While SF-TDDFT rigorously cures the topology problem around CXs, it tends to significantly worsen the spin contamination as compared to LR-TDDFT, because some double excitations are admitted into the excitation space but not in a manner that introduces all of the complementary determinants needed to form spin-pure Ŝ2 eigenstates. In the (4e,4o) example of Fig. , the o-o subspace in spin-complete and contains a minimalist description of the S 0 /S 1 intersection, however the remaining subspaces lack some of the determinants needed to form Ŝ2 eigenstates. Any excited state that contains significant contributions from outside the o-o subspace is likely to exhibit significant spin contamination. It is possible to minimally augment the excitation space to restore spin symmetry, and this approach has been used to construct a spin-complete version of SF-CIS. Notably, this can be done without increasing the formal complexity of the method; the number of determinants remains O(N occ N virt ), albeit with a somewhat larger prefactor as compared to conventional CIS. More automated versions of this approach are discussed in Section 3, including methods that incorporate a DFT treatment of dynamical correlation.