Static correlated functionals for reduced density matrix functional theory

Based on recent progress on fermionic exchange symmetry we propose a way to develop new functionals for reduced density matrix functional theory. For some settings with an odd number of electrons, by assuming saturation of the inequalities stemming from the generalized Pauli principle, the many-body wave-function can be written explicitly in terms of the natural occupation numbers and the natural orbitals. This leads to an expression for the two-particle reduced density matrix and therefore for the correlation energy functional. This functional is tested for a three-electron Hubbard model where it shows excellent performance both in the weak and strong correlation regimes.