Taking Eq. ( ) as an ansatz for the excited-state wavefunction, analytic expressions can then be derived for h JK using standard analytic gradient theory, which essentially means careful application of the chain rule. The relevant expressions will not be repeated here; see Zhang and Herbert for a concise derivation and for a generalization beyond the TDA. The results are in good agreement with derivative couplings computed via quadratic response theory, which is the formally correct way to obtain h JK within TDDFT, at least when quadratic response is well-behaved. That method, however, is vulnerable to spurious divergences, 58,71-73 a fact that was actually noted long ago in the context of time-dependent Hartree-Fock theory. As explained later by Furche and co-workers, these are artifacts of approximate response theory in general, not limited to TDDFT, and they complicate the application of quadratic response to the point that the pseudo-wavefunction approach is the much more widely-used method. Similarly, the topology problem around a CX is not unique to LR-TDDFT and is also an artifact of response theory, and in particular the unbalanced (and non-variational) manner in which it treats the reference and response states. Correlated Green's functions methods also afford wrong topology at any CX involving the reference state, whereas SF versions of those methods restore the correct topology. Derivative couplings computed within the pseudo-wavefunction formalism show good agreement with exact (full CI) results for small molecules, good agreement with LR theory for derivative couplings d 0K that involve the ground state, and (for couplings between two excited states) good agreement with quadratic response theory, provided that the latter is well-behaved. Some exemplary data are shown in Fig. , where derivative couplings d JK computed within the pseudo-wavefunction approach are compared to results from quadratic response theory for a set of small molecules, and also to exact (full CI) results for linear H 3 as a function of internuclear distance. Derivative couplings based on the pseudo-wavefunction formalism also correctly reproduce the branching plane and the Berry phase around a CX, for which the orbital response contributions to d JK prove to be crucial. Results presented below demonstrate that MECPs located with the aid of pseudo-wavefunction h JK vectors afford good agreement with benchmark results from multireference electronic structure methods. Within the TDA, the pseudo-wavefunction formalism also affords the same result for d JK as does the equation-of-motion formalism developed by Li and Liu. All of these features argue in favor of using the pseudo-wavefunction approach, to the exclusion of quadratic response theory.