where again we invoke the fiction that ⟨Ψ ab ij |LAS⟩ = 0 for the sake of argument. However, within that constraint, every possible spin microstate of each fragment is considered. The individual microstates of each spin multiplet are not optimized separately; rather, a single microstate is optimized and spin-raising and spin-lowering operators are applied to the state thus optimized in order to generate the rest of the spin multiplet. This guarantees that the LASSIS eigenstates always have good spin quantum numbers in the absence of spin-orbit coupling.