Local density functional theory of atoms and molecules

Abstract

A local density functional theory of the ground electronic states of atoms and molecules is generated from three assumptions: (i) The energy functional is local. (ii) The chemical potential of a neutral atom is zero. (iii) The energy of a neutral atom of atomic number Z is -0.6127 Z ^7/3. The energy functional is shown to have the form [Formula: see text] where A ₀=6.4563 and B ₀=1.0058. The first term represents the electronic kinetic energy, the second term represents the electron-electron repulsion energy for N electrons, and the third term is the nucleus-electron attraction energy. The energy E and the electron density ρ are obtained and discussed in detail for atoms; their general properties are described for molecules. For any system the density becomes zero continuously at a finite distance from nuclei, and contours of the density are contours of the bare-nuclear potential v. For an atomic species of fractional charge q = 1 - (N/Z), an energy formula is obtained, [Formula: see text] which fits Hartree-Fock energies of 625 atoms and ions with root-mean-square error of 0.0270. A more general local density functional involving a coefficient B(N) = B₀ N ^2/3 + B₁ is briefly considered.