Mean-field molecular dynamics with surface hopping

Molecular dynamics simulations of many degree of freedom systems are often comprised of classical evolutions on quantum adiabatic energy surfaces with intermittent instantaneous hops from one surface to another. However, since quantum transitions are inherently nonadiabatic processes, the adiabatic approximation underlying the classical equations of motion does not hold in the regions where quantum transitions take place, and the restriction to classical trajectories for adiabatic quantum states is an approximation. Alternatives which employ classical paths that account more fully for nonadiabaticity can be computationally expensive and algorithmically complicated. Here, we propose a new method, which combines the surface hopping idea with the mean-field approximation for classical paths. Applied to three test systems, the method is shown to outperform the methods based on an adiabatic force without significant extra effort. This makes it an appealing alternative for modeling complex quantum–classical processes.