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Research Article  |  Open Access  |  2 Jan 2024

High hydrogen evolution activities of dual-metal atoms incorporated N-doped graphenes achieved by coordination regulation

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J Mater Inf 2024;4:1.
10.20517/jmi.2023.34 |  © The Author(s) 2024.
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Electrolysis of water to produce hydrogen (H) can solve the current energy crisis and environmental problems. However, efficient hydrogen evolution reaction (HER) catalysts are still limited to a few noble metals, thus prohibiting their broad applications. Herein, first-principles calculations were carried out to investigate the theoretical HER performances of a series of N-doped graphenes containing inexpensive single- and dual-metal atoms. Among them, MN4-gra (M = Fe, Co, Ni), homonuclear MMN6-gra, and heteronuclear M1M2N6-gra mostly exhibit low HER activities due to the weak H adsorption, and only CoN4-gra, NiNiN6-gra, and CoNiN6-gra show better ΔG*H values of 0.19, 0.15 and 0.27 eV, respectively. In contrast, low-coordinated MMN5-gra and M1M2N5-gra both have rather high HER activities. In particular, the ΔG*H values of FeNiN5-gra and CoNiN5-gra are as low as -0.04 and -0.06 eV, respectively, very close to the ideal 0 eV. Detailed analyses reveal that such high activity mainly stems from the reduced metal coordination and the synergistic effect between the two metals, which greatly enhance the adsorption ability of the active center. More interestingly, the strong H adsorption of MMN5-gra/M1M2N5-gra could enable them to further adsorb a second H atom and generate a stable HMH intermediate to yield the final product H2. Under this novel mechanism, the two-step |ΔG*H| values of FeNiN5-gra and CoNiN5-gra are all no more than 0.10 eV. Our work not only discloses the important effect of coordination regulation and site synergy on enhancing the catalytic activity but also finds a new HER path on the metal-embedded N-doped graphenes.


Hydrogen evolution reaction, density functional calculations, N-doped graphene, dual-atom catalyst, coordination regulation


The massive consumption of fossil resources and the increasingly serious environmental problems prompt people to search for suitable alternative energy sources and develop efficient energy conversion technologies. However, the lack of cheap and high-efficiency catalysts largely restricts the overall efficiency of energy conversion devices and is the main bottleneck for realizing the transformation of energy supply forms. As important chemical reactions, hydrogen evolution reactions (HER) and oxygen evolution reactions (OER) form the whole reaction of water electrolysis to produce hydrogen (H)[1-4]. The generated hydrogen can then be used in fuel cells as a carrier of clean energy due to its high mass energy density[5-7]. Unfortunately, the current utilization of hydrogen energy is still in its infancy due to the lack of cheap and efficient HER catalysts. As an optimal HER catalyst, platinum (Pt) requires only negligible overpotentials in acidic solutions to achieve high reaction rates[8-11]. However, the scarcity limits its large-scale application. Although many HER catalysts such as transition-metal phosphides[12-14], carbides[15-17] and sulfides[18,19] have been developed, the excellent performance as that of Pt/C is still hard to achieve.

In recent years, single-atom catalysts (SACs), exemplified by the metal atoms anchored on nitrogen (N)-doped graphenes (M-N-C), exhibit excellent catalytic activities in many important electrocatalytic processes[20-22]. The unique structure of SACs achieves nearly 100% atomic utilization and excellent catalytic performance[23-25]. Thus, they become promising catalyst materials for HER[26-32]. For example, Lu et al. prepared a Ru and N co-doped carbon material (RuCxNy) as an efficient HER catalyst[33]. When the overpotential is only -12 mV, the current density can reach 10 mA·cm-2, and the catalytic performance is significantly better than that of commercial Pt-based catalysts. Its excellent catalytic activity is mainly attributed to the embedded Ru atoms in the carbon matrix. First-principles calculations indicate that RuCxNy has a lower hydrogen binding energy and a lower dissociation kinetics energy barrier than the Ru nanoparticles.

