Nonadiabatic proton-coupled electron transfer reactions: Impact of donor-acceptor vibrations, reorganization energies, and couplings on dynamics and rates

Fundamental aspects of proton-coupled electron transfer (PCET) reactions in solution are analyzed with molecular dynamics simulations for a series of model systems. The analysis addresses the impact of the solvent reorganization energy, the proton donor-acceptor mode vibrational frequency, and the distance dependence of the nonadiabatic coupling on the dynamics of the reaction and the magnitude of the rate. The rate for nonadiabatic PCET is expressed in terms of a time-dependent probability flux correlation function. The time dependence of the probability flux correlation function is determined mainly by the solvent reorganization energy and is not significantly influenced by the proton donor-acceptor frequency or the distance dependence of the nonadiabatic coupling. The magnitude of the PCET rate becomes greater as the solvent reorganization energy decreases, the proton donor-acceptor frequency decreases, and the distance dependence of the nonadiabatic coupling increases. The approximations underlying a previously derived analytical PCET rate expression are also investigated. The short-time approximation for the solvent is valid for these types of systems. In addition, solvent damping effects on the proton donor-acceptor motion are not significant on the time scale of the probability flux. The rates calculated from the molecular dynamics simulations agree well with those calculated from the analytical rate expression.