Atomic energies from electrostatic potentials at nuclei: direct evaluation

We have calculated the energies of a series of atoms by means of an exact relationship that formally requires integrating over the electrostatic potentials at the nuclei of sequences of isoelectronic negative ions. In doing so, we made use of the fact that gaseous atoms do not form more than singly charged negative ions ( except perhaps some for quite large nuclear charges). The results obtained support the validity of this approach, and its possible application in other situations involving isoelectronic negative systems.