Compared with SACs, dual-atom catalysts (DACs) not only maintain the high atomic utilization and good selectivity and stability but also have higher metal loading and more complex and flexible active sites. The possible synergistic effect, orbital coupling, and electron redistribution between adjacent metal centers and their functionality complementarity provide more opportunities for better catalytic performance[34-36]. Thus, they have attracted more interest than SACs. For example, Zheng et al. constructed a series of N-doped porous graphene (NPG)-based diatomic catalysts MM’-NPG and studied their HER activity[37]. Due to the dual active centers and controllable electronic structure, FeV-NPG and NiV-NPG could replace the noble metal HER catalysts under alkaline conditions. Zhou et al. synthesized the Rh-Fe dual atoms-embedded N-doped carbon hollow spheres, which exhibit a low overpotential of 36 mV for HER due to the electron redistribution promoted by Fe on the active Rh site[38]. Zhao et al. reported that the presence of C1-Pt-Ru-N2 structures in Pt1Ru1/NMHCS-A (activated N-doped mesoporous hollow carbon spheres) can greatly accelerate the H2 generation with a rather low overpotential of 22 mV to achieve a current density of 10 mA·cm-2[39]. However, the formation of atomic-scale metal sites without obvious aggregation remains as a large challenge for DACs. On the other hand, the coordination environment of the catalyst active center also greatly affects the H adsorption and desorption. By carefully adjusting the coordination environment of the active center, the performance of the catalyst can be further improved[40].

To obtain potential HER catalysts, we herein constructed a series of single-/dual-metal atom-incorporated N-doped graphenes with different coordination environments and systematically investigated their HER activities by density functional theory (DFT) calculations. The potential active centers of various catalysts and the adsorption structures of the key *H intermediate were investigated in detail. The HER activity of each catalyst was evaluated by calculating the free energy of H adsorption, and some very promising HER catalysts were then proposed. Finally, in-depth electronic structure analyses revealed the activity origins of the catalysts to provide a theoretical guide for the rational design of related catalytic materials.


DFT calculations considering spin polarization were carried out by using the Vienna ab initio simulation package (VASP)[41]. The Perdew-Burke-Ernzerhof (PBE)[42] functional and the projector augmented wave (PAW) method are used. The dispersion interactions during adsorption were considered by using the popular Grimme’s DFT-D3 correction method[43]. The convergence thresholds are 10-5 eV and 0.02 eV/Å for the energy and force, respectively, and the cutoff energy for the plane wave basis set is 500 eV. A vacuum space of 15 Å was applied along the z-direction to avoid the interactions between slabs. A 2 × 2 × 1 Monkhorst-Pack k-point mesh was used because the cell is as large as 17.22 Å × 17.22 Å × 15.04 Å. All these parameters have been carefully tested in our recent work[44]. All the results were visualized with the aid of the VESTA software[45].

To evaluate the structural stability of metal atoms in the N-doped graphene, the formation energy (taking low-coordinated ones as an example) was calculated as:

$$ E_{\mathrm{f}}=E_{\mathrm{MN} 3 \text {-gra }}-E_{\mathrm{N} 3 \text {-gra }}-E_{\mathrm{M}} $$


$$ E_{\mathrm{f}}=E_{\mathrm{MMN} 5 \text {-gra }}-E_{\mathrm{N} 5 \text {-gra }}-2 E_{\mathrm{M}} $$

where EMN3-gra and EN3-gra are the calculated energies of SACs and corresponding N-doped graphene without the metal atom, respectively. Similarly, EMMN5-gra and EN5-gra are the homonuclear DAC and corresponding metal-free structures, respectively. EM denotes the calculated energy of a metal atom in its stable bulk structure. Therefore, a more stable metal site has a more negative Ef value.

