The expression V-ee[Gamma(1)] = (1/2)Sigma(p not equal q)[n(p)n(q)J(pq)-Omega(n(p),n(q))K-pq], where {n(p)} are the occupation numbers of natural spin orbitals, and {J(pq)} and {K-pq} are the corresponding Coulomb and exchange integrals, respectively, generalizes both the Hartree-Fock approximation for the electron-electron repulsion energy V-ee and the recently introduced Goedecker-Umrigar (GU) functional. Stringent constraints upon the form of the scaling function Omega(x,y) are imposed by the properties of a homogeneous electron gas. The stability and N-representability of the 1-matrix demand that 2/3