Treatments of the exchange energy in density-functional theory

Details Treatments of the exchange energy in density-functional theory Treatments of the exchange energy in density-functional theory

2007-08-03

arxiv.org/abs/0708.0576v2

Int. J. Mod. Phys. B 22, 2225 (2008)

Physics

Chemical Physics

19 pages; original manuscript from 2001 (v1) revised for publication, with presentation substantially improved, some errors co

Scientific paper

10.1142/S0217979208039344

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.

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