NiN4/Cr修饰的石墨烯电化学固氮电极

工业上应用哈伯工艺法合成氨过程要求严苛, 需要消耗大量能源且二氧化碳排放量大。因此, 开发在常规环境条件下通过电催化氮还原反应的清洁技术, 对未来可持续的能源转化进程具有重要意义。本研究采用密度泛函理论计算方法, 对TM₁N₄/TM₂嵌入石墨烯的氮还原反应进行了全面研究。在充分考虑活性和稳定性的情况下, 研究结果表明, NiN₄/Cr锚定石墨烯通过酶促反应途径表现出最佳的催化活性, 其中第一次加氢为电位决定步骤, 起始电位为0.57 V, 优于商业Ru基材料。此外, 与单一的Cr原子修饰的石墨烯相比, 引入NiN₄官能团降低了ΔG_max并提高了电催化性能。根据Mulliken电荷分析, 催化剂的催化活性主要来源于载体和反应中间体之间的电子转移。上述结果为高效合成氨提供了电极候选材料, 进一步深化了相应的电催化机理。

Abstract

Owing to the heavy energy consumption and the massive CO₂ emission during ammonia synthesis via Haber-Bosch process, a clean technology of nitrogen reduction electrocatalysis under ambient conditions is of significance for the sustainable energy conversion progress in future. In the study, the nitrogen reduction reaction of TM₁N₄/TM₂ embedded graphene is comprehensively investigated using density functional theory calculations. Fully considering the activity and stability, our results reveal that NiN₄/Cr anchored graphene exhibits the best catalytic activity via the enzymatic reaction pathway wherein the potential determining step is located at the first hydrogenation with an onset potential of 0.57 V, being superior to the commercial Ru-based material. Furthermore, compared with the isolated Cr atom decorated nitrogen functionalized graphene, the introduction of NiN₄ moiety decreases ΔG_max and enhances the electrocatalytic performance. According to the Mulliken charge analysis, the physical origin of the catalytic activity is ascribed to the electron transition between the supports and reaction intermediates. Overall, these results pave a way for the design of the high efficient electrode material for ammonia synthesis and provide a fundamental insight into the electrocatalysis.

Ammonia is an important chemical material that is widely used in industrial and agricultural production^{[1⇓⇓⇓-5]}. Currently, ammonia is mainly produced via the Haber- Bosch process in industry by using nitrogen and hydrogen as raw materials^[6⇓⇓-9]. In order to break the inherent inert N≡N triple bond, the Haber-Bosch process using Fe and Ru metal-based catalysts with promoters under the harsh reaction environment, leading to the heavy energy consumption and the massive CO₂ emission^{[10⇓⇓-13]}. Naturally, ammonia synthesis via nitrogen reduction reaction under mild conditions becomes an economic and eco-friendly way, which is inspired by the soybean rhizobium and bacteria nitrogenase^[14]. Based on this strategy, exploring efficient catalysts that can effectively facilitate electrochemical nitrogen reduction reaction (NRR) is desirable, however, it remains a big challenge.

Graphene has shown attractive catalytic activity due to its extraordinary electronic, thermal and mechanical properties^[15]. Considering its electron neutrality, the common strategy to activate the inert graphene is the direct introduction of the TM/N heteroatoms as the active sites. For example, Choi et al.^[4] have reported that several single atom catalysts (SACs) including TiN₄ and VN₄ embedded graphene exhibits better activity in comparison with Ru (0001) stepped surface. Furthermore, Yang et al.^[16] have reported that among varied TMN₄ embedded graphene (TM = Fe, Co, Mo, W, Ru, Rh), the MoN₄ site exhibits outstanding catalytic activity for ammonia synthesis with small reaction energy barrier of 0.67 eV. Analogously, Riyaz et al.^[17] have demonstrated that the best activity is offered by CrN₄ site among different TMN₄ (TM=Cr, Mn, Fe, Mo, Ru) embedded graphene.

