The electron-electron repulsion energy as a functional of the Hartree-Fock one-electron density matrix

The recently proposed expression that yields approximate electron-electron repulsion energy as a functional V-ee[Gamma(HF)] of the Hartree-Fock one-electron reduced density matrix rw is studied in detail. A scaling property of the screening function that enters V-ee[Gamma(HF)] is deduced from the long-range electron correlation effects incorporated in the functional. The resulting dependence of V-ee[Gamma(HF)] on the HOMO-LUMO gap is shown to give rise to two distinct asymptotics of the correlation energy of atoms and monoatomic ions at the limit of a large nuclear charge that are not reproduced by the presently known functionals of electron density. (C) 1999 Elsevier Science B.V. All rights reserved.