Theoretical insights into the electroreduction mechanism of N₂ to NH₃ from an improved Au(111)/H₂O interface model

Abstract

An improved H coverage-dependent Au(111)/H₂O electrochemical interface model is proposed in this paper, which is firstly used to study electroreduction mechanisms of N₂ into NH₃ at the thermodynamical equilibrium potential in cooperation with electronic structure analysis. The results show that the associative mechanism is more favorable on Au(111) and therein alternating and distal pathways may be able to parallelly occur in gas phase and the present simulated electrochemical interface. The initial N₂ reduction into the N₂H intermediate is the rate determining step, which may be able to be regarded as the origin of the observed experimentally high overpotential during N₂ electroreduction. The presence of an electrochemical environment can significantly change the N₂ reduction pathway and decrease the barrier of the rate determining step, which can be ascribed to the significant electron accumulation and interaction between N₂ molecules and H₂O clusters. The theoretical results display excellent consistency with the available experimental data, confirming the rationality of the present proposed electrochemical model. The comparison of the barrier between the hydrogen evolution reaction and rate determining step well explains why the activity of Au electrodes is usually unsatisfactory. Accordingly, a single descriptor can be proposed, in which an ideal electrocatalyst should be able to reduce the barrier for initial N₂ electroreduction into N₂H. In this way, N₂ electroreduction pathways can be facilitated and the yield of NH₃ can be enhanced. We believe that the present study can represent progress to study N₂ electroreduction mechanisms from an improved electrochemical model.

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1. Introduction

NH₃ as a promising carbon-free alternative energy carrier can be employed in fertilizers, production of important chemicals, NH₃ fuel cells and indirectly hydrogen fuel cells.^1–3 At present, NH₃ is synthesized primarily by reaction of N₂ with H₂ on an Fe/Ru-based catalyst through the industrial Haber–Bosch (HB) process under harsh conditions such as high temperatures and pressures,^4,5 which is an energy intensive chemical process and consumes ca. 2% of annual global energy because of the stability and chemical inertness of N₂ molecule.^6–8 By contrast, the electrochemical reduction of N₂ into NH₃ with proton and electron transfer in an aqueous environment is more energy efficient and attracts extensive interest in recent years since it can be operated at ambient conditions and powered by renewable electricity.^9–14 Unfortunately, the required large overpotential and competing hydrogen evolution reaction lead to low faradaic efficiency and poor selectivity for N₂ electroreduction into NH₃ on most electrocatalysts, thus impeding its practical applications.^15–18 The poor activity of the cathode electrocatalyst may put a major limitation on production of NH₃ product in significant yields at ambient conditions. To achieve the rational design of more selective and active electrocatalysts, the system understanding on electroreduction mechanism of N₂ into NH₃ is extremely urgent and essential.

Although tremendous efforts in recent years, N₂ electroreduction mechanism remains elusive. The present most studies on N₂ electroreduction reaction primarily focus on the synthesis of electrocatalysts including metals such as Pt, Ru, Fe, Au, Pd, Rh, Fe, Ni, Mo and Bi,^19–30 alloys such as Pt–Ru,³¹ metal nitrides and sulfides,^32,33 and carbon-based materials.^34–38 However, these reported electrocatalysts suffer from low NH₃ faradaic efficiency and N₂ electroreduction reaction is still plagued. Based on these previous studies, the development of more active and selective electrocatalysts is highly desired but remains challenging. Study of N₂ electroreduction reaction mechanism will help design electrocatalysts with high activity and selectivity. In the most recent reviews from Shao et al. and Zhang et al.,^39,40 N₂ electroreduction mechanisms and reaction intermediates that obtained in experiments by various spectroscopy techniques are summarized. Currently, it is generally accepted that there are two main reaction mechanisms for N₂ electroreduction into NH₃, namely, dissociative pathways and associative pathways. N≡N bond in N₂ molecule is broken to form N atoms on electrocatalyst surface before hydrogenation in dissociative mechanism, whereas the hydrogenation of N₂ molecule occurs before N≡N bond is broken in associative mechanism. It is currently believed that the dissociative mechanism is dominant in the HB process of N₂ reduction into NH₃.^15,41 An associative distal or alternating mechanism may be followed during N₂ electroreduction into NH₃ through experimental identification of some intermediates. For example, using surface-enhanced infrared absorption spectroscopy, Shao et al., studied for the first time N₂ electrochemical reduction reaction mechanism on Au thin film, in which the adsorbed N₂H_y (1 ≤ y ≤ 4) species was detected at potentials below 0 V (vs. RHE),⁴² thus indicating that N₂ electroreduction may follow the associative alternating and distal mechanisms on Au surface. Combing surface-enhanced infrared absorption spectroscopy with electrochemical measurements, the adsorbed N₂H_x (0 ≤ x ≤ 2) species was detected at potentials below 0.2 V (vs. RHE) on Ru thin film in the subsequent study from Shao et al., and notably increased coverage of N₂H_x was observed as the potential decreasing from 0.2 to −0.4 V, thus the associative distal mechanism may be able be concluded.²⁰ By performing isotope-labelled experiments, Yin et al., found only a trace amount of N₂H₄ intermediate during N₂ electroreduction on bismuth surface, suggesting that associative distal mechanism may be more favorable.³⁰ Despite of understanding of N₂ electroreduction reaction mechanism is of importance for rationally designing more efficient electrocatalysts, the experimental studies are very rare at present in this area since low selectivity makes experimental determination of mechanism rather difficult.

