Density functional theory: beyond or within Dirac's desire?

Jacek Karwowski

Abstract Some consequences of using multicomponent wave functions are analyzed. In particular, paradoxical properties of a density functional derived from Dirac and Lévy‐Leblond equations are discussed. The application of a recently formulated N‐electron “relativistic Schrödinger theory,” based on a 4N‐component wave function, to the construction of a Lorentz and gauge covariant density functional theory is suggested. © 2012 Wiley Periodicals, Inc.

Eugene S. Kryachko

Eugene S. Kryachko, Eduardo V. Ludeña

Mohamed Barhoumi

Density Functional Theory is one of the most widely used methods in quantum calculations of the electronic structure of matter in both condensed matter physics and quantum chemistry. Despite the importance of the density functional theory to find the correlation-exchange energy, but this quantity remains inaccurate. So we have to go beyond DFT to correct this quantity. In this framework, the random phase approximation has gained importance far beyond its initial field of application, condensed matter physics, materials science, and quantum chemistry. RPA is an approach to accurately calculate the electron correlation energy.

Walter Kohn

I. A. Howard, Norman Henry March

In density functional theory, the single-particle kinetic energy is still not known in an orbital-free form. The natural tool to calculate such kinetic energy for a given one-body potential V is the Dirac density matrix y. Here, by first taking solvable one-dimensional examples, and in particular the sech 2 (x) potential, forms for the Dirac density matrix are exhibited in terms of the potential.This in turn generates the Legendre transform of the single-particle kinetic energy. Finally, one-dimensional perturbation theory for the kinetic energy density, summed to all orders in V, is presented in the appendix.