Assessment of trajectory surface hopping methods in long-time nonadiabatic dynamics

We present an assessment of an extensive set of trajectory surface hopping methodologies for modeling long-time population dynamics in a two-level spin-boson model. The considered methodological recipes involve combinations of three surface hopping approaches with five decoherence correction methods, several decoherence-time computation schemes, and two initial-condition sampling methods. In addition to these combinations, the phase correction approach of Shenvi, Subotnik, and Yang (SSY) is considered. By exploring a wide range of meta-parameters controlling decoherence and dephasing times, we determine the optimal performance of such methods and provide a ranking of the best-performing approaches. We find that inclusion of the SSY correction generally over-accelerates the population relaxation dynamics. We also find a strong dependence of the trajectory surface hopping (TSH) calculations on the type of initial-condition sampling: Wigner sampling leads to overestimated population transfer rates and requires decoherence corrections. The simplified decay of mixing approach is found to perform well in this situation. In contrast, Boltzmann sampling leads to a surprisingly remarkable performance of bare TSH schemes without decoherence, which may be a consequence of error cancellation. We provide a critical discussion of the observed trends in different methods' performance and suggest possible avenues for their further improvement.