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

Simple density functional theory gives the following relation between the energy E Z , N of an ion of nuclear charge Z and N electrons, the potential V (0) created at the nucleus by the electronic cloud, and the chemical potential μ\documentclass{article}\pagestyle{empty}\begin{document}$$ E_{Z,N} = \frac{3}{7}(ZV(0) + N_\mu). $$\end{document}Using Hartree—Fock values for V (0) and μ, this equation has been tested in several isoelectronic series with 3 ≤ N ≤ 28. The importance of the term 3 N μ/7 increases as the degree of ionization increases.