Revisiting the Recoherence Problem in the Fewest Switches Surface Hopping Algorithm.

We isolate and dissect exactly how and why Tully's fewest switches surface hopping (FSSH) algorithm fails when two wave packets come together at a crossing and "recohere". Using two different one-dimensional avoided crossing models and an initial wave function, which is a superposition of wave packets on different adiabats, we show that the key failures pertain to asymptotic nuclear momenta rather than electronic populations. Moreover, these FSSH failures stem from the fundamental assumption of independent trajectories with time-local hopping. As such, there is no possible means to correct FSSH without either (i) introducing time-nonlocal dynamics (i.e., allowing trajectories to move forward and backward in time) or (ii) requiring that trajectories interact.