Nitrogen (N₂) is abundant, cheap, and readily available. Although the atmosphere contains more than 78% N₂, it cannot be used or absorbed directly by humans, animals, or plants. N₂ can be consumed only as nitrogen-containing compounds that can be obtained in food and by industrial production [1]. Ammonia (NH₃) is an important nitrogen-containing compound, which is widely used in agriculture, pharmaceutical production, and other industrial processes. Currently, industrial N₂ fixation for producing NH₃ mainly relies on the Haber–Bosch process, which not only requires high energy consumption, but also generates a large number of greenhouse gases [2-5]. Therefore, the search for highly efficient and low-energy-consuming alternative catalysts has been a major focus area for researchers [6-16]. Over the years, several alternatives to the Haber–Bosch method have been developed, including chemical [6, 7], electrochemical [8-11] and photochemical routes [12-14].

Among other methods, electrochemical NRR has been extensively studied (ideally at room temperature) in recent years as a green technology for NH₃ production. Compared with the traditional Haber–Bosch process, electrochemical NRR technology has many advantages, such as the use of renewable resources, moderate reaction conditions, and low equipment costs. This process is also fuelled by water rather than fossil fuels. However, due to the intrinsically inert properties of N₂, its cleavage and reduction under ambient conditions presents several challenges. For example, (1) N₂ has negative electron affinity (−1.8 eV) and high ionisation potential (15.85 eV), which can reduce its reactivity, (2) N≡N bond dissociation is difficult because of the high total bond energy (941 kJ/mol) and the thermodynamically high energy (410 kJ/mol) required for cleavage of the first bond, and (3) the large HOMO–LUMO energy gap (10.82 eV) is not favourable for electron transfer [17-19]. Therefore, it is necessary to use catalysts to weaken the bond energy of N₂ and reduce the activation energy to achieve high efficiency and low energy consumption during NH₃ synthesis. For this reason, the NRR process still poses great challenges for researchers and demands highly efficient electrocatalysts [20, 21]. The key factors governing the performance of electrochemical catalysts are as follows: (1) N₂ adsorption and NH₃ desorption on the catalyst; (2) the competitive relationship between the NRR and hydrogen evolution reaction (HER); and (3) the high equilibrium potential (−3.2 V in theory). Therefore, the design of novel and efficient electrocatalysts is a major technical challenge facing the scientific community. To date, many kinds of electrocatalysts for the NRR have been designed both theoretically and experimentally [22-47], especially transition metal (TM)-based catalysts [28-35, 40], which have been studied extensively in recent years.

It is well known that the chemisorption of N₂ molecules onto the active centres, and subsequent activation with electrons transferred from the catalysts, are considered prerequisite steps for the NRR. The good reduction capability of TMs is commonly attributed to the combination of filled and empty d orbitals in their electronic structure. TM atoms have empty d orbitals to accept the lone-pair electrons from the N₂ molecule, while simultaneously donating d electrons back to the antibonding π^* orbitals of N₂ to weaken the N≡N triple bond. Recently, various traditional TM electrocatalysts have been reported to be effective for the NRR. Many studies have reported that Fe is one of the most active TM catalysts for electrochemical synthesis of NH₃. In 2017, Zhao et al. synthesized several metal-organic frameworks (MOFs) using a hydrothermal process. The prepared MOFs exhibited excellent catalytic activity for electrochemical NH₃ synthesis at low temperatures and ambient pressure. Among these, the MOF (Fe) displayed the best catalytic activity; the highest NH₃ formation rate and the highest current efficiency were 2.12 × 10⁻⁹ mol s⁻¹ cm⁻² and 1.43%, respectively, at 1.2 V and 90 ℃, when using pure N₂ and H₂O as raw materials [33]. Chen et al. studied Fe₂O₃ supported on carbon nanotubes (CNTs) as the catalyst, using which a rate of NH₃ formation of 2.2 × 10⁻³ g m⁻² h⁻¹ was obtained at room temperature and atmospheric pressure with a flow of N₂ gas and an applied potential of 2.0 V. Their results also indicated that the active sites in NH₃ electrocatalytic synthesis may be associated with specific carbon sites formed at the interface between Fe particles and CNT. These were able to activate N₂, making it more reactive towards hydrogenation [34]. Du et al. revealed that the NRR process can proceed preferentially with Fe in the presence of S, and the conversion of ^*NH₂ to ^*NH₃ was the potential-determining step, with an energy barrier of 0.45 eV according to density functional theory (DFT) calculations [35].

