The LRC-ωPBE and LRC-ωPBEh functionals do not perform particularly well at the ∆SCF level but afford the smallest MAEs for the STM approach. Note that LRC functionals have been used in the past to improve the agreement between valence Kohn-Sham energy lev-els and ionization energies, 72,104,105 but these functionals are inferior to B3LYP for K-edge excitation energies in TD-DFT. It is possible that "optimal tuning" of these functional, 107 by adjusting ω such that ε HOMO = -∆E IP , might improve the performance even further. We have not pursued this, however, in the interest of obtaining a black-box method that does not need to be adjusted for each new molecule. (Optimally-tuned values of ω are often strongly dependent on system size, even for homologous systems. ) With other functionals, MAEs of 1-2 eV are observed and this includes CAM-B3LYP, which uses range separation but sacrifices correct asymptotic behavior in its parameterization. In previous work on core-level binding energies, we showed that STM is not competitive with ∆SCF but that GSTM results can approach the accuracy of ∆SCF. This can be understood based on the fact that GSTM amounts to a higher-order Taylor series approximation (as compared to Slater's original method), or as a higher-order quadrature scheme in a form of thermodynamic integration. The same is true for these Kedge excitations, where all functionals tested except for SRC1-r1 afford MAEs smaller than 1 eV at the GSTM level. Using B3LYP, the GSTM and ∆SCF results are quite similar.