an approximate expression for the generalized moments which incorporates the width of the transition with arbitrary initial condition far from equilibrium. For low barriers, we derive an analytical expression for the rate corresponding to harmonic potential surfaces in the overdamped regime. For Fokker-Planck operators of Smoluchowski type, we introduce a new method to solve all of the generalized moments by using the eigenfunction expansion method.
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