Surface Hopping by Consensus

We present a new stochastic surface hopping method for modeling molecular dynamics with electronic transitions. The approach, consensus surface hopping (CSH), is a numerical framework for solving the semiclassical limit Liouville equation describing nuclear dynamics on coupled electronic surfaces using ensembles of trajectories. In contrast to existing techniques based on propagating independent classical trajectories that undergo stochastic hops between the electronic states, the present method determines the probabilities of transition of each trajectory collectively with input from the entire ensemble. The full coherent dynamics of the coupled system arise naturally at the ensemble level and ad hoc corrections, such as momentum rescaling to impose strict trajectory energy conservation and artificial decoherence to avoid the overcoherence of the quantum states associated with independent trajectories, are avoided.