Nonequilibrium Fermi's Golden Rule Charge Transfer Rates via the Linearized Semiclassical Method

Nonequilibrium Fermi's golden rule (NE-FGR) describes the transition between a photoexcited bright donor electronic state and a dark acceptor electronic state when the nuclear degrees of freedom start out in a nonequilibrium state. In this article, we derive a new expression for NE-FGR within the framework of the linearized semiclassical approximation. The new expression opens the door for applications of NE-FGR in complex condensed-phase molecular systems described in terms of anharmonic force fields. We show that the linearized semiclassical expression for NE-FGR yields the exact fully quantum-mechanical result for the canonical Marcus model, where the coupling between donor and acceptor is assumed constant (the Condon approximation) and the donor and acceptor potential energy surfaces are parabolic and identical except for a shift in the equilibrium energy and geometry. For this model, we also present a comprehensive comparison between the linearized semiclassical expression and a hierarchy of more approximate expressions, in both normal and inverted regions and over a wide range of initial nonequilibrium states, temperatures, and frictions.