N-dependence of electronic energies in atoms and molecules: Mulliken and exponential interpolations

The unphysical artifact of the Mulliken (parabolic) interpolation of the dependence of the electronic energy of atoms and molecules on the system average number of electrons N is identified. To remedy this shortcoming a smooth exponential interpolation between the energies of the neutral system, its cation and anion is suggested. The trends exhibited by the associated electronegativity and chemical hardness scales are examined.