On the evaluation of the rigorous electrostatic potential/atomic energy relationship

A series of atomic energy formulas that relate atomic energies to the electrostatic potentials V-0 at nuclei are obtained by a series of polynomial and series fits of V0 versus nuclear charge (Z). Density functional and Hartree-Fock V-0 are used for a series of fits that involve an isoelectronic series of anions, cations, and neutral ground state atoms to approximate atomic energies. Comparisons to the exact energies were performed in order to demonstrate the efficacy of the rigorous expressions.