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Overcoming positivity violations for density matrices in surface hopping

Fewest-switches surface hopping (FSSH) has emerged as one of the leading methods for modeling the quantum dynamics of molecular systems. While its original formulation was limited to adiabatic populations, the growing interest in the application of FSSH to coherent phenomena prompts the question how one should construct a complete density matrix based on FSSH trajectories. A straightforward solution is to deﬁne adiabatic coherences based on wavefunction coe ﬃ cients. In this Paper, we demonstrate that inconsistencies introduced in the density matrix through such treatment may lead to a violation of positivity. We furthermore show that a recently proposed coherent generalization of FSSH results in density matrices that satisfy positivity, while yielding an improved accuracy throughout much (but not all) of parameter space.