Mechanism of ammonia synthesis on Fe 3 Mo 3 N †

Ammonia (NH 3 ) synthesis is an essential yet energy-demanding industrial process. Hence, there is a need to develop NH 3 synthesis catalysts that are highly active under milder conditions. Metal nitrides are promising candidates, with the h -carbide Co 3 Mo 3 N having been found to be more active than the industrial Fe-based catalyst. The isostructural Fe 3 Mo 3 N catalyst has also been identi ﬁ ed as highly active for NH 3 synthesis. In the present work, we investigate the catalytic ammonia synthesis mechanisms in Fe 3 Mo 3 N, which we compare and contrast with the previously studied Co 3 Mo 3 N. We apply plane-wave density functional theory (DFT) to investigate surface N vacancy formation in Fe 3 Mo 3 N, and two distinct ammonia synthesis mechanisms. The calculations reveal that whilst N vacancy formation on Fe 3 Mo 3 N is more thermodynamically demanding than for Co 3 Mo 3 N, the formation energies are comparable, suggesting that surface lattice N vacancies in Fe 3 Mo 3 N could facilitate NH 3 synthesis. N 2 activation was found to be enhanced on Fe 3 Mo 3 N compared to Co 3 Mo 3 N, for adsorption both at and adjacent to the vacancy. The calculated activation barriers suggest that, as for Co 3 Mo 3 N, the associative Mars van Krevelen mechanism a ﬀ ords a much less energy-demanding pathway for ammonia synthesis, especially for initial hydrogenation processes.


Introduction
Ammonia (NH 3 ) synthesis is one of the most important industrial chemical processes, most notably for the production of fertilisers, which are crucial to supporting agriculture, and therefore ensuring global food security.][35][36] The Fe 3 Mo 3 N system, which is isostructural to Co 3 Mo 3 N, has also been found to be highly active for ammonia synthesis. 37,38However, experimental studies show that, in contrast to the isostructural Co system, Fe 3 Mo 3 N appears to be highly resistant to reduction, with no appreciable loss of lattice N being observed even under harsh conditions. 39Furthermore, experimental studies also show that the quaternary metal nitride system (Co 3−x Fe x Mo 3 N) is highly active towards ammonia synthesis, 38 opening the possibility to nely tune ammonia synthesis activity by determining the optimal Co : Fe ratio.Clearly, a detailed understanding of both the Co and Fe ternary systems is required before embarking on the rational design of an optimal quaternary metal nitride catalyst.
It is therefore of considerable interest to explore the mechanisms for ammonia synthesis on Fe 3 Mo 3 N, analogous to the previous studies for Co 3 Mo 3 N, both to rationalise the high activity of the Fe 3 Mo 3 N ternary metal nitride, and to inform future investigations into the quaternary Co 3−x Fe x Mo 3 N system.In the present work, plane-wave density functional theory techniques are applied to explore surface N vacancy formation, and both the dissociative LH mechanism, and associative ER-MvK mechanism, for Fe 3 Mo 3 N.The calculations reveal that surface N vacancy formation is feasible for the Fe 3 Mo 3 N system, and that N 2 activation takes place both at and adjacent to surface N vacancy sites.The calculations also show that, as for Co 3 Mo 3 N, the associative ER-MvK mechanism provides a more energetically accessible mechanistic pathway for ammonia synthesis.The present work, in addition to providing key insights into the behaviour of the Fe 3 Mo 3 N system, will serve as a benchmark study for future work exploring promotion of the Fe 3 Mo 3 N catalyst, and (in tandem with the previous work for the Co 3 Mo 3 N system) for investigations concerning the quaternary Co 3−x Fe x Mo 3 N system, supporting the rational design of optimal metal nitride catalysts for ammonia synthesis.

