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We investigate two well-known approaches for extending the fewest switchessurface hopping (FSSH) algorithm to periodic time-dependent couplings. Thefirst formalism acts as if the instantaneous adiabatic electronic states werestandard adiabatic states, which just happen to evolve in time. The secondformalism replaces the role of the usual adiabatic states by thetime-independent adiabatic Floquet states. For a set of modified Tully modelproblems, the Floquet FSSH (F-FSSH) formalism gives a better estimate for bothtransmission and reflection probabilities than the instantaneous adiabatic FSSH(IA-FSSH) formalism. More importantly, only F-FSSH predicts the correct finalscattering momentum. Finally, in order to use Floquet theory accurately, wefind that it is crucial to account for the interference between Floquet states.Our results should be of interest to all those interested in laser inducedmolecular dynamics.

Non-adiabatic Dynamics in a Laser Field with Floquet Fewest Switches  Surface Hopping: The Need for An Accurate Treatment of Coherence and  Decoherence Remains