Direct Nonadiabatic Dynamics of Ammonia with Curvature-Driven Coherent Switching with Decay of Mixing and with Fewest Switches with Time Uncertainty: An Illustration of Population Leaking in Trajectory Surface Hopping Due to Frustrated Hops

Mixed quantum-classical nonadiabatic dynamics is a widely used approach to simulate molecular dynamics involving multiple electronic states. There are two main categories of mixed quantum-classical nonadiabatic dynamics algorithms, namely, trajectory surface hopping (TSH) in which the trajectory propagates on a single potential energy surface, interrupted by hops, and self consistent-potential (SCP) methods, such as semiclassical Ehrenfest, in which propagation occurs on a mean-field surface without hops. In this work, we will illustrate an example of severe population leaking in TSH. We emphasize that such leaking is a combined effect of frustrated hops and long-time simulations that drive the final excited-state population toward zero as a function of time. We further show that such leaking can be alleviated-but not eliminated-by the fewest switches with time uncertainty TSH algorithm (here implemented in the SHARC program); the time uncertainty algorithm slows down the leaking process by a factor of 4.1. The population leaking is not present in coherent switching with decay of mixing (CSDM), which is an SCP method with non-Markovian decoherence included. Another result in this paper is that we find very similar results with the original CSDM algorithm, with time derivative CSDM (tCSDM), and with curvature-driven CSDM (kappa CSDM). Not only do we find good agreement for electronically nonadiabatic transition probabilities but also we find good agreement of the norms of the effective nonadiabatic couplings (NACs) that are derived from the curvature-driven time-derivative couplings as implemented in kappa CSDM with the time-dependent norms of the nonadiabatic coupling vectors computed by state-averaged complete-active-space self-consistent field theory.

Automated summary

Mixed quantum-classical nonadiabatic dynamics is widely used for simulating molecular dynamics involving multiple electronic states. Trajectory surface hopping (TSH) and self-consistent potential (SCP) methods are the two main categories of such dynamics algorithms. This work illustrates an example of severe population leaking in TSH, which is caused by frustrated hops and long-time simulations driving the excited-state population towards zero over time. The leaking can be partially alleviated by the fewest switches with time uncertainty (TSH) algorithm, but not completely eliminated.