Boosting hydrazine electrooxidation on Ru-coordinated heteronuclear double metal atom catalysts

Abstract

The hydrazine oxidation reaction (HzOR) is considered as an efficient alternative anodic reaction to the oxygen evolution reaction for low-energy hydrogen production. Consequently, developing highly efficient electrocatalysts for the HzOR is important. By using density functional theory (DFT) calculations, we evaluate the HzOR activity of dual-metal atom catalysts (DACs), specifically Ru coordinated with 3d–5d transition metals, anchored on nitrogen-doped graphene (RuM@N₆C, where M = Ti–Cu, Zr–Mo, Ru–Pd, W, Ir and Pt). Among these DACs, RuCo@N₆C and RuCu@N₆C exhibit high catalytic activity with low limiting potential values of −0.13 and 0.00 V, respectively. The electron transfer, crystal orbital Hamiltonian population and electron localization function are further analyzed to prove that the moderate metal coordination favored the reduction of the strong adsorption of the Ru site to the *N₂H₃ intermediate. In addition, the excellent thermodynamic stability of RuCo@N₆C and RuCu@N₆C was also identified. These findings underscore the crucial role of electron transfer in the HzOR and highlight the potential of Ru-coordinated heteronuclear DACs in bridging the gap between the sustainable hydrogen production and ecosystem governance technologies.

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1. Introduction

Hydrazine (N₂H₄) is a versatile liquid energy carrier that has gained significant attention due to its excellent energy density, ease of storage and transport and favourable thermodynamic properties.¹ As a clean and efficient fuel, N₂H₄ has become a focus of research in energy technologies. In recent years, renewable hydrogen production via direct water splitting has achieved a series of advancements.^2–5 In traditional electrochemical water splitting for hydrogen production, the high thermodynamic barrier of 1.23 V (vs. RHE) for the anodic oxygen evolution reaction (OER) imposes a huge energy consumption, whereas the hydrazine oxidation reaction (HzOR) is considered as an efficient alternative pathway to the OER due to its 0.33 V theoretical potential.^6,7 However, the catalytic activity of the HzOR catalysts remains unsatisfactory, highlighting the need for the development of highly efficient materials. In addition, theoretical insights into the underlying mechanisms of new materials are essential for advancing materials chemistry.

As for HzOR electrocatalysis, single-atom catalysts (SACs) show commendable performances.^8–12 Jiao et al. investigated a series of 14 SACs (single transition metal atoms anchored on the C₂N monolayer, TM@C₂N) using the first-principles calculations and identified Ru@C₂N as the best catalyst with the lowest limiting potential of −0.24 V.¹³ Dual-atom catalysts (DACs) have atomically dispersed active sites and exhibit similar advantages to SACs in terms of maximum utilization efficiency of metal sites. Moreover, DACs possess two adjacent metal atoms as the active center, potentially resulting in a new catalytic mechanism and greatly improved structural adjustability compared with SACs.^14–16 Theoretical studies of DACs have already demonstrated their application potential in numerous fields, such as the carbon dioxide reduction reaction (CO₂RR)^17,18 and the nitrogen reduction reaction (NRR).¹⁹ Furthermore, the cooperative interaction between the two adjacent metal atoms results in a unique electronic structure of both metal atoms that is different from the corresponding single-atom counterparts, which potentially optimizes HzOR performance by adjusting intermediate adsorption.^20,21 On the other hand, nitrogen-doped graphene has attracted widespread attention for its ability to provide anchor sites for metals due to its high carrier density and mobility.²² In particular, FeZn@N₆C,²³ CoCu@N₆C,²⁴ and RuCo@N₆C²⁵ have been successfully synthesized, where RuCo@N₆C was used as a bifunctional oxygen electrocatalyst for oxygen electrocatalysis, demonstrating the potential of nitrogen-doped graphene as an ideal support for DACs. Given the excellent HzOR catalytic performance of the Ru-containing catalysts discussed above, constructing Ru-based DACs on nitrogen-doped graphene is promising for obtaining high catalytic activity, and the corresponding reaction mechanism deserves further investigation.

