Density functional theory (DFT) calculations are performed to investigate the energetics of the CO₂ electrochemical reduction on metal (M) porphyrin-like motifs incorporated into graphene layers. The objective is to develop strategies that enhance CO₂ reduction while suppressing the competitive hydrogen evolution reaction (HER). We find that there exists a scaling relation between the binding energy of the catalyst to hydrogen and that to COOH, a key intermediate in the reduction of CO₂ to CO; however, the M–H bond is stronger than the M–COOH bond, driving the reaction toward the HER rather than the reduction of CO₂ to CO. This scaling relation holds even with axial ligation to the metal cation coordinated to the porphyrin ring. When 4f lanthanide or 5f actinide elements are used as the reactive center, the scaling relation still holds but the M–COOH bond is stronger than the M–H bond, and the reaction favors the reduction of CO₂ to CO. By contrast, there is no scaling relation between the binding energy of the catalyst to H and that to OCHO, the key intermediate in CO₂ reduction to formic acid. Interestingly, we find that coordination of a ligand to an unoccupied axial site can make the M–OCHO bond stronger than the M–H bond, resulting in preferential formic acid formation. This means that the axial ligand effectively enhances CO₂ reduction to formic acid and suppresses the HER. Our DFT calculations have also identified several promising electrocatalysts for CO₂ reduction to HCOOH with almost zero overpotentials.