Interestingly, the non-metal B-based molecular catalyst also reacted favourably with N₂. Notably, sp³-hybridised B also contains both occupied and empty orbitals, indicating its potential for N₂ fixation. More importantly, sp³-hybridised B can bind N₂ through a side-on pattern due to the compatibility of the orbitals [26, 27, 37-40]. For example, Ji et al. concluded that a boron-interstitial (Bint)-doped C₂N layer can act as a metal-free electrocatalyst for N₂ fixation and reduction to NH₃ after performing extensive DFT computations. Their computations revealed that the Bint-doped C₂N layer could sufficiently activate the N₂ molecule via the "acceptance-donation" process due to its significant positive charge and the magnetic moment of the B dopant [26]. Liu et al. reported boron sheets doped with single Ru atoms exhibited outstanding catalytic activity for NH₃ synthesis under ambient conditions via the distal reaction pathway, with a small activation barrier (0.42 eV) [27]. Qiu et al. fabricated a B₄C nanosheet, which could be utilized as a superior metal-free electrocatalyst for the NRR with excellent selectivity at room temperature and ambient pressure [39]. These studies highlight the value of B as a substrate for the design of highly efficient electrocatalysts for the NRR. In summary, Fe is one of the most active metal catalysts and B forms a strong bond with N₂. Therefore, Fe and B can be used in combination to form a new electrocatalyst, which can achieve high stability and high loading of active sites simultaneously. Despite the high N₂ fixation capacity of Fe-B electrocatalysts, only a limited number have been reported. To our knowledge, only Li et al. have explored FeB, FeB₂, FeB₆ (alpha), and FeB₆ (beta) as potential NRR catalysts under the framework of DFT. Their results revealed that FeB₆ (beta) offered the best performance in terms of the lowest maximum energy required for the elementary steps (0.68 eV) [40]. Due to a gap in the literature regarding Fe-B electrocatalysts, we will design a new Fe-B electrocatalyst and study the NRR in the hope of achieving an improved catalytic effect.

In this study, we explore the potential of Fe₂B₂ as an NRR electrocatalyst using DFT. The theoretical calculations not only facilitate the exploration of efficient catalysts and predict trends in chemical reaction rates, but also provide an emerging understanding of the mechanisms and allow interpretation of experimental data with mechanistic insights and structure-reactivity correlations. Herein, our results demonstrate that the enzymatic mechanism is the most favourable NRR pathway of those tested, because it provides a lower limiting potential (−0.44 V), lower free energy (only 0.02 eV) of the first step hydrogenation reaction (^*N–N to ^*NH–N), and more electron transfer from Fe₂B₂ to the reaction species. In addition, both vacancies and dopants can assist in reducing the energy barrier of the potential-determining step. This indicates that Fe-B catalysts have superior qualities which can enhance NRR via enzymatic pathways.

All the calculations are performed using spin-polarized DFT with the projected augmented wave (PAW) formalism, using the Vienna Ab initio Simulation Package (VASP) [48-51]. Electronic exchange and correlation effects are described by the generalized gradient approximation (GGA) as given by the Perdew, Burke, and Ernzerhof (PBE) equation. The cut-off energy for the plane-wave basis set is assumed to be 500 eV. The Brillouin-zone integration is conducted using a 5 × 5 × 1 Monkhorst-Pack grid. The convergence of the total energy is calculated to an accuracy of 10⁻⁵ eV and the Fermi smearing of the electronic levels is calculated using a width of 0.02 eV/Å. The Fe₂B₂ comprises a 2 × 2 supercell containing eight Fe and eight B atoms. A vacuum space exceeding 20 Å is employed to avoid interaction between two periodic units. The free NRR species are simulated using a unit cell with the dimensions 10 × 10 × 10 ų. During the geometry optimisation, all atoms are allowed to relax.

