where Ψ 0 (r 1 , . . . , r N ) is the ground-state wave function. The definition of T (r, r ′ ) in Eq. (2.8) is valid for correlated wave functions also. It has been argued that eigenvalue differences ε a -ε i should be good approximations to true excitation energies in exact Kohn-Sham theory, albeit without spin coupling so there is no distinction between excitations to different spin multiplicities. As such, one might imagine that configuration mixing in Eq. (2.7) occurs to a lesser extent in TD-DFT as compared to CIS, and indeed this is observed to be the case. For example, Figs. 1a and 1b compare amplitudes x ia for S 0 → S 1 excitation of formaldehyde, computed using TD-DFT/TDA with the PBE functional and also with the Hartree-Fock functional (i.e., exact exchange and no correlation), the latter of which is equivalent to the CIS method. The TD-PBE eigenstate consists almost exclusively of the 2b 2 → 2b 1 amplitude whereas for a converged CIS calculation (including all virtual orbitals), this amplitude accounts for less than 20% of the norm of the transition eigenvector. (These calculations were performed using a real-space electronic structure code, 92 so there is not finite-basis approximation. CIS with conventional Gaussian basis sets are shown in Fig 1c .) Truncating the virtual space leads to a more compact expansion and a 2b 2 → 2b 1 coefficient in the CIS case, but has a disastrous effect on the excitation energy (Fig ). This is not a useful strategy. That said, significant configuration mixing may be an unavoidable consequence of the use of hybrid functionals that contain some fraction of "exact" (Hartree-Fock) exchange. Because the Hartree-Fock virtual orbitals experience an N -electron potential rather than a (N -1)-electron potential, the virtual levels ε a are upshifted such that even frontier virtual orbitals are often unbound (ε a > 0). These are discretized continuum states, and a large number of them will need to mix together in order to generate the localized wave function of a bound excited state. Inclusion of diffuse basis functions, which are often necessary to obtain converged excitation energies, 8 also generate significant configuration mixing as shown in Fig. .