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Exploration of efficient catalysts is a priority for the electrochemical nitrogen reduction reaction (NRR) in order to receive a high product yield rate and faradaic efficiency of NH₃, under ambient conditions. In the present contribution, the binding free energy of N₂, NNH, and NH₂ were used as descriptors to screen the potential NRR electrocatalyst among different single or binuclear transition metal atoms on N-doped nanoporous graphene. Results showed that the binuclear Mo catalyst might exhibit the highest catalytic activity. Further free energy profiles confirmed that binuclear Mo catalysts possess the lowest potential determining step (hydrogenation of NH₂* to NH₃). The improved activities could be ascribed to a down-shift of the density of states for Mo atoms. This investigation could contribute to the design of a highly active NRR electrocatalyst.