On the basic homogeneity characteristic of atomic and molecular electronic energies

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Abstract
A homogeneity property of electronic energy with respect to atomic number, known to hold to a certain accuracy for neutral atoms, is extended and applied to neutral diatomic and polyatomic molecules. Two alternative hypotheses are examined. Homogeneity of the total energy, W, including repulsions between nuclei, leads to total Hartree–Fock energies at equilibrium proportional to the sum of orbital energies, and a linear first-order differential equation for the energy, for a diatomic molecule having the form R (dW/dR) +(3−k) W=Σεi, where k is the homogeneity parameter (about 7/3). A second, preferred hypothesis is homogeneity of the electronic energy E: ΣαZα(∂ E/∂ Zα)R=kE. It leads to a total energy equation in which appear both the sum of orbital energies and the repulsion between nuclei, and the differential equation R (dW/dR)+(3−k) W=Σεi+(2−k)(ZαZβ/R). The two hypotheses are tested on a number of atomic and molecular species, and their consequences are discussed. A constrained Hartree–Fock method in which the second hypothesis holds exactly is developed and shown to take the form of the extended Hückel method.