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Page 8 of 14 Zhang et al. J Mater Inf 2024;4:1 https://dx.doi.org/10.20517/jmi.2023.34

Figure 5. Adsorption Gibbs free energy of the first (ΔG ) and second H (ΔG ) in the HMH intermediates on different catalyst sites.
*H1 *H2

Dual-H co-adsorption path
When the metal coordination of the catalyst is unsaturated, the HER may also occur along a new reaction
pathway [52-57] : after the formation of a usual MH species on the catalyst surface, a second H atom continues
to be adsorbed on the same metal site to form a stable HMH intermediate. Thus, with low metal
coordination numbers, the possibility for MMN -gra/M1M2N -gra to adsorb a second H atom was further
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investigated. The corresponding optimized structures are summarized in Supplementary Table 19. Indeed,
all these catalysts formed stable HMH structures with one H atom on a metal and one H atom between two
metals. The corresponding H-H distances are all no more than 1.86 Å. We calculated the adsorption free
energy of the second H to evaluate its adsorption strength [Supplementary Table 20]. Most catalysts show
favorable adsorption for the second H, especially the Ni site of NiNiN -gra (ΔG = -0.09 eV) and the Co
*H2
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site of FeCoN -gra (ΔG = -0.11 eV), suggesting that stable HMH structures could form on the surface of
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*H2
these catalysts.
Recently, Liberto et al. found that if the H generation involves two reaction intermediates, MH and HMH,
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an excellent HER catalyst should be thermoneutral for every H adsorption [58,59] . Namely, the ΔG values for
*H
both adsorption steps (ΔG and ΔG ) should be close to 0 eV. We further evaluated the catalyst activity
*H1
*H2
under this HER mechanism. As shown in Figure 5, FeNiN -gra may have the best activity under this
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mechanism via the adsorption at its Ni site. In addition, CoNiN -gra can achieve rather high catalytic
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activity either through Co sites (ΔG : -0.06 and ΔG : 0.10 eV) or through Ni sites (ΔG : -0.06 and ΔG :
*H2
*H1
*H1
*H2
0.18 eV). The other two promising candidates are FeFeN -gra and FeCoN -gra via their Fe and Co sites,
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respectively.
In conclusion, most of the MMN -gra/M1M2N -gra exhibited excellent HER activity through the MH
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intermediate reaction mechanism or through the HMH intermediate mechanism. In particular, the |ΔG |
*H
values of FeNiN -gra and CoNiN -gra under both reaction mechanisms are all no more than 0.1 eV,
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