In this study, we employed density functional theory (DFT) based first-principles calculations to explore the performance and mechanisms of Ru paired with transition metals (TM) supported on nitrogen-doped graphene for the HzOR. The investigated catalysts, denoted as RuM@N₆C DACs (containing TMs including Ti–Cu, Zr–Mo, Ru–Pd, W, Ir and Pt) had different adsorption sites for the activation of N₂H₄. Furthermore, we identified an optimized volcano-shaped correlation between the adsorption free energy of the N₂H₄ molecule and the limiting potential (U_L) for hydrazine oxidation to nitrogen synthesis across all heteronuclear RuM@N₆C DACs. Notably, RuCo@N₆C and RuCu@N₆C exhibited excellent HzOR catalytic activity, with limiting potentials of −0.13 V and 0.00 V, respectively. Additionally, we use the electron transfer (Q) and the crystal orbital Hamilton population (COHP) to demonstrate the mechanism of how TMs with moderate chemical activity atoms (e.g. Co, Cu) coordinated with Ru in DACs can reduce U_L by effectively modulating the adsorption capacity of the reaction intermediates. These results give an insight into how the HzOR selectivity can be modulated by the dual metal coordination composition and further provide theoretical guidance for designing catalysts for hydrazine assisted hydrogen production.

2. Computational details

Spin-polarized first-principles calculations have been performed based on DFT implemented in the Vienna Ab initio Simulation Package (VASP),^26,27 and the data were post-processed using VASPKIT.²⁸ The interaction between the valence electrons and the ionic core is treated using the projector augmented wave (PAW) method²⁹ and the exchange–correlation effect is accounted by the Perdew–Burke–Ernzerhof (PBE) functional³⁰ with the DFT-D3 method to correct the van der Waals interaction.³¹ The plane wave energy cutoff was set to be 450 eV. The convergence criteria for Hellmann–Feynman force and energy are set to be 0.02 eV Å⁻¹ and 10⁻⁵ eV, respectively. A 4 × 4 graphene supercell with a vacuum space of ∼15 Å is adopted to build the atomic model of RuM@N₆C, for which the Monkhorst–Pack (MP) grids of 3 × 3 × 1 and 6 × 6 × 1 are adopted to perform structural optimization and the calculation of densities of states (DOS),³¹ respectively. The COHP was calculated with the Local Orbital Basis Suite Towards Electronic-Structure Reconstruction (LOBSTER) program.³² Bader charge analysis was performed to quantitate the electron transfer.³³Ab initio molecular dynamics (AIMD) simulation was adopted to evaluate the thermal stability of the proposed catalysts, for which the simulation was performed under a constant volume and temperature (NVT) ensemble. The total simulation time we adopted is 6 ps with a time step of 2 fs.³⁴ During the AIMD simulations, the temperature is controlled using a Nosé–Hoover thermostat. The total electronic energies of various HzOR intermediates (N_xH_y) and adsorption energy (ΔE_ads(*N_xH_y)) for N_xH_y on the catalyst are defined as:

E(N_xH_y) = E(N₂H₄) − [(4 − y)/2E(H₂)] (1)

ΔE_ads(*N_xH_y) = E(*N_xH_y) − E(*) − E(N_xH_y) (2)

where x = 2, y = 0, 1, 2, 3 and 4 and the E(N₂H₄) and E(H₂) are the total electronic energies of the isolated N₂H₄ and H₂ molecules in a vacuum, respectively, and ΔE(*N_xH_y) and E(*) are the total electronic energies of the catalyst with and without intermediates, respectively. The computational hydrogen electrode (CHE) model³⁵ is used to calculate the free energy change of the reaction elementary step based on the following formula:

ΔG = ΔE + ΔE_ZPE − TΔS (3)

where ΔE was calculated based on the DFT total energy, and ΔE_ZPE and TΔS are the contributions of zero-point energy and entropy difference of the reactants and products (298.15 K, 1 atm.), respectively. E_ZPE and TS of the free molecules (Table S1, SI) and the adsorbates (Table S2, SI) were obtained by calculating the vibrational frequencies. The reaction free energies of each step during the HzOR process are denoted in Table S3 (SI). The U_L was calculated with:

U_L = −ΔG_max/e (4)

where ΔG_max is the free energy change of the potential determining step (PDS), which is the most endothermic one among all elementary steps along the lowest-energy pathway.

