Treatments of the exchange energy in density-functional theory
Abstract
Following a recent work [Gal, Phys. Rev. A 64, 062503 (2001)], a simple derivation of the density-functional correction of the Hartree-Fock equations, the Hartree-Fock-Kohn-Sham equations, is presented, completing an integrated view of quantum mechanical theories, in which the Kohn-Sham equations, the Hartree-Fock-Kohn-Sham equations and the ground-state Schrodinger equation formally stem from a common ground: density-functional theory, through its Euler equation for the ground-state density. Along similar lines, the Kohn-Sham formulation of the Hartree-Fock approach is also considered. Further, it is pointed out that the exchange energy of density-functional theory built from the Kohn-Sham orbitals can be given by degree-two homogeneous N-particle density functionals (N=1,2,...), forming a sequence of degree-two homogeneous exchange-energy density functionals, the first element of which is minus the classical Coulomb-repulsion energy functional.
Keywords
Cite
@article{arxiv.0708.0576,
title = {Treatments of the exchange energy in density-functional theory},
author = {Tamas Gal},
journal= {arXiv preprint arXiv:0708.0576},
year = {2008}
}
Comments
19 pages; original manuscript from 2001 (v1) revised for publication, with presentation substantially improved, some errors corrected, plus an additional summarizing figure (Appendix B) included