Methodology
1][42][43] A thin-lm Fe 3 Mo 3 N (111) model was constructed exposing a nitrogen-rich termination, based on the model successfully developed for the isostructural Co 3 Mo 3 N system reported in previous computational studies. 15,33,35The optimised lattice parameter for bulk Fe 3 Mo 3 N was determined in previous studies 33 and was used to dene the dimensions of the surface slab periodic cell.The thin-lm slab consists of a 2 × 2 surface supercell, to minimise lateral interactions between adsorbed species in adjacent periodic images, and three N-containing layers forming a non-stoichiometric symmetric slab model, as illustrated in Fig. 1.The thin lm slab was centred in the periodic cell, with a vacuum separation of 30 Å between slabs in adjacent periodic images, ensuring sufficient slab separation to avoid any spurious interactions.During geometry optimisation, all atomic positions were allowed to relax.In line with the previous computational studies for Co 3 Mo 3 N, a G-centred (4 × 4 × 1) Monkhorst-Pack k-point sampling scheme was used. 15,44Inner electrons were replaced by projector-augmented waves (PAW), 45,46 and the valence states were expanded in plane-waves with a cut-off energy of 650 eV.The revised PBE (RPBE) exchange correlation functional was used throughout, having previously been demonstrated to accurately reproduce N 2 bond dissociation energy, 15 with a dispersion correction applied using the D3 scheme devised by Grimme, and Becke-Johnson damping, in order to account for the weak van der Waals interactions responsible for the physisorption behaviour of species such as N 2 . 47,48n order to investigate the elementary reaction processes involved in the LH and ER-MvK mechanisms for ammonia synthesis, optimised geometries were obtained for all adsorbed reactants, products, and intermediates, on the Fe 3 Mo 3 N (111) surface model featuring a single surface N vacancy, with atomic forces converged to within 0.01 eV Å−1 .In each case, electronic wavefunctions were converged such that the total energy was converged to within 10 −5 eV.Transition states were identied using the climbing image nudged elastic bands (CI-NEB) and dimer methods, with vibrational analysis conrming that a saddle point had indeed been located.
For the ab initio thermodynamics study, calculated DFT electronic energies were combined with gas-phase thermochemistry data (obtained from the NIST Webbook 49 ) using the general approach described by Reuter et al. 50to obtain the Gibbs free energy of vacancy formation as a function of H 2 partial pressure and temperature, to estimate typical surface N vacancy concentrations under a range of hydrogenating conditions.Further details of the ab initio thermodynamics model can be found in the ESI.†

Formation of surface N vacancies
As illustrated in the previous studies investigating the Co 3 Mo 3 N system, the possibility of an associative MvK-type mechanism depends on the presence of surface N vacancies to activate adsorbed N 2 .As such, it is of interest to calculate the N vacancy formation energy, both with respect to N 2 and NH 3 arising from hydrogenation of surface lattice N under appropriate conditions, to determine the overall thermodynamic feasibility of the vacancy formation.The calculated nitrogen vacancy formation energies are presented in Table 1, for both a single N

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vacancy, and two adjacent N vacancies to determine the extent of lateral instability; Fig. 2 illustrates both the surface with a single N vacancy and two adjacent N vacancies.The calculated vacancy formation energies show that, with respect to the formation of N 2 , the formation of a single N vacancy on the model surface is endothermic by 1.893 eV.For the formation of two adjacent vacancies, a value of 4.247 eV was obtained, giving a formation energy per N vacancy of 2.124 eV, indicating that there is only a moderate extent of repulsive interaction between adjacent N vacancies, with the vacancy formation energy per vacancy differing by only 0.231 eV; hence, it may be possible to achieve appreciable surface N vacancy concentrations under appropriate conditions.
For the vacancy formation energies with respect to H 2 and NH 3 , we nd that the vacancy formation energy is considerably less endothermic, with a vacancy formation energy of only 0.972 eV for a single N vacancy, and 1.203 eV per vacancy for two adjacent N vacancies, suggesting that, under ammonia synthesis conditions where H 2 is present, formation of N vacancies via evolution of NH 3 should be more thermodynamically feasible compared to the formation of N vacancies via evolution of N 2 under comparable conditions where H 2 is not present.

