with h ≡ h CIS 01 defined in Eq. ( ). The results are plotted as the blue curve in Fig. . This time, degeneracy between the S 0 and S 1 states is preserved along the z direction. Even at the distance of 0.02 bohr from the MECP geometry, the energy gap between the two states remains quite small (≈ 0.0003 eV). Finally, starting from the MECP geometry we performed two-dimensional potential energy scans along the directions ĝ and ŷ, with results plotted in Fig. . It can be seen that the intersection seam a closed curve encompassing a small area around the MECP, which is located at the origin. This behavior results from the fact that the HF reference state is unstable in the vicinity of the CX, leading to negative excitation energies. (In the absence of instabilities, one would expect a double-cone shape around the MECP.) Although these results are computed at the CIS level, one can expect the same behavior for intersections between the Kohn-Sham ground state and the LR-TDDFT excited states, at least within the pseudo-wave function formalism for DFT derivative couplings that is described herein.