A simple example for a (4e,4o) model is shown in Fig. . There, a triplet (S = 1) reference configuration is used to generate a singlet (S = 0) excitation manifold. For the proper qualitative description of a S 0 /S 1 intersection, the minimal excitation space is labeled "o-o" in Fig. and consists of excitations within the halffilled orbitals of the reference configuration, including de-excitations. (Notably, if the molecule in question has a singlet ground state then the lowest SF-TDDFT excitation energy starting from a triplet reference is negative.) The o-o space contains a closed-shell configuration that resembles S 0 . It also contains two open-shell determinants with M S = 0, linear combinations of which will generate either an open-shell singlet (S 1 ) or else the M S = 0 component of the triplet state, depending on whether these determinants are added (triplet) or subtracted (singlet). Lastly, the o-o space contains a determinant that is doubly-excited with respect to S 0 , which provides coupling between S 0 and S 1 . The four determinants in the o-o space thus constitute a minimalist model that can describe the S 0 /S 1 intersection correctly. Notably, the doublyexcited determinant that is required is not contained in the usual LR-TDDFT excitation manifold starting from a closed-shell S 0 reference state, because that excitation manifold consists of single excitations only.