3.4.1. Core-to-Valence (K-Edge) Transitions. Unlike the situation for wave function methods, core-level excitations in TD-DFT need not require specialized basis sets or modifications to the core functions, 134 though we do invoke the CVS approximation. Errors in TD-DFT/def2-TZVPD excitation energies for a set of small organic molecules, 131 at the K-edge of carbon, nitrogen, and oxygen, are provided in histogram form in Fig. for the B(α)LYP functionals. Previous work demonstrates that hybrid functionals including B3LYP, PBE0, and CAM-B3LYP consistently underestimate core-to-valence excitation energies, with errors that increase as a function of atomic number for the elemental K-edge in question. This trend can be understood in terms of differential SIE between core and valence orbitals, with greater SIE for the 1s orbitals of heavier elements. Meanwhile, the CIS method overestimates these same transition energies. This is mostly an effect of incomplete orbital relaxation, 97 a shortcoming that is shared by TD-DFT but exposed in the CIS case because SIE is absent. This points to orbital relaxation errors partially cancelling SIE for core-to-valence TD-DFT calculations, as quantified elsewhere. Using the one-parameter B(α)LYP ansatz, Besley and co-workers suggested α = 57 as the optimal value to cancel SIE and minimize errors in K-edge transition energies, although others have suggested that 70% HF exchange is optimal for K-shell excitations, as compared to 50% for L-shell transitions and 20% for valence excitations. For the present data set, the value α = 60 in Fig. leads to signed errors that are approximately symmetric about zero, whereas smaller values systematically underestimate the transition energies (suggesting residual SIE that is more significant than neglected orbital relaxation) whereas larger values of α lead to overestimated excitation energies whose errors are likely dominated by orbital relaxation effects.