To fully explore nonadiabatic photochemistry with TDDFT (or any other electronic structure method) it is necessary to possess not only an analytic gradient but also nonadiabatic coupling vectors h JK [Eq. ( )]. As compared to the gradient, the couplings are more complicated to derive and implement, and as a result they are available only in selected quantum chemistry programs and only for a limited number of electronic structure models, which includes TDDFT. A survey of implementations can be found in Ref. 22, although it omits the implementation in the Q-Chem program. The latter is the joint product of the Herbert group and the Subotnik group. Semi-empirical implementations have also been reported recently. Out of a variety of formalisms for computing nonadiabatic couplings within TDDFT, the one that is conceptually and computationally simplest is the "pseudo-wavefunction" approach. Working within the TDA, both for conceptual simplicity and for the practical reasons discussed above, one might write the wavefunction for the Kth excited state as a linear combination of singly-excited Slater determinants, as in the CIS method: