Nonadiabatic dynamics of photoinduced proton-coupled electron transfer: comparison of explicit and implicit solvent simulations.

Theoretical approaches for simulating the ultrafast dynamics of photoinduced proton-coupled electron transfer (PCET) reactions in solution are developed and applied to a series of model systems. These processes are simulated by propagating nonadiabatic surface hopping trajectories on electron-proton vibronic surfaces that depend on the solute and solvent nuclear coordinates. The PCET system is represented by a four-state empirical valence bond model, and the solvent is treated either as explicit solvent molecules or as a dielectric continuum, in which case the solvent dynamics is described in terms of two collective solvent coordinates corresponding to the energy gaps associated with electron and proton transfer. The explicit solvent simulations reveal two distinct solvent relaxation time scales, where the faster time scale relaxation corresponds to librational motions of solvent molecules in the first solvation shell, and the slower time scale relaxation corresponds to the bulk solvent dielectric response. The charge transfer dynamics is strongly coupled to both the fast and slow time scale solvent dynamics. The dynamical multistate continuum theory is extended to include the effects of two solvent relaxation time scales, and the resulting coupled generalized Langevin equations depend on parameters that can be extracted from equilibrium molecular dynamics simulations. The implicit and explicit solvent approaches lead to qualitatively similar charge transfer and solvent dynamics for model PCET systems, suggesting that the implicit solvent treatment captures the essential elements of the nonequilibrium solvent dynamics for many systems. A combination of implicit and explicit solvent approaches will enable the investigation of photoinduced PCET processes in a variety of condensed phase systems.