Overcoming positivity violations for density matrices in surface hopping

TL;DR

This paper addresses the challenge of maintaining positivity in density matrices constructed from surface hopping trajectories, proposing a coherent generalization of FSSH that improves accuracy and positivity.

Contribution

It introduces a coherent generalization of FSSH that ensures positivity of the density matrix and enhances accuracy in quantum molecular dynamics simulations.

Findings

The straightforward adiabatic coherence approach can violate positivity.

The proposed coherent generalization maintains positivity.

The new method improves accuracy in many parameter regimes.

Abstract

Fewest-switches surface hopping (FSSH) has emerged as one of the leading methods for modeling the quantum dynamics of molecular systems. While its original formulation was limited to adiabatic populations, the growing interest in the application of FSSH to coherent phenomena prompts the question how one should construct a complete density matrix based on FSSH trajectories. A straightforward solution is to define adiabatic coherences based on wavefunction coefficients. In this Paper, we demonstrate that inconsistencies introduced in the density matrix through such treatment may lead to a violation of positivity. We furthermore show that a recently proposed coherent generalization of FSSH results in density matrices that satisfy positivity, while yielding an improved accuracy throughout much (but not all) of parameter space.