The relation between orbital SCF energies and total SCF energies in molecules

The Hartree–Fock electronic energy of a molecule may be approximated as 1/4 times the sum of orbital energies of an artificial system obtained by holding the number of electrons fixed, doubling all nuclear charges, and halving all internuclear distances in the molecule. The approximation is shown to give a rigorous upper bound to the Hartree–Fock energy. Rationalization of schemes such as Walsh’s Rules, Woodward–Hoffmann correlation diagrams, and Hückel methods in which total energy is replaced by an orbital sum is thus suggested.