Ab initio thermodynamics of vacancy formation under hydrogenation conditions
Whilst the calculated vacancy formation energies for both Co 3 Mo 3 N and Fe 3 Mo 3 N are endothermic, the DFT calculated energies do not account for temperature and pressure dependent thermodynamic contributions under real conditions; in the case of lattice N being evolved into the gas phase to form surface vacancies, it is clear that entropy contributions arising both from translational and rotational  degrees of freedom of gas phase molecules, and congurational entropy arising from many possible permutations of larger numbers of surface vacancies, will have a considerable impact on the thermodynamic feasibility of vacancy formation.To this end, we apply ab initio thermodynamics techniques to extrapolate the DFT results to provide approximate insights into the extent of surface N vacancy formation under a range of possible experimental conditions, based on the established approach detailed in previous works investigating a variety of different systems; [51][52][53][54]  (for a single vacancy) to 4.83 × 10 22 cm −2 (for the maximum surface vacancy concentration, i.e. all 24 surface N atoms in the thin lm model having been removed).Fig. 3 shows the approximate vacancy concentration for varying H 2 partial pressure and temperatures, 55 based on the calculated Gibbs free energy of vacancy formation for each vacancy concentration representable within the thin-lm model.
The ab initio thermodynamic studies summarised in Fig. 3 show that N vacancy concentration is higher at higher H 2 partial pressures and higher temperatures, as expected.Whilst the model is necessarily limited to a minimum vacancy concentration of 2.01 × 10 21 cm −2 (this being the vacancy concentration corresponding to a single surface N vacancy within the 2 × 2 thin lm model), it Fig. 3 Surface N vacancy concentration as a function of H 2 partial pressure (where p°is ambient pressure) and temperature, as estimated from ab initio thermodynamics.

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Faraday Discuss.This journal is © The Royal Society of Chemistry 2023 can still be seen that one would not necessarily expect an appreciable number of vacancies to be formed under ambient pressure ln p H2 p y 0 for any range of temperatures.However, even at relatively modest H 2 partial pressures, such as 10 mPa, 56,57 which is at the lower range of pressures applied for ammonia synthesis using the industrially well-establish Fe-based catalysts ln p H2 p y 4:5 , the ab initio thermodynamics suggest that the 2.01× 10 21 cm −2 vacancy concentration threshold would be reached at 650 °C.It is therefore highly plausible that lower concentrations of surface N vacancies would be present at somewhat lower temperatures and pressures and could therefore facilitate ammonia synthesis via the ER-MvK mechanism.

Associative Eley-Rideal-Mars-van-Krevelen mechanism
As illustrated from the DFT calculations for vacancy formation, and resulting ab initio thermodynamics studies, it is likely that there is an appreciable vacancy concentration on the Fe 3 Mo 3 N (111) surface under relatively mild experimental conditions.Hence, it is of interest to explore the energetics of the ER-MvK mechanism for this system that was found to afford a more kinetically accessible pathway for ammonia synthesis for the isostructural Co 3 Mo 3 N system. 35he calculated reaction energies and activation barriers with corresponding frequencies for the unstable mode are presented in Table 2.
The mechanism proceeds with the initial associative adsorption of the N 2 molecule at the vacancy site (process 1), as illustrated in Fig. 4.This adsorption process is highly exothermic, at −1.746 eV, and induces a considerable elongation of the N 2 bond, to 1.320 Å, compared to the 1.098 Å determined experimentally, 58 indicating a substantial degree of activation of the N 2 molecule.
The initial hydrogenation process takes place via an Eley-Rideal mechanism with direct hydrogenation of the adsorbed N 2 species by H 2 from the gas phase Table 2 DFT calculated reaction energies, activation barriers, and vibrational frequencies for unstable modes corresponding to the reaction coordinate, for all elementary processes associated with the Eley-Rideal-Mars-van-Krevelen mechanism for ammonia synthesis.The N vacancy adsorption site is indicated by the symbol , in the chemical equations for each elementary process, with intermediates adsorbed at the vacancy site indicated using this symbol in superscript.Co-adsorbed species located at adsorption sites other than the N vacancy site are indicated by *

