The SF-TDDFT excitation manifold also consists of determinants involving the virtual orbitals ("o-v" and "c-v" subspaces in Fig. ), along with the "c-o" space of excitations between doubly-occupied and singlyoccupied orbitals. Unlike the o-o space, none these other subspaces is spin-complete, meaning that they are missing one or more determinants needed to construct Ŝ2 eigenstates but which cannot be generated from the reference state via a single excitation combined with a single spin-flip. These are the subspaces that are responsible for spin contamination. We will return to this point later in this chapter.