• Strong spin correlation is one of possibly many components of the as-yet mysterious quantity of interest: strong correlation. Thus, ⟨S 2 ⟩ UCCSD is, by construction, incomplete. In addition, there are a small number of known cases (e.g., two-electron systems including stretched H 2 ) where ⟨S 2 ⟩ UCCSD will always be spin-pure, despite qualitatively different correlation regimes being traversed.