Cavity-Modified Nonequilibrium Fermi's Golden Rule Rate Coefficients from Cavity-Free Inputs

The Nonequilibrium Fermi's Golden Rule (NE-FGR) provides a convenient theoretical framework for calculating the charge transfer rate between a photoexcited bright donor electronic state and a dark acceptor electronic state, when the nuclear degrees of freedom start out in a nonequilibrium initial state. In this paper, we show that NE-FGR rates can be significantly modified by placing the molecular system inside an electromagnetic microcavity, even when the coupling with the cavity modes is weak. In this case, cavity-modified NE-FGR rates can also be estimated from the same inputs needed for calculating the cavity-free NE-FGR rates, thereby bypassing the need for an explicit simulation of the molecular system inside the cavity. We also introduce an approximate limit of the cavity-modified NE-FGR, which we denote cavity-modified Instantaneous Marcus Theory, since it is based on the same assumptions underlying Marcus theory. The utility of the proposed framework for calculating cavity-modified NE-FGR rates is demonstrated by applications to photo-induced charge transfer in the carotenoid-porphyrin-C$_{60}$ molecular triad dissolved in liquid tetrahydrofuran and the Garg-Onuchic-Ambegaokar model for charge transfer in the condensed phase.