Compared with single-metal atom catalysts, double atom catalysts (DACs) with synergetic interatomic interactions and flexible active sites, can maximize the potentials of catalysts, which makes the optimization of activity and selectivity feasible. They have emerged as more beneficial catalysts for electrochemical reactions. For instance, Sun et al.^[18] have revealed that VFe-N-C shows the best catalytic activity for electrochemical NRR with limiting potential of -0.36 V. Analogously, Zheng et al.^[19] have reported that only Fe/Mn-N-C catalyst is identified to be a promising candidate for NRR. The fascinating activity modification motivates our interest on the NRR reactivity catalyzed by DACs. Interestingly, Zhou et al.^[20] have successfully introduced the secondary Rh atom into the FeN₄ pre-embedded graphene experimentally and the obtained FeN₄/Rh sample delivers the superior electrocatalytic activity. Therefore, we are interested in the N₂-to-NH₃performance of TM₁N₄/TM₂ combination induced by the introduction of the second TM heteroatom into the TMN₄ pre-doping graphene. However, it has not been explored yet.

In this study, the NRR performance of the TM₁N₄/TM₂ embedded graphene is systematically investigated by density function theory calculations. According to our results, the NiN₄/Cr combination is a potential electrocatalyst for the N₂-to-NH₃ conversion. Besides, the Mulliken charge analysis identifies the electron transfer between the functional graphene and the NRR intermediates. The presented results provide a theoretical guide for the catalyst synthesis experimentally.

1 Computational method

All calculations are performed within the density functional theory (DFT) framework as implemented in DMol³ code^[21-22]. The generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) functional is employed to describe exchange-correlation interactions^[23]. The DFT Semi-core Pseudopotential (DSPP) core treat method is implemented for relativistic effects, which replaces core electrons by a single effective potential and introduces some degree of relativistic corrections into the core^[24]. The double numerical atomic orbital augmented by a polarization function (DNP) is chosen as the basis set^[21]. A smearing of 0.005 Ha (1 Ha=27.21 eV) to the orbital occupation is applied to achieve accurate electronic convergence. In the geometry structural optimization, the convergence tolerances of energy, maximum force and displacement are 1.0×10^-5 Ha, 0.02 Ha/nm and 0.0005 nm, respectively. The spin- unrestricted method is used for all calculations. A conductor-like screening model (COSMO) was used to simulate a H₂O solvent environment for all calculations^[25]. COSMO is a continuum model in which the solute molecule forms a cavity within the dielectric continuum. The DMol³/COSMO method has been generalized to periodic boundary cases. The dielectric constant is set as 78.54 for H₂O. During the geometrical optimization, the systems are free to relax.

The 4×4 supercell is an appropriate choice in the consideration of avoiding the interaction among images and reducing the cumbersome calculation^{[26⇓⇓-29]}. The 2 nm-thick vacuum is added to avoid the artificial interactions between the catalyst and its images in the Z direction. The adsorption energies (E_ads) of NRR intermediates are calculated by

(1)E_ads=E_system-E_catalyst-E_m

where E_system, E_catalyst and E_m represent the total energy of the adsorption system, the catalyst and the adsorbates, respectively.

Six proton-electron transfer steps were involved in the electrochemical NH₃ synthesis from N₂, i.e., N₂+6H⁺+ 6e^-→2NH₃. Gibbs free energy change (ΔG) of each elementary step was computed by computational hydrogen electrode model (CHE) raised by Nørskov et al., which the chemical potential of (H⁺+e^-) pairs equaled to one-half of H₂ at standard condition^[30-31]. The ΔG was determined by

(2)ΔG=ΔE+ΔZPE-TΔS+ΔG_U+ΔG_pH

where ΔE is the reaction energy analyzed directly from the DFT computations, ΔZPE and ΔS are the zero point- energy and the entropy difference at room temperature (T=298.15 K), respectively. The zero-point energies and entropies of the NRR intermediates are calculated from the vibrational frequencies according to standard methods. Following the suggestion of Wilcox, et al.^[32], the substrates are fully constrained for the frequency calculation. The term of ΔG_U=-eU corresponds to the free energy contribution caused by the variation of electrode potential. ΔG_pH is the pH correction of the free energy, which could be expressed as ΔG_pH=2.303×k_BT×pH, where k_B is the Boltzmann constant and pH is set to zero. ΔG<0 corresponds to an exothermic adsorption process vice versa. Furthermore, the onset potential was defined as the applied potential (U) required such that every step in the specified mechanism is exergonic.

