▎ 摘　　要

The development of stable and efficient non-noble metal catalysts for the hydrogen evolution reaction (HER) can greatly promote the utilization of hydrogen energy. Herein, we investigated four potential model catalysts of the atomic cluster M-4 supported on MN4-graphene substrates (M = Fe, Ni) from first-principles, i.e., Fe-4@FeN4-Gr, Fe-4@NiN4-Gr, Ni-4@FeN4-Gr and Ni-4@NiN4-Gr, respectively. Using density functional theory (DFT) calculations, the synergistic effect enhances the stability and HER activity of these supported M-4@MN4-Gr. It is found that the Gibbs free energy of hydrogen adsorption (Delta G(H*)) of Ni-4@FeN4-Gr is only -0.168 eV with the best exchange current. We further explored the pH effect on the HER performance and determined the ideal pH range of these potential model catalysts. Four model catalysts can follow the Volmer-Tafel pathway if considering the implicit solvation effect. These results provide an effective guidance for the rational design of electro-catalysts.