Current density functional framework for spin–orbit coupling

Abstract

Relativistic two-component density functional calculations are carried out in a non-collinear formalism to describe spin–orbit interactions, where the exchange–correlation functional is constructed as a generalization of the non-relativistic density functional approximation. Contrary to non-relativistic density functional theory (DFT), spin–orbit coupling, however, leads to a non-vanishing paramagnetic current density. Density functionals depending on the kinetic energy density, such as meta-generalized gradient approximations, should therefore be constructed in the framework of current DFT (CDFT). The latter has previously exclusively been used in the regime of strong magnetic fields. Herein, we present a consistent CDFT approach for relativistic DFT, including spin–orbit coupling. Furthermore, we assess the importance of the current density terms for ground-state energies, excitation energies, nuclear magnetic resonance shielding, and spin–spin coupling constants, as well as hyperfine coupling constants, Δg-shifts, and the nuclear quadrupole interaction tensor in electron paramagnetic resonance (EPR) spectroscopy. The most notable changes are found for EPR properties. The impact of the current-dependent terms rises with the number of unpaired electrons, and consequently, the EPR properties are more sensitive toward CDFT. Considerable changes are observed for the strongly constrained and appropriately normed functionals, as well as the B97M family and TASK. The current density terms are less important when exact exchange is incorporated. At the same time, the current-dependent kernel ensures the stability of response calculations in all cases. We, therefore, strongly recommend to use the framework of CDFT for self-consistent spin–orbit calculations.