Natural orbital functional for the many-electron problem

The exchange-correlation energy in Kohn-Sham density functional theory is expressed as a functional of the electronic density and the Kohn-Sham orbitals. An alternative to Kohn-Sham theory is to express the energy as a functional of the reduced first-order density matrix or equivalently the natural orbitals. We present an approximate, simple, and parameter-free functional of the natural orbitals, based solely on scaling arguments and the near satisfaction of a sum rule. Our tests on atoms show that it yields on average more accurate energies and charge densities than the Hartree-Fock method, the local density approximation, and the generalized gradient approximations.