Process number
Process DE/eV  2, process 4), with this process having a much higher activation barrier (1.269 eV), reecting the saturation of the N-N bond with successive hydrogenation, although the process is only mildly endothermic (0.290 eV), as illustrated in Fig. 6.
Dissociation of the N-N bond of the N 2 H , 3 intermediate evolves the rst equivalent of ammonia, the process is exothermic (Table 2, process 5, −0.274 eV)   and leaves the remaining N atom originating from the adsorbed N 2 molecule in process 1 located in the vacancy site, essentially replacing the lattice N lost during vacancy formation, and a co-adsorbed H atom.These co-adsorbed species subsequently form the NH , intermediate (Table 2, process 6, Fig. 7), the process being moderately exothermic (−0.812 eV), and again, only weakly activated (0.373 eV).
The third and nal equivalent of H 2 required to complete the catalytic cycle is then adsorbed exothermically (−0.315 eV) in a similar manner to process 3 (Table 2, process 7), before again dissociating and forming a second N-H bond to yield the NH , 2 (Table 2, process 8); the process is moderately endothermic (1.013 eV) and has a considerable activation barrier of 1.590 eV, making this the most energy-demanding elementary process in the ER-MvK mechanism by a considerable margin, and thus we would expect this process to also be the rate determining elementary step in this catalytic cycle (Fig. 8).It must also be noted that whilst the activation barrier for this hydrogenation process is high, and therefore represents a signicant kinetic obstacle to formation of the second equivalent of ammonia to regenerate the surface vacancy, at this stage in the reaction mechanism a rst equivalent of ammonia has already been evolved.Hence, it is entirely possible that ammonia synthesis could proceed identically to that described by processes 1 to 5 in Table 2 at a different N vacancy site.Such behaviour would correspond to N looping, rather than true catalysis, since in this scenario the N vacancies are not regenerated within the same cycle, but could be under a different set of conditions.
The remaining hydrogenation process then takes place, yielding the NH , 3 intermediate (Table 2, process 9), which is conversely mildly exothermic (−0.229 eV) and has only a moderate activation barrier (0.430 eV), illustrated in Fig. 9.   Evolution of the second equivalent of ammonia completes the catalytic cycle, regenerating the surface lattice N vacancy, this process being considerably endothermic by 1.272 eV.
The calculated reaction prole for the ER-MvK mechanism reveals that the presence of a surface lattice N vacancy is indeed able to signicantly activate N 2 , and the initial hydrogenation processes are facile, with generally low activation barrier.Conversely, higher activation barriers and more energy-demanding processes are observed for the nal hydrogenation processes and evolution of the second equivalent of ammonia.Hence, whilst the surface lattice N vacancies are clearly highly active, their formation (with the latter processes of the mechanism essentially corresponding to the hydrogenation of lattice N to yield the surface vacancy) presents a greater challenge for overall feasibility of the reaction mechanism.

Dissociative Langmuir-Hinshelwood mechanism
Having explored the associative ER-MvK mechanism, it is also of interest to consider the possibility of the dissociative LH mechanism providing an alternative pathway for ammonia synthesis, to afford comparison both with the ER-MvK   on Fe 3 Mo 3 N, and the LH mechanism on the Co 3 Mo 3 N system which has been extensively investigated previously. 35he calculated reaction energies and activation barriers with corresponding frequencies for the unstable mode are presented in Table 3.The initial process, as for the associative ER-MvK mechanism, consists of adsorption of the N 2 molecule, although in the associative LH mechanism, N 2 is adsorbed adjacent to, rather than at, the surface N vacancy site.
The adsorption of N 2 adjacent to the vacancy site is weakly exothermic (−0.172 eV, Table 3, process 1), considerably less so than for adsorption at the vacancy, although notably there is still evidence of N 2 activation even when the N 2 molecule is merely adsorbed near, rather than at, the surface N vacancy site, with an elongation of the N 2 bond length being observed, 1.359 Å compared to 1.098 Å determined experimentally, 58 even greater than that observed for N 2 adsorbed at the N vacancy site as investigated in the ER-MvK mechanism.This result suggests that the presence of surface N vacancies is able to facilitate N 2 activation even when adsorption takes place outside the immediate vicinity of surface N vacancies.
The dissociation of the adsorbed N 2 molecule (Table 3, process 2), which has been identied as the rate-limiting elementary process for ammonia synthesis on Fe 11,12 and Ru 13,14 based catalysts, is only moderately activated on the Fe 3 Mo 3 N (111) surface, with a calculated activation barrier of 0.708 eV, and the process is exothermic by −0.436 eV, reecting the considerable N 2 activation even when N 2 is not adsorbed directly at the surface N vacancy site (Fig. 10).The resulting N* species are adsorbed at two distinct surface sites: the rst being a 3-coordinate Mo-Fe-Mo site, subsequently referred to as the Fe-Mo interface; whilst the second is located at a 3-coordinate Mo-only site, adjacent to the lattice N vacancy.We will rst consider hydrogenation of N* at the Fe-Mo interfacial site.3, process 4).

