The left-eigenstate completely renormalized coupled-cluster (CC) method with singles, doubles, and noniterative triples [CR-CC(2,3)] and a few representative density functional theory (DFT) approaches have been applied to methanol oxidation to formic acid on a Au-8(-) cluster, which is a model for aerobic oxidations on gold nanoparticles. It is demonstrated that CR-CC(2,3) supports the previous exothermic reaction mechanism, placing the initial rate-determining transition state, which corresponds to hydrogen transfer from the methoxy species to the molecular oxygen, at about 20 kcal/mol above the reactants, less than 40 kcal/mol above the O-2 and CH3O- species coadsorbed on Au-8(-), and considerably above the remaining two transition states along the reaction pathway. The DFT calculations using the previously exploited M06 hybrid functional show reasonable agreement with CR-CC(2,3), but B3LYP offers additional improvements in the description of the relevant activation energies. Pure functionals, including M06-L, BP86, and TPSS, do not work well, significantly underestimating the activation barriers, but dispersion corrections, as in B97-D, bring the results closer to the M06 accuracy level.