A Comparison of the Mechanisms and Activation Barriers for Ammonia Synthesis on Metal Nitrides (Ta 3 N 5 , Mn 6 N 5 , Fe 3 Mo 3 N, Co 3 Mo 3 N)

: In this study we perform a comparison of the reaction mechanism and the activation barrier for the rate-determining step in various metal nitrides (Ta 3 N 5 , Mn 6 N 5 , Fe 3 Mo 3 N, Co 3 Mo 3 N) for the ammonia synthesis reaction. The reactions are explained with simpliﬁed schematics and the energy proﬁles for the various reaction mechanisms are given in order to screen the catalytic activity of the catalysts for the ammonia synthesis reactio n. We ﬁnd that the catalytic activity ranks in the following order: Co 3 Mo 3 N > Fe 3 Mo 3 N > Ta 3 N 5 > Mn 6 N 5. We also ﬁnd that the reaction mechanism proceeds either by a Langmuir–Hinshelwood and an Eley–Rideal/Mars–van Krevelen mechanism. This is an overview of about 10 years of computational research conducted to provide an overview of the progress established in this ﬁeld of study.


Introduction
The ammonia synthesis reaction is one of the milestones of chemistry, spanning a history of over 100 years of industrial development [1][2][3].Currently, the catalyst most used industrially is a potassium oxide-promoted iron catalyst which operates at high temperatures (450-550 °C) and pressures (100-200 atm) and undergoes a Langmuir-Hinshelwood (L-H) mechanism [4,5].The