Unlike LR-TDDFT, the SF-TDDFT approach treats electron correlation on a consistent footing for both the ground and excited states of the target multiplicity, and in particular affords correct topology in the vicinity of any CX, including ones that involve the ground state of the target multiplicity. However, the usual SF-TDDFT approach contains only single spin flips, which often leads to significant spin contamination especially as one moves away from the Franck-Condon region of the excited state and starts to explore bond-breaking geometries. The more pervasive spin contamination in SF-TDDFT as compared to (spin-conserving) LR-TDDFT can be understood using the simple model that is shown in Fig. . Here, a high-spin triplet configuration is used as the reference determinant in order to target states of singlet multiplicity via single excitations combined with a single α → β spin flip. The figure depicts the SF-TDDFT excitation manifold that is generated in this manner. Amongst the Slater determinants contained in this manifold, only the four that are depicted in Fig. ) are able to form spin-pure states, i.e., eigenfunctions of Ŝ2 , and these can be combined to form three singlet states and one triplet. These states include both the nominal S 0 configuration as well as the two determinants necessary to form the properly spin-adapted open-shell S 1 configuration, corresponding to excitation between frontier MOs. Also present in the "o-o" space of Fig. ) is a double excitation that couples S 0 and S 1 and is needed in order to obtain proper topology at the S 1 /S 0 CX. The determinants shown in Fig. )-(e) are also part of the SF-TDDFT excitation manifold, however, and each of these is missing one or more of its "spin complements", meaning the determinants that are necessary to form a Ŝ2 eigenstate with S = 0. The missing determinants cannot be formed by any single excitation and single spin flip from the high-spin triplet reference state in Fig. . Any SF-TDDFT state that has a significant contribution from one or more of the determinants in Fig. )-(e) will exhibit significant spin contamination.