For Co atoms adsorbed at the preferred oxygen sites of MgO(001), we find that the bind- In contrast, embedded EOM-CCSD calculations on two cluster models of different size predict a non-aufbau, doubly degenerate quartet ground state with nearly unquenched orbital angular momentum (L ≈ 3) and strong spin-orbit coupling (SOC). The resulting spinorbit splitting favors states with the highest angular momentum projections (M J = ±9/2), which are the lowest in energy, in agreement with experimental observations of easy-axis magnetic anisotropy. The agreement between embedded EOM-CCSD and all-atom EOM-CCSD and CC2 predictions for state ordering and magnetic properties (SOC, spin-inversion energy barrier, and susceptibility) improves when the oxygen adsorption site is included in the high-level treatment. For this partitioning scheme-but independently of cluster sizethe predicted spin-inversion energy barrier of 427 cm -1 closely matches the experimentally reported magnetic anisotropy energy of 469 cm -1 . Our ab initio estimate of spin-inversion energy barrier also corroborates the results obtained through parametrized multiplet ligand field theory. These findings establish the reliability of embedded EOM-CCSD for magnetic properties of magnetic adsorbates.