The adsorption Gibbs free energies were calculated as:

$$ \Delta G=\Delta E+\Delta \mathrm{ZPE}-T \Delta S $$

where the adsorption energies of the first and second H atoms are calculated as ΔE*H1 = E*H1- E* - 1/2EH2 and ΔE*H2 = E*H2- E*H1- 1/2EH2, respectively. E*H1 and ΔE*H2 are the energies of the systems with one and two adsorbed H atoms, respectively. E* is the energy of the catalyst. EH2 is the energy of a free H2 molecule. ΔZPE is the change in zero-point energy upon adsorption, while ΔS represents the change in entropy. They were obtained from the vibrational frequency calculations and standard thermodynamic data, as done in the recent literature[46]. T is the temperature (298.15 K). We assume pH = 0 and applied potential U = 0 V vs. Standard hydrogen electrodes (SHE) in the calculations. The computational hydrogen electrode (CHE) model[47] was used to calculate the Gibbs free energy change, namely assuming the free energy of an isolated H2 molecule is twice that of a proton-electron pair. For simplicity, the hydrogen coverage was not considered, and it is assumed to have a negligible effect as it does on other catalyst surfaces[46].



We first investigated the nine MN4-gra (M = Fe, Co, Ni), MMN6-gra, and M1M2N6-gra catalysts, and Figure 1 gives their typical structures with each metal surrounded by four N atoms. Our recent study revealed that some MMN6-gra and M1M2N6-gra catalysts exhibit excellent OER activity due to the rich site synergy effects[44]. They are all planar, and their structural stabilities have been confirmed. Herein, we turned to investigate their possible HER activities.

High hydrogen evolution activities of dual-metal atoms incorporated N-doped graphenes achieved by coordination regulation

Figure 1. Potential active centers of each type of catalyst. (A) MN4-gra (M = Fe, Co, Ni); (B) MMN6-gra; (C) M1M2N6-gra.

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*H) of the adsorption process being the most critical activity descriptor of a HER catalyst[8]. The ideal catalyst should have a zero ΔG*H value as a result of balanced adsorption and desorption. 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[44], the N atoms coordinating with metals were also 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*H values on all these active sites of 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 FeNiN6-gra is slightly close to the Fe site. The adsorption behavior of hydrogen on metal sites is basically consistent with the d-band center theory[49]. Compared with FeN4-gra, the adsorption at Fe sites of FeFeN6-gra, FeCoN6-gra, and FeNiN6-gra is weakened due to the formation of M-M bonds and the lowered metal d-band center (εd, Supplementary Table 10). They, thus, show lower HER catalytic activity (ΔG*H ≥ 0.37 eV) than FeN4-gra (ΔG*H: 0.34 eV). Consistent with the d-band center order of Co atoms (CoN4-gra > CoNiN6-gra > FeCoN6-gra > CoCoN6-gra)[44], their corresponding ΔG*H values are 0.19, 0.62, 0.79, and 0.84 eV, respectively. Among them, CoN4-gra has the best HER catalytic activity with ΔG*H of only 0.19 eV, which is well consistent with its high activity in recent experiments[48]. Interestingly, the hydrogen atom tends to adsorb on the non-metal sites (N or C sites) of NiN4-gra instead of the Ni site. Compared with NiN4-gra, the Ni site on NiNiN6-gra exhibits enhanced H adsorption owing to its upshifted d-band center. Nevertheless, its H adsorption is still weak (ΔG*H: 1.34 eV). The Ni sites of FeNiN6-gra and CoNiN6-gra exhibit weaker H adsorption due to the relatively strong Fe-Ni and Co-Ni interactions and the 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 MN4-gra have weak H adsorption (ΔG*H ≥ 1.05 eV, Figure 2), implying their low HER activity. For the N sites with two different coordination environments (N1, N2) on MMN6-gra, the ΔG*H of the N2 site is always smaller than that of the N1 site. It is worth noting that the ΔG*H value at the N2 site of NiNiN6-gra is only 0.15 eV, much lower than that of the Ni site (1.34 eV). Such a moderate H adsorption behavior suggests that the reaction could preferentially occur at this site, accompanied by a rather low ΔG*H value (0.15 eV). Similarly, for M1M2N6-gra, the N2 site directly coordinated with two metal atoms also has a strong H adsorption capacity. The ΔG*H value for the N2 site on CoNiN6-gra is 0.27 eV, much smaller than that of the Co site (0.62 eV) and the Ni site (1.69 eV). For all the C sites, however, hydrogen atoms are always vertically adsorbed on their top, and the adsorptions are all weak G*H ≥ 1.14 eV), indicating that the C sites of all catalysts are inactive for catalyzing HER.

