which is the exact Hilbert space in a minimal basis. In the case of no instabilities, the various Hartree-Fock solutions are identically a determinant constructed from θ 0,0 4,1 . When an instability with respect to Ŝ2 arises, the UHF state, which is still constrained by S z = 0, consists of only the right-most term in Eq. 13, i.e., |U HF ⟩ = Âθ 1,0 2,1 θ 1,0 2,1 |Φ⟩. As before, we find that UHF captures some intra-pair correlations by breaking total spin symmetry. In the absence of non-collinearity, this constrained function represents both UHF and GHF, and no additional lowering of energy is obtained from the latter. With the onset of a Ŝz instability, GHF is able to recapture the two missing terms of θ 0,0 4,2 which give rise to opposite triplet-pair spin correlations; indeed, all possible ways to couple triplet geminals to overall singlets are represented. Rather beautifully, GHF's ability to break Ŝz symmetry to obtain subsets of the interpair correlations gives rise to the method's size-consistency regardless of the instabilities.