The present chapter describes a solution to these dilemmas based on the "spin-flip" (SF) approach to TDDFT. The formalism of SF-TDDFT is described in Section 2 but the essential idea is rather simple: we recognize that the shortcomings described above are limited to CXs that involve the reference state that is used in LR theory, which is typically the ground state but it need not be. SF-TDDFT uses a sacrificial reference state with a different spin multiplicity as compared to the target states of interest, e.g., a triplet reference is used to simulate singlet photochemistry or a quartet reference for the doublet H 3 radical. The change in multiplicity is accomplished via single excitations in conjunction with a single α → β spin flip, so that states having the target multiplicity (including the ground state) appear in the excitation manifold and are described in a variational manner with respect to one another. This cures the topology problem. (In fact, the double cones in Fig. were generated using SF-TDDFT calculations.) In Fig. ), the SF-CIS approach repairs the incorrect RO-CIS description of the conical intersection in H 3 . Adding dynamical correlation, SF-TDDFT recovers a double cone as well; see Fig. .