Time-dependent density functional theory (TDDFT), in its conventional linear-response (LR) formulation, 1-3 fails to describe the topology of any conical intersection (CX) that involves the reference state (typically the ground state), for which the branching space is onedimensional rather than two-dimensional. Depending upon one's point of view, this behavior arises either due to a lack of double excitations in the ansatz for the TDDFT "wave function", or else simply due to an imbalance in the nature of how LR-TDDFT describes the variational ground state versus the response (excited) states, leading to problems in regions of configuration space where the ground state becomes degenerate. A simple example is H 3 radical, which is a Jahn-Teller system in its D 3h geometry and for which LR-TDDFT predicts highly distorted potential energy surfaces that fail to reproduce the ground-state degeneracy. In contrast, CXs between two excited states are topologically correct in LR-TDDFT, which can be understood by considering the configuration interaction singles (CIS) method as a special case and examining its wave function ansatz,