The quantity ρ 0I (r; R) is the transition density, which is a parametric function of the nuclear coordinates R, and v ne (r; R) is the nuclear-electron Coulomb (or "external") potential. Upon invoking the TDA, one finds that h DFT 0I in Eq. ( ) vanishes whenever E I = E 0 , just like the situation for CIS. (See Appendix A.) In summary, the nonadiabatic coupling at an approximate conical intersection that involves the reference state does not vanish in general for either CIS or LR-TDDFT, meaning that the branching space is not solely determined by the vector g 0I , as shown in detail in Appendix B along with a numerical example. Nevertheless, the magnitude of these couplings remains small, which is a direct consequence of the absence of proper interactions between the reference state and the response states. The practical consequence is incorrect local topology and large curvature of potential energy surfaces in the vicinity of CXs that involve the reference state. Presumably, this should have consequences for NMD simulations.