For the eigenvalue-based methods the MAEs are 2 eV, even when using SCAN, SCAN0, and B3LYP, and even for the IP-TPM@1/3 that performed well for 1s → LUMO transitions. The lone exception to this trend is XGTPM used in conjunction with B3LYP, for which the MAE is 1.0 eV, but in view of the other statistics this much lower error does not seem reliable. At some level, these larger errors for higher-lying transitions may not be surprising given that we are using a ground-state theory to simulate excited states, and it is possible that DFT simply cannot describe higher-lying states very well, absent some additional constraints or a different strategy. Thus we turn to an empirical shifting scheme that proved quite successful for core-level electron binding energies. C. Empirically-Shifted Method. In previous work, we demonstrated that introduction of a single, functional-specific shifting parameter turned the primitive STM approach into the most accurate electronic structure method for K-shell binding energies, outperforming both ∆SCF but also more expensive methods including variants of GW . In a similar spirit, we introduce an empirically-shifted version of the XTPM approach (eq 11):