Photoexcited electron transfer: Short-time dynamics and turnover control by dephasing, relaxation, and mixing

In the usual parabolic, spin-boson approximation, understanding the dynamics of electron transfer reduces to following the coupled electron/vibration system throughout its exploration of the coupled potential energy surfaces. We discuss such an analysis for a very simple model for photoexcited electron transfer, consisting of two electronic states, one coupled vibration, and bath terms that describe solvent relaxation and dephasing. The current results are numerically exact. They correspond to the evolution of the system reduced density matrix, with relaxation and dephasing contributions from the environment. We observe control elements due to electronic and vibrational dephasing and relaxation, nonadiabatic coupling, and temperature. Many of these parameters exhibit a turnover phenomenon (nonmonotonic behavior of the rate change as the appropriate interaction strength varies). The onset of irreversible (rate-type) behavior, short time quantum beats, multiple time scales, and other characteristic phenomena appear clearly in this very simplified and reduced structural model. The differences between this full dynamical analysis and the very useful transition-state or equilibrium vibronic model arises from the nonequilibrium nature of the initial photoexcited state, whose decay is effected by dephasing and relaxation dynamics as well as energetics.