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 Vee[ΓHF] of the Hartree–Fock one-electron reduced density matrix ΓHF is studied in detail. A scaling property of the screening function that enters Vee[ΓHF] is deduced from the long-range electron correlation effects incorporated in the functional. The resulting dependence of Vee[ΓHF] 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.