Electron transfer in confined electromagnetic fields: A unified Fermi’s golden rule rate theory and extension to lossy cavities

With the rapid development of nanophotonics and cavity quantum electrodynamics, there has been growing interest in how confined electromagnetic fields modify fundamental molecular processes such as electron transfer. In this paper, we revisit the problem of nonadiabatic electron transfer (ET) in confined electromagnetic fields studied in Semenov and Nitzan [J. Chem. Phys. 150, 174122 (2019)] and present a unified rate theory based on Fermi's golden rule. By employing a polaron-transformed Hamiltonian, we derive analytic expressions for the ET rate correlation functions that are valid across all temperature regimes and all cavity mode time scales. In the high-temperature limit, our formalism recovers the Marcus and Marcus-Jortner results, while in the low-temperature limit, it reveals the emergence of the energy gap law. We further extend the theory to include cavity loss by using an effective Brownian oscillator spectral density, which enables closed-form expressions for the ET rate in lossy cavities. As applications, we demonstrate two key cavity-induced phenomena: (i) resonance effects, where the ET rate is strongly enhanced with certain cavity mode frequencies, and (ii) electron-transfer-induced photon emission, arising from the population of cavity photon Fock states during the ET process. These results establish a general framework for understanding how confined electromagnetic fields reshape charge transfer dynamics and suggest novel opportunities for controlling and probing ET reactions in nanophotonic environments.