A semi-focused multi-state variant of the mapping approach to surface hopping

The mapping approach to surface hopping (MASH) is one of the most promising methods for simulating nonadiabatic dynamics in molecular systems, in a mixed quantum/classical framework. In its original formulation, MASH is limited to the treatment of two-state systems. Here, we present a generalization of MASH to multiple electronic states, which we call semi-focused MASH (SMASH). A key distinguishing aspect of our approach is that only a selected subset of electronic states, identified through an appropriate clustering procedure, is initially populated. Test simulations of the ultrafast photodynamics of three molecular systems (spiropyran, thioguanine, and azobenzene) show that SMASH gives results closely matching those of decoherence-corrected fewest-switches surface hopping, while eliminating the need for any ad hoc corrections.