3. Results and discussion

3.1. Structure and stability of RuM@N₆C DACs

The structure model of RuM@N₆C DACs consists of two parts, namely, nitrogen-doped graphene and the Ru-metal dimer. For the optimized structure of the substrate nitrogen-doped graphene, which contains six pyridine N atoms, the lattice parameters are given in Fig. S1 (SI). The active centre consists of the Ru-metal dimer as shown in Fig. 1a, where a Ru atom is paired with a TM atom, and each TM is coordinated with 3 N atoms. The TM atoms selected to coordinate with Ru are shown in Fig. 1b, and considering the strength of adsorption, not too strong (Sc, Ti, Y and Zr) and not too weak (Zn, Ag, Cd, Au and Hg), combined with the commonness of TMs (except Tc, Ta, Re and Os), the middle TMs with moderate chemical activity have been considered to constitute heteronuclear RuM@N₆C DACs. The optimized geometric configuration is presented in Fig. S2 (SI). To evaluate the stability of RuM@N₆C DACs, we first use the formation energy (E_f) as the first screening factor. The value of E_f and the energy of TM atoms in their bulk (E_TM-bulk) are listed in Table S4 (SI). All RuM@N₆C DACs exhibit E_f < 0, indicating their thermodynamic stability.³⁶ The structure parameters are given in Table S5 (SI). Both the largest bond lengths between TM atoms and their neighbouring N atoms and the Ru–M bond lengths are smaller than sum of their corresponding covalent radii. The stability of the RuM@N₆C DACs is further confirmed by the calculated total density of states (TDOS) and COHP. As shown in Fig. S3 (SI) and Fig. 1e, f, there is significant electronic state hybridization spanning a large energy range for the bonded atoms, confirming the formation of strong chemical bonds.

Fig. 1 (a) Schematic diagram of RuM@N₆C DACs, showing the Ru atom (purple sphere) paired with a transition metal (green sphere), each metal atom coordinated with three nitrogen atoms (grey spheres), and nitrogen-doped graphene (brown spheres). (b) The TM selected to coordinate with Ru. (c) Formation energy and binding energy of the studied RuM@N₆C DACs. The COHP of (e) RuCo@N₆C and (f) RuCu@N₆C.

3.2. Adsorption and activation of N₂H₄

Due to the special spatial configuration of the N₂H₄ molecule, we investigated the role of different metal sites in the adsorption and activation of N₂H₄, and the calculated adsorption free energies and optimized adsorption configuration for *N₂H₄ are shown in Table S6 and Fig. S4–S6 (SI), respectively. The corresponding energies of the optimal adsorption sites are shown in Fig. 2a. Interestingly, the adsorption energies have a periodic pattern, and the TM located on the left side of the periodic table of elements paired with Ru made RuM@N₆C DACs have a strong adsorption energy for *N₂H₄, which also means that it is difficult for further HzOR dehydrogenation to occur. Thus, we speculate that the RuM@N₆C DACs, where TM on the right side of the periodic table is paired with Ru as the optimal adsorption site, show high catalytic activity for the HzOR.

Fig. 2 (a) The energies of the optimal adsorption sites. The CDD of (b) RuCo@N₆C and (c) RuCu@N₆C. The PDOS of (d) RuCo@N₆C and (e) RuCu@N₆C. The PDOS of (f) RuCo@N₆C and (g) RuCu@N₆C with N₂H₄. The COHP of (h) RuCo@N₆C and (i) RuCu@N₆C with N₂H₄. (j) Schematic diagram of the activation mechanism of N₂H₄.

To gain fundamental insight into the N₂H₄ adsorption and activation mechanism, the charge density difference (CDD), DOS and COHP were investigated. Considering the moderate chemical activity, RuCo@N₆C and RuCu@N₆C are chosen as representatives. As shown in Fig. 2b and c, N₂H₄ adsorption and activation should follow the typical Blyholder model.³⁷ The electron depletion (cyan region) can be seen on the Ru atom and σ* orbitals of N₂H₄, which indicates that Ru site back-donates electrons to the σ* orbitals of N₂H₄ and the σ orbitals of N₂H₄ donate electrons to the empty d states of the Ru site. Overall, the N₂H₄ molecule gains 0.15e and 0.14e from the active sites of RuCo@N₆C and RuCu@N₆C, respectively. The CDD diagram of N₂H₄ on Ru₂@N₆C is shown in Fig. S7 (SI), the N₂H₄ molecule gains 0.17e from the active site of Ru₂@N₆C. Compared to the above moderate chemical system, the Ru₂@N₆C system has a stronger bond between the active site and the N₂H₄ molecule, which may be detrimental to the next step of the dehydrogenation reaction. In order to explore the adsorption and bonding strength between the active site and the N₂H₄ molecule, we further evaluated the partial densities of states (PDOS) and COHP. The calculated PDOS diagrams of the Ru–M d orbital of RuM@N₆C DACs are shown in Fig. S8 (SI), and the PDOS of selected RuCo@N₆C and RuCu@N₆C are presented in Fig. 2d and e, respectively. For the RuCo@N₆C system, significant orbital overlap was observed between Co-3d and Ru-4d, indicating that strong hybridization in RuCo@N₆C arises between Co-3d and Ru-4d. For the RuCu@N₆C system, due to the characteristics of the electronic structure of the Cu atom, the overlap between Cu-3d and Ru-4d is not as large as the former, but there is still a significant overlap in the 2 eV to −2 eV energy region. Meanwhile, the d-band center (ε_d) of the Ru atom for RuCo@N₆C is −0.64 eV, which is higher than that of the Co atom (ε_d = −0.81 eV). The d-band center of the Ru atom in RuCu@N₆C follows a similar trend compared with RuCo@N₆C, where the ε_d values of Ru and Cu are −0.16 and −2.22 eV, respectively. According to the d-band center theory, the higher d-band center will contribute to the stronger adsorption. The d-band center of different metal atoms shows a consistent trend with adsorption free energies at different adsorption sites.

