| Summary: | The catalytic conversion of CO<sub>2</sub> to C<sub>2</sub> products through the CO<sub>2</sub> reduction reaction (CO<sub>2</sub>RR) offers the possibility of preparing carbon-based fuels and valuable chemicals in a sustainable way. Herein, various Fe<sub>n</sub> and Co<sub>5</sub> clusters are designed to screen out the good catalysts with reasonable stability, as well as high activity and selectivity for either C<sub>2</sub>H<sub>4</sub> or CH<sub>3</sub>CH<sub>2</sub>OH generation through density functional theory (DFT) calculations. The binding energy and cohesive energy calculations show that both Fe<sub>5</sub> and Co<sub>5</sub> clusters can adsorb stably on the N-doped carbon (NC) with one metal atom anchored at the center of the defected hole via a classical MN<sub>4</sub> structure. The proposed reaction pathway demonstrates that the Fe<sub>5</sub>-NC cluster has better activity than Co<sub>5</sub>-NC, since the carbon–carbon coupling reaction is the potential determining step (PDS), and the free energy change is 0.22 eV lower in the Fe<sub>5</sub>-NC cluster than that in Co<sub>5</sub>-NC. However, Co<sub>5</sub>-NC shows a better selectivity towards C<sub>2</sub>H<sub>4</sub> since the hydrogenation of CH<sub>2</sub>CHO to CH<sub>3</sub>CHO becomes the PDS, and the free energy change is 1.08 eV, which is 0.07 eV higher than that in the C-C coupling step. The larger discrepancy of d band center and density of states (DOS) between the topmost Fe and sub-layer Fe may account for the lower free energy change in the C-C coupling reaction. Our theoretical insights propose an explicit indication for designing new catalysts based on the transition metal (TM) clusters supported on N-doped carbon for multi-hydrocarbon synthesis through systematically analyzing the stability of the metal clusters, the electronic structure of the critical intermediates and the energy profiles during the CO<sub>2</sub>RR.
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