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Page 12 of 14 Zhang et al. J Mater Inf 2024;4:1 https://dx.doi.org/10.20517/jmi.2023.34

atoms leads to strong interactions between them. This is further confirmed by the COHP analysis of N-H,
which has the most negative ICOHP of -7.29 and -7.23 on NiNiN -gra and CoNiN -gra, respectively
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6
[Supplementary Figure 13]. Similar to the linear relationship between ICOHP of M-H and H adsorption
free energy, the ICOHP between N2-H on MMN -gra and M1M2N -gra also has a good linear relationship
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6
with the H adsorption free energy [Supplementary Figure 14A]. In addition, the linear relationship between
the p-band center of the N2 atom and the free energy of H adsorption shows that the adsorption at the N2
site also follows the p-band center theory [Supplementary Figure 14B]. Overall, the optimization of the
electronic structure of the N2 site due to the doping of bimetallic atoms enhances its H-trapping ability,
which, in turn, improves the HER activity of NiNiN -gra and CoNiN -gra.
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6
CONCLUSIONS
In summary, we investigated the HER activity of a series of SACs/DACs formed by embedding inexpensive
Fe/Co/Ni atoms into N-doped graphene by systematic DFT calculations and found a variety of potential
HER materials. Besides the CoN -gra, the ΔG values of NiNiN -gra and CoNiN -gra are also as low as 0.15
6
*H
4
6
and 0.27 eV, respectively. Reducing the coordination number of the metal in the active center can
significantly enhance its H-trapping ability, and FeFeN -gra, FeCoN -gra, FeNiN -gra, and CoNiN -gra,
5
5
5
5
thus, exhibit excellent HER catalytic activity with |ΔG | ≤ 0.18 eV. Importantly, the reduced metal
*H
coordination of MMN -gra/M1M2N -gra and the synergy between metal atoms allow them to
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5
simultaneously adsorb two hydrogen atoms to form a stable HMH intermediate toward the final product
H . Especially for FeNiN -gra and CoNiN -gra, both the |ΔG | and |ΔG | are ≤ 0.10 eV. The effective
2
5
5
*H2
*H1
coordination regulation and site synergy revealed by this work provide deep insights into the HER process
on diatomic catalysts and could guide the design of low-cost catalysts with activity comparable to noble-
metal ones.
DECLARATIONS
Authors’ contributions
Conceptualization, investigation, writing - original draft: Zhang C
Conceptualization, supervision, resources, writing - review and editing: Jin P
Investigation and data analysis and interpretation: Qin S, Gao H
Availability of data and materials
Not applicable.
Financial support and sponsorship
This work was supported by the National Natural Science Foundation of China (No. 22171068) and the
Natural Science Foundation of Hebei Province (No. B2022202036).

Conflicts of interest
All authors declared that there are no conflicts of interest.

Ethical approval and consent to participate
Not applicable.

Consent for publication
Not applicable.