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Faraday Discussions Exothermic dissociative adsorption of H 2 (−1.372 eV, Table 3, process 3) is followed by hydrogenation of one of the N* resulting from N 2 dissociation (Table 3, process 4).Whilst the process is almost thermoneutral (0.027 eV), it also has a high activation barrier (1.480 eV), presenting a signicant energetic barrier to initial N hydrogenation, as illustrated in Fig. 11.
This pattern continues for the second hydrogenation process to yield NH * 2 (Fig. 12), which is also mildly endothermic (0.104 eV) and has a high activation barrier of 1.143 eV (Table 3, process 5), albeit somewhat lower than for the preceding hydrogenation process.It was also seen that during the hydrogenation process, NH* shis from the 3-coordinate Fe-Mo interfacial site with NH * 2 being formed at a 2-coordinate Fe-Mo site.
A second equivalent of H 2 is then dissociatively adsorbed on the surface exothermically (−0.885 eV, Table 3, process 6), and subsequently hydrogenation of the NH * 2 intermediate takes place to yield NH * 3 (Table 3, process 7).As for the preceding hydrogenation processes, NH * 3 formation is only slightly endothermic (0.282 eV) but has a high activation barrier of 1.329 eV.During hydrogenation, NH * 2 shis once again such that the resulting NH * 3 species adopts a 1-coordinate adsorption environment located slightly offset from the top of the Fe atom, as illustrated in Fig. 13.
Evolution of the rst equivalent of ammonia is strongly endothermic (1.405 eV, Table 3, process 8), and is followed by the rst hydrogenation of the second N* (Table 3, process 9); in contrast to the corresponding process for the rst N* (Table 3, process 4), this process is exothermic by −0.600 eV, and has only a moderate activation barrier of 0.532 eV.It is notable that the rst series of hydrogenation processes (Table 3, processes 4, 5, 7), which were all determined to be endothermic and highly activated, took place at the N* species located at the Fe-Mo interface, whilst hydrogenation of the second N* species (Table 3, process 9; Fig. 14), involves N* migrating from a 3-coordinate Mo site to the Fe-Mo  2 hydrogenation process (Table 3, process 7).

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Faraday Discuss.This journal is © The Royal Society of Chemistry 2023 interface.This implies that the N*, NH*, and NH * 2 species are more stabilised at the Fe-Mo interface site, and therefore these species are more resistant to hydrogenation at this site, compared to at the 3-coordinate Mo site.
Dissociative adsorption of the third and nal equivalent of H 2 takes place exothermically (−1.349 eV, Table 3, process 10).Subsequently, NH* undergoes hydrogenation to NH * 2 (Table 3, process 11), this process being found to be almost thermoneutral (−0.012 eV), and return to the high activation barriers calculated for the rst series of hydrogenation processes is observed, with an activation barrier of 1.206 eV being determined; once again, during hydrogenation the NH* species moves from the 3-coordinate Fe-Mo interfacial site to form NH * 2 at the adjacent 2-coordinate Fe-Mo bridging site (Fig. 15), in a manner virtually identical to that determined for process 4.
The nal hydrogenation process (Table 3, process 12; Fig. 16) to form NH * 3 occurs analogously to process 7, being even more endothermic (0.910 eV) and having a high activation barrier of 1.636 eV, making this the most energydemanding elementary process in the dissociative LH mechanism.Finally, evolution of the second equivalent of ammonia (Table 3, process 13) completes the catalytic cycle, and is mildly endothermic at 0.258 eV.The calculations for the dissociative LH mechanism for ammonia synthesis reveal that whilst the initial adsorption and dissociation of N 2 is enhanced on the Fe 3 Mo 3 N (111) surface, subsequent hydrogenation processes are largely highly activated and endothermic, especially at the Mo-Fe interfacial surface site; indeed the only hydrogenation process that deviates from this is process 9, which involves hydrogenation of the N* species from the Mo-only site, with the remaining endothermic hydrogenation processes largely being compensated by highly exothermic dissociative adsorption of H 2 .

