  A practical electronic structure method in which a two-body functional is the
fundamental variable is constructed. The basic formalism of our method is
equivalent to Hartree-Fock density matrix functional theory [M. Levy in {\it
Density Matrices and Density Functionals}, Ed. R. Erdahl and V. H. Smith Jr.,
D. Reidel, (1987)]. The implementation of the method consists of solving
Hartree-Fock equations and using the resulting orbitals to calculate two-body
corrections to account for correlation. The correction terms are constructed so
that the energy of the system in the absence of external potentials can be made
to correspond to approximate expressions for the energy of the homogeneous
electron gas. In this work the approximate expressions we use are based on the
high-density limit of the homogeneous electron gas. Self-interaction is
excluded from the two-body functional itself. It is shown that our pair density
based functional does not suffer from the divergence present in many density
functionals when homogeneous scaling is applied. Calculations based on our pair
density functional lead to quantitative results for the correlation energies of
atomic test cases.
