Inter- and Intra-Atomic Correlation Energies and Theory of Core-Polarization

Atomic and molecular energies depend strongly on the correlation in the motions of electrons. Their complexity necessitates the treatment of a chemical system in terms of small groups of electrons and their interactions, but this must be done in a way consistent with the exclusion principle. To this end, a nondegenerate many-electron system is treated here by a generalized second-order perturbation method based on the classification of all the Slater determinants formed from a complete one-electron basis set. The correlation energy of the system is broken down into the energies of pairs of electrons including exchange. Also some nonpairwise additive terms arise which represent the effect of the other electrons on the energy of a correlating pair because of the Pauli exclusion principle. All energy components are written in approximate but closed forms involving only the initially occupied H.F. orbitals. Then each term acquires a simple physical interpretation and becomes adoptable for semiempirical usage. The treatment is applied in detail to two particular problems: (a) The correlation energy between an outer electron in any excited state and the core electrons, e.g., in the Li atom, is represented by a potential acting on the outer one. This potential can be regarded as the mean square fluctuation of the Hartree-Fock potential of the core, and applies even when the outer electron penetrates into the core. The magnitudes of some of the correlation effects are calculated for Li. (b) Starting from a complete one-electron basis set of SCF MO's, the energy of a molecule is separated into those of groups of electrons and of intra-molecular dispersion forces acting between the groups. The assumptions that are usually made in discussing dispersion forces at such short distances are then removed and generally applicable formulas are given. Some three or more electron-correlation effects and limitations in the use of ``many electron group functions'' for overlapping systems are also discussed.