Numerical tests of coherence-corrected surface hopping methods using a donor-bridge-acceptor model system

Surface hopping (SH) is a popular mixed quantum-classical method for modeling nonadiabatic excited state processes in molecules and condensed phase materials. The method is simple, efficient, and easy to implement, but the use of classical and independent nuclear trajectories introduces an overcoherence in the electronic density matrix which, if ignored, often leads to spurious results, such as overestimated reaction rates. Several methods have been proposed to incorporate decoherence into SH simulations, but a lack of insightful benchmarks makes their relative accuracy unknown. Herein, we run numerical simulations of common coherence-corrected SH methods including Truhlar's decay-of-mixing (DOM) and Subotnik's augmented SH using a Donor-bridge-Acceptor (DbA) model system. Numerical simulations are carried out in the superexchange regime, where charge transfer proceeds from a donor to an acceptor as a result of donor-bridge and bridge-acceptor couplings. The computed donor-to-acceptor reaction rates are compared to the reference Marcus theory results. For the DbA model under consideration, augmented SH recovers Marcus theory with quantitative accuracy, whereas DOM is only qualitatively accurate depending on whether predefined parameters in the decoherence rate are chosen wisely. We propose a general method for parameterizing the decoherence rate in the DOM method, which improves the method's reaction rates and presumably increases its transferability. Overall, the decoherence method of choice must be chosen with great care and this work provides insight using an exactly solvable model.