The adsorption energy, E_ad, which measures the stability of the adsorption configurations, is defined as (Eq. 1):

(1)

where E_T, E_Fe2B2 and E_species are the total energies of the adsorption system, Fe₂B₂ catalyst, and free NRR species, respectively. With this definition, a negative value indicates that the adsorption systems are energetically exothermic. The computational hydrogen electrode model [52] was used to calculate the free energy change (ΔG) in each of the reaction steps as follows (Eq. 2):

(2)

where ΔE is obtained directly from DFT calculations, ΔZPE is the zero-point energy correction, and TΔS is the entropy change at room temperature (T = 298.15 K). ΔG_U is the contribution of electrode potential (U) to ΔG. ΔG_pH = k_BT × ln10 × pH, where k_B is the Boltzmann constant, T = 298.15 K and pH = 0 for the acid medium. The free energy of (H⁺ + e⁻) at standard conditions is assumed to be the energy of 1/2 H₂ according to a computational hydrogen electrode model.

To catalyse the NRR, N₂ molecules must be adsorbed on the catalyst surface; this is a prerequisite for initializing the NRR. The possible sites for adsorption of N₂ on Fe₂B₂, include the top sites on Fe/B (T_Fe and T_B), the hollow site on Fe/B (H_Fe and H_B), and the bridge sites on Fe-B (T_Fe-T_B for B₁ and T_Fe-H_B for B₂) (Fig. 1a). Considering all forms of adsorption, including all end-on and side-on configurations, there are twelve adsorption sites. After optimisation, the most stable adsorption site is found to be the T_Fe site with end-on and side-on configurations (Fig. S1 in Supporting information). Through the adsorption energy calculation, we find that the end-on configuration (−1.107 eV) is more stable than the side-on configuration (−0.222 eV) with ΔE_ad = 0.885 eV. For both end-on and side-on configurations, the N-N bond distance after adsorption of N₂ is elongated to 1.133 and 1.148 Å for end-on and side-on configurations, respectively, compared with 1.092 Å for free N₂ gas, leading to the activation of the adsorbed N₂ molecule. This happens because the charge transferred from Fe₂B₂ to N₂ occupies the anti-bonding 2π^* orbital of N₂, lengthening the N-N bond. To gain more insight into the bonding nature and stability of Fe₂B₂, we plotted the partial density of states (PDOS), (Fig. 1b). The PDOS can not only reflect the distribution of electrons in each orbital, but also reveal the interaction between atoms and the information of chemical bonds. Fig. 1b demonstrates that the PDOS crosses the Fermi level, which indicates that Fe₂B₂ belongs to the metal system. In addition, there are two peaks on two sides of the Fermi level, and the relative width between the two peaks further demonstrates the high stability of Fe₂B₂ system. During the NRR, the high stability of Fe₂B₂ can also ensure an improved catalytic reaction.

In general, there are three possible reaction pathways in the NRR process, the distal and alternating reaction pathways that involve end-on configurations and the enzymatic reaction pathway, which uses a side-on configuration (Fig. S2 in Supporting information). All possible adsorption structures of the various reaction species on Fe₂B₂ involved in the NRR mechanism have been studied; they include: ^*N₂, ^*N=NH, ^*NH=NH, ^*NH–NH₂, ^*NH₂–NH₂, ^*NH₂–NH₃, ^*N=NH₂, ^*N, ^*NH, ^*NH₂ and ^*NH₃. The bond length and the calculated adsorption energy (E_ad) for each species on Fe₂B₂ are listed in Table 1. In the following sections, we will describe these reaction pathways in detail.

