Understanding the Relativistic Generalization of Density Functional Theory (DFT) and Completing It in Practice

In 2014, 50 years following the introduction of density functional theory (DFT), a rigorous understanding of it was published [AIP Advances, 4, 127,104 (2014)]. This understanding includes two features that complete the theory in practice, inasmuch as they are necessary for its correct application in electronic structure calculations; this understanding elucidates what appears to have been the crucial misunderstanding for 50 years, namely, the confusion between a stationary solution, attainable with most basis sets, following self-consistent iterations, with the ground state solution. The latter is obtained by a calculation that employs the well-defined optimal basis set for the system. The aim of this work is to review the above understanding and to extend it to the relativistic generalization of density functional theory by Rajagopal and Callaway [Phys. Rev. B7, 1912 (1973)]. This extension straightforwardly follows similar steps taken in the non-relativistic case, with the four-component current density, in the former, replacing the electronic charge density, in the latter. This new understanding, which completes relativistic DFT in practice, is expected to be needed for the study of heavy atoms and of materials (from molecules to solids) containing them—as is the case for some high temperature superconductors.