2 Results and discussion

The atomic structure is illustrated in Fig.1(a). TM₁ denotes the TM atom in TMN₄ moiety and TM₂ is the secondary dopant wherein TM₁ considers Mn, Fe, Co and Ni elements according to the experimental accessibility and TM₂ screens 3d/4d/5d TM elements^[20,33-34]. For simplicity, the TM₁N₄/TM₂ embedded graphene is referred as TM₁N₄/TM₂. Fig. 1 (b) provides the screening criterion. In order to reduce the cumbersome calculations, the competition between NRR and the side hydrogen evolution reaction (HER) is firstly considered via comparing the strengths of the adsorption energies E_ads. Herein, E_ads(N₂) is greater than E_ads(H), indicating the favorable nitrogen adsorption. The preferential N₂ adsorption could suppress the adverse HER and boost the electrochemical NH₃ synthesis^[8]. Subsequently, in order to ensure the activation of N₂ molecule, the E_ads(N₂) should be stronger than -0.6 eV^[35]. Herein, the three-coordination TM₂ site is identified as the active site. The strong adsorption ability originates from the donation-back-donation mechanism that accepting the lone-pair electrons of N₂with the empty orbitals of TM site and thereby donating the occupied orbital electrons into the antibonding orbitals of N₂. The data of E_ads(N₂) and E_ads(H) are listed in Table S1- S4 in the supporting materials for clear reference. According to the mentioned consideration, there are total 55 combinations identified.

图 1.

Fig. 1. (a) Atomic structure of TM₁N₄/TM₂ and (b) screening criterion for TM₁N₄/TM₂ combination

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According to literature data, the potential determining step (PDS) of NRR is usually located at the first protonation process, the formation of NNH^[35-36]. For a quick screening, the free energy of the NNH formation (∆G_N2-NNH) is evaluated in priority. The data are presented in Fig.2 where the ∆G_N2-NNH value of the commercial Ru is added as reference since it is the optimal pure metal catalyst for the industrial process^[37]. Therein, the most exergonic step in the reduction to form ammonia on Ru(0001) is the addition of the first hydrogen atom to form NNH and the step is 1.08 eV uphill in free energy^[37].

图 2.

Fig. 2. Gibbs free energy difference between N₂ and NNH with the orange line at 1.08 eV Colorful figures are available on website

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According to the results, we focus our attention on the systems with relatively low ∆G_N2-NNH, including MnN₄/W, MnN₄/Re, FeN₄/W, FeN₄/Re, CoN₄/Re, NiN₄/Cr, NiN₄/Mo, NiN₄/Ta, NiN₄/W and NiN₄/Re. Noteworthy, it is necessary to test the stability of materials against the agglomeration of dispersible metal atoms. The thermodynamic stability of atomic distribution is evaluated via the binding energy E_b^[38]. Fig. S1 in the supporting materials reveals that E_b of NiN₄/Cr, NiN₄/Mo and NiN₄/Ta exceed the corresponding cohesive energy E_c, indicating the good resistance against clustering. According to the mentioned discussion, the potential electrode materials are identified as NiN₄/Cr, NiN₄/Mo and NiN₄/Ta. Therefore, we perform the complete free energy profiles of the NRR progress focused on the three candidates in the following discussion.

Fig. 3 shows the reaction mechanisms including distal, alternating and enzymatic mechanisms^[35,39-40]. The end- on adsorption of nitrogen molecule prefers a distal or alternating mechanism. In distal mechanism, the pair of electrons continuously attacks the nitrogen atom farthest from the catalyst's surface, releasing an ammonia molecule, which then attacks a second nitrogen atom to form another ammonia molecule. In alternating mechanism, the hydrogenation step alternates between two nitrogen atoms on the surface of the catalyst. Nitrogen molecules adsorbed by side-on manner can be reduced to ammonia by enzymatic mechanism, in which two nitrogen atoms alternately hydrogenated on the catalyst surface by proton-electron pairs and release the first ammonia molecule, thereby forming the second one. The free energy changes ΔG of the elementary steps of NiN₄/Cr, NiN₄/Mo and NiN₄/Ta are summarized in Table S5 in the supporting materials.

