  Fermionic natural occupation numbers do not only obey Pauli's exclusion
principle but are even stronger restricted by so-called generalized Pauli
constraints. Whenever given natural occupation numbers lie on the boundary of
the allowed region the corresponding $N$-fermion quantum state has a
significantly simpler structure. We recall the recently proposed natural
extension of the Hartree-Fock ansatz based on this structural simplification.
This variational ansatz is tested for the lithium atom. Intriguingly, the
underlying mathematical structure yields universal geometrical bounds on the
correlation energy reconstructed by this ansatz.