Discussion
The computed reaction proles for the two mechanisms are presented in Fig. 17.It is clear that whilst N 2 adsorption and activation (and dissociation, for the LH type mechanism) is enhanced both at and adjacent to the surface N vacancy, the subsequent hydrogenation processes are far less activated for the associative ER-MvK mechanism, at least for the initial hydrogenation processes; indeed, the only elementary process in the ER-MvK mechanism with an activation barrier greater than 1 eV is the second NH* hydrogenation process (Table 2, process 8), whilst for the LH mechanism, the only hydrogenation process with an activation barrier less 1 eV is the second N* hydrogenation process (Table 3, process 9).Hence, it appears likely that the high activity of Fe 3 Mo 3 N can be attributed to this mechanism, and therefore N vacancy formation in Fe 3 Mo 3 N is conned to the surface (as suggested by the bulk N/vacancy diffusion calculations), explaining the negligible loss of lattice N in Fe 3 Mo 3 N reported experimentally, in stark contrast with Co 3 Mo 3 N.Here, we will compare the two mechanisms and the two ternary metal nitride systems, comparing and contrasting the results, and offering some insight to rationalise the experimentally reported phenomena in light of the calculations presented in the present work and previous literature.

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Surface formation and bulk diffusion of N vacancies
In comparison with the vacancy formation energies for Co 3 Mo 3 N in the literature, 15 the corresponding Co 3 Mo 3 N(111) surface N vacancy formation energy was calculated to be 1.68 eV, only 0.21 eV less endothermic than for Fe 3 Mo 3 N. Whilst this is in agreement with the experimental ndings that lattice N in Fe 3 Mo 3 N is generally less active compared to Co 3 Mo 3 N, 38,39,59 it is notable that the modest difference in the calculated vacancy formation energies for the two compounds suggests that formation of surface N vacancies on Fe 3 Mo 3 N is at the very least highly plausible, which is consistent with the experimental observation that bulk lattice N in Fe 3 Mo 3 N is inactive, if loss of lattice N is conned only to the surface layers, and therefore accounts for only a negligible loss of total lattice nitrogen from the experimental sample.Hence, this nding suggests that the experimentally observed resistance of Fe 3 Mo 3 N to loss of lattice N under high temperature hydrogenation conditions can be attributed to the diffusion of bulk and subsurface lattice nitrogen to the surface being kinetically, rather than thermodynamically, unfeasible.

N 2 activation
Comparison of the N 2 adsorption process between the Fe 3 Mo 3 N and Co 3 Mo 3 N shows that N 2 activation is considerably enhanced on Fe 3 Mo 3 N, with N 2 adsorption both at the surface N vacancy site, and adjacent to the N vacancy site, being more exothermic than for Co 3 Mo 3 N. Adsorption of N 2 at the surface N vacancy is exothermic by −1.746 eV (Table 2, process 1), compared to a mere ∼−0.73 eV for Co 3 Mo 3 N, whilst at the site adjacent to the vacancy, the process is exothermic by −0.172 eV for Fe 3 Mo 3 N (Table 3, process 1), and slightly endothermic for Co 3 Mo 3 N (+0.42 eV). 35The enhanced N 2 activation for Fe 3 Mo 3 N can be interpreted in terms of its more endothermic vacancy formation energy (Table 1) compared to Co 3 Mo 3 N, implying that the defective system is inherently less stable, and therefore more active, for the Fe system compared to the Co system.Despite the considerably more exothermic adsorption energies on the Fe 3 Mo 3 N surface, the elongation of the N 2 bond is comparable between the Fe and Co systems, both when N 2 is adsorbed at the N vacancy site (1.320Å for Fe 3 Mo 3 N, compared to 1.297 Å for Co 3 Mo 3 N) and when N 2 is adsorbed adjacent to the vacancy site (1.359Å for Fe 3 Mo 3 N, compared to 1.363 Å for Co 3 Mo 3 N).For both the Fe and Co systems, activation of N 2 adjacent to the N vacancy also can be seen to play a key role in facilitating N 2 dissociation (Table 3, process 2), a key process in the LH mechanism for ammonia synthesis; for the Fe system the process has an activation barrier of 0.708 eV, and is exothermic by −0.436, whereas a lower barrier and even greater exothermicity was reported for the Co system (E A = 0.24 eV, DE = −1.86eV).Whilst N 2 dissociation appears to be both more kinetically and thermodynamically favourable over the Co system compared to the Fe system, one must bear in mind that the preceding N 2 adsorption is more exothermic for the Fe system, hence it is likely that the overall pathway for N 2 adsorption from the gas phase, and subsequently dissociation, is more facile for the Fe system, given that both processes are moderately exothermic and the dissociation process has only a moderate activation barrier.