High hydrogen evolution activities of dual-metal atoms incorporated N-doped graphenes achieved by coordination regulation

Figure 2. Gibbs free energy of H adsorption (ΔG*H) at different sites on MN4-gra/MMN6-gra/M1M2N6-gra. For the non-metal sites, only the values with the strongest adsorption are shown. Carbon: brown; Iron: golden; Cobalt: dark blue; Nickel: silvery; Nitrogen: light blue.

In summary, the metal sites of the above catalysts mostly exhibit weak adsorptions, and only the Co site of CoN4-gra shows potential high HER activity (ΔG*H: 0.19 eV). For the same reason, all the carbon sites are unsuitable for HER. Interestingly, owing to the dual-atom doping, the N2 sites simultaneously coordinated with the two metal atoms present enhanced H adsorption. In particular, the moderate H adsorptions on these N sites render NiNiN6-gra as a potential HER catalyst with ΔG*H as low as 0.15 eV. The overall weak H adsorptions on the above catalysts [Figure 2] necessitate further tailoring of their structures to achieve better activity.


Theoretically, the HER performance of the above catalysts could be improved by reducing the number of coordinating N atoms because it will endow the central metal with a stronger coordination ability to enhance its H adsorption. We then constructed a series of SACs and DACs with three N atoms around each metal: MN3-gra, MMN5-gra, and M1M2N5-gra[50,51]. However, the metal atoms in MN3-gra (M = Fe, Co, Ni) SACs all protrude from the catalyst surface upon structural optimization [Supplementary Figure 1]. The formation energies of MN3-gra are also positive, suggesting that they may be unstable and unsuitable for electrocatalytic reactions.

By comparison, the optimized structures of MMN5-gra/M1M2N5-gra DACs are all basically planar [Figure 3], with each metal atom well incorporated in the graphene plane. The metal atom and three nearby N atoms have average distances between 2.03~2.14 Å, all close to the sum of the covalent atomic radii [Supplementary Table 11]. This structural feature suggests that M-N covalent bonds may be formed, which are supported by the electron localization functions (ELFs), where substantial electron accumulation was found in the M-N regions [Supplementary Figure 2]. Consistently, the formation energies of these DACs are all negative (-0.61 to -0.06 eV), further confirming their energetic stabilities [Figure 3]. Moreover, the distances between two metal neighbors are all smaller than their covalent radii sum [Supplementary Table 11], indicating that M-M covalent bonds are formed, which are consistent with the ELF results in Supplementary Figure 2. The crystal orbital Hamiltonian population (COHP, Supplementary Figure 3) reveals that there are strong M-M bonding interactions under the Fermi level, which are largely due to the σ-type overlap of the metal 3dx2-y2 orbitals [Supplementary Table 12]. The large and negative integral-COHP (ICOHP) values of -5.03, -3.70, -2.74, -4.36, -3.15, and -2.97 for Fe-Fe, Co-Co, Ni-Ni, Fe-Co, Fe-Ni, and Co-Ni, respectively, further support the formation of M-M bonds. The metal atoms all donate some electrons to the N-doped graphene, as indicated by the charge density difference and Bader charges [Supplementary Figure 4].

High hydrogen evolution activities of dual-metal atoms incorporated N-doped graphenes achieved by coordination regulation

Figure 3. Optimized structures (two views) and formation energies (Ef) of (A-C) MMN5-gra (M = Fe, Co, Ni) and (D-F) M1M2N5-gra. The first column gives the different active sites considered for each kind of catalyst.

The electronic properties were then investigated by the density of states (DOSs) and electronic band structures. As shown in Supplementary Figure 5, substantial hybridization was observed between the N-2p state and the M-3d state. Compared with MMN6-gra/M1M2N6-gra, the metal d-band centers (εd) in MMN5-gra/M1M2N5-gra all shift to higher energy levels [Supplementary Figure 5]. This difference can be understood from the lifted energy level of the metal 3dx2-y2 orbitals in projected DOSs (PDOS, Supplementary Figure 6). Meanwhile, the metals also exhibit lower spin states [Supplementary Figure 6]. In addition, there are rich electronic states around the Fermi level with small band gaps of 0 to 0.04 eV (Supplementary Figure 7; note that the gaps are generally underestimated at the PBE level). Thus, rapid electron transfer between the catalyst surface and the adsorbates is expected to speed up the electrocatalytic reaction.

