), portions of the operator. When the constrained internally-stable RHF wavefunction is not externally-stable to these rotations, the symmetry dilemma arises, as in the domain of triplet instabilities. The GHF determinant, | ΦGHF ⟩, may be conceived as further introducing the possible rotations of c † a,↑ c i,↓ and c † a,↓ c i,↑ , allowing for a linear combination of spin-restricted determinants now of varying S z . This set, which can be written as a single Slater determinant of generalized orbitals, is not an eigenfunction of Ŝ2 nor Ŝz .