that Cu(111) surfaces favor methane formation, which is a dominant C 1 product of CORR, whereas Cu(100) surfaces preferentially produce ethylene , both having little to no methanol products. From many DFT studies on reaction pathways involving COH* and CHO* intermediates, the most current interpretation leads to the conclusion that COH* preferentially leads to methane and higher hydrocarbons. In contrast, the CHO* pathway should indicate the production of methanol and oxygenated products . However, the precise mechanisms remain unclear due to the absence of direct experimental identification of these transient species on single crystals. To address these uncertainties, more advanced methods such as the RPA for Cu(100) and the embedding approach for Cu(111) have been employed to provide a more accurate description of the reaction pathways. In this study, we complement these efforts by using a benchmark FNDMC method to provide further insights.