In the approach proposed by Harbola and Sahni for the determination of electronic structure, the correlations between the interacting electrons are directly related to the local effective many-body potential in which they move by Coulomb’s law. As such this potential is the work required to move an electron in the force field of its Fermi-Coulomb-hole-charge distribution. In this paper we have applied this approach within the Pauli-correlated approximation, in which only correlations between the electrons due to the Pauli exclusion principle are considered, to atoms from He (Z=2) to Rn (Z=86). For open-shell atoms the central-field model is assumed. The calculations are also spin restricted and nonrelativistic. The self-consistently-determined atomic properties presented are the total ground-state energy, the highest-occupied-orbital eigenvalue, and the expectation value of the single-particle operators r,${\mathit{r}}^2$, ${\mathit{r}}^{\mathrm{-}1}$,${\mathit{r}}^{\mathrm{-}2}$, and δ(r). The total ground-state energies and expectation values are essentially equivalent to those of Hartree-Fock theory, with the relative differences diminishing with increasing atomic number. The total ground-state energies lie above, as must be the case, and within parts per million of the Hartree-Fock theory results. By ${}_{}{}^9{}_{}{}^{}\mathrm{F}$ this difference is 50 ppm, by ${}_{}{}^{35}{}_{}{}^{}\mathrm{Br}$ 10 ppm, and by ${}_{}{}^{72}{}_{}{}^{}\mathrm{Hf}$ less than 5 ppm.

The most remarkable results, however, are those for the highest-occupied-orbital eigenvalues. In the Harbola-Sahni approach, the asymptotic structure of the effective potential in the Pauli-correlated approximation is that of the fully correlated system, in which correlations between the electrons due to Coulomb repulsion are also considered. This is manifested by the fact that in comparison with Hartree-Fock theory, the highest-occupied-orbital eigenenergies for the majority of atoms are closer to the experimental ionization potentials. For the remaining atoms, the differences between the two theories are of the order of hundredths of a rydberg or less. Furthermore, we note that in the central-field model the density-functional-theory exchange-energy-potential sum rule due to Levy and Perdew is rigorously satisfied by the potentials and orbitals of this approach. For the present calculations this sum rule is satisfied numerically from six to eight significant figures, as is the virial theorem. Finally, the Harbola-Sahni approach in the Pauli-correlated approximation is contrasted to Hartree-Fock theory, and directions for future research to go beyond it within this framework are indicated.

• Received 13 September 1991

DOI:https://doi.org/10.1103/PhysRevA.45.1434