The electron pairs alternately attack two N atoms with the alternating mechanism. Our optimised structures of the reaction species are shown in Fig. 2a and the bond lengths are listed in Table 1. Generally, the bond length represents bonding stability. The more electrons participating in the bonding, the shorter the bond length is. Overall, the Fe-N bond length increased as the hydrogenation proceeded. However, there are exceptions with ^*NH=NH and ^*NH₂, such as when ^*NH=NH reacts with the side-on configuration and NH₂ adsorbs on the H_Fe site. Next, to evaluate the structural stability of various reaction species on Fe₂B₂, we have calculated the corresponding adsorption energy (Table 1). The adsorption energy reflects the strength of adsorption. Eq. 1 represents the positive correlation between the absolute value of adsorption energy and the strength of the interaction force, which is also an indicator of the stability of the system. As shown in Table 1, the adsorption energy is negative, and the absolute value is greater than 1 eV, which suggests that the reaction species are chemisorbed on Fe₂B₂ and have high stability. The NRR activity is further examined by Gibbs free energy profiles. Finally, we plotted the free energy (ΔG) (Fig. 2b). The highest energy barrier (ΔG_max), viz. the barrier for the potential-determining step (PDS), determines the thermodynamic feasibility of the electrocatalytic process. As depicted in Fig. 2b, despite the effective adsorption of N₂ on Fe₂B₂ with a negative ΔG value (−0.61 eV), the first hydrogenation step is very difficult due to the weak N₂H binding, requiring a high energy input (ΔG = 1.26 eV) for ^*N₂ → ^*N₂H (^*N–N + H⁺ + e⁻ = ^*N–NH). This is the PDS and the corresponding limiting potential is as high as −1.26 V.

In contrast to the alternating mechanism, the electron pairs attack one N atom preferentially to produce NH₃, followed by the other N atom in the case of the distal mechanism. Figs. 3a and b display the optimised structures of reaction species and the distal mechanism free energy diagrams. The corresponding bond lengths and adsorption energy are summarised in Table 1. The data for adsorption energy and bond length for the adsorption of various species on Fe₂B₂ demonstrates that the absolute value of adsorption energy is highest (−4.229 eV) for the N atom and the bond length is shortest for Fe-N (1.557 Å). In addition, we observed that the distal mechanism results in a higher adsorption energy and shorter bond length than the alternating mechanism for the steps where the two methods differ from one another. This indicates that the adsorption process is more stable when using the distal mechanism. We also analysed the whole hydrogenation process. The results reveal that the first step (^*N–N + H⁺ + e⁻ = ^*N–NH) and second step (^*N–NH + H⁺ + e⁻ = ^*N–NH₂) are endothermic and the rest of the hydrogenation steps are exothermic. However, the first hydrogenation step with the free energy of 1.26 eV is still the PDS. Therefore, the efficiency of the NRR on Fe₂B₂ via the alternating or distal mechanism is very low.

In the enzymatic mechanism, N₂ can adsorb on Fe₂B₂ through the side-on configuration, and subsequently two N atoms are hydrogenated alternately. The second NH₃ molecule will be released immediately following the generation of the first one. From the change in adsorption energy and bond length (Table 1), we concluded that shorter bond length corresponds to stronger adsorption energy. Figs. 4a and b show the optimised structures of the reaction species and the corresponding free energy diagrams. Based on the calculated free energy of each elementary step, our results reveal that the hydrogenation of ^*N–^*NH to ^*NH–^*NH (^*N–^*NH + H⁺ + e⁻ = ^*NH–^*NH) is the PDS with the most positive free energy change (ΔG = 0.44 eV). Thus, the limiting potential of the whole process is −0.44 V, which is much lower than that for the alternating and distal mechanisms (−1.26 V). Thus, once an extra potential of U = −0.44 V is applied to eliminate the PDS barrier, the whole NRR process becomes energetically preferable. Although the configuration with the N₂ adsorbed side-on is less stable than the end-on configuration, the free energy of the first hydrogenation step (^*N–^*N + H⁺ + e⁻ = ^*N–^*NH) is only 0.02 eV, which is far lower than the free energy values for the alternating and distal mechanism (1.26 eV). The subsequent steps are all exothermic. Previous DFT studies have revealed that the first hydrogenation step for generating or binding ^*N₂H is the most important for the entire NRR process [53-55]. Therefore, the catalytic activity of the electrocatalyst depends on the strength of N₂ adsorption and the difficulty of ^*N₂H formation. This conclusion is consistent with those derived from previous results [26]. The above results reveal that the free energy for the Fe₂B₂ catalytic reaction via the enzymatic mechanism is lower than that of FeB₆ (beta) (ΔG = 0.68 eV) [40] and close to that of Ru atom doped boron sheets (ΔG = 0.42 eV) [27], suggesting that Fe₂B₂ is a promising catalyst for the NRR.

