The Dirac equation and its implications for density functional theory-based calculations of materials containing heavy elements

Electronic structure calculations based on density functional theory (DFT) typically give quantitatively accurate predictions for ground-state properties of materials containing light elements. For materials containing heavy elements, relativistic effects play an increasingly important role and in principle, a formulation of DFT based on the Dirac equation is needed to properly incorporate relativistic effects. Working towards that goal, we have developed a code, called dirac-fp, that solves the Dirac-Kohn-Sham equations under the assumption of a vanishing orbital current. The dirac-fp code is based on the full potential linear muffin tin orbital (FP-LMTO) code RSPt, but solves the Dirac-Kohn-Sham equations throughout the entire computational cell. To assess the results of the Dirac-Kohn-Sham (Dirac) approach, we compare the ground state properties to the scalar relativistic (SR) and scalar relativistic+spin-orbit coupling (SR+SO) approaches for three different non-magnetic FCC materials: thorium, aluminum, and gold, in which relativistic effects should be strong, negligible, and intermediate, respectively. We find that only the Dirac approach is able to provide consistent results in the electronic structure and ground state properties across all three materials.