On the performance of multi-state transition filtering in mixed quantum-classical Liouville surface-hopping simulations: beyond two- and three-state quantum subsystems

Abstract

In two recent studies [(i) Dell’Angelo, D.; Hanna, G. J. Chem. Theory Comput., 2016, 12: 477 and (ii) Dell’Angelo, D.; Hanna, G. AIP Conf. Proc., 2016, 1790: 020009], we developed a transition filtering approach for reducing the number of trajectories required in mixed quantum-classical Liouville surface-hopping calculations of time-dependent expectation values. This approach was successfully applied to two relatively simple systems (viz., two quantum states coupled to twenty classical degrees of freedom (DOF) and three quantum states coupled to one classical DOF), yielding substantial reductions in the number of trajectories required for converged results. However, because the number of trajectories scales with the number of states in the quantum subsystem, it is not obvious how well this scheme would work for subsystems with larger numbers of states. Therefore, in this work, we examine the feasibility and efficacy of our transition filtering scheme for computing quantum state populations in a model of an alpha-helical polypeptide containing six quantum and six classical DOF. For this model, we find that it is possible to obtain accurate, numerically stable results with more than one order of magnitude fewer trajectories than the number of trajectories used to generate the results without any filtering. This level of performance is consistent with that observed in our previous applications to systems of lower complexity, pointing to the applicability of this scheme to systems with an arbitrary number of quantum states.