To put the accuracy in context with other state-ofthe-art approaches, Fig. illustrates the errors alongside some of the competing alternatives, including BSE@G 0 W 0 results from Ref. 35. We compare 29 K-edge and near-edge excitation energies, corresponding to the data set for which the BSE@G 0 W 0 results are available. Those results are compared alongside ∆SCF and four As compared to BSE@G 0 W 0 calculations (MAE = 0.7 eV), we observe that each of the eigenvalue-based methods exhibits larger errors, including XTPM (MAE = 1.6 eV), XGTPM (MAE = 0.8 eV), and IP-TPM@1/3 (MAE = 1.3 eV). The ∆SCF approach is also slightly less accurate, with MAE = 0.9 eV. However, shifting reduces the error associated with XTPM by more than 1 eV, affording a MAE of 0.5 eV that is comparable to what is obtained by shifting TD-DFT results based on a single ∆SCF calculation. MAEs for this same data set, using the shifted-XTPM approach in conjunction with other density functionals, are 0.6 eV for SCAN0, 0.7 eV for CAM-B3LYP, and 0.8 eV for both SCAN and LRC-ωPBEh. D. Other Applications. As illustrative applications, we use several B3LYP-based methods to compute carbon, oxygen, and nitrogen K-edge excitation energies for the thymine and oxazole molecules. Errors (relative to experiment) in several K-edge transitions are listed in Table , using a variety of methods but all based on the B3LYP functional. The transitions in question represent the lowest dipole-allowed excitation from each indicated 1s orbital. In the case of thymine, all methods except XTPM perform well, with MAEs ≤ 0.5 eV. The smallest errors (0.3 eV) are obtained from the ∆SCF and shifted-XTPM approaches. For oxazole, the same two methods afford MAEs of 0.2 eV, as does the IP-TPM@1/3 technique. The advantage of the shifted-XTPM approach over IP-TPM@1/3 is that the former uses a charge-neutral excitation whereas the latter does not.