  Non-adiabatic chemical reactions involving continuous circularly polarized
light (cw CPL) have not attracted as much attention as dynamics in
unpolarized/linearly polarized light. However, including circularly (in
contrast to linearly) polarized light allows one to effectively introduce a
complex-valued time-dependent Hamiltonian, which offers a new path for control
or exploration through the introduction of Berry forces. Here, we investigate
several inexpensive semiclassical approaches for modeling such nonadiabatic
dynamics in the presence of a time-dependent complex-valued Hamiltonian,
beginning with a straightforward instantaneous adiabatic fewest-switches
surface hopping (IA-FSSH) approach (where the electronic states depend on
position and time), continuing to a standard Floquet fewest switches surface
hopping (F-FSSH) approach (where the electronic states depend on position and
frequency), and ending with an exotic Floquet phase-space surface hopping
(F-PSSH) approach (where the electronic states depend on position, frequency,
and momentum). Using a set of model systems with time-dependent complex-valued
Hamiltonians, we show that the Floquet phase-space adiabats are the optimal
choice of basis as far as accounting for Berry phase effects and delivering
accuracy. Thus, the F-PSSH algorithm sets the stage for modeling nonadiabatic
dynamics under strong externally pumped circular polarization in the future.
