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

Diola Bagayoko

doi:10.4236/jmp.2016.79083

Abstract

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.

Highlights

From its introduction by Hohenberg and Kohn [1], fifty one years ago, to 2014, density functional theory (DFT) and its local density approximation (LDA) [2] seemed to have serious limitations for an accurate description or the prediction of electronic and related properties of atoms, molecules, semiconductors, and insulators
The argument has been that, without the self-interaction correction and the addition of the derivative discontinuity of the exchange correlation energy to the band gap obtained with a DFT potential, one is not expected to get an agreement with experiment
The above steps in the derivation of density functional theory (DFT) directly lead to its rigorous, mathematical and physical understanding articulated by Bagayoko [21], namely, for the results of electronic structure calculations to possess the full physical content of DFT, it is (a) necessary to keep the number of particles constant and (b.1) to employ the exact, three dimensional ground state charge density or (b.2) to search for and to attain the absolute minima of the occupied energies

Summary

Introduction

From its introduction by Hohenberg and Kohn [1], fifty one years ago, to 2014, density functional theory (DFT) and its local density approximation (LDA) [2] seemed to have serious limitations for an accurate description or the prediction of electronic and related properties of atoms, molecules, semiconductors, and insulators. Self-interaction [3] and the derivative discontinuity of the exchange correlation energy [4]-[6] were respectively introduced in 1981 and 1983 to explain the perceived limitations of DFT and of its local density approximation (LDA) version. The argument has been that, without the self-interaction correction and the addition of the derivative discontinuity of the exchange correlation energy to the band gap obtained with a DFT potential, one is not expected to get an agreement with experiment. Understanding Non-Relativistic Density Functional Theory (DFT) and Completing It in Practice

Understanding Non-Relativistic Density Functional Theory

Completing DFT in Practice

Experimental Confirmation of Our Understanding of DFT

Understanding Relativistic DFT and Completing It in Practice

Conclusion