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Page 10 of 14 Zhang et al. J Mater Inf 2024;4:1 https://dx.doi.org/10.20517/jmi.2023.34

Figure 6. Charge density difference and Bader charge values during the hydrogen evolution reaction, (A) CoN -gra and (B) CoCoN -gra.
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COHP and DOS between M-H in *H of (C) CoN -gra and (D) CoCoN -gra. COHP: Crystal orbital Hamiltonian population; DOS: density
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of state.

Figure 7. (A) Linear relationship between ICOHP and free energy of H adsorption for MN -gra/MMN -gra/M1M2N -gra; (B) Linear
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relationship between the d-band centers of the metals and free energy of H adsorption. ICOHP: M-H crystal orbital Hamiltonian
population integral.
Finally, the HER activity of NiNiN -gra and CoNiN -gra is mainly due to the optimized electronic structure
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of the N2 site by doping bimetallic atoms. Specifically, the p-band center (ε ) of the N2 site in MMN -gra
[60]
p
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and M1M2N -gra is upshifted relative to that of MN -gra due to the direct coordination with two metal
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atoms [Figure 9]. This leads to a significant enhancement of the H adsorption capacity of N2 sites on
MMN -gra and M1M2N -gra, especially NiNiN -gra (ε : -3.07 eV, ΔG : 0.15 eV) and CoNiN -gra (ε :
p
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*H
p
-3.43 eV, ΔG : 0.27 eV). The charge density difference and Bader charge analyses reveal that, unlike the H
*H