Because of the experimental limitations to identify intermediates and complexity of N₂ electroreduction process involving 6 elementary reaction steps, theoretical calculations have become a powerful tool for studying electrocatalytic reactions by employing density functional theory (DFT).^43,44 DFT calculations can give mechanistic information that is not accessible based on experiments alone and identify favored reaction intermediates. Theoretical work by Skúlason et al. and Montoya et al. thermodynamically indicated that the associative distal mechanism would be more favorable since more positive reaction free energies are expected for the associative alternating mechanism by combining DFT calculations with the computational hydrogen electrode model.^15,45 Their findings had shown that the potential limiting step is N₂ reductive protonation to the adsorbed N₂H species on the transition metal surface with relatively weak N adsorption such as Pt, Pd, Ag, Au, Ni, Co and Ru during N₂ electroreduction into NH₃, whereas the potential limiting step is determined by the protonation of the adsorbed NH into NH₂ species for more reactive transition metals, such as Mo. On the basis of DFT-based computational hydrogen electrode model, the electrocatalytic activity of various binary transition metals are systematically examined in recent theoretical work from Zhao et al.,⁴⁶ and the binary FeRh catalyst was thought to have the optimal catalytic performance due to its lowest limiting potential and best suppressing effect on hydrogen evolution reaction during N₂ electroreduction reaction. Furthermore, their study indicated that N₂ reduction reaction prefers to proceed through associative distal mechanisms than alternating pathways on the FeRh catalyst. These above theoretical studies assumed that activation barriers of reaction pathways is related with reaction free energies on different transition metal surfaces and only considered various elementary step thermodynamics, whereas the potential-dependent kinetic barriers that predicting catalytic activity were not further calculated. Most recently, Janik et al. calculated explicitly the potential-dependent activation barriers for elementary electroreduction reactions included in associative distal and alternating pathways during N₂ electroreduction using their previously developed method,^47–49 and concluded that the alternating mechanism by direct surface hydrogenation may be more favorable on late transition metals due to smaller barriers at 0 V (vs. RHE),^50,51 in which N₂ electroreduction into N₂H species is rate determining step of overall reaction. However, despite various theoretical efforts, N₂ electroreduction mechanisms are still not systematically understood and mechanistic inconsistencies remain exist. Furthermore, the key factor such as solvent effect was not included in previous theoretical studies on N₂ electroreduction mechanisms. Thus, the modeling of electrocatalytic reaction systems occurred at the complex electrode/aqueous interfaces remains a subject of ongoing discussion.

In the present paper, Au electrocatalyst is selected due to its excellent durability, relatively high faradaic efficiency and low hydrogen evolution reaction activity in N₂ electroreduction. Furthermore, electrocatalytic N₂ reduction reaction on the Au surface is indeed possible under ambient conditions.^25,52 Our previous validated explicit solvation model with two relaxed H₂O bilayer structure is employed to simulate solvent effect,^53–55 which allows us to better model the interactions among adsorbates, surface and solvents and determine the kinetic barriers for various elementary reaction steps. Thus, an improve H coverage-dependent Au(111)/H₂O electrochemical interface model is proposed, by which the electroreduction mechanisms of N₂ into NH₃ can be identified. Simultaneously, solvation effect on N₂ reduction mechanisms is also considered in this work. Our present used model is differentiated from previous theoretical work on N₂ electroreduction into NH₃. The available experimental results on Au electrodes will be used to examine whether the currently employed computational model is enough accurate by comparing with our present theoretical study.

