Incorporating backflow into a relaxation theory treatment of the dynamics of nonequilibrium nonadiabatic transition processes

Abstract

An approximate method for computing the leakage of population from an initial (‘‘donor’’) electronic state, prepared in a nonequilibrium nuclear coordinate distribution, onto a second, nonadiabatically coupled (‘‘acceptor’’), electronic state is presented. This proposed solution, which utilizes a set of coupled integrodifferential equations (commonly referred to as Generalized Master Equations) is an extension of a nonequilibrium golden rule formula derived previously [R. D. Coalson, D. G. Evans, and A. Nitzan, J. Chem. Phys. 101, 486 (1994)]. The Generalized Master Equation approach is able to describe situations where the donor and acceptor potential energy surfaces have similar energy origins, and hence irreversible flow of population from the donor state to the acceptor state is not expected. The accuracy of the method is demonstrated for an exactly solvable spin–boson model of inner sphere electron transfer. In the regime of small nonadiabatic coupling, agreement of the proposed method and path integral calculations is nearly quantitative for symmetric electron transfer processes and systems with weak bias between the energy origins of the donor and acceptor electronic states. Unlike the nonequilibrium golden rule formula, appropriately constructed Generalized Master Equations are capable of capturing the backflow of electronic population from the acceptor to the donor surface and relaxation to Boltzmann equilibrium at long times.