Relation between total energy,electronic potential at the nucleus and chemical potential. Application to the helium isoelectronic series in Hartree-Fock theory

A formal relation between the total energy, the electronic potential at the nucleus and the chemical potential is derived within the context of density functional theory of atomic ions, using the homogeneity properties of the energy functional. An explicit application is then performed for two-electron ions in the context of the Hartree-Fock approximation.