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

               RESULTS AND DISCUSSION
               MN -gra/MMN -gra/M1M2N -gra
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               We first investigated the nine MN -gra (M = Fe, Co, Ni), MMN -gra, and M1M2N -gra catalysts, and
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               Figure 1 gives their typical structures with each metal surrounded by four N atoms. Our recent study
               revealed that some MMN -gra and M1M2N -gra catalysts exhibit excellent OER activity due to the rich site
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               synergy effects . They are all planar, and their structural stabilities have been confirmed. Herein, we turned
                           [44]
               to investigate their possible HER activities.
                                                        +
               In the acidic solution (pH = 0), the abundant H  in the electrolyte can be adsorbed on the catalyst under a
               certain external voltage to form a *H-rich surface, which then reacts to generate hydrogen molecules.
               Therefore, it is important to study the adsorption behavior of hydrogen on the catalyst surface, with the free
               energy change (ΔG ) of the adsorption process being the most critical activity descriptor of a HER
                                *H
               catalyst . The ideal catalyst should have a zero ΔG  value as a result of balanced adsorption and desorption.
                     [8]
                                                         *H
               Figure 1 shows all possible H adsorption sites of these catalyst models. The geometric optimization of the H
               adsorption configuration on their surfaces was carefully performed to ensure that the most favorable H
               adsorption structure and adsorption site were found for each of them. Note that besides the metal and
               carbon sites considered in our recent OER study , the N atoms coordinating with metals were also
                                                           [44]
               included in this work because they are widely regarded as potential HER active centers [33,37,48] . Supplementary
               Tables 1-9 summarize the adsorption structures and corresponding ΔG  values on all these active sites of
                                                                            *H
               the above nine catalysts.
               First, for the metal sites, the hydrogen atom tends to be vertically adsorbed on most metals except that the
               one on the Ni site of FeNiN -gra is slightly close to the Fe site. The adsorption behavior of hydrogen on
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               metal sites is basically consistent with the d-band center theory . Compared with FeN -gra, the adsorption
                                                                    [49]
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               at Fe sites of FeFeN -gra, FeCoN -gra, and FeNiN -gra is weakened due to the formation of M-M bonds and
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               the lowered metal d-band center (ε , Supplementary Table 10). They, thus, show lower HER catalytic
                                               d
               activity (ΔG  ≥ 0.37 eV) than FeN -gra (ΔG : 0.34 eV). Consistent with the d-band center order of Co
                          *H
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                                                      *H
                                                                    [44]
               atoms (CoN -gra > CoNiN -gra > FeCoN -gra > CoCoN -gra) , their corresponding ΔG  values are 0.19,
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                                                                                           *H
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                          4
               0.62, 0.79, and 0.84 eV, respectively. Among them, CoN -gra has the best HER catalytic activity with ΔG  of
                                                                                                      *H
                                                              4
                                                                                        [48]
               only 0.19 eV, which is well consistent with its high activity in recent experiments . Interestingly, the
               hydrogen atom tends to adsorb on the non-metal sites (N or C sites) of NiN -gra instead of the Ni site.
                                                                                  4
               Compared with NiN -gra, the Ni site on NiNiN -gra exhibits enhanced H adsorption owing to its upshifted
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                                 4
               d-band center. Nevertheless, its H adsorption is still weak (ΔG : 1.34 eV). The Ni sites of FeNiN -gra and
                                                                     *H
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               CoNiN -gra exhibit weaker H adsorption due to the relatively strong Fe-Ni and Co-Ni interactions and the
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               downshifted d-band center of Ni atoms. Thus, the Ni sites on these catalysts may be unsuitable for HER.
               Then, all the non-metal active sites, namely the N atoms coordinating with metals and the C atoms
               coordinating directly with N atoms, were investigated. Supplementary Tables 1-9 show that besides the
               vertical adsorption on top of the N atom, the hydrogen atom on the N site may also reside slightly towards
               the metal site in some cases. The H adsorption strengths of N sites in different coordination environments
               are quite different. The N sites on MN -gra have weak H adsorption (ΔG  ≥ 1.05 eV, Figure 2), implying
                                                                              *H
                                                 4
               their low HER activity. For the N sites with two different coordination environments (N1, N2) on
               MMN -gra, the ΔG  of the N2 site is always smaller than that of the N1 site. It is worth noting that the ΔG
                                                                                                         *H
                               *H
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               value at the N2 site of NiNiN -gra is only 0.15 eV, much lower than that of the Ni site (1.34 eV). Such a
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               moderate H adsorption behavior suggests that the reaction could preferentially occur at this site,
               accompanied by a rather low ΔG  value (0.15 eV). Similarly, for M1M2N -gra, the N2 site directly
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                                             *H
               coordinated with two metal atoms also has a strong H adsorption capacity. The ΔG  value for the N2 site
                                                                                       *H
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