Momentum rescaling for collapse to a block Ehrenfest dynamics

The Ehrenfest with collapse to a block (TAB) algorithm has recently been demonstrated to efficiently and accurately simulate nonadiabatic molecular dynamics in dense manifolds of electronic states. TAB employs an Ehrenfest force for the classical nuclei, accompanied by stochastic collapses of the electronic density matrix to account for decoherence. Energy conservation dictates that the nuclear momentum be adjusted during such a collapse. In this paper, we present a prescription for rescaling the component of the nuclear momentum that projects into the branching plane between arbitrary superposition states. This prescription yields accurate branching ratios and phase-space distributions when compared to alternative methods in which scaling is performed in the nonadiabatic coupling direction or the momentum direction. We justify this direction by deriving an effective nonadiabatic coupling vector from the localized Pechukas force during a collapse step.