图 3.

Fig. 3. Schematic reaction mechanismsColorful figure is available on website

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Fig. 4 gives the free energy profile of NiN₄/Cr combination as an illustration. Wherein, the free energy of the *N₂ end-on adsorption is downhill by 0.41 eV indicating its spontaneity. In distal mechanism, the free energy of the *N-NH formation is uphill by 0.98 eV. In the second protonation step, the exothermic character of *N-NH₂ formation is observed with the ΔG of -0.28 eV. Subsequently, the release of the first NH₃ requires overcoming 0.17 eV of energy. The second *NH₃ is formed by the *N consecutive reduction where *NH, *NH₂ and *NH₃ formation is downhill trend with the ΔG of -1.08, -1.09 and -0.23 eV. Finally, desorption of the second *NH₃ is hindered by the endothermic ΔG of 1.04 eV. Noteworthy, NH₄⁺ reacted from *NH₃ protonation would be desorbed easily with aid of the solution^[4]. Therefore, the elementary step of the *NH₃ desorption is not a problematic obstacle in NRR^[41]. Herein, the PDS in the distal pathway is located at the first protonation with the ΔG_max of 0.98 eV. Analogously, ΔG of the first protonation step via the alternating mechanism is uphill by 0.98 eV. In the second protonation step, the endothermic character of *NH-NH formation is observed with the ΔG of 0.05 eV, indicating the stability of *N-NH structure. Later, an exothermic trend was found in the following protonation, with ΔG values of -0.31, -0.25, -1.29 and -0.71 eV, respectively. Herein, the PDS is also identified at the first protonation for the alternating mechanism with the same ΔG_max of 0.98 eV. Furthermore, for enzymatic mechanism, the free energy of the *N₂ side-on adsorption decreased by 0.10 eV. Subsequently, the formation of *N-*NH and *NH-*NH requires overcoming 0.57 and 0.16 eV of energy. In the following protonation process, the downhill trends are revealed by the corresponding ΔG of -0.56, -0.12, -1.51 and -0.38 eV, respectively. Herein, the PDS is located at the first protonation of *N-*NH formation with the value of 0.57 eV. In order to overcome the thermodynamic barrier, the applied U is shifted to 0.98, 0.98 and 0.57 V for distal, alternating and enzymatic mechanism, respectively. The lower onset potential corresponds to the better activity. Therefore, the preferred mechanism of NRR on NiN₄/Cr is the enzymatic pathway. Herein, it is noteworthy that our discussion is based on the abundant proton in the acid solution. However, the efficiency of aqueous NRR is complicatedly dependent on the proton supply. The proton-poor neutral/alkaline solutions are generally used to lower the proton accessibility for a suppressed HER in order to improve the NRR efficiency. On the other hand, the limited proton from water splitting also deteriorates NH₃ formation since NRR is essentially related to the hydrogenation reactions. Therefore, the variation of the NRR performance caused by different pH solution is still under the debate^[42⇓-44].

图 4.

Fig. 4. Free energy diagrams and the corresponding configuration of the NRR intermediates on NiN₄/Cr NRR mechanisms are (a) distal, (b) alternating and (c) enzymatic

