Polariton-Mediated Electron Transfer Rate Constant from Non-Equilibrium Fermi’s Golden Rule

We provide a time-domain derivation of the population transfer rates for the polariton-mediated electron transfer (PMET) reaction under the collective coupling regime. Our theoretical analysis leads to the corresponding Marcus theory rates under the high-temperature and Markovian bath approximations. In addition to including the non-Markovian effect and the low-temperature limits, the theory is also generalized to include the multiple donor-to-acceptor case, as well as including multiple cavity modes. The derivations reveal a comprehensive framework of master equation-based reduced dynamics methods for PMET and other polariton-mediated reactions, providing a promising balance between numeric accuracy and computational efficiency, as well as a step closer to fully scalable simulations of realistic PMET processes.