The Berry curvature in the framework of current density functional theory for molecules in external magnetic fields

Abstract

In this work, we investigate the quantum geometry framework for molecules in external magnetic fields. For electronic ground states, the linear response formalism through which the quantum geometric tensor can be computed was described by Culpitt et al. [J. Chem. Phys. 156, 044121 (2022)], and this work expands their framework to current density functional theory. We show that for nuclear displacements, the Fubini–Study metric can be connected to the diagonal Born–Oppenheimer correction. Furthermore, we examine the effects of external magnetic fields on the molecular Berry curvature. For selected systems, we investigate how different density functional approximations compare to both full configuration interaction and Hartree–Fock theory. Finally, the convergence of the Berry curvature with respect to the numerical grid is estimated for different functionals, highlighting some known deficiencies of modern density functional approximations.