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The free energy profiles of NiN₄/Mo and NiN₄/Ta are presented in Fig. S2 and Fig. S3 in the supporting materials, respectively. As for the former, the PDS are preserved at the first protonation step with the ΔG_max of 0.92, 0.92 and 0.60 eV, respectively. Therefore, NRR follows the enzymatic pathway on NiN₄/Mo with the overpotential of 0.60 V. As for the latter, the PDS is the first protonation step for the distal and alternating pathway and the ΔG_max of 0.69 eV, meanwhile the high ΔG_max is located at the *NH₂-*NH₂ formation with the value of 0.58 eV for the enzymatic pathway. However, the enzymatic pathway of NiN₄/Ta is unfavorable considering the endothermic character of the *N-*N adsorption. Therefore, the preferred mechanism of NRR on NiN₄/Ta is the distal or alternating. According to the above analysis, ∆G_max is ordered by NiN₄/Cr (0.57 eV)4/Mo (0.60 eV) < NiN₄/Ta (0.69 eV). Therefore, the mentioned candidates show outstanding activities, being promising alternatives to the commercial Ru(0001)^[37]. Furthermore, the potential determining step and the free energy change ΔG_max are summarized in Table S6. We further add the data of Cr/Mo/Ta embedded nitrogen functionalized graphene, which are from the free energy profiles in Fig. S4-S6. In comparison with Cr single- atom catalyst, NiN₄/Cr decreases the ΔG_max from 0.66 to 0.57 eV, indicating a boosted activity caused by synergetic interatomic interactions. In contrast, the combination of NiN₄/Mo as well as NiN₄/Ta inversely deteriorates the NRR efficiency due to the increased ΔG_max. Therefore, NiN₄/Cr is a promising candidate for experimental synthesis.

In order to further reveal the catalytic effect, the Mulliken charge analysis was performed. In line with previous reports^{[40,45⇓-47]}, there are three moieties, including moiety 1 (the graphene substrate), moiety 2 (active center) and moiety 3 (NRR intermediates). Fig. 5 presents the charge variation of NiN₄/Cr, NiN₄/Mo and NiN₄/Ta during the protonation steps. The charge transfer is observed between the adsorbent and the substrate, in consistent with previous reports^[45]. Besides, Fig. 5(d) monitors the N-N bond lengths of the NRR intermediates. Therein, the stretch of N-N bond is obvious, indicating that the protonation continuously activates the inert N-N bonds and leads to the energetic feasibility of the N₂-to-NH₃ conversion under the mild condition.

图 5.

Fig. 5. (a-c) Charge variation of the three moieties along the optimal pathway and (d) N-N bond length change in NRR along preferred pathwayMoieties 1, 2, 3 represent the graphene substrate, active center, and NRR intermediates, respectively

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In the end, it is noteworthy that the N vacancy would be created during the reduction environment and act as the active site, besides the transition metal site discussed above. Herein, we further consider the role of nitrogen vacancy. Fig. S7 in the supporting materials presents the corresponding free energy profiles of N₂-to-NH₃ conversion. For convenience, four different N vacancies are donated as 1N, 2N, 3N and 4N, respectively. The results reveal that the 1N and 2N sites are unable to capture N₂ molecule due to the endothermic character meanwhile the first protonation on the 4N site is energetically limited. Differently, the free energy profile of 3N site is continuously declined, demonstrating its feasibility to boost N₂-to-NH₃ conversion. Therefore, the 3N vacancy would act as an active site for ammonia synthesis. However, according to the reaction of N₄*+3(H⁺+e^-)→ N₃*+NH₃, the formation energy of 3N site is 3.70 eV. It is energy-demanding process, implying the difficulty for the vacancy formation. It stems from the strong interaction between N atom and its surrounding, as reflected by the binding energy with the value of 9.91 eV. Furthermore, Fig. S8 in the supporting materials reveals that the nitrogen atom is accessible for one hydrogen atom but it is unable to capture more hydrogen atoms. Therefore, the creation of the N vacancy via protonation steps is energetically adverse. Considering the mentioned discussion, we do not further devote our attention on the N vacancy.

3 Conclusions

In summary, the NRR performance of the TM₁N₄/TM₂ embedded graphene is systematically investigated by means of density functional theory calculation. Considering activity and stability, our results reveal that NiN₄/Cr, NiN₄/Mo and NiN₄/Ta exhibit outstanding performance toward NRR, being promising alternatives to the commercial Ru(0001). Herein, ∆G_max is ordered by NiN₄/Cr (0.57 eV)4/Mo (0.60 eV)4/Ta (0.69 eV). Besides, the Mulliken charges analysis certifies that the activation of the NRR intermediates is ascribed to the electron transfer between the graphene substrate and NRR intermediates. This study provides the potential graphene-based nanomaterial for electrocatalytic synthesis of ammonia.

