We next consider the transition potential approaches, TPM and GTPM. These methods modify only the core occupancy n c and do not put any electrons into the virtual space, resulting in underestimation of electron-hole attraction and a shift to higher excitation energies. This is evident in the data presented in Table , where GTPM errors are generally smaller than those exhibited by TPM yet even the GTPM errors remain larger than 2 eV for all functionals tested. FCHM, which likewise does not place electrons into the virtual space, affords similarly larger errors. Given that these methods also create a charged system, and are therefore problematic under periodic boundary conditions, neither TPM nor GTPM can be recommended. The XCHM approach (eq 9) creates a charge-neutral excitation but we find that results are erratic, improving somewhat with respect to other TPMtype methods for certain functionals (e.g., SCAN and CAM-B3LYP), yet seriously degraded for other functionals (e.g., BH&HLYP, for which the XCHM error exceeds 7 eV). The magnitude of these absolute errors is disturbing, given the continued use of TPM approaches in modern DFT. The performance of IP-TPM@1/2 and IP-TPM@1/3, on the other hand, is quite interesting. For a given functional, these methods typically afford smaller errors as compared to any of the TPM-based approaches that do not place electrons in the virtual space, and they also perform better than XCHM in many cases. The IP-TPM@1/3 method, in particular, is consistently better than other eigenvalue-based approaches. In conjunction with SCAN, SCAN0, or B3LYP, the IP-TPM@1/3 method affords MAEs below 1 eV. For B3LYP the MAE is 0.3 eV, essentially identical to the MAE for the ∆SCF approach based on the same functional.