Fewest switches surface hopping with decoherence in the Marcus inverted regime: correct rates but wrong thermal populations

TL;DR

This paper analyzes the augmented-FSSH method in the Marcus inverted regime, showing it predicts correct rate constants but fails to accurately reproduce thermal populations due to a self-consistency issue.

Contribution

It provides an analytical derivation explaining why AFSSH yields correct rates but incorrect populations in the Marcus inverted regime.

Findings

AFSSH predicts correct rate constants due to resonance effects.

AFSSH yields incorrect thermal populations because of self-consistency issues.

An analytical expression for the quantum correction factor is derived.

Abstract

Fewest switches surface hopping (FSSH) is a well benchmarked dynamical method for simulating nonadiabatic systems. In particular, the literature shows that for the spin-Boson model Hamiltonian, FSSH with appropriate corrections usually captures the detailed balance well and obtains rate constants within a factor of 2 compared to numerically exact results. In this study, we show that in the deep inverted Marcus regime, the augmented-FSSH (AFSSH, one version that includes decoherence) yields reasonably accurate rate constants but incorrect thermal populations over a broad range of parameters. We present an analytical derivation to understand the AFSSH behavior, and therefore, show that AFSSH obtains correct rate constants owing to the resonance of the time derivative coupling with the exothermicity, but obtains an incorrect thermal population owing to the self-consistency issue. The presented derivation provides an analytical expression for the quantum correction factor for AFSSH simulations in the Marcus inverted regime.