Density-Functional Formalism

Abstract

Abstract A new Density-Functional (DF) formula is constructed for atoms. The kinetic energy of the electrons is divided into two parts: the kinetic self-energy and the orthogonalization energy where these concepts are borrowed from the pseudopotential theory. For the radial part of the ortho-gonalization energy which replaces the radial part of the Fermi-energy of the Thomas-Fermi model we derived the expression where p is the momentum, the ak's are constants and pε is the momentum width associated with the self-energy for which an expression is derived. Calculations were made for the total energies of neutral atoms, positive ions and for the He isoelectronic series. For neutral atoms the results match the Hartree-Fock energies within 1 % for atoms with N < 36; for atoms with N > 36 the results generally match the HF energes within 0.1%. For positive ions the results are fair; for the He series we achieved four or five-digit agreement between our energies and the HF results. For molecular applications a simplified model is developed in which the kinetic energy consist of the Weizsäcker term plus the Fermi energy reduced by a continuous function η(N). It is shown that the η(N) can be constructed in such a way that the energies computed closely approximate the HF energies for all neutral atoms.