  We present a preliminary extension of the fewest switches surface hopping
(FSSH) algorithm to the case of complex Hamiltonians as appropriate for
modeling the dynamics of photoexcited molecules in magnetic fields. We make
ansatze for the direction of momentum rescaling and we account for Berry's
phase effects through "magnetic" forces as applicable in the adiabatic limit.
Because Berry's phase is a nonlocal, topological characteristic of a set of
entangled potential energy surfaces, we find that Tully's local FSSH algorithm
can only partially capture the correct physics.