8 Supporting materials

Supporting materials related to this article can be found at https://doi.org/10.15541/jim20220033.

9 Supporting Materials:

NiN₄/Cr Embedded Graphene for Electrochemical Nitrogen Fixation

WU Jing¹, YU Libing¹, LIU Shuaishuai¹, HUANG Qiuyan¹, JIANG Shanshan¹, Anton Matveev², WANG Lianli³, SONG Erhong⁴, XIAO Beibei¹

(1. School of Energy and Power Engineering, Jiangsu University of Science and Technology, Zhenjiang 212003, China; 2. National Research Ogarev Mordovia State University, Saransk 430005, Russia; 3. School of Materials Science and Engineering, Xi’an University of Science and Technology, Xi’an 710054, China; 4. The State Key Laboratory of High Performance Ceramics and Superfine Microstructure, Shanghai Institute of Ceramics, Chinese Academy of Sciences, Shanghai 200050, China)

表 1.
Adsorption energies E_ads on Mn₁N₄/TM₂ (E_ads in eV)

Table 1.
Adsorption energies E_ads on Mn₁N₄/TM₂ (E_ads in eV)

3d	Sc	Ti	V	Cr	Mn	Fe	Co	Ni
E_ads(TM₂) N₂ end-on	-0.22	-0.36	-0.62	-0.72	-1.02	-1.07	-0.89	-0.59
E_ads(TM₂) N₂ side-on	0.12	-0.02	-1.17	-0.35	-0.59	-0.51	-0.33	-0.19
E_ads(TM₂) H	0.75	0.20	-0.18	-0.14	-0.19	-0.20	-0.22	-0.38
4d	Y	Zr	Nb	Mo	Tc	Ru	Rh	Pd
E_ads(TM₂) N₂ end-on	-0.14	-0.22	-1.05	-0.70	-0.73	-0.99	-0.73	-1.30
E_ads(TM₂) N₂ side-on	-0.13	0.11	-0.42	-0.43	-0.47	-0.44	-0.25	-0.96
E_ads(TM₂) H	0.78	0.25	-0.87	-0.38	0.51	-0.11	-0.33	-1.06
5d	Lu	Hf	Ta	W	Re	Os	Ir	Pt
E_ads(TM₂) N₂ end-on	-0.21	-0.35	-0.60	-1.57	-1.23	-1.30	-1.08	-0.52
E_ads(TM₂) N₂ side-on	0.07	0.02	-0.32	-1.48	-0.88	-0.68	-0.44	-0.23
E_ads(TM₂) H	0.65	-0.01	-1.33	-0.92	-0.88	-0.81	-0.87	-0.99

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表 2.
Adsorption energies E_ads on Fe₁N₄/TM₂(E_ads in eV)

Table 2.
Adsorption energies E_ads on Fe₁N₄/TM₂(E_ads in eV)

3d	Sc	Ti	V	Cr	Mn	Fe	Co	Ni
E_ads(TM₂) N₂ end-on	-0.21	-0.75	-0.26	-0.52	-0.94	-1.06	-0.88	-0.53
E_ads(TM₂) N₂ side-on	-0.21	-0.37	-0.35	-0.41	-0.59	-0.54	-0.25	-0.56
E_ads(TM₂) H	0.93	0.33	0.27	-0.02	-0.14	-0.25	-0.11	-0.37
4d	Y	Zr	Nb	Mo	Tc	Ru	Rh	Pd
E_ads(TM₂) N₂ end-on	-0.14	-0.22	-0.20	-0.62	-0.88	-0.96	-0.76	-0.49
E_ads(TM₂) N₂ side-on	0.22	-0.20	-0.20	0.01	-0.58	-0.41	-0.27	0.01
E_ads(TM₂) H	0.90	0.21	0.17	-0.23	-0.12	-0.12	-0.09	-0.33
5d	Lu	Hf	Ta	W	Re	Os	Ir	Pt
E_ads(TM₂) N₂ end-on	-0.20	-0.31	-0.64	-0.91	-1.15	-1.27	-1.09	-0.26
E_ads(TM₂) N₂ side-on	-0.20	0.07	-0.49	-0.77	-0.94	-0.68	-0.48	0.22
E_ads(TM₂) H	0.77	0.01	-0.73	-0.84	-0.68	-0.78	-0.72	-0.99

