Mixed quantum-classical dynamics

We present a unified derivation of the mean-field (Ehrenfest) and surface-hopping approaches to mixed quantum-classical dynamics that elucidates the underlying approximations of the methods and their strengths and weaknesses. We then report a quantitative test of alternative mixed quantum-classical methods against accurate quantum mechanical calculations for a simple one-dimensional curve-crossing model. We conclude that, for this model, surface-hopping with the adiabatic representation is decidedly superior to either mean-field or surface-hopping with the diabatic representation.