We will test some of the STM and STM approaches using the "CORE65" data set, which consists of 65 experimental K-shell CEBEs for the elements carbon (30 CEBEs in the data set), oxygen (21 CEBEs), nitrogen (11 CEBEs) and fluorine (3 CEBEs). Various density functional approximations are tested, including the SCAN functional along with its hybrid SCAN0, the latter of which includes 25% Hartree-Fock exchange (HFX); the B3LYP functional; 86, Becke's "half-andhalf" functional (BH&HLYP), which contains 50% HFX; the range-separated hybrid functional ωB97X-V; and two long-range corrected (LRC) functionals, namely, LRC-ωPBE and LRC-ωPBEh, the latter of which includes 20% HFX at short range. We also examine the short-range corrected (SRC) functional SRC1-r1, which was parameterized for XAS at the K-edge of "first row" elements (meaning C, O, N, and F) and contains 50% HFX on a length scale of < 1 Å. Range separation parameters for the two LRC functionals were set to ω = 0.3 bohr -1 (LRC-ωPBE) and ω = 0.2 bohr -1 (LRC-ωPBEh), which are the statistically-optimized values for a data set that includes both thermochemistry and excitation energies. The def2-QZVP basis set is used for all production calculations. It has been suggested that additional core functions are required for CEBE calculations, in order to describe orbital relaxation associated with the core hole, but we find that def2-QZVP is sufficiently close to the basis-set limit as to make this unnecessary. For ∆SCF methods, a completely uncontracted version of def2-QZVP, which should better describe core-hole relaxation, affords K-shell CEBEs that differ by an average of only 0.03 eV as compared to conventional def2-QZVP results (Table ). For the def2-TZVP basis, the ∆SCF results change by an average of 0.4 eV upon uncontracting the basis set (Table ), meaning that uncontracting the basis set is a good option when lower-quality basis sets are used, in order to reach the basis-set limit more rapidly. For the purpose of this benchmark study, we use the conventional (contracted) def2-QZVP basis set because we subscribe to the idea that new theoretical methods should first be assessed near the basis-set limit before basis-set approximations are introduced, in order to avoid conflating method error with basis-set error. Calculations with GGA functionals and their hybrids use the SG-1 quadrature grid, whereas SG-2 is used for meta-GGA functionals. Calculations reported below were performed using a locally-modified version of Q-Chem 5.4, 101 which contains several different algorithms that can be used to optimize a non-aufbau determinant that contains a core hole or fractional core hole. The simplest of these is the maximum overlap method (MOM), and for the present calculations we have found it sufficient to use the "initial MOM" (IMOM) algorithm. This differs from the original MOM procedure only in that the reference orbitals used for computing overlaps are not updated during the SCF iterations, but are taken from an initial closed-shell, integer-occupancy SCF calculation that is used to obtain E initial 0 (N ) in Eq. (1). For the core-ionized states considered here, we find that IMOM avoids variational collapse in all cases.