The PDOS diagrams for N₂H₄ adsorbed on RuCo@N₆C, RuCu@N₆C and free N₂H₄ are shown in Fig. 2f, g and Fig. S9 (SI), respectively. The electronic state hybridization between the molecular orbitals of N₂H₄ and the d orbitals of Ru and other metal atoms can be observed at ∼5 eV. The COHP analysis could give more quantitative information on the chemical bond between N₂H₄ and the dominant metal active sites, and the details of more negative integrated COHP (ICOHP) values are shown in Tables S9–S11 (SI). As shown in Fig. 2h and i, the ICOHP values (−1.06 eV) of Ru–N for the RuCo@N₆C system indicate that Ru is the dominant adsorption metal active site for adsorbing N₂H₄, proving the generation of a d–σ bond during adsorption. For the RuCu@N₆C system, the ICOHP values (−0.66 and −0.01 eV for Ru–N and Cu–N) are lower than those of RuCo@N₆C system, which confirms the stronger adsorption of N₂H₄ on RuCo@N₆C. The PDOS and COHP of the Ru₂@N₆C system are shown in Fig. S10 and S11 (SI), respectively. For the Ru₂@N₆C system, the stronger d–σ bond than those of RuCo@N₆C and RuCu@N₆C leads to difficulties in the first dehydrogenation step to generate *N₂H₃, resulting in a higher energy barrier for the RDS. The ICOHP values (−0.14 and −1.26 eV for Ru₁–N and Ru₂–N) further prove the excessive N₂H₄ adsorption ability of the Ru₂@N₆C system. Overall, a schematic diagram of the activation mechanism of N₂H₄ is shown in Fig. 2j. The adsorption process causes the empty orbital (band no. 8) of N₂H₄ to shift downwards, approaching the Fermi energy level (E_f), which is conducive to electron transfer from the metal active site, thus causing molecule activation, while the orbital splits out the d–σ bond, and N₂H₄ of the RuCo@N₆C system has a larger orbital width and overlap than that of RuCu@N₆C system, indicating a higher activation intensity.

