Theoretical computation of C–C coupling reactions by different C₁ intermediates at Cu_<i>n</i> and Cu_<i>n</i>−1Ag clusters supported on TiO₂

*CO dimerization is a well-known pathway for C-C bond formation, producing C₂₊ products. However, the mechanisms of C-C coupling between other C₁ intermediates remain less explored. In this study, we investigate C-C bond formation involving *CO, *CHO, *COH, and other C₁ intermediates on Cu_<i>n</i> and Cu_<i>n</i>-1Ag clusters supported on TiO₂. Interestingly, our results reveal that the activation energy for *CO dimerization is not the lowest, indicating that it is not the dominant pathway for C-C bond formation. Coupling reactions involving *CHO, *COH, and other C₁ intermediates exhibit lower activation energies. Furthermore, the activation energy for the same reaction varies across different Cu_<i>n</i> clusters, emphasizing the role of cluster selection in C-C coupling. Notably, on certain clusters, such as Cu₈, the activation energy for C-C bond formation at the Ag site is lower than that at the Cu site, suggesting that Ag doping can enhance C-C coupling. However, in larger clusters like Cu₁₃, the activation energy at the Ag site exceeds that at the Cu site, highlighting that the effect of Ag doping is cluster size dependent. This study provides new insights into C-C bond formation, offering guidance for designing efficient co-catalysts to produce high-value C₂₊ products.