Structure optimizations were carried out using the PBE 68 functional, augmented by the D3 dispersion correction scheme. We employed a plane-wave basis set with a 520 eV energy cutoff, along with projector-augmented wave (PAW) pseudopotentials for the core electrons. For the surface models, the first Brillouin zone was sampled using a 2×2×1 k-point grid centered at the Γ point, while a 1×1×1 k-point grid was used for gas-phase Co atom calculations. At the PBE+D3 equilibrium structure of Co/Mg(O)(001), we performed singlepoint calculations using PBE+U , 68,72 HSE06, and RPA. For PBE+U , we adopted U = 6.9 eV, following Ref. 54. RPA calculations employed a frequency integration grid density of 8 points for the surface models and 16 points for the isolated Co atoms. Due to computational constraints, RPA calculations were performed using a 1×1×1 Γ-centered k-point grid and a vacuum space in the z-direction reduced by 7 Å. Using a smaller k-point mesh affects the binding energy by 8 kJ/mol, whereas reducing the vacuum height affects it by 2 kJ/mol only (see Table ). Electronic energy thresholds were set to 1×10 -6 eV for DFT and 1×10 -8 eV for RPA calculations. The magnetic anisotropy energy (MAE) for Co/Mg(O)(001) was computed by carrying out self-consistent, non-collinear PBE and PBE+U calculations, including spin-orbit coupling and considering magnetization directions [0,0,1] and [1,0,0]. A 2×2×1 Γ-centered k-point grid was used for periodic models and a 1×1×1 k-point for finite clusters, with denser k-point meshes having a negligible effect on the MAE (see Table ). To improve convergence, the linear mixing parameter for the magnetization density was set to 0.2. MAE calculations with the HSE06 functional failed to converge, highlighting the challenges DFT-based methods face in adequately describing the multiconfigurational spin states of Co adatoms. See Section II C for further details on MAE calculations. PBE+D3 structure optimizations were carried out until all forces on relaxed atoms were converged below 0.005 eV/ Å. DFT and RPA calculations were conducted using the Vienna ab initio simulation package (VASP version 6.3.0). All relevant Cartesian coordinates are provided in the Supporting Information (SI).