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表 3.
Adsorption energies E_ads on Co₁N₄/TM₂ (E_ads in eV)

Table 3.
Adsorption energies E_ads on Co₁N₄/TM₂ (E_ads in eV)

3d	Sc	Ti	V	Cr	Mn	Fe	Co	Ni
E_ads(TM₂) N₂ end-on	-0.21	-0.37	-0.68	-0.84	-1.01	-1.05	-0.85	-0.46
E_ads(TM₂) N₂ side-on	-0.20	-0.37	-0.29	-0.51	-0.64	-0.53	-0.26	-0.56
E_ads(TM₂) H	1.02	0.37	-0.09	-0.08	-0.36	-0.13	-0.07	-0.28
4d	Y	Zr	Nb	Mo	Tc	Ru	Rh	Pd
E_ads(TM₂) N₂ end-on	-0.12	-0.19	-0.44	-0.61	-0.82	-0.93	-0.75	-0.48
E_ads(TM₂) N₂ side-on	-0.13	-0.20	-0.03	-0.29	-0.57	-0.42	-0.25	-0.48
E_ads(TM₂) H	1.03	0.42	-0.12	-0.22	-0.07	-0.07	-0.03	-0.26
5d	Lu	Hf	Ta	W	Re	Os	Ir	Pt
E_ads(TM₂) N₂ end-on	-0.20	-0.29	-0.62	-0.86	-1.08	-1.23	-1.07	-0.49
E_ads(TM₂) N₂ side-on	-0.21	-0.29	-0.28	-0.63	-0.89	-0.67	-0.46	-0.48
E_ads(TM₂) H	0.82	0.23	-0.50	-0.75	-0.63	-0.72	-0.69	-0.87

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表 4.
Adsorption energies E_ads on Ni₁N₄/TM₂ (E_ads in eV)

Table 4.
Adsorption energies E_ads on Ni₁N₄/TM₂ (E_ads in eV)

3d	Sc	Ti	V	Cr	Mn	Fe	Co	Ni
E_ads(TM₂) N₂ end-on	-0.21	-0.41	-0.72	-0.91	-1.04	-1.07	-0.79	-0.58
E_ads(TM₂) N₂ side-on	-0.19	0.02	-0.41	-0.63	-0.66	-0.50	/	-0.58
E_ads(TM₂) H	0.97	0.19	-0.14	-0.40	-0.23	-0.22	-0.18	-0.27
4d	Y	Zr	Nb	Mo	Tc	Ru	Rh	Pd
E_ads(TM₂) N₂ end-on	-0.12	-0.24	-0.51	-0.70	-0.91	-0.98	-0.73	-0.48
E_ads(TM₂) N₂ side-on	-0.13	-0.20	-0.23	-0.63	-0.61	-0.44	-0.21	-0.48
E_ads(TM₂) H	0.97	0.15	-0.33	-0.22	-0.12	-0.13	-0.16	-0.25
5d	Lu	Hf	Ta	W	Re	Os	Ir	Pt
E_ads(TM₂) N₂ end-on	-0.20	-0.33	-0.74	-0.98	-1.17	-1.30	-1.06	-0.65
E_ads(TM₂) N₂ side-on	-0.20	0.06	-0.49	-0.94	-0.95	-0.68	-0.41	-0.65
E_ads(TM₂) H	0.85	0.02	-0.71	-0.66	-0.69	-0.82	-0.81	-0.93

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表 5.
Free energy change ΔG (ΔG in eV), R_i stands for the i^th protonation step

Table 5.
Free energy change ΔG (ΔG in eV), R_i stands for the i^th protonation step

