  We introduce a novel energy functional for ground-state electronic-structure
calculations. Its fundamental variables are the natural spin-orbitals of the
implied singlet many-body wave function and their joint occupation
probabilities. The functional derives from a sequence of controlled
approximations to the two-particle density matrix. Algebraic scaling of
computational cost with electron number is obtainable in general, and
Hartree-Fock scaling in the seniority-zero version of the theory. Results
obtained with the latter version for saturated small molecular systems are
compared with those of highly-accurate quantum-chemical computations. The
numerical results are variational, capturing most of the correlation energy
from equilibrium to dissociation. Their accuracy is considerably greater than
that obtainable with current density-functional theory approximations and with
current functionals of the one-particle density matrix only.