The changed electronic structure caused by the reduced metal coordination number will inevitably affect the adsorption of *H. Supplementary Tables 13-18 summarize the adsorption structures and corresponding ΔG*H on different active sites of all these low-coordinated DACs. For the metal sites, the H atom prefers to adsorb on the bridge site between two metal atoms of MMN5-gra/M1M2N5-gra as compared to a single metal site on MMN6-gra/M1M2N6-gra. Owing to such a novel dual-atom synergy, the ΔG*H values decrease significantly [Figure 4] and are very close to 0 eV on the metal sites of FeFeN5-gra (-0.16 eV), FeCoN5-gra (-0.18 eV), FeNiN5-gra (-0.04 eV), and CoNiN5-gra (-0.06 eV). Thus, they, especially FeNiN5-gra (ΔG*H: -0.04 eV) and CoNiN5-gra (ΔG*H: -0.06 eV), may exhibit high catalytic activity.

High hydrogen evolution activities of dual-metal atoms incorporated N-doped graphenes achieved by coordination regulation

Figure 4. Gibbs free energy of H adsorption (ΔG*H) at different sites on MMN5-gra/M1M2N5-gra. For the non-metal sites, only the values with the strongest adsorption are shown.

For the C sites, their overall adsorptions are still weak because their coordination environments in MMN5-gra/M1M2N5-gra are not significantly changed compared with MMN6-gra/M1M2N6-gra. Note that the C1 site of MMN5-gra and the C1/C10 sites of M1M2N5-gra exhibit strong H adsorption G*H ≤ -0.64 eV,Figure 4) due to the deformation of the catalyst structure during the H adsorption. For the N sites, although, such as MMN6-gra/M1M2N6-gra, the N sites coordinated to two metals (i.e., N1 sites) in MMN5-gra/M1M2N5-gra mostly have the strongest H adsorption capacity, they are still weak G*H ≥ 0.77 eV), not suitable for catalyzing HER. In summary, with rather low |ΔG*H| values of less than 0.2 eV,FeFeN5-gra, FeCoN5-gra, FeNiN5-gra, and CoNiN5-gra are promising HER catalysts due to the high activity of their metal sites.

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 MMN5-gra/M1M2N5-gra to adsorb a second H atom was further 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 NiNiN5-gra (ΔG*H2 = -0.09 eV) and the Co site of FeCoN5-gra (ΔG*H2 = -0.11 eV), suggesting that stable HMH structures could form on the surface of these catalysts.

Recently, Liberto et al. found that if the H2 generation involves two reaction intermediates, MH and HMH, an excellent HER catalyst should be thermoneutral for every H adsorption[58,59]. Namely, the ΔG*H values for both adsorption steps (ΔG*H1 and ΔG*H2) should be close to 0 eV. We further evaluated the catalyst activity under this HER mechanism. As shown in Figure 5, FeNiN5-gra may have the best activity under this mechanism via the adsorption at its Ni site. In addition, CoNiN5-gra can achieve rather high catalytic activity either through Co sites (ΔG*H1: -0.06 and ΔG*H2: 0.10 eV) or through Ni sites (ΔG*H1: -0.06 and ΔG*H2: 0.18 eV). The other two promising candidates are FeFeN5-gra and FeCoN5-gra via their Fe and Co sites, respectively.

High hydrogen evolution activities of dual-metal atoms incorporated N-doped graphenes achieved by coordination regulation

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

In conclusion, most of the MMN5-gra/M1M2N5-gra exhibited excellent HER activity through the MH intermediate reaction mechanism or through the HMH intermediate mechanism. In particular, the |ΔG*H| values of FeNiN5-gra and CoNiN5-gra under both reaction mechanisms are all no more than 0.1 eV, indicating that they are potential HER catalysts. Supplementary Figure 8 depicts the calculated exchange currents for the above catalyst models based on their adsorption free energies. Among them, CoN4-gra, NiNiN6-gra, FeNiN5-gra, CoNi-N5-gra, FeFeN5-gra, and FeCoN5-gra reside much closer to the volcano peak with high activity.

