  We carried out extensive studies to examine the performance of the
fewest-switches surface hopping method in the description of the ultrafast
intersystem crossing dynamic of various singlet-triplet (S-T) models by
comparison with the results of the exact full quantum dynamics. Different
implementation details and some derivative approaches were examined. As
expected, it is better to perform the trajectory surface hopping calculations
in the spin-adiabatic representation or by the local diabatization approach,
instead of in the spin-diabatic representation. The surface hopping method
provides reasonable results for the short-time dynamics in the S-T model with
weak spin-orbital coupling (diabatic coupling), although it does not perform
well in the models with strong spin-orbital coupling (diabatic coupling). When
the system accesses the S-T potential energy crossing with rather high kinetic
energy, the trajectory surface hopping method tends to produce the good
description of the nonadiabatic intersystem crossing dynamics. The impact of
the decoherence correction on the performance of the trajectory surface hopping
is system dependent. It improves the result accuracy in many cases, while its
influence may also be minor for other cases.
