Improved partition-expansion of two-center distributions involving Slater functions.

The calculation of the electronic structure of large systems is facilitated by the substitution of the two-center distributions by their projections on auxiliary basis sets of one-center functions. An alternative is the partition-expansion method in which one first decides what part of the distribution is assigned to each center, and next expands each part in spherical harmonics times radial factors. The method is exact, requires neither auxiliary basis sets nor projections, and can be applied to Gaussian and Slater basis sets. Two improvements in the partition-expansion method for Slater functions are reported: general expressions valid for arbitrary quantum numbers are derived and the efficiency of the procedure is increased giving analytical solutions to integrals previously computed by numerical quadrature. The efficiency of the new version is assessed in several molecules and the advantages over the projection methods are pointed out.

A reinterpretation of the nature of the Fermi hole.

A reinterpretation of the Boyd-Coulson [R. J. Boyd and C. A. Coulson, J. Phys. B 7, 1805 (1974)] definition of the Fermi hole is presented. Through this reinterpretation, which makes no reference to the hypothetical Hartree level, we are able to show the essentially identical character of the Boyd-Coulson definition with the one based on a conditional probability analysis. The basis-set dependence of the Fermi hole is emphasized and the effect of canonical, localized and delocalized Kohn-Sham and Hartree-Fock basis sets is examined for selected atoms and molecules.