2. H coverage-dependent Au(111)/H₂O interface model

2.1 Determination method of equilibrium potentials

Surface and solvation model, and computational parameters included in computational details have been represented in detail in ESI (see Fig. S1).† It is known that the hydrogen evolution reaction and proton-coupled electron transfer usually occur during N₂ electroreduction on the Au electrodes, thereby the surface adsorbed H atoms as the intermediate may be involved.^24,25,53 Moreover, the difference of electrostatic potential in electric double layer can be controlled and adjusted by changing number of the surface adsorbed H atoms.^56–58 Thus, the H coverage-dependent equilibrium potentials can be determined and potential-dependent N₂ electroreduction mechanisms can be speculated. The surface adsorbed H atom can be formed during N₂ electroreduction by following eqn (1):

H⁺ + e⁻ → ½H₂ → H* (1)

At different H coverage conditions, the Gibbs free energy of eqn (1), ΔG(θ) can be calculated by eqn (2) on the basis of the methodology proposed by Nørskov et al., Chen et al. and Strasser et al. for oxygen reduction, hydrogen evolution and CO₂ electrochemical reduction reactions,^56,59–63 in which ΔE(θ), ΔS(θ), ΔZPE and k_BT ln(θ/1 − θ) represent the differential adsorption energy of surface adsorbed H atoms, entropy change, zero-point energy change and the contributions of configuration entropy to ΔG(θ), respectively. Herein, coverage θ = n/N, in which n is the number of surface adsorbed H atoms and N is the total number of surface Au atoms. Thus, the H coverage-dependent equilibrium potential U (vs. RHE) can be determined at Au(111)/H₂O interface when the Gibbs free energy, ΔG(θ) is equal with zero.

ΔG(θ) = ΔE(θ) + eU − TΔS(θ) + ΔZPE + k_BT ln(θ/1 − θ) (2)

According to eqn (3), the differential adsorption energy of surface adsorbed H atoms, ΔE(θ) can be calculated, where is the total energy of the Au surface with different coverage of adsorbed H atoms.

The contributions from ZPE and entropy changes together to ΔG(θ) are estimated to be ca. 0.24 eV at standard temperature (298 K) based on the available data from previous literature.⁶⁴ Therefore, combining eqn (2) with eqn (3), the eqn (4) can be obtained. The values of and is directly available via DFT calculations. A series of values of can be calculated by changing the coverage of surface adsorbed H atoms on Au(111). At the different coverages, the values of ΔE(θ) can be obtained by differentiating the plots of against θ on the basis of eqn (3).

2.2 Relationship between H coverage and equilibrium potentials

In the present study, we consider various possible surface adsorption configurations of H atoms and coverage dependence. It is observed that H atoms prefer to adsorb at 3-fold face-centered cubic hollow (fcc) sites on Au(111) so that they can stay away from each other in order to minimize the repulsive reactions when H coverage (θ_H) is below and equal with 1 monolayer (ML) (see Fig. S2†). The coverages of H atoms above 1 ML are not further analyzed on Au(111) because of the observed spontaneous formations of hydrate proton by adsorbed H atoms with adjacent H₂O molecules caused by strong repulsive interactions among adsorbed H atoms. Fig. 1(a) exhibits a reasonable polynomial relationship between the differential adsorption energy of surface adsorbed H atoms, ΔE(θ) and θ_H, indicating that the Langmuir adsorption isotherms may be followed on Au(111). Thereby, ΔE(θ) can be calculated at any θ_H through polynomial fitting of ΔE(θ) ∼ θ_H data. We can calculated the equilibrium potentials (U) based on the eqn (4) at any θ_H and then the polynomial relationships between θ_H and U can be obtained on Au(111). It is found that the more negative equilibrium potentials can be obtained with the increasing H coverage, as shown in Fig. 1(b). In fact, the previous theoretical study from Skúlason et al. also showed that most surfaces will be fully covered with the adsorbed H atoms at more negative electrode potentials,⁵⁶ confirming the reasonability of our present proposed H coverage-dependent Au(111)/H₂O electrochemical interface model to some degree. The equilibrium potential is calculated as ca. −0.22 V (vs. RHE) when θ_H is equal with zero based on the polynomial relationship between θ_H and U, which is the closest to the thermodynamical value of ca. −0.06 V (vs. RHE) for N₂ electroreduction under ambient conditions,²⁰ thus being regarded as the thermodynamical equilibrium potential. Our present study will focus on the electroreduction mechanisms of N₂ into NH₃ at the thermodynamical required equilibrium potential with the aim of applying the present proposed H coverage-dependent Au(111)/H₂O interface model. The mechanistic understanding on N₂ electroreduction can provide scientific guideline for rational design of efficient electrocatalysts. The potential-dependent N₂ electroreduction mechanisms will be further studied in our future work.

