The fully converged vacuum FNDMC calculations reveal that the COH* intermediate binds most strongly at the FCC and HCP hollow sites on the Cu(111) surface, slightly less strongly at the bridge site, and weakest at the top site (Figure ). In contrast, the CHO* intermediate binds strongest at the top site, less strongly at the bridge site, and weakest at the FCC/HCP hollow sites (Figure ). Differences between all sites for CHO* are within 0.2 eV, compared to COH*, where we found a significant difference (∼1 eV) between the top site and other sites. The difference in FNDMC adsorption ener-gies between the most preferred binding sites for COH* and CHO* is 0.67 eV, indicating that COH* is more weakly bound than CHO*. This energy difference varies among different density functional approximations: PBE predicts 0.36 eV, PBE-VdW 0.43 eV, RPBE 0.52 eV, and BEEF-VdW 0.70 eV. Notably, only the BEEF-VdW functional closely agrees with the FNDMC result for energy difference between the strongest bonding sites. The discrepancies in absolute adsorption energies between all DFT functionals and FNDMC highlight the limitations of these density functional approximations. This underscores the need for high-accuracy many-body methods, as correct absolute adsorption energies are essential for accurately predicting reaction pathways.