Electron gas models and density functional theory

Abstract

A functional for representing the kinetic and exchange energies of the ground state of an N electron atom or ion in terms of its electron density is derived by:(i) considering explicitly the variation of the charge density in an atom, and (2) approximating the pair correlation function for parallel spin electrons by that of a uniform free-electron gas, but including the corrections to the momentum at the Fermi level and the appropriate boundary conditions that result from taking into account that the number of electrons in an atom is finite. The first consideration leads in a natural way to the full Weizsacker correction in the kinetic energy expression, while the second consideration yields the Thomas-Fermi term (kinetic) and the Dirac plus the Fermi-Amaldi terms (exchange) multiplied by different functions of N.The quality of such functional is analyzed usingHartree-Fock densities.

Energy Density Functional Theory of Many-Electron Systems

“…There is a rather long list of articles which review different aspects of density functional theory: Almbladh and von Barth (1985b), Appelbaum and Hamann (1976), von Barth (1984), von Barth and Williams (1983), Bamzai and Deb (1981), Brack et al (1985), Bader and Essen (1984), ClaYerie (1978), Care and : 'Iarch (1975), Connolly (1977), Callaway and March (1984), Das (1983), Deb (1984a,b), Donnelly 1-1 CHAPTER 1 (1983), Ellis and Painter ('1971,1984), EYans (1979), Gazquez (1983), Ghosh and Deb (1982a), Golden (1960), Gunnarsson (1979), Gunnarsson and Jones (1984), Gupta and Rajagopal (1982), Harriman (1983c), Hedin (1972), Hedin and Lundqvist (1969), Herman and Schwarz (1972), Johnson (1975), Johnson et al (1973), Jones and ;\Iarch (1973), Keller (1973), Keller and Amador (1~83), Keller et al (1981Keller et al ( ,1985, Kirzhnitz (1971), Kirzhnits et al (197.S), , Kohn (1975bKohn ( , 1968Kohn ( , 1985a, Kohn and \'ashista (198:3), , …”

“…Other candidates for boundaries have been proposed by Alonso and Girifalco (1978a), Tal and Bader (1978), Ohwada (1983b), Ludena (1982Ludena ( , 1983b, Haq et al (1984), Chattaraj andDeb (1984, 1985). The contents of the l[p(T)] "black box" have been reviewed by Parr (1983Parr ( , 1984, Kryachko (198"1), Gazquez (1983), Keller and Amador (1983) and Chattaraj and Deb (1984). It is interesting to notice that just about all the kinetic energy density functionals, used in formulating equivalent variational principles, have been of the local type.…”

“…where the nature of the nonlocal term has not been completely elucidated so far (r- Iarch and Young, 1958;Gombas, 1969a;Miiller et al, 1970;Gazquez and Ludena, 1981;Ludella, 1983bLudella, , 1984aGazquez, 1983). The same conclusion has been reached by Reznik and Shatalov (1981), who haye analyzed that part oft[p(r)] having a functional dependence of the fnllO\\"ing type: THE THO?lIAS-FER}'II ENERGY-DENSITY FUNCTIO~AL ....…”