Expansions of density functionals in terms of homogeneous functionals:Justification and nonlocal representation of the kinetic energy, exchange energy,and classical Coulomb repulsion energy for atoms

For atoms or molecules, a general argument is given justifying expanding well behaved density functionals in series of functionals that are homogeneous to different degrees with respect to density scaling. Employing only appropriate local homogeneous functionals 〈ρᵏ〉, few-term fits of atomic Hartree-Fock T[{ρ}],nEₓ[{ρ}], and J[{ρ}] (kinetic energy, exchange energy, and classical Coulomb repulsion energy density functionals) are shown to give excellent results, as do self-consistent calculations on atoms using this Eₓ[{ρ}] plus an earlier obtained representation of Ec[{ρ}]. The representations may be local (as the one for Ec) or nonlocal, where nonlocal products of two or more 〈ρᵏ〉 can be included.