Energy and environmental concerns demand development of more efficient and selective electrodes for electrochemical reduction of CO2 to form fuels and chemicals. Since Cu is the only pure metal exhibiting reduction to form hydrocarbon chemicals, we focus here on the Cu (111) electrode. We present a methodology for density functional theory calculations to obtain accurate onset electrochemical potentials with explicit constant electrochemical potential and pH effects using implicit solvation. We predict the atomistic mechanisms underlying electrochemical reduction of CO, finding that (1) at acidic pH, the C1 pathway proceeds through COH to CHOH to form CH4 while C2 (C3) pathways are kinetically blocked; (2) at neutral pH, the C1 and C2 (C3) pathways share the COH common intermediate, where the branch to C-C coupling is realized by a novel CO-COH pathway; and (3) at high pH, early C-C coupling through adsorbed CO dimerization dominates, suppressing the C1 pathways by kinetics, thereby boosting selectivity for multi-carbon products.