Fig. 1 (a) The relationship between the differential adsorption energy of H atoms and H coverage (θ_H), ΔE(θ); (b) the relationship between the calculated equilibrium potentials (U) and H coverage (θ_H).

3. Results and discussion

3.1 N₂ reduction mechanism on Au(111) in gas phase

For comparison and consideration of solvation effect on N₂ reduction mechanisms, we firstly present calculated results of N₂ reduction to NH₃ via dissociative and associative mechanisms on Au(111) in gas phase. In dissociative mechanism, N₂ is initially dissociated to form the adsorbed N atoms on Au(111) with an extremely high activation barrier of ca. 6.02 eV, as can be seen in Fig. 2. Subsequently, the adsorbed N atoms are further reduced to form NH₃ molecules via serial surface hydrogenation steps with corresponding barriers of ca. 0.40, 0.47 and 0.57 eV, respectively. By comprehensively scrutinizing the overall energy pathway diagram of N₂ reduction into NH₃ in gas phase, N₂ dissociation pathway is rate determining step of overall reaction in dissociative mechanism on Au(111).

Fig. 2 Overall energy pathway diagram of N₂ reduction and electroreduction into NH₃ via dissociative mechanism on Au(111) in gas phase and the present simulated Au(111)/H₂O electrochemical interface.

Fig. 3 shows the overall energy pathway diagram of N₂ reduction into NH₃ via associative alternating and distal mechanisms in gas phase. In these both mechanisms, the activation barrier is calculated as ca. 2.10 eV for the first hydrogenation step of N₂ molecule into the adsorbed N₂H species. Beginning with the further reduction of N₂H, there may be two possibilities to occur. One is N₂H hydrogenation to form the surface adsorbed NHNH species, which is defined alternating pathways; another is N₂H hydrogenation to form the surface adsorbed NNH₂ species, being defined as distal pathways. The required barrier for the formation of NHNH species is ca. 0.17 eV in alternating pathways. NHNH species can further be reduced to form the adsorbed NHNH₂ species with an activation barrier of ca. 0.26 eV. Two possibilities are considered for NHNH₂ subsequent further reduction, the adsorbed NH₂NH₂ and NHNH₃ species may be formed via surface hydrogenation. The corresponding barrier is 0.31 and 0.21 eV, respectively, which is extremely low and surmountable at room temperature, indicating that NHNH₂ further reduction into NH₂NH₂ and NHNH₃ species may be parallel pathways in alternating pathways. NH₂NH₂ further reduction to form the first NH₃ molecule may be able to be separated into two elementary reaction steps, namely, NH₂NH₂ species surface hydrogenation into the adsorbed NH₂NH₃ species, and subsequent formation of the adsorbed NH₂ species and NH₃ product via N–N bond cleavage. The calculated barrier is ca. 0.37 and 1.66 eV, respectively, as shown in Fig. 3(a). Surface hydrogenation of NH₂ intermediate can finally leads to production of the second NH₃ molecule.

Fig. 3 Overall energy pathway diagram of N₂ reduction into NH₃ via associative mechanism on Au(111) in gas phase: (a) alternating pathways; (b) distal pathways.

In distal pathways, surface hydrogenation of NNH₂ intermediate is possible to form the adsorbed NNH₃ and NHNH₂ species. However, the significant higher barrier for formation of NNH₃ than NHNH₂ is observed (0.72 eV vs. 0.24 eV), indicating that the NNH₃ formation is kinetically inhibited, as shown in Fig. 3(b). Starting with NHNH₂ further reduction, the first NH₃ molecule may be produced via two elementary reaction steps involving hydrogenation into the adsorbed NHNH₃ species and its subsequent N–N bond scission with the formations of the adsorbed NH species and NH₃ product, and the corresponding barrier is calculated as ca. 0.21 and 0.65 eV. The adsorbed NH₂NH₂ intermediate is also possible to be formed through NHNH₂ surface hydrogenation with the surmountable barrier of ca. 0.31 eV at room temperature in distal pathways. As above elaborated, NH₂NH₂ species can further be reduced into the adsorbed NH₂ species and the first NH₃ molecule via surface hydrogenation and N–N bond scission. The adsorbed NH and NH₂ intermediates can finally lead to the second NH₃ molecule via surface hydrogenation in distal pathways. However, we note that the extremely high barrier is required for N–N bond cleavage in NH₂NH₃ species to form NH₃ product (ca. 1.66 eV) in associative alternating and distal mechanisms, thereby it can be concluded that NH₂NH₃ species is only a spectator during N₂ reduction in gas phase due to its easy formation via NHNH₃ and NH₂NH₂ hydrogenation. The corresponding energetics of for the possible elementary reaction steps involved in N₂ reduction pathways on Au(111) in gas phase are summarized in Table 1.

