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The quantum-classical Liouville equation offers a rigorous approach tononadiabatic quantum dynamics based on surface hopping type trajectories.However, in practice the applicability of this approach has been limited toshort times owing to unfavorable numerical scaling. In this paper we show thatthis problem can be alleviated by combining it with a formally exactgeneralized quantum master equation treatment. This allows dramaticimprovements in the efficiency of the approach in nonadiabatic regimes, makingit computationally tractable to treat the quantum dynamics of complex systemsfor long times. We demonstrate our approach by applying it to a model ofcondensed phase charge transfer where our method is shown to be numericallyexact in regimes where fewest-switches surface hopping and mean fieldapproaches fail to obtain the either the correct rates or long-timepopulations.

Efficient and accurate surface hopping for long time nonadiabatic quantum dynamics