To explore the binding nature of the NRR mechanism, we have performed Bader charge analyses [56]. As shown in Figs. 5a-c, all the reaction species are negatively charged due to the high electronegativity of the N atom. The amounts of charge transfer are 0.354e and 0.331e for N₂ adsorbed with end-on and side-on configurations, respectively. We also plotted the charge difference density diagram, which can be used to analyse the bonding properties and the orbital properties of the electron cloud. The charge accumulation (yellow) is distributed around two N atoms and Fe-N bonds, while the charge depletion (cyan) is distributed around the N-N bonds and the bonded surface metal atoms could be observed in two adsorption configurations (Fig. S3 in Supporting information). This conclusion supports our calculation results. The charge transfer revealed that 0.331e is injected into ^*N₂, which effectively activated ^*N₂. In addition, due to the formation of the Fe-N bond, the separated electrons in the Fe atoms are donated into the anti-bonding orbital, forming an electron transfer route that weakened the N≡N bond and made the subsequent hydrogenation easier. Generally speaking, more charge transfer corresponds to larger adsorption energy. Although our charge transfer and adsorption energy results do not completely conform to a linear relationship, the results do support a weak positive correlation between charge transfer and adsorption energy. Based on the information in Table 1 and Fig. 5, it can be concluded that strong adsorption indicated larger adsorption energy and more charge transfer. The results are as follows: −2.390 eV and 0.493e of ^*NH-NH@Fe₂B₂ for the alternating mechanism; −4.229 eV and 0.564e of ^*N@Fe₂B₂ for the distal mechanism; −2.522 eV and 0.848e of ^*NH₂-^*NH₂@Fe₂B₂ for the enzymatic mechanism. Previous studies have reported that the donated electrons reduced the strength of the N≡N triple bond and the energy barrier of the PDS of hydrogenation [9, 10]; this supports our calculated results, indicating that there is more charge transfer using the enzymatic mechanism. For example, the ^*N₂H gained more electrons via the enzymatic mechanism than with any of the other two mechanisms, and these extra donated electrons are further transmitted into the antibonding orbital of ^*N₂H to strengthen the ^*N₂H binding, leading to a lower free energy (0.02 eV). Thus, the substantial electron transfer should significantly improve the electronic transport properties, which can improve the catalytic activity.

Upon adsorption of all the reaction species, the total magnetic moment is significantly reduced by 1–2 μ_B, the decline is more than 2 μ_B for some species. The magnetic moment is mostly influenced by the d orbitals of Fe atoms, which are not filled with electrons. Therefore, the main reason for the reduction of total magnetic moment is that the empty d orbitals in the Fe atoms could receive the lone-pair electrons of N₂, which led to a decrease in the number of unpaired electrons in Fe atoms after adsorption. Finally, we compared the relationship between charge transfer and magnetic moment. Generally, greater charge transfer between atoms corresponds to more distinct orbital hybridisation, implying that the charge transfer and orbital hybridisation affect the magnetic moment of the entire system. In our calculation, considering the end-on configuration using either the alternating or distal mechanism, the charge transfer is indirectly proportional to the magnetic moment, which means that the two curves in Figs. 5a and b display opposing trends. In contrast to the end-on configuration, more charge transfer do not result in significant reduction in magnetic moment for the side-on configuration of the enzymatic mechanism. This can be attributed to the different adsorption site and the relatively lower limiting potential.