Table 1 Activation barriers (ΔE_act, eV) and reaction energies (ΔE_reac, eV) for the possible elementary reaction steps involved in N₂ reduction pathways on Au(111) in gas phase

Elementary reaction steps^a	ΔEact, eV	ΔEreac, eV
a The asterisk (*) indicates that the species is adsorbed on the Au(111) surface.
N2 + * → N* + N*	6.02	5.67
N* + H* → NH*	0.40	−1.87
	0.47	−1.52
	0.57	−2.05
N2 + H* → N2H*	2.10	1.75
N2H* + H* → NHNH*	0.17	−0.79
	0.22	−0.48
	0.26	−0.92
	0.24	−1.23
	0.72	0.48
	0.31	−1.42
	0.21	−0.45
	0.21	−1.52
	0.37	−0.40
	0.24	−1.37
	0.65	−1.23
	1.66	−1.38

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By scrutinizing the overall energy pathway diagram of associative alternating and distal mechanisms (see Fig. 3), N₂ hydrogenation into N₂H species is rate determining step with the barrier of ca. 2.10 eV, suggesting that both alternating and distal pathways may be parallel and operable on Au(111) in gas phase. It is found that the barrier of rate determining step for the associative mechanism is notably lower than that of dissociative mechanism by comparing the barriers between these both mechanisms (ca. 2.10 eV vs. 6.02 eV), suggesting that the associative mechanism including the adsorbed NHNH, NNH₂, NH₂NH₂, NHNH₃ and NH₂NH₃ intermediates is more favorable. The optimal associative mechanisms including alternating and distal pathways on Au(111) in gas phase are summarized in Fig. 4. Images of reactants, products and transition states for N₂ reduction into NH₃ via the optimal associative mechanisms are included in ESI, as shown in Fig. S3–S13.† However, we also note that the required barrier for initial N₂ hydrogenation is extremely high, which may be able to ascribed to weakly bonded N₂ molecule on Au(111) with the adsorption energy of ca. −0.03 eV. Furthermore, N≡N bond length of N₂ on Au(111) is almost identical with that of isolated N₂ molecule, ca. 1.11 Å.

Fig. 4 The optimal associative mechanisms on Au(111) in gas phase: (a) alternating pathways via NHNH species; (b) distal pathways via NNH₂ species (* represents surface adsorption).

3.2 N₂ electroreduction mechanism at Au(111)/H₂O interface

Our present proposed H coverage-dependent Au(111)/H₂O electrochemical interface model is utilized to simulate N₂ electroreduction pathways, including dissociative and associative mechanisms. The present calculated thermodynamically required equilibrium potential of ca. −0.22 V (vs. RHE) when θ_H is equal with zero is focused. Fig. 1 shows the overall energy pathway diagram of N₂ electroreduction into NH₃ through dissociative mechanism. The largest barrier for this mechanism is initial N≡N bond scission to form the adsorbed N atoms with an activation barrier of ca. 4.90 eV at −0.22 V (vs. RHE), thus being rate determining step of overall reaction. Although the barrier for N₂ dissociation is significantly decreased at Au(111)/H₂O electrochemical interface by comparing with that in gas phase (4.90 eV vs. 6.02 eV), it is still extremely high and difficult to be overcome. An activation barrier of ca. 1.75 eV is required for initial N₂ electroreduction into N₂H species at the present simulated Au(111)/H₂O interface in associative mechanisms, as can be seen in Fig. 5. The barrier for N₂H further electroreduction into the surface adsorbed NHNH and NNH₂ species in alternating and distal pathways is calculated as ca. 0.22 and 0.01 eV, respectively, suggesting that both NHNH and NNH₂ species are possible key intermediates during N₂ electroreduction on Au(111) because of extremely low formation barriers.

Fig. 5 Overall energy pathway diagram of N₂ electroreduction into NH₃ via associative mechanism at the present proposed Au(111)/H₂O interface: (a) alternating pathways; (b) distal pathways.

