Comparison of dynamical aspects of nonadiabatic electron, proton, and proton-coupled electron transfer reactions

The dynamical aspects of a model proton-coupled electron transfer (PCET) reaction in solution are analyzed with molecular dynamics simulations. The rate for nonadiabatic PCET is expressed in terms of a time-dependent probability flux correlation function. The impact of the proton donor-acceptor and solvent dynamics on the probability flux is examined. The dynamical behavior of the probability flux correlation function is dominated by a solvent damping term that depends on the energy gap correlation function. The proton donor-acceptor motion does not impact the dynamical behavior of the probability flux correlation function but does influence the magnitude of the rate. The approximations previously invoked for the calculation of PCET rates are tested. The effects of solvent damping on the proton donor-acceptor vibrational motion are found to be negligible, and the short-time solvent approximation, in which only equilibrium fluctuations of the solvent are considered, is determined to be valid for these types of reactions. The analysis of PCET reactions is compared to previous analyses of single electron and proton transfer reactions. The dynamical behavior is qualitatively similar for all three types of reactions, but the time scale of the decay of the probability flux correlation function is significantly longer for single proton transfer than for PCET and single electron transfer due to a smaller solvent reorganization energy for proton transfer.