System	Mechanisms	N₂ adsorption	R₁	R₂	R₃	R₄	R₅	R₆	NH₃ desorption
NiN₄/Cr	Distal	-0.41	0.98	-0.28	0.17	-1.08	-1.09	-0.23	1.04
	Alternating	-0.41	0.98	0.05	-0.31	-0.25	-1.29	-0.71	1.04
	Enzymatic	-0.10	0.57	0.16	-0.56	-0.12	-1.51	-0.38	1.04
NiN₄/Mo	Distal	-0.27	0.92	-0.08	-0.22	-1.14	-0.71	-0.20	1.04
	Alternating	-0.27	0.92	0.16	-0.56	0.06	-1.52	-0.49	1.04
	Enzymatic	-0.11	0.60	0.18	-0.89	0.50	-1.54	-0.44	1.04
NiN₄/Ta	Distal	-0.18	0.69	-0.37	-0.06	-1.22	-1.02	0.22	1.04
	Alternating	-0.18	0.69	0.05	-0.88	0.11	-1.78	0.05	1.04
	Enzymatic	0.04	0.11	-0.23	-0.70	0.58	-1.70	-0.04	1.04

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表 6.
Potential determining step and its free energy change ΔG_max(ΔG_max in eV)

Table 6.
Potential determining step and its free energy change ΔG_max(ΔG_max in eV)

	Distal		Alternating		Enzymatic
	RDS	ΔG_max	RDS	ΔG_max	RDS	ΔG_max
Cr	N₂+H→NNH	1.03	N₂+H→NNH	1.03	NN+H→NNH	0.66
NiN₄/Cr	N₂+H→NNH	0.98	N₂+H→NNH	0.98	NN+H→NNH	0.57
Mo	N₂+H→NNH	1.27	N₂+H→NNH	1.27	NN+H→NNH	0.43
NiN₄/Mo	N₂+H→NNH	0.92	N₂+H→NNH	0.92	NN+H→NNH	0.60
Ta	NNH₂+H→N	0.72	N₂+H→NNH	0.66	NHNH₂+H→NH₂NH₂	0.49
NiN₄/Ta	N₂+H→NNH	0.69	N₂+H→NNH	0.69	NHNH₂+H→NH₂NH₂	0.58

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图 6.

Fig. 6. Comparison of binding energy and bulk cohesive energy of the selected complexes

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图 7.

Fig. 7. Free energy diagrams and the corresponding configuration of the NRR intermediates on NiN₄/Mo NRR mechanisms are (a) distal, (b) alternating, and (c) enzymatic, respectively

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图 8.

Fig. 8. Free energy diagrams and the corresponding configuration of the NRR intermediates on NiN₄/Ta NRR mechanisms are (a) distal, (b) alternating, and (c) enzymatic, respectively

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图 9.

Fig. 9. Free energy diagrams and the corresponding configuration of the NRR intermediates on Cr embedded nitrogen functionalized grapheneNRR mechanisms are (a) distal, (b) alternating, and (c) enzymatic, respectively

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图 10.

Fig. 10. Free energy diagrams and the corresponding configuration of the NRR intermediates on Mo embedded nitrogen functionalized grapheneNRR mechanisms are (a) distal, (b) alternating, and (c) enzymatic, respectively

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图 11.

Fig. 11. Free energy diagrams and the corresponding configuration of the NRR intermediates on Ta embedded nitrogen functionalized grapheneNRR mechanisms are (a) distal, (b) alternating, and (c) enzymatic, respectively

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图 12.

Fig. 12. Free energy profiles of N₂-to-NH₃ conversion on the N vacancy

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图 13.

Fig. 13. Atomic configurations of the hydrogen adsorption on the nitrogen embedded in graphene after geometry optimization

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1 Computational method

2 Results and discussion

3 Conclusions

8 Supporting materials

9 Supporting Materials:

吴静, 余立兵, 刘帅帅, 黄秋艳, 姜姗姗, ANTON Matveev, 王连莉, 宋二红, 肖蓓蓓. NiN4/Cr修饰的石墨烯电化学固氮电极[J]. 无机材料学报, 2022, 37(10): 1141. Jing WU, Libing YU, Shuaishuai LIU, Qiuyan HUANG, Shanshan JIANG, Matveev ANTON, Lianli WANG, Erhong SONG, Beibei XIAO. NiN₄/Cr Embedded Graphene for Electrochemical Nitrogen Fixation [J]. Journal of Inorganic Materials, 2022, 37(10): 1141.