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

Abstract

With the definition of a "screening factor" σ k transforming the nuclear charge Z k of an atom k into an "effective" nuclear charge Z k * = Z k σ k , the total energy E = E(Z k *, Z*,...) of a molecule at equilibrium can be expressed as a homogeneous function of degree γ/α in Z k *, Z l *,..., i.e. E = −∑ k Z k * γ/α , where α is the average of the α k 's(α k = ∂ ln Z k σ k/ ∂ ln Z k ) and γ = (V ne + 2V nn )/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 K k mol factors of the energy formula E = ∑ k K k mol V(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 K k mol' s, can be estimated in a simple way from atomic data.