Nonadiabatic Coupling in Trajectory Surface Hopping: Accurate Time Derivative Couplings by the Curvature-Driven Approximation

Trajectory surface hopping (TSH) is a widely used mixed quantum-classical dynamics method that is used to simulate molecular dynamics with multiple electronic states. In TSH, time-derivative coupling is employed to propagate the electronic coefficients and in that way to determine when the electronic state on which the nuclear trajectory is propagated switches. In this work, we discuss nonadiabatic TSH dynamics algorithms employing the curvature-driven approximation and overlap-based time derivative couplings, and we report test calculations on six photochemical reactions where we compare the results to one another and to calculations employing analytic nonadiabatic coupling vectors. We correct previous published results thanks to a bug found in the software. We also provide additional, more detailed studies of the time-derivative couplings. Our results show good agreement between curvature-driven algorithms and overlap-based algorithms.