In Figure we provide comparisons of adsorption energies from FNDMC (including Hsing et al. results) alongside various DFT functionals -PBE , PBE with Van der Waals correction (PBE-VdW), BEEF-VdW 48 , RPBE , as well as previously done RPA calculations and experimental data (-0.59 eV) . The DFT calculations were performed with Quantum Espresso code , using a relaxed, symmetric 8-layer slab, optimized with the respective functional, with adsorbates placed on both sides. As expected, PBE-based functionals significantly overestimate adsorption energies on FCC, HCP, and bridge sites and underestimate the top site, predicting only minor differences (∼0.1 eV) between adsorption sites. Both RPBE and BEEF-VdW functionals that have been fitted for surface reactions improve the adsorption energies but still do not predict the correct site ordering (the top site being the most stable one). In contrast, as shown in Figure , RPA calculations predict relatively higher adsorption energies for the top site (-0.37 eV 40 ; -0.42 eV ) and show a more noticeable distinction between the top site and other sites. However, compared to experimental energies, the RPA calculations still underestimate the adsorption energies by approximately 0.22 eV 40 and 0.17 eV , corresponding to relative errors of 37% and 29%, respectively.