A symmetrical quasi-classical windowing model for the molecular dynamics treatment of non-adiabatic processes involving many electronic states

In the previous work of Cotton and Miller [J. Chem. Phys. 145, 144108 (2016)], an improved symmetrical quasi-classical (SQC) windowing model for the molecular dynamics treatment of electronically non-adiabatic processes was developed in order to extend the original SQC approach to the regime of weak-coupling between the electronic states. The improved SQC model-based on triangular-shaped window functions-handled the weak-coupling limit as intended and, as a bonus, was shown to be universally superior to the original square/histogram SQC windowing model over all coupling regimes, but only for treating systems of two electronic states, as no higher-dimensional generalization was evident. This paper, therefore, provides a generalized version for treating an arbitrary number of electronic states. By construction, the benefits of the two-state triangle model-seamless treatment of weak-coupling and improved accuracy in all coupling regimes-carry over to the generalized version. Far more significant, however, is that the new model provides vastly improved windowing statistics in higher dimensions, enabling the SQC simulation of electronically non-adiabatic processes involving many more relevant electronic states than was previously practical. Capabilities are demonstrated with respect to a 24 pigment trimer model of the Fenna-Matthews-Olson light-harvesting complex, as well as treating similar 48- and 96-electronic state model problems, illustrating the scaling properties of the new method.