  Chemical relaxation phenomena, including photochemistry and electron transfer
processes, form a vigorous area of research in which nonadiabatic dynamics
plays a fundamental role. Here, we show that for nonadiabatic dynamics with two
electronic states and a complex-valued Hamiltonian that does not obey
time-reversal symmetry, the optimal semiclassical approach is to run surface
hopping dynamics on a set of phase-space adiabatic surfaces. In order to
generate such phase-adiabats, one must isolate a proper set of diabats and
apply a phase gauge transformation, before eventually diagonalizing the total
Hamiltonian (which is now parameterized by both R and P). The resulting
algorithm is valid in both the adiabatic and nonadiabatic limits, incorporates
all Berry curvature effects, and allows for the study of semiclassical
nonadiabatic dynamics in the presence of spin-orbit coupling and/or external
magnetic fields.
