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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 fieldmultiplied by an effective charge so that the resulting Berry force behaveslike a Lorentz force during the simulations. Here we investigate whether theseeffective charges can provide insight into the electronic structure of a givenmolecule or, in other words, whether we can perform a population analysis basedon the Berry curvature. To develop our approach, we first rewrite the Berrycurvature in terms of charges that partially capture the effective charges andtheir dependence on the nuclear velocities. With these Berry charges and chargefluctuations, we then construct our population analysis yielding atomic chargesand overlap populations. Calculations at the Hartree$-$Fock level reveal thatthe atomic charges are similar to those obtained from atomic polar tensors.However, since we additionally obtain an estimate for the fluctuations of thecharges and a partitioning of the atomic charges into contributions from allatoms, we conclude that the Berry population analysis is a useful alternativetool to analyze the electronic structure of molecules.

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