Beginning with NHNH further electroreduction in alternating pathways, we find that the adsorbed NHNH₂ species is unstable at Au(111)/H₂O interface, which can be spontaneously electrochemically reduced to form the surface adsorbed NH₂NH₂ species by proton-coupled electron transfer with the surmountable barrier of ca. 0.24 eV at room temperature, as shown in Fig. 5(a). The first NH₃ molecule can be produced by further electroreduction of NH₂NH₂ species through two elementary reaction steps including NH₂NH₃ formation and its subsequent N–N bond scission. The corresponding barrier is calculated as ca. 0.48 and 0.69 eV, respectively. It is noted that the barrier for NH₂NH₃ further electroduction into the adsorbed NH₂ species and NH₃ product is significantly decreased at Au(111)/H₂O interface compared with that in gas phase (0.69 eV vs. 1.66 eV), suggesting that the presence of electrochemical interface may be able to alter N₂ reduction mechanisms. The formed NH₂ species can finally lead to production of the second NH₃ molecule with an activation barrier of ca. 0.56 eV. Starting with NNH₂ intermediate formed in distal pathways, it is found that the adsorbed NHNH₂ and NNH₃ species observed in gas phase are unstable at Au(111)/H₂O interface, which can be also spontaneously electrochemically reduced to form the surface adsorbed NH₂NH₂ and NHNH₃ intermediates by proton-coupled electron transfer process. The required barrier for NNH₂ electroreduction into NH₂NH₂ and NHNH₃ is calculated as only ca. 0.11 and 0.05 eV, respectively, as shown in Fig. 5(b), suggesting that NH₂NH₂ and NHNH₃ species is possible intermediate in distal pathways. Similarly, NH₂NH₂ intermediate can be further electrochemically reduced to form the adsorbed NH₂ species and the first NH₃ molecule via abovementioned two elementary reaction steps. Two possibilities are also considered for further electroreduction of NHNH₃ intermediate at Au(111)/H₂O interface, one is NH₂NH₃ formation, and another is formation of the adsorbed NH species and production of the first NH₃ molecule via N–N bond scission. It is found that the required barrier for the former is notably lower than that of the latter (0.24 eV vs. 0.94 eV), indicating that NH₂NH₃ formation is more favorable. Thus, we can concluded that the first NH₃ molecule is possible to be produced by N–N bond scission of NH₂NH₃ species at Au(111)/H₂O interface, rather than NHNH₃ species as observed in gas phase, again suggesting that the influence of electrochemical interface containing solvation effect on N₂ reduction pathways. The corresponding energetics of for various possible reaction steps involved during N₂ electroreduction at Au(111)/H₂O interface are summarized in Table 2.

Table 2 Activation barriers (ΔE_act, eV) and reaction energies (ΔE_reac, eV) for various possible reaction steps involved in N₂ electroreduction pathways at Au(111)/H₂O interface

Reaction steps^a	ΔEact, eV	ΔEreac, eV
a The asterisk (*) indicates that the species is adsorbed on the Au(111) surface.
N2 + * → N* + N*	4.93	4.92
N* + (H + e^−) → NH*	0.33	−1.37
	0.73	−1.78
	0.56	−1.51
	1.75	1.65
	0.22	−1.30
	0.01	−0.75
	0.24	−1.25
	0.11	−1.80
	0.05	−1.34
	0.48	−0.85
	0.24	−1.31
	0.94	−0.21
	0.69	−0.68

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By scrutinizing the overall energy pathway diagram, our present simulation results reveal that the rate determining step for N₂ electroreduction into NH₃ via associative alternating and distal mechanisms at Au(111)/H₂O interface is N₂ electroreduction into form the adsorbed N₂H species, suggesting that these both mechanisms may be able to parallelly occur. The corresponding barrier is significantly lower than that of rate determining step in the dissociative mechanism (1.75 eV vs. 4.90 eV). Thus, it can be concluded that the associative mechanisms are more facile to occur at the present simulated Au(111)/H₂O interface. The optimal associative alternating and distal mechanisms are summarized in Fig. 6. Images of reactants, products and transition states for N₂ electroreduction into NH₃ via the optimal associative mechanisms at the present simulated Au(111)/H₂O interface are included in ESI, as shown in Fig. S14–S23.†

Fig. 6 The optimal associative mechanisms at the present simulated Au(111)/H₂O interface: (a) alternating pathways via NHNH species; (b) distal pathways via NNH₂ species (* represents surface adsorption).

