The direct correlation functionc(r)is divided into two parts, following the work of Kumaret al.One part,c(r)potential≡cp(r), contributes the entire compressibility and decays at largeras-(r)/KBT, with (r) the density independent pair potential. The definition ofcp(r) as–(r)/KBT{(1/6ρr2)∂2/∂ρ∂r[ρ2r3g(r)]{ is motivated by the condition of thermodynamic consistency, and for a hard core liquid leads tocp(r) small inside an atomic diameter.