When the excitation energy is small, we observe that the slope of the potential surfaces becomes unrealistically large near the seam, because the energy gradient has contributions that vary as ω - I . This is clear by comparing Figs. 12 and 13, where the latter provides the analogous plot computed using SF-TDDFT around the same MECP. Here, a proper double cone is obtained. We conclude that the potential surfaces close to a crossing point involving the ground state generally exhibit incorrect topologies, at both the CIS level and at the LR-TDDFT level. This can be expected to have consequences in NMD simulations.