Our present calculated N₂ electroreduction mechanisms at Au(111)/H₂O electrochemical interface are partially inconsistent with the previous theoretical study from Janik et al., in which only alternating pathway via NHNH species is favorable on late transition metals at 0 V (vs. RHE) with rate determining step of N₂ electroreduction into N₂H species by calculating explicitly the potential-dependent barriers for elementary electroreduction reactions (see Fig. 7).⁵¹ Furthermore, the predicted NHNH₂ species on late transition metals at 0 V (vs. RHE) is found to may be unstable at Au(111)/H₂O interface, which can be spontaneously reduced to form adsorbed NH₂NH₂ species by proton-coupled electron transfer with the surmountable barrier at room temperature. The difference of interface model may lead to partially inconsistent N₂ electroreduction mechanisms, in which only a H₂O molecule is employed to simulate solvent effect in previous theoretical work from Janik et al., being insufficient to model interactions among solvent, adsorbates and surface. However, our present theoretical results can be confirmed by the most recent experimental study from Shao et al., in which the adsorbed intermediates such as N₂H, NHNH, NNH₂, NH₂NH₂, NH₂NH₃ and NH₂ may be able to be formed during N₂ electroreduction on the Au electrodes at potentials of ca. −0.10 V (vs. RHE) or lower due to detected N₂H_y (1 ≤ y ≤ 4) reaction species using the surface-enhanced infrared absorption spectroscopy technique,⁴² further validating the rationality of our present employed Au(111)/H₂O interface model. Simultaneously, we also note that the presence of electrochemical interface makes the barrier of rate determining step in the associative mechanisms decrease compared with that in gas phase (1.75 eV vs. 2.10 eV), indicating that the presence of solvent effect could help stabilize the adsorbed N₂H species and lower the corresponding barrier value to ca. 1.75 eV. Even so, barrier of 1.75 eV is still high for N₂ electroreduction, making this process be still challenging, which may be able to be regarded as origin of experimentally observed high overpotential. The almost not changed N≡N bond length of ca. 1.11 Å at Au(111)/H₂O interface again shows weakly adsorbed N₂ molecule compared with that of isolated N₂ molecule.

Fig. 7 The optimal associative alternating pathways via NHNH species on late transition metal surfaces at 0 V (vs. RHE) from previous work conducted by Janik et al. (* represents surface adsorption).⁵¹

The potential of the hydrogen evolution reaction is very approximate to the thermodynamically required potential for N₂ electroreduction under ambient conditions. Therefore, overcoming the undesirable hydrogen evolution reaction competition may become the critical challenge during N₂ electroreduction at present, which can greatly reduce the faradaic efficiency of reaction. Herein, the barrier of hydrogen evolution reaction is evaluated by using our present proposed H coverage-dependent Au(111)/H₂O interface model at −0.22 V (vs. RHE) and compared with that of rate determining step for the optimal associative mechanisms during N₂ electroreduction into NH₃ to quantify the challenge in designing the high efficient electrocatalysts. As can be seen in Fig. 8, the calculated activation barrier of ca. 0.24 eV is remarkably lower than that of initial N₂ electroreduction into N₂H intermediate (ca. 1.75 eV). Furthermore, we also observe that the formed N₂H intermediate may be unstable, which can be facile to back to N₂ molecule with extremely low barrier of ca. 0.10 eV. The present comparison and analysis can well explain why the catalytic activity of Au electrodes is usually unsatisfactory although the relatively high faradaic efficiency can be achieved experimentally during N₂ electroreduction.^24,25,42 Accordingly, the single descriptor may be able to be proposed to scale catalytic activity of electrocatalysts for N₂ electroreduction, in which an ideal electrocatalyst should be able to reduce barrier for initial N₂ electroreduction into N₂H intermediate. In this way, N₂ electroreduction pathways can be facilitated and the yield of NH₃ can be enhanced.

Fig. 8 Energy pathway diagram of competitive hydrogen evolution reaction and initial N₂ electroreduction into N₂H species at the present proposed Au(111)/H₂O electrochemical interface.

3.3 Origin of solvation effect on N₂ reduction mechanisms

As above discussed, the presence of electrochemical interface including solvation effect could change N₂ reduction mechanism, especially it can reduce the barrier of rate determining step. To ascertain the origin of difference of N₂ reduction mechanisms at gas phase and the present simulated electrochemical interface on Au(111), the charge density difference analyses are carried out in our present work taking example for N₂ adsorption on Au(111). It is observed that there is almost not significant electron accumulation and interaction between N₂ molecule and surface Au atoms under gas- and aqueous-phase environment, as shown in Fig. 9, confirming the above-mentioned weakly binding N₂ molecule on Au(111) and almost identical N≡N bond length compared with isolated N₂ molecule, thus explaining why high barrier is required for initial N₂ reduction. However, the significant electron interactions are found between N₂ and H₂O cluster at the present simulated electrochemical interface. The existence of H bonds and interactions of N₂ with H₂O molecules at the Au(111)/H₂O interface may lead to easier initial N₂ electroreduction, as observed decreased barrier value.

