Analytical Switching Algorithms for Global Trajectory Surface Hopping Molecular Dynamics Simulation

The on-the-fly trajectory surface hopping molecular dynamics in which nuclear motions are based on the classical trajectory is a suitable method for simulating nonadiabatic dynamics in large and complex photochemical systems. However, the nonadiabatic switching probability that comes from a pure quantum effect must be formulated from quantum mechanics. The Landau-Zener and Zhu-Nakamura switching probabilities are analytically solved under a mixed quantum/classical method with T̂_N = 0 and a semiclassical method with T̂_N ≠ 0 (where T̂_N is a quantum nuclear kinetic operator), respectively. Both switching probabilities are actually exact solutions under its T̂_N assumption for the same two-state linear curve crossing model. Moreover, the global switching and fewest switching algorithms are extensively compared by on-the-fly trajectory surface hopping molecular dynamics simulation for cis-to-trans and trans-to-cis azobenzene photoisomerization. Both algorithms agree pretty well for quantum yields, lifetimes, hopping spot distributions, and population decay distributions.