An approximate universal energy functional in density functional theory

Using Harriman’s orthonormal set, a closed expression for the reduced first order density operator γ1(1,2)=ρ(1)1/2ρ(2)1/2G(1,2) is obtained in the context of the independent particle approximation. It is shown that G(1,2) is given by G(1,2)=(1/n)exp{i[(n+1)/2]F(1,2)}[sin 1/2 nF(1,2)]/sin 1/2 F(1,2)], where F(1,2)=f(r2)−f(r1). Using this representation of γ1(1,2), an approximate universal functional of the energy which is given solely in terms of ρ is constructed. In particular, closed analytic expressions for the kinetic and exchange energies are explicitly derived. The simplifications brought about in these expressions by spherical symmetry are also discussed.