A multi-state mapping approach to surface hopping

TL;DR

This paper introduces a multi-state surface hopping method that accurately models electronic populations and coherences, outperforming traditional approaches in complex systems and applicable to a broader range of problems.

Contribution

It extends the mapping approach to multiple electronic states, ensuring correct long-term populations and coherences, and demonstrates superior accuracy over existing surface hopping methods.

Findings

More accurate populations and coherences than fewest switches surface hopping.

Comparable or better accuracy than existing methods in benchmark tests.

Applicable to multi-state systems beyond two-state models.

Abstract

We describe a multiple electronic state adaptation of the mapping approach to surface hopping introduced recently by Mannouch and Richardson (J. Chem. Phys. 158, 104111 (2023)). This adaptation treats populations and coherences on an equal footing and is guaranteed to give populations in any electronic basis that tend to the correct quantum-classical equilibrium values in the long-time limit (assuming ergodicity). We demonstrate its accuracy by comparison with exact benchmark results for three- and seven-state models of the Fenna-Matthews-Olson complex, obtaining electronic populations and coherences that are significantly more accurate than those of fewest switches surface hopping and at least as good as those of any other semiclassical method we are aware of. Since these results were obtained by adapting the scheme of Mannouch and Richardson, we go on to compare our results with theirs for a variety of problems with two electronic states. We find that their method is sometimes more accurate, and especially so in the Marcus inverted regime. However, in other situations the accuracies are comparable, and since our scheme can be used with multiple electronic states it can be applied to a wider variety of systems.