A Reciprocal-Space Formulation of Surface Hopping

TL;DR

This paper introduces a reciprocal-space formulation of surface hopping that enhances the simulation of band-like electronic phenomena in materials, making it compatible with band structure calculations and efficient for large systems.

Contribution

It develops a reciprocal-space surface hopping method compatible with band structure calculations, enabling efficient simulation of band-like phenomena in materials.

Findings

Formal equivalence between real-space and reciprocal-space surface hopping.

Accurate results demonstrated against mean-field and exact methods.

Method suitable for band structure calculations and large systems.

Abstract

Surface hopping has seen great success in describing molecular phenomena where electronic excitations tend to be localized, but its application to materials with band-like electronic properties has remained limited. Here, we derive a formulation of fewest-switches surface hopping where both the quantum and classical equations of motion are solved entirely in terms of reciprocal-space coordinates. The resulting method is directly compatible with band structure calculations, and allows for the efficient description of band-like phenomena by means of a truncation of the Brillouin zone. Using the Holstein and Peierls models as examples, we demonstrate the formal equivalence between real-space and reciprocal-space surface hopping, and assess their accuracy against mean-field mixed quantum--classical dynamics and numerically-exact results.