3.3. HzOR catalytic mechanism

To clarify the HzOR mechanism, we calculated ΔG profiles for all intermediates on RuM@N₆C DACs. In addition to the previously mentioned optimized adsorption geometry configuration for N₂H₄ (Fig. S5 and S6, SI), the configuration of the rest of the reaction intermediates (*N₂H₃–*N₂) is shown in Fig. S12—S15 (SI). As evidenced in Fig. 3a and Table S7 (SI), the rate-determining step (RDS) of RuM@N₆C DACs is mainly the step2 (N₂H₄–N₂H₃, ΔG₂) and step3 (N₂H₃–N₂H₂, ΔG₃), which may be due to selective modulation of the *N₂H₃ intermediates by the moderate RuM@N₆C DACs, such as RuCo@N₆C and RuCu@N₆C, indicating that the inclusion of Cu and Co atoms as the TMs to coordinate with Ru significantly improves the adsorption of the intermediates. In addition, the U_L values for RuCo@N₆C (−0.13 V) and RuCu@N₆C (0.00 V) are less negative than those of the other RuM@N₆C and Ru₂@N₆C (−0.41 V) catalysts, indicating the thermodynamic advantage of these two materials. We further explored the relationship between ΔG_ads(*N₂H₄) and ΔG₂ and ΔG₃, respectively. As shown in Fig. 3b and c, linear correlations can be observed, thus ΔG_ads(*N₂H₄) can be selected as a descriptor. A volcano plot of limiting potential on RuM@N₆C DACs is shown in Fig. 3d, where RuCo@N₆C and RuCu@N₆C exactly stand near the top of the volcano, confirming that the moderate adsorption of N₂H₄ is pivotal for the HzOR. Since the electrochemical HzOR occurs in an aqueous solution, we used the VASPsol implicit solvation model to include by default the effects of solvation on catalytic activity, which was validated for the key DACs (RuCo@N₆C, RuCu@N₆C and Ru₂@N₆C),³⁸ as shown in Fig. S16 and Table S8, with respective overpotentials (U_L) of −0.14, 0.07 and −0.40 V. These values are nearly consistent with those obtained without taking into account of solvation effects. Meanwhile, ΔG_ads(*N₂H₄) of RuCo@N₆C and RuCu@N₆C is stable under different U values, indicating the exchange–correlation functional using PBE is sufficient to explain the relationship of volcano plot for HzOR, as shown in Fig. S17 and S18 (SI).

Fig. 3 (a) Summary of the limiting potentials of the HzOR on RuM@N₆C DACs. (b) The relationship between ΔG_ads(*N₂H₄) and ΔG₂ (N₂H₄–N₂H₃). (c) The relationship between ΔG_ads(*N₂H₄) and ΔG₃ (N₂H₃–N₂H₂). (d) HzOR volcano plot of RuM@N₆C DACs with a descriptor (ΔG_ads(*N₂H₄)), where the red hexagon represents Ru₂@N₆C, the outline of the volcano plot are composed of two function lines in red gained by Fig. 3(b) and (c).

3.4. HzOR performance of RuCo@N₆C and RuCu@N₆C

As plotted in Fig. 4a and b, the detailed free energy diagrams of the HzOR on RuCo@N₆C and RuCu@N₆C are further analyzed to validate their hydrazine-to-nitrogen performance. The top views of the corresponding structures are shown in Fig. 4c and d. The free energy diagram of the HzOR on Ru₂@N₆C is shown in Fig. S19 (SI) for comparison. N₂H₄ can be stably adsorbed with a Ru–N bond and then goes through the first dehydrogenation step to form *N₂H₃ with energy changes of 0.13 eV for RuCo@N₆C and −0.13 eV for RuCu@N₆C. In the subsequent steps (*N₂H₃–*N₂H₂–*N₂H–*N₂), stepwise dehydrogenation occurs and the corresponding energies drop by 0.36, 0.17 and 0.38 eV for RuCo@N₆C and 0.26, 0.00 and 0.40 eV for RuCu@N₆C, respectively. Eventually, *N₂ species desorb from RuM@N₆C, and the energies of of RuCo@N₆C and RuCu@N₆C are −0.19 and −0.30 eV, respectively.

Fig. 4 Free energy diagrams of (a) RuCo@N₆C and (b) RuCu@N₆C, respectively. The top view of the optimized geometry adsorption configuration of (c) RuCo@N₆C and (d) RuCu@N₆C, respectively. The charge variation between the metal atoms and the intermediates of (e) RuCo@N₆C and (f) RuCu@N₆C, respectively.

To quantify the electron transfer contribution of the active center Ru–M metal pair to the intermediates, charge variations of metal atoms during the HzOR on RuCo@N₆C, RuCu@N₆C and Ru₂@N₆C are shown in Fig. 4e, f and Fig. S20 (SI). It is found that the tendency of charge variations on RuCo@N₆C and RuCu@N₆C is analogous. Specially, in the first step the Ru atom is the dominant metal active site for both systems, which is consistent with the previous discussion. For the RuCu@N₆C system, the electronic contribution of the Cu atom to the intermediates increases gradually during the steps 1–6 (*N₂H₄–*N₂H₃–*N₂H₂–*N₂H–*N₂), indicating that the inclusion of the Cu atom as the TM to coordinate with Ru significantly improved the adsorption of the intermediates. For the RuCo@N₆C system, the harmonious coordination of Co and Ru atoms leads to an increase in the electron transfer number of the Ru–Co pair compared with the Ru₂@N₆C system, resulting in the activation of the intermediates, thus the energy barrier can be efficiently decreased.

