The treatment of classically forbidden electronic transitions in semiclassical trajectory surface hopping calculations

A family of four weakly coupled electronically nonadiabatic bimolecular model photochemical systems is presented. Fully converged quantum mechanical calculations with up to 25 269 basis functions were performed for full-dimensional atom–diatom collisions to determine the accurate scattering dynamics for each of the four systems. The quantum mechanical probabilities for electronically nonadiabatic reaction and for nonreactive electronic deexcitation vary from 10−1 to 10−5. Tully’s fewest-switches (TFS) semiclassical trajectory surface-hopping method (also called molecular dynamics with quantum transitions or MDQT) is tested against the accurate quantal results. The nonadiabatic reaction and nonreactive deexcitation events are found to be highly classically forbidden for these systems, which were specifically designed to model classically forbidden electronic transitions (also called frustrated hops). The TFS method is shown to systematically overestimate the nonadiabatic transition probabilities due to the high occurrence of frustrated hops. In order to better understand this problem and learn how to best minimize the errors, we test several variants of the TFS method on the four new weakly coupled systems and also on a set of three more strongly coupled model systems that have been presented previously. The methods tested here differ from one another in their treatment of the classical trajectory during and after a frustrated hopping event. During the hopping event we find that using a rotated hopping vector results in the best agreement of semiclassical and quantal results for the nonadiabatic transition probabilities. After the hopping event, we find that ignoring frustrated hops instead of reversing the momentum along the nonadiabatic coupling vector results in the best agreement with the accurate quantum results for the final vibrational and rotational moments. We also test the use of symmetrized probabilities in the equations for the TFS hopping probabilities. These methods systematically lead to increased error for systems with weakly coupled electronic states unless the hopping probabilities are symmetrized according to the electronic state populations.