Comparison of hydrogenation processes and insights into activity of quaternary metal nitrides
Whilst an examination of the reaction proles for the two mechanisms for both the Fe system investigated in the present work, and the Co system in previous computational studies, shows broadly similar behaviour, there are a few key differences that could help to identify limitations to the activity of both catalysts, and thus inform the future development of, for example, highly active ammonia synthesis catalysts based on the quaternary Co 3−x Fe x Mo 3 N system, with an optimal Co : Fe ratio.
As has already been discussed, the N 2 activation behaviour of the Co and Fe systems is broadly similar, although in terms of hydrogenation, it appears that these processes are activated more for the Fe system.Indeed, examining the LH pathways for the two systems, it can be seen that activation barriers are consistently higher for the Fe system than the corresponding activation barriers for the Co system.The key structural difference appears to lie in the coordination environment of the NH*, NH * 2 and NH * 3 intermediates, with the calculations implying a greater stabilisation of these intermediates at the Fe-Mo interfacial sites compared to the corresponding Co-Mo sites in the Co system.Similarly, whilst the ER-MvK mechanism provides a less activated mechanistic pathway for both systems, it can be seen that whilst the initial hydrogenation processes are less activated for the Fe system, the latter hydrogenation processes are more so, once again reecting the greater stability of these intermediates at the N vacancy site.

Faraday Discussions Paper
To compare the more accessible ER-MvK mechanism for both the Fe 3 Mo 3 N and Co 3 Mo 3 N systems, a reaction prole illustrating this mechanism for the two systems is presented in Fig. 18, based on the results presented in this work and the previous literature on Co 3 Mo 3 N. 35 Whilst the reaction proles are broadly similar, the general trend of the initial hydrogenation processes being less activated, and latter ones more activated, for the Fe 3 Mo 3 N system is clearly evident.In particular, it is notable that the highest activation barriers, which are likely to correspond to the overall rate-limited elementary processes, are comparable, even if they do not correspond to the same process.Namely, the activation barrier for the NH* hydrogenation process is much higher for Fe 3 Mo 3 N than for Co 3 Mo 3 N, and is the most energy-demanding process for Fe 3 Mo 3 N (Table 1, process 8); yet as illustrated in Fig. 18, the most energy-demanding processes for Co 3 Mo 3 N correspond to NH * 2 hydrogenation, and evolution of the second equivalent of NH 3 are comparable to that of the most energy-demanding process for Fe 3 Mo 3 N.This explains the high activity observed for Fe 3 Mo 3 N experimentally; indeed, it seems likely, based on the calculations performed in the present work, that the key difference between the two systems lies primarily in the greater resistance of Fe 3 Mo 3 N to loss of lattice N, which in turn reduces the concentration of active N vacancy sites compared to Co 3 Mo 3 N, resulting in overall lower ammonia production.
Based on these observations, we can suggest that a possible means by which the mixed quaternary Co/Fe system can enhance ammonia synthesis is by combining the greater ease of N vacancy formation (thereby increasing the concentration of active sites for the ER-MvK mechanism, which is the less activated for both the Fe and Co systems) associated with the Co system, along with the weaker binding of key intermediates at the Co-Mo interface and N vacancy site, with the greater extent of N 2 activation and lower barriers for initial hydrogenation processes associated with the Fe system.We therefore speculate that optimal catalytic activity could be tuned by careful control of the Co : Fe ratio in the quaternary system, which combined with the promotion and doping strategies applied to the ternary systems, could enable highly active and stable ammonia synthesis catalysts that can operate under mild conditions.

