Berry Population Analysis: Atomic Charges from the Berry Curvature in a Magnetic Field

TL;DR

This paper introduces a novel Berry population analysis method that derives atomic charges from Berry curvature, providing insights into electronic structure and charge fluctuations in molecules.

Contribution

It develops a new approach to extract atomic charges from Berry curvature, offering an alternative to traditional population analysis methods.

Findings

Atomic charges from Berry analysis resemble those from atomic polar tensors.

The method estimates charge fluctuations and contributions from all atoms.

Berry charges provide a useful electronic structure analysis tool.

Abstract

The Berry curvature is essential in Born$-$Oppenheimer molecular dynamics, describing the screening of the nuclei by the electrons in a magnetic field. Parts of the Berry curvature can be understood as the external magnetic field multiplied by an effective charge so that the resulting Berry force behaves like a Lorentz force during the simulations. Here we investigate whether these effective charges can provide insight into the electronic structure of a given molecule or, in other words, whether we can perform a population analysis based on the Berry curvature. To develop our approach, we first rewrite the Berry curvature in terms of charges that partially capture the effective charges and their dependence on the nuclear velocities. With these Berry charges and charge fluctuations, we then construct our population analysis yielding atomic charges and overlap populations. Calculations at the Hartree$-$Fock level reveal that the atomic charges are similar to those obtained from atomic polar tensors. However, since we additionally obtain an estimate for the fluctuations of the charges and a partitioning of the atomic charges into contributions from all atoms, we conclude that the Berry population analysis is a useful alternative tool to analyze the electronic structure of molecules.