Past exam of the chemistry course of the year 3 of the natural sciences course of the University of Cambridge / 2022 / Paper 2A / Section A / 17 / c

The fixed localized determinant is unsuitable near equilibrium. It does not develop the correct shared bonding orbital and is not a pure singlet: for one alpha and one beta orbital, $⟨S^2⟩/{\hslash }^2=1-|⟨A|B⟩{|}^2$, which is nonzero unless the occupied spatial orbitals coincide. At dissociation it is an equal singlet/triplet mixture, though their energies become degenerate there. Near equilibrium the physical ground state is a bonding singlet. An optimized UHF calculation can recover the restricted, spin-pure solution by making its two occupied spatial orbitals equal; that does not rescue the particular fixed atomic-orbital determinant written here. A spin-adapted multideterminant description is needed to combine good bonding near equilibrium with correct singlet dissociation.