A mapping approach to surface hopping

TL;DR

This paper introduces MASH, a new surface hopping method that combines the strengths of FSSH and mapping dynamics, providing more accurate nonadiabatic simulations with a rigorous quantum-mechanical foundation.

Contribution

MASH is a novel surface hopping approach that ensures internal consistency and is rigorously derived from quantum mechanics, improving accuracy over FSSH.

Findings

MASH outperforms FSSH in accuracy across various models.

MASH maintains computational cost similar to FSSH.

The method provides a systematic way to include decoherence corrections.

Abstract

We present a nonadiabatic classical-trajectory approach that offers the best of both worlds between fewest-switches surface hopping (FSSH) and quasiclassical mapping dynamics. This mapping approach to surface hopping (MASH) propagates the nuclei on the active adiabatic potential-energy surface, like in FSSH. However, unlike in FSSH, transitions between active surfaces are deterministic and occur when the electronic mapping variables evolve between specified regions of the electronic phase space. This guarantees internal consistency between the active surface and the electronic degrees of freedom throughout the dynamics. MASH is rigorously derivable from exact quantum mechanics, as a limit of the quantum-classical Liouville equation (QCLE), leading to a unique prescription for momentum rescaling and frustrated hops. Hence, a quantum-jump procedure can in principle be used to systematically converge the accuracy of the results to that of the QCLE. This jump procedure also provides a rigorous framework for deriving approximate decoherence corrections similar to those proposed for FSSH. We apply MASH to simulate the nonadiabatic dynamics in various model systems and show that it consistently produces more accurate results than FSSH, at a comparable computational cost.