Nonadiabatic quantum molecular dynamics with detailed balance

We present an approach for carrying out nonadiabatic molecular dynamics simulations of systems in which nonadiabatic transitions arise from the coupling between the classical atomic motions and a quasicontinuum of electronic quantum states. Such conditions occur in many research areas, including chemistry at metal surfaces, radiation damage of materials, and warm-dense-matter physics. The classical atomic motions are governed by stochastic Langevin-like equations, while the quantum electron dynamics is described by a master equation for the populations of the electronic states. These working equations are obtained from a first-principles derivation. Remarkably, unlike the widely used Ehrenfest and surface-hopping methods, the approach naturally satisfies the principle of detailed balance at equilibrium and therefore can describe the evolution to thermal equilibrium from an arbitrary initial state. A practical algorithm is cast in the form of the widely used fewest-switches surface-hopping algorithm but with switching probabilities that are not specified ad hoc like in the standard algorithm but are instead derived.