Conclusions
The calculations reported in the present work reveal that, like the isostructural Co 3 Mo 3 N system, the Fe 3 Mo 3 N system affords low activation barriers for ammonia synthesis via the ER-MvK mechanism, and in particular the Fe system has lower barriers for initial hydrogenation processes via the hydrazine-like intermediate.However, the vacancy formation energy for Fe 3 Mo 3 N is more endothermic than for Co 3 Mo 3 N, and as illustrated by the ab initio thermodynamics study, it is anticipated that Fe 3 Mo 3 N would feature lower concentrations of surface N vacancies compared to Co 3 Mo 3 N, in line with the experimentally wellobserved tendency of the Fe system to be resistant to loss of lattice nitrogen.It is also notable that whilst the ER-MvK mechanism was determined to be the less activated pathway for both systems, the dissociative LH mechanism is more accessible on the Fe system since the initial adsorption of N 2 is considerably more exothermic compared to the Co system, thus enabling the initial N 2 activation process, although higher activation barriers were reported for latter hydrogenation processes in the LH mechanism.Considering this, and the broadly similar features of the ammonia synthesis mechanisms for the two ternary metal nitride systems, it seems likely that the high activity of the Fe 3 Mo 3 N system reported experimentally can be attributed to the lower vacancy concentration, and thus lower concentration of active sites for the favoured ER-MvK mechanism, being partially compensated by the existing possibility for N 2 hydrogenation to take place via the LH mechanism, reecting the well-established high activity of promoted Fe catalysts used in industry.
The present work provides useful insights into the activity of metal nitride catalysts and it is intended that future work will explore not only promotion of the Fe 3 Mo 3 N system, but also the quaternary Co 3−x Fe x Mo 3 N system, which will be informed by the present work and the existing previous literature for the Co 3 Mo 3 N system.

Fig. 1
Fig. 1 Graphic illustrating the symmetric, non-stoichiometric thin-film slab model used to model the Fe 3 Mo 3 N surface, from the top (left) and side (right), as viewed across the cell diagonal.The pristine surface is illustrated, i.e. no N vacancies are present.Key: green, Mo; brown, Fe; blue, N.

Fig. 2
Fig. 2 Graphic illustrating the model surface with a single N vacancy present (left) and two adjacent N vacancies (right).The locations of the N vacancies are highlighted by the red circles.
details of the ab initio thermodynamics model are described in detail in the ESI.† The thin-lm Fe 3 Mo 3 N (111) model used in the present work consists of two surfaces of 248.46 Å2 , which corresponds to 2.49 × 10 −22 cm 2 , giving a total surface area of 4.97 × 10 −22 cm 2 .The (2 × 2) surface supercell presents a total of 24 surface lattice N atoms, 12 for each side of the slab.Hence, the range of vacancy concentrations represented by the model spans from 2.01 × 10 21 cm −2

Fig. 4
Fig. 4 Graphic illustrating the associative adsorption of N 2 at the surface N vacancy site.

Fig. 5
Fig. 5 Graphic illustrating the adsorption configuration of the N 2 H , 2 intermediate.

Fig. 7
Fig.7Graphics illustrating the initial (left), transition (centre), and final (right) state geometries associated with hydrogenation of surface lattice N (regenerated after the evolution of a first equivalent of NH 3 ) to yield the NH , intermediate (Table2, process 6).

Fig. 8
Fig. 8 Graphics illustrating the initial (left), transition (centre), and final (right) state geometries associated with hydrogenation of the NH , intermediate to yield the NH , 2 intermediate (Table 2, process 8).

Fig. 17
Fig. 17Computed reaction profile for the two mechanisms for ammonia synthesis on Fe 3 Mo 3 N, for the associative Eley-Rideal-Mars-van-Krevelen mechanism (black) and the dissociative Langmuir-Hinshelwood mechanism (red).

Fig. 18
Fig.18Computed reaction profiles comparing the ER-MvK mechanism for ammonia synthesis on Fe 3 Mo 3 N (red) and for Co 3 Mo 3 N (black).35

Table 1
Calculated N vacancy formation energies, for a single vacancy and two adjacent vacancies, with respect to both evolution of N 2 , and evolution of NH 3 by reacting with H 2 .The vacancy formation energy per N vacancy is also presented

Table 2 ,
process 2), yielding the N 2 H , 2 intermediate (Fig.5).The process is exothermic by −0.753 eV and lacks an intrinsic barrier due to the high energy of the incident H 2 molecule.Subsequently, a second equivalent of H 2 is exothermically adsorbed (−0.286 eV) adjacent to the N 2 H , , þ H 2 ðgÞ/NH , þ H * 2 (

Table 2 ,
process 3), undergoing dissociation synchronously with the formation of a new N-H bond to yield the N - 2 H ,3 intermediate (Table

Table 3
DFT calculated reaction energies, activation barriers, and vibrational frequencies for unstable modes corresponding to the reaction coordinate, for all elementary processes associated with the dissociative Langmuir-Hinshelwood mechanism for ammonia synthesis