The "spin-flip" (SF) approach to TDDFT has been used as a means to fix (or at least circumvent) the topology problem. SF-TDDFT starts from a ground-state calculation with higher spin multiplicity as compared to the states of interest, e.g., a triplet state if targeting singlet photochemistry, or a quartet state for the aforementioned doublet H 3 radical. This high-spin state is used as a reference for a LR-TDDFT calculation that also involves a one-electron α → β spin flip, thus affording states with the target multiplicity, at least in favorable cases. (As discussed later in this work, SF-TDDFT is often beset by significant spin contamination. ) The SF-TDDFT approach cures the topology problem around a CX by introducing a limited set of double excitations that couple ground and excited states, or (from a different point of view) because all of the states having the target multiplicity are generated by response theory and are thus described in a balanced fashion. Challenging cases such as H 3 in D 3h symmetry are described correctly by SF-TDDFT. Despite its topology problems, however, conventional LR-TDDFT remains a widely-used approach in the context of trajectory surface hopping simulations of nonadiabatic molecular dynamics (NMD). Provided that trajectories are halted before they can undergo internal conversion (IC) to the ground state, problems associated with incorrect topology may be avoided, but this con- straint is rather limiting insofar as the timescale for IC is one of the most basic questions that one might wish to answer using NMD simulations. As a counterpoint, there might be reason for optimism given that most nonadiabatic events likely occur near conical seams, where the energy gap is small, as opposed to occurring at a conical seam, where the energy gap is zero but which occupies a vanishingly small volume in the configuration space of a polyatomic molecule. A recent side-by-side comparison of NMD simulations using LR-and SF-TDDFT, for cis → trans photoisomerization azobenzene, seems to corroborate the optimistic viewpoint. That study found very little difference between the two approaches when it comes to predicting either the IC timescale or the branching ratio of cis versus trans photoproducts. It is worth noting, however, that the excited-state trajectories in that study are significantly more oscillatory when LR-TDDFT is used, which may reflect warping of the potential energy surfaces in the vicinity of the S 1 /S 0 intersection. In addition, 41 of the 300 LR-TDDFT trajectories had to be discarded due to convergence failure, whereas none of the SF-TDDFT trajectories suffered this problem. These observations are consistent with the problematic description of CXs involving the ground state in LR-TDDFT. In the present work, we contribute to this ongoing discussion by comparing NMD simulations using both LR-and SF-TDDFT, for a well-studied photochemical problem: photoisomerization of the protonated Schiff base C 5 H 6 NH + 2 . This molecule has been suggested 22,23 as a minimalist model of the rhodopsin chromophore, namely, 11-cis-retinal protonated Schiff base (PSB11). The full chromophore is depicted in Fig. (a) and the truncated model, trans-C 5 H 6 NH + 2 (PSB3), is shown in Fig. ). PSB3 has become something of a benchmark case for excited-state electronic structure theory, and is used here to probe difference between trajectory surfacehopping results at the LR-and SF-TDDFT levels of theory.