defined as the difference in adsorption energy between the periodic (pbc) and cluster models, decreases by 4.7 kJ/mol. The smaller Co/Mg 9 O 9 cluster exhibits a higher PBE contribution to the binding, with the D3 correction accounting for only 6% of the total adsorption energy, compared to 15% in the periodic calculations. In contrast, the larger Co/Mg 25 O 25 cluster yields a ratio between the PBE and D3 contributions that is closer to that of the periodic system. However, both cluster models provide an accurate description of the chemisorption of Co onto MgO(001), with errors of less than 5% on the total binding. Furthermore, at both the PBE and PBE+U level, and regardless of whether the periodic or cluster model was used, the MAE calculated using Eq. ( ) remains positive, ranging between 30 and 54 cm -1 (Table ). Positive MAEs are indicative of in-plane magnetic anisotropy, which is qualitatively incorrect for Co adatoms on MgO(001). This discrepancy in the computed MAE, the challenging convergence behavior of the non-collinear DFT calculations, and the DOS, indicating fully occupied d xy , d x 2 -y2 orbitals and thus quenching of the orbital angular momentum, showcase the difficulties that approximate exchange and correlation density functionals face in capturing the multiconfigurational, non-aufbau character of the spin states in Co/MgO(001). These issues suggest that beyond-DFT approaches are necessary to accurately describe the system. For Co/Mg 9 O 9 , using EOM-EE-CCSD, we compute an orbital angular momentum of ), in accordance with El-Sayed's rule. The agreement between EOM-EE-CCSD and EOM-EE-CCSD-in-DFT is excellent, with SOCC differences between the two levels of theory of less than 20 cm -1 . Moving from the C1 to the C2 partitioning scheme reduces both the orbital angular momentum and SOCC values, improving the agreement with EOM-EE-CCSD even further.