Proton-coupled electron transfer reactions in solution: Molecular dynamics with quantum transitions for model systems

A general minimal model for proton-coupled electron transfer (PCET) reactions in solution is presented. This model consists of three coupled degrees of freedom that represent an electron, a proton, and a solvent coordinate. Altering the parameters in this model generates a wide range of PCET dynamics. This paper focuses on three model systems corresponding to three different mechanisms: a concerted mechanism in which the proton and electron are transferred simultaneously, a sequential mechanism in which the proton is transferred prior to the electron, and a sequential mechanism in which the electron is transferred prior to the proton. The surface hopping method 'molecular dynamics with quantum transitions' (MDQT) is applied to these model systems. The proton and electron coordinates are treated quantum mechanically, and the solvent coordinate is treated classically. Thus the adiabatic quantum states are two-dimensional wavefunctions that depend on both the electron and the proton coordinates. The MDQT method incorporates nonadiabatic transitions between these mixed proton/electron adiabatic quantum states. The MDQT simulations presented in this paper provide insight into the fundamental physical principles and the dynamical aspects of PCET reactions. Nonadiabatic effects are shown to play an important role in determining the rates and mechanisms of PCET reactions. This represents the first application of MDQT to a system in which both a proton and an electron are treated quantum mechanically.