Origins of HER activity

The above calculation results show that CoN4-gra, NiNiN6-gra, CoNiN6-gra, and MMN5-gra/M1M2N5-gra all have better activities for catalyzing HER. However, the underlying reasons for their enhanced activities may be different.

For CoN4-gra, its excellent HER activity can be attributed to the moderate adsorption of H on Co sites. To understand the huge difference in the H adsorption capacity of different metal sites, the charge transfer between metal atoms as HER active sites and adsorbed hydrogen atoms was further investigated. The charge density difference shows that charge accumulation (yellow area) mainly occurs on the adsorbed H atoms, whereas charge depletion (cyan area) is concentrated around the metal atoms [Supplementary Figure 9]. In addition, the results of Bader charge analysis show that the adsorption free energy of H increases with the decrease of the negative charge it carries; that is, the adsorption gradually weakens. For example, the negative charges carried by H on CoN4-gra and CoCoN6-gra are -0.07 and -0.03 [Figure 6A and B], respectively, and the adsorption free energies of H are correspondingly 0.19 and 0.84 eV.

High hydrogen evolution activities of dual-metal atoms incorporated N-doped graphenes achieved by coordination regulation

Figure 6. Charge density difference and Bader charge values during the hydrogen evolution reaction, (A) CoN4-gra and (B) CoCoN6-gra. COHP and DOS between M-H in *H of (C) CoN4-gra and (D) CoCoN6-gra. COHP: Crystal orbital Hamiltonian population; DOS: density of state.

The COHP between the metal atoms and the adsorbed H atoms was further calculated [Supplementary Figure 10]. The activation of H was also quantitatively assessed using the ICOHP. In general, a more negative ICOHP corresponds to a stronger H adsorption. For example, the Co-H interaction in CoN4-gra (ICOHP: -3.28, Figure 6C) is much stronger than that in CoCoN6-gra (ICOHP: -3.08, Figure 6D). A clear linear correlation between the ICOHP of M-H and the free energy of H adsorption for all MN4-gra/MMN6-gra/M1M2N6-gra can be found in Figure 7A. This is also consistent with the above analyses that the downshifted d-band center of Co atoms in CoCoN6-gra leads to the decreased H adsorption capacity of Co sites [Supplementary Table 10]. The DOS results also show slightly more obvious hybridization between the states of CoN4-gra and adsorbed hydrogen [Figure 6C and D]. In addition, Figure 7B also plots the linear relationship between the metal d-band center and the H adsorption free energy, and the adsorption capacity of the metal site for H is in good agreement with the change of the d-band center.

High hydrogen evolution activities of dual-metal atoms incorporated N-doped graphenes achieved by coordination regulation

Figure 7. (A) Linear relationship between ICOHP and free energy of H adsorption for MN4-gra/MMN6-gra/M1M2N6-gra; (B) Linear relationship between the d-band centers of the metals and free energy of H adsorption. ICOHP: M-H crystal orbital Hamiltonian population integral.

The enhanced H adsorption capacity of MMN5-gra/M1M2N5-gra is consistent with the reduced coordination number and upshifted d-band center of the central metal [Supplementary Figure 5 and Supplementary Table 10]. Besides, the bridge site between two metals of MMN5-gra/M1M2N5-gra also helps to enhance their capture abilities. Further charge density difference and Bader charge analyses revealed that both metal atoms on MMN5-gra/M1M2N5-gra transfer electrons to the adsorbed H atoms, which results in a significant increase in the amount of charge on H (≤ -0.15, Figure 8) compared to the less negative charge of H on MMN6-gra/M1M2N6-gra (≥ -0.11, Supplementary Figure 9). In addition, according to the COHP analyses [Supplementary Figure 11], the bimetallic atoms on MMN5-gra/M1M2N5-gra simultaneously have bonding interactions with the adsorbed H atoms. This further confirms that the dual atoms in MMN5-gra/M1M2N5-gra both contribute to the H adsorption. Meanwhile, the excellent HER activity of MMN5-gra/M1M2N5-gra to generate H2 through HMH intermediates can also be attributed to the enhancement of H adsorption capacity after reducing the coordination number of metal active centers and the synergistic effect of bimetallic site on H adsorption.

