  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 coefficients. 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.
