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The Berry connection and curvature are key components of electronic structurecalculations for atoms and molecules in magnetic fields. They ensure thecorrect translational behavior of the effective nuclear Hamiltonian and thecorrect center-of-mass motion during molecular dynamics in these environments.In this work, we demonstrate how these properties of the Berry connection andcurvature arise from the translational symmetry of the electronic wave functionand how they are fully captured by a finite basis set of London orbitals butnot by standard Gaussian basis sets. This is illustrated by a series ofHartree-Fock calculations on small molecules in different basis sets. Based onthe resulting physical interpretation of the Berry curvature as the shieldingof the nuclei by the electrons, we introduce and test a series ofapproximations using the Mulliken fragmentation scheme of the electron density.These approximations will be particularly useful in ab initio moleculardynamics calculations in a magnetic field, since they reduce the computationalcost, while recovering the correct physics and up to 95% of the exact Berrycurvature.

Magnetic-Translational Sum Rule and Approximate Models of the Molecular Berry Curvature