Trajectory-based nonadiabatic molecular dynamics without calculating nonadiabatic coupling in the avoided crossing case: trans ⇆ cis photoisomerization in azobenzene

We develop a novel method to simulate analytical nonadiabatic switching probability based on effective coupling and effective collision energy by using only electronic adiabatic potential energy surfaces and its gradients in the case of avoided crossing types of nonadiabatic transitions. In addition, the present method can keep the same time step for computing both on-the-fly trajectory and nonadiabatic transitions accurately. The present method is most useful for localized nonadiabatic transitions induced by conical intersection. We employ the on-the-fly surface hopping algorithm with an ab initio quantum chemistry calculation to demonstrate a dynamic simulation for photoisomerization in azobenzene. Simulated quantum yield and lifetime converge to 0.39 and 53 femtosecond, respectively (0.33 and 0.81 picosecond) for cis-to-trans (trans-to-cis) photoisomerization with up to 800 (600) sampling trajectories. The present results agree well with those of the experiment, as well as results simulated with use of nonadiabatic coupling within Tully's fewest switching method. The present trajectory-based nonadiabatic molecular dynamics free from nonadiabatic coupling greatly enhances the simulation power of molecular dynamics for large complex chemical systems.