3.5. Origin of the enhanced HzOR activity of RuCo@N₆C and RuCu@N₆C

The CDD diagrams of N₂H₃ on RuCo@N₆C, RuCu@N₆C and Ru₂@N₆C are shown in Fig. 5a–c. Pronounced charge redistribution between Co, Cu and Ru and N₂H₃ indicates a strong orbital interaction between Ru–M metal pairs and N₂H₃. To evaluate the N₂H₃ adsorption stability, we also calculate the COHP, further demonstrating the bonding strength between N of N₂H₃ and the metal d orbital. As shown in Fig. 5d–f, for RuCo@N₆C, RuCu@N₆C and Ru₂@N₆C, significant orbital overlap was observed among Co-3d, Cu-3d, Ru-4d and N-2p, further indicating a strong interaction between the intermediates and active sites. The values of ICOHP are −2.77, −2.25 and −2.57 eV for RuCo@N₆C, RuCu@N₆C and Ru₂@N₆C, respectively (Tables S12–S14, SI). The RuCu@N₆C system has a more negative ICOHP value, representing a more stable adsorption configuration, thus the next dehydrogenation step of N₂H₃ can be accelerated. The electron localization function (ELF) was analyzed to further prove the bonding characteristics. The results showed active interactions between the active sites (Ru and TM) and the N of N₂H₃. Charge transfer predominantly occurred from Ru or TM atoms to the nitrogen atoms, forming the stronger bonds (Ru–N or TM–N), which enhanced the stability of the adsorption of N₂H₃, shown in Fig. 5-i and Fig. S21–S23 (SI). This illustrates that the TM atom (moderate active site) of RuCo@N₆C and RuCu@N₆C can more effectively adjust the adsorption of the key intermediate (N₂H₃) than that of Ru₂@N₆C, resulting in the enhancement of the HzOR activity.

Fig. 5 The charge density difference of (a) RuCo@N₆C, (b) RuCu@N₆C and (c) Ru₂@N₆C, respectively. The COHP of TM–N (between N of N₂H₃ and the metal d orbital) on (d) RuCo@N₆C, (e) RuCu@N₆C and (f) Ru₂@N₆C, respectively. The electron localization function (ELF) diagrams of (g) RuCo@N₆C, (h) RuCu@N₆C and (i) Ru₂@N₆C, respectively.

3.6. Electrochemical stability of RuCo@N₆C and RuCu@N₆C

To further confirm the thermodynamic stability of RuCo@N₆C and RuCu@N₆C, AIMD simulations were performed and the results are shown in Fig. 6a and b, respectively. RuCo@N₆C and RuCu@N₆C maintained their complete structures during the simulations at 300 K for 6 ps. In addition, the energies of RuCo@N₆C and RuCu@N₆C remained relatively stable, indicating their good thermodynamic stability. The excellent thermal stabilities of RuCo@N₆C and RuCu@N₆C suggest that they could serve as durable electrocatalysts for the HzOR.

Fig. 6 Temperature and energy evolution during the AIMD simulation of (a) RuCo@N₆C and (b) RuCu@N₆C, respectively. Insets show the top and side views of the snapshots after 6 ps simulation.

4. Conclusions

In summary, we systematically investigated Ru-coordinated 3d–5d TM atoms, anchored on the nitrogen-doped graphene DACs for the HzOR. RuCo@N₆C and RuCu@N₆C showed significantly enhanced catalytic performance due to their good stability, moderate adsorption ability, and significant electron transfer for N₂H₄. Through the cooperative interaction of TM atoms with Ru, RuCo@N₆C and RuCu@N₆C effectively modulate the adsorption of the key *N₂H₃ intermediate, and exhibit the limiting potentials of −0.13 and 0.00 V, which are much lower than that of Ru₂@N₆C (−0.41 V). The excellent thermal stability of RuCo@N₆C and RuCu@N₆C was further verified through AIMD simulations. These findings underscore the potential of DACs containing Ru coordinated with a moderate TM atom and are expected to inspire further experimental and theoretical research in this area.

Conflicts of interest

The authors declare no conflicts of interest.

Data availability

The data supporting this article have been included as part of the supplementary information (SI). Supplementary information: the optimized structure and related data are shown in SI. See DOI: https://doi.org/10.1039/d5cp03046c.

Acknowledgements

The authors appreciate the support from the National Natural Science Foundation of China (No. 52371161, 52371232, 52271152).

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