Fig. 9 The charge density difference maps for N₂ (a) in gas-phase and (b) at the Au(111)/H₂O interface.

Based on the above conclusions, we can conclude that the decreased barrier for rate determining step may be able to be ascribed to electronic interactions between N₂ and H₂O cluster. Therefore, the quantitative analysis of electronic structures will facilitate well understanding the origin of solvation effect on N₂ electroreduction mechanisms. According to projected electron densities of states, the Löwdin charge (the number of valence electron) of N₂ can be obtained from Löwdin population analyses on Au(111) in gas phase and at the present simulated electrochemical interface. Table 3 gives the electron gains (Δq) for N₂ molecule, respectively, which could be obtained by subtracting the Löwdin charge of isolated N₂ molecule from that in the optimized structure. Simultaneously, Δq of H₂O cluster at the present simulated electrochemical interfaces are also given in Table 3 compared with that of free N₂ adsorbed Au(111)/H₂O interface. A positive value of Δq will imply a gain of electron by the component. It can be found that only slight electron transfer occurs between N₂ molecule and Au(111) surface in gas phase due to little electron gains of total, s and p orbitals of N₂, as found weakly bonded N₂ molecule on Au(111) with the adsorption energy of only ca. −0.03 eV, confirming the above observed no significant electron accumulation and interaction based on the charge density difference analyses. However, we notice that the nature of electronic interactions at the Au(111)/H₂O interface is practically not the same as that observed in gas phase. The significant electron transfer occurs between N₂ molecule and H₂O cluster, namely, the total net electrons of H₂O cluster are positive because s orbital can gain more electrons although p orbital loses electrons, whereas the total net electrons of N₂ is negative, in which s orbital loses electrons and p orbital gains electrons. Thus, it can be concluded that the notable different electron interactions on Au(111) in gas phase and at the electrochemical interface may result in the difference of N₂ reduction mechanisms.

Table 3 The electron gains (Δq) of total, s and p orbitals of N₂ molecule on Au(111) and at the present simulated Au(111)/H₂O interface; Δq of total, s and p orbitals of H₂O cluster in N₂ adsorbed Au(111)/H₂O interface

		Difference of electron (Δq)
		Total	s	p
Au(111)	N2	−0.0284	−0.0271	−0.0013
Au(111)/H2O interface	N2	−0.0147	−0.0385	+0.0238
	H2O cluster	+0.0188	+0.0384	−0.0195

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4. Conclusions

In the present paper, an improved H coverage-dependent Au(111)/H₂O electrochemical interface model is proposed, which is firstly used to study electroreduction mechanisms of N₂ to NH₃ at the thermodynamical equilibrium potential cooperated with electronic structure analysis. The calculated results show that the associative mechanism is more favorable on Au(111) and therein alternating and distal pathways may be able to parallelly occur in gas phase and the present simulated electrochemical interface. The initial N₂ reduction into N₂H intermediate is rate determining step, which may be able to be regarded as the origin of observed experimentally high overpotential during N₂ electroreduction. However, the presence of electrochemical environment can significantly change N₂ reduction pathway and decrease the barrier of rate determining step, in which NHNH₂ and NNH₃ species observed in gas phase are unstable at Au(111)/H₂O interface, which can be spontaneously electrochemically reduced to form adsorbed NH₂NH₂ and NHNH₃ intermediates by proton-coupled electron transfer process. The significant electron accumulation and interaction between N₂ molecule and H₂O cluster may result in different N₂ electroreduction pathways and the decreased barrier of rate determining step. The theoretical results display excellent consistency with the available experimental data, confirming the rationality of the present used Au(111)/H₂O interface model. The comparison of barrier between hydrogen evolution reaction and rate determining step well explains why the catalytic activity of Au electrodes is usually unsatisfactory although the relatively high faradaic efficiency can be experimentally achieved. Accordingly, the single descriptor may be able to be proposed, in which an ideal electrocatalyst should be able to reduce barrier for initial N₂ electroreduction into N₂H intermediate. In this way, N₂ electroreduction pathways can be facilitated and the yield of NH₃ can be enhanced. We believe that the present study represents a progress to systematically study N₂ electroreduction mechanisms based on an improved electrochemical interface model.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was supported by the Key Program of Education Department of Hunan Province (Grant No. 19A337); Hunan Provincial Natural Science Foundation of China (Grant No. 2018JJ2273); Key Program of Hunan University of Arts and Science (19ZD06) and National Natural Science Foundation of China (Grant No. 21303048).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/d1ra01978c

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