Charge distributions and chemical effects. XXV. On the homogeneity of total molecular energies and the relationships between electronic, orbital, and total energies

With the definition of a "screening factor" σk transforming the nuclear charge Zk of an atom k into an "effective" nuclear charge Zk* = Zkσk, the total energy E = E(Zk*, Z*,...) of a molecule at equilibrium can be expressed as a homogeneous function of degree γ/α in Zk*, Zl*,..., i.e. E = −∑kZk*γ/α, where α is the average of the αk's(αk = ∂ ln Zkσk/∂ ln Zk) and γ = (Vne + 2Vnn)/E is a function of the nuclear-electronic, nuclear-nuclear, and total energies. Molecular energies calculated in this manner agree within 0.045% (average deviation) with their SCF counterparts. The sums of the orbital energies are correctly predicted from the equation [Formula: see text] A separation of the individual nuclear–electronic and nuclear–nuclear contributions to the total potential energy V(k, mol) of each nucleus k indicates that the Kkmol factors of the energy formula E = ∑kKkmolV(k, mol) are constant for each type of atom, thus stressing the basic homogeneity of the total energy rather than of the electronic energy only. The γ function, which is the inverse of the molecular average of the Kkmol's, can be estimated in a simple way from atomic data.