Density, Total Energy and Chemical Potential of Atomic Ions and some Molecules

Abstract

In this article we shall review some recent work on the electron density (ρ(r→)) description of atomic ions and some molecules with π-electrons, In section 2, we briefly consider first the one-electron treatment of atoms and molecules given by Thomas and Fermi1–3 in terms of ρ(r→), with its extension to include exchange, first given by Dirac.4 This treatment is formally generalized to yield the Euler equation of the density functional theory which however contains an as yet unknown functional consisting of kinetic plus exchange and correlation energy. Separation into single-particle kinetic energy allows the Euler equation to be recast into a one-electron framework, following the earlier work of Slater,5 which was completed by Kohn and Sham,6 The existence of a one-body potential energy allows approximations of Thomas-Fermi nature in the kinetic energy to be avoided, if desired by direct solution of the Schrodinger equation with the one-body potential (with exchange and correlation suitably approximated).