In summary, we have identified that the first hydrogenation step for generating ^*N₂H is key, and we have elucidated the PDS for the entire NRR process via the alternating and distal mechanisms. However, these mechanisms possess very large ΔG values (^*N–N + H⁺ + e⁻ = ^*N–NH) (1.26 eV); hence, it is difficult to bind ^*N₂H. In order to solve this problem, we attempted to change the catalyst, by introducing defects or doping heteroatoms. Effective use of vacancies is considered to be one of the most effective defect strategies to improve catalytic behaviours in the NRR [57]. It has been revealed that the presence of various vacancies can effectively regulate the intrinsic properties including the electronic structure, charge transport, and surface adsorption capacity [58, 59]. Consequently, we can remove the B atom nearest to the T_Fe atom on the surface of Fe₂B₂ to form a B vacancy and calculate the free energy for generating ^*N₂H (^*N-N + H⁺ + e^- = ^*N-NH). ΔG =1.01 eV indicates that the free energy barrier is reduced by 0.25 eV due to the B-vacancy (Fig. S4a in Supporting information). In addition, doping with a heteroatom is considered another effective approach to tailor electronic structures, reduce the reaction barrier, and modify chemical composition of catalysts [60-62]. We chose Al, Ga, and In to act as heteroatoms; they all belong to the same main group as B. It is well known that the atomic number, the number of electron layers, the atomic radius, the ease of electron loss and the metallicity of elements for the same group increase gradually from top to bottom. Increasing ease of electron loss played a positive role in weakening the N≡N triple bond, and this can help to reduce the ΔG by 0.26 eV, 0.06 eV and 0.10 eV after doping with Al, Ga and In, respectively (Figs. S4b-d in Supporting information).

Furthermore, the change in N-N bond length could also indicate the activation degree of N₂. The N-N bond length of N₂ and N₂H adsorbed on pristine, defective, and doped Fe₂B₂ are summarised in Table S1 (Supporting information). These data indicated that the N-N bonds are all stretched due to the introduction of vacancies and dopants, illustrating that N-N bonds are activated more effectively. Especially in the case of Al doping, the N-N bond length is elongated to 1.254 Å, consistent with the lower free energy barrier of 1.00 eV (Fig. S4b). Accordingly, these vacancies and dopants help improve the catalytic activity, which opened up new opportunities for us to design and develop highly efficient and highly selective catalysts for NRR under ambient conditions. In future, we will study and report the effects of vacancies and dopants in detail.

In conclusion, we have performed first-principles calculations to systematically investigate the catalytic performance of Fe₂B₂. The following results demonstrate that the enzymatic mechanism is more favourable: (1) The limiting potential of −0.44 V; (2) the lower free energy (only 0.02 eV) of the first hydrogenation step (^*N–N + H⁺ + e⁻ = ^*N–^*NH); and (3) the increased electron transfer for the whole NRR process. Therefore, efficient and stable electrocatalysts of Fe₂B₂ can promote N₂ adsorption and accelerate electron transfer using an enzymatic mechanism to activate the NRR with a low free energy. In addition, considering all the reaction species adsorption, the total magnetic moment is significantly reduced by 1–2 μ_B, the decline range of some species is more than 2 μ_B. Both vacancies and dopants can be helpful to reduce the reaction energy barrier of the potential-determining step. We also hope that the insights obtained from this theoretical study offer guidance for the design of new and efficient electrocatalysts for the NRR.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

The authors thank the National Natural Science Foundation of China for financial support (Nos. 21603109, 11904081 and 21876104). This research is also supported by Henan Joint Funds of the National Natural Science Foundation of China (No. U1404216), the Special Fund of Tianshui Normal University, China (No. CXJ2020-08), the Scientific Research Program Funded by Shaanxi Provincial Education Department (No. 20JK0676).

Appendix A. Supplementary data

Supplementary material related to this article can be found, in the online version, at doi:https://doi.org/10.1016/j.cclet.2021.02.043.