  We introduce an energy functional for ground-state electronic structure
calculations. Its variables are the natural spin-orbitals of singlet many-body
wave functions and their joint occupation probabilities deriving from
controlled approximations to the two-particle density matrix that yield
algebraic scaling in general, and Hartree-Fock scaling in its seniority-zero
version. Results from the latter version for small molecular systems are
compared with those of highly accurate quantum-chemical computations. The
energies lie above full configuration interaction calculations, close to doubly
occupied configuration interaction calculations. Their accuracy is considerably
greater than that obtained from current density-functional theory
approximations and from current functionals of the one-particle density matrix.