High hydrogen evolution activities of dual-metal atoms incorporated N-doped graphenes achieved by coordination regulation

Figure 8. Charge density difference and Bader charge when the hydrogen evolution reaction occurs on the metal site for MMN5-gra/M1M2N5-gra.

Finally, the HER activity of NiNiN6-gra and CoNiN6-gra is mainly due to the optimized electronic structure of the N2 site by doping bimetallic atoms. Specifically, the p-band center (εp)[60] of the N2 site in MMN6-gra and M1M2N6-gra is upshifted relative to that of MN4-gra due to the direct coordination with two metal atoms [Figure 9]. This leads to a significant enhancement of the H adsorption capacity of N2 sites on MMN6-gra and M1M2N6-gra, especially NiNiN6-gra (εp: -3.07 eV, ΔG*H: 0.15 eV) and CoNiN6-gra (εp: -3.43 eV,ΔG*H: 0.27 eV). The charge density difference and Bader charge analyses reveal that, unlike the H adsorption on metal sites, the accumulation of charges mainly occurred around the N atoms, while the depletion of charge was mainly concentrated on the adsorbed H atoms [Supplementary Figure 12]. Moreover, when the N2 sites on NiNiN6-gra and CoNiN6-gra adsorb H, they have the largest amount of charge transfer, which are 0.44 and 0.43 e, respectively. Such massive electron transfer between N2 and H 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 NiNiN6-gra and CoNiN6-gra, respectively [Supplementary Figure 13]. Similar to the linear relationship between ICOHP of M-H and H adsorption free energy, the ICOHP between N2-H on MMN6-gra and M1M2N6-gra also has a good linear relationship 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 NiNiN6-gra and CoNiN6-gra.

High hydrogen evolution activities of dual-metal atoms incorporated N-doped graphenes achieved by coordination regulation

Figure 9. 2p projected density of states of N1 atoms in MN4-gra and N2 atoms in MMN6-gra/M1M2N6-gra. DOS: Density of state.


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 CoN4-gra, the ΔG*H values of NiNiN6-gra and CoNiN6-gra are also as low as 0.15 and 0.27 eV, respectively. Reducing the coordination number of the metal in the active center can significantly enhance its H-trapping ability, and FeFeN5-gra, FeCoN5-gra, FeNiN5-gra, and CoNiN5-gra, thus, exhibit excellent HER catalytic activity with |ΔG*H| ≤ 0.18 eV. Importantly, the reduced metal coordination of MMN5-gra/M1M2N5-gra and the synergy between metal atoms allow them to simultaneously adsorb two hydrogen atoms to form a stable HMH intermediate toward the final product H2. Especially for FeNiN5-gra and CoNiN5-gra, both the |ΔG*H1| and |ΔG*H2| are ≤ 0.10 eV. The effective 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.


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.


© The Author(s) 2024.

Supplementary Materials


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Cite This Article

OAE Style

Zhang C, Qin S, Gao H, Jin P. High hydrogen evolution activities of dual-metal atoms incorporated N-doped graphenes achieved by coordination regulation. J Mater Inf 2024;4:1.

AMA Style

Zhang C, Qin S, Gao H, Jin P. High hydrogen evolution activities of dual-metal atoms incorporated N-doped graphenes achieved by coordination regulation. Journal of Materials Informatics. 2024; 4(1): 1.

Chicago/Turabian Style

Zhang, Cunjin, Shuaibo Qin, Hui Gao, Peng Jin. 2024. "High hydrogen evolution activities of dual-metal atoms incorporated N-doped graphenes achieved by coordination regulation" Journal of Materials Informatics. 4, no.1: 1.

ACS Style

Zhang, C.; Qin S.; Gao H.; Jin P. High hydrogen evolution activities of dual-metal atoms incorporated N-doped graphenes achieved by coordination regulation. J. Mater. Inf. 2024, 4, 1.

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