Mathematical derivations of linear-response TD-DFT, starting from an explicitly time-dependent theory of a perturbed Kohn-Sham ground state, can be found elsewhere; see Ref. 1 for a pedagogical version. The linear-response formalism is what is most often implied by "TD-DFT", as it is (by far) the most common form. An explicitly time-dependent or "real-time" formalism also exists, which can be used to describe attosecond electron dynamics in an external electric field. For excitation energies and most molecular electronic spectroscopy applications, however, the real-time method is much less efficient. Realtime methods are not considered here, and visualization tools are somewhat different for that approach. Starting from the ground-state solution of the Kohn-Sham eigenvalue problem, 58