Relation between total energy, electronic potential at the nucleus, and chemical potential of positive ions

Abstract

Simple density functional theory gives the following relation between the energy EZ,N of an ion of nuclear charge 2 and N electrons, the potential V ( 0 ) created at the nucleus by the electronic cloud, and the chemical potential y, EZ,N = $ ( Z V ( O ) + N p ) .Using Hartree-Fock values for V ( 0 ) and y, this equation has been tested in several isoelectronic series with 3 5 N 5 28. The importance of the term 3Np/7 increases as the degree of ionization increases.The knowledge of the relation between the ground-state energy E of an atom or ion and the electrostatic potential V(O), created at the nucleus by the electronic cloud,has potentially interesting applications. p(r) in Eq. (1) where 2 is the nuclear charge, and E is the one-electron energy eigenvalue. The treatment of ions or atoms with more than two electrons is more difficult. The simplest version of the density functional theory, that is, the Thomas-Fermi (TF) approximation, gives the following result for an ion with N electrons [5]

Energy Density Functional Theory of Many-Electron Systems

“…Naturally one can extend the domain of validity of Eq. (5.3-27) we have prowd that the chemical potential at the Hartree-Fock level is precisely A program for testin~ the adequacy of the above expression has been carried out by Alonso et al(1982) and Balbas et a!. (5.3-1)).…”