Novel pseudomomentum-translational sum rule for the molecular Berry curvature

The molecular Berry curvature plays an important role for electronic structure calculations within the adiabatic Born– Oppenheimer approximation and is connected to many magnetic phenomena such as the Aharanov–Bohm and the chirality-induced spin selectivity (CISS) effect. For molecules in external magnetic fields, the Berry curvature is essential to achieve a qualitatively correct description of nuclear motion. Here, it is responsible for screening the Lorentz forces acting on moving nuclear charges. This connection has recently been exploited to derive a new type of population analysis known as Berry charges. In this work, we derive a novel sum rule for the molecular Berry curvature. This pseudomomentum-translational sum rule is then used to reveal the connection between Berry charges and the well-known generalized atomic polar tensor (GAPT) charges. Furthermore, we present an efficient integral-direct implementation of the molecular Berry curvature for molecules in finite magnetic fields into the TURBOMOLE program suite. This is used to further demonstrate the connection between Berry and GAPT charges for a variety of larger molecules, comparing the results to other established types of partial charges.