Theorem of Brillouin

The UHF formalism becomes inconvenient for open-shell configurations of atoms or molecules with point-group symmetry. Unless specific restrictions are imposed, the self-consistent occupied orbitals fall into sets that are nearly but not quite transformable into each other by operations of the symmetry group. By imposing equivalence and symmetry restrictions, these sets become symmetry-adapted basis states for irreducible representations of the symmetry group. This makes it possible to construct symmetry-adapted /V-clcctron functions, as described in Section 4.4. The constraints in general invalidate the theorems of Brillouin and Koopmans. This restricted theory (RHF) is described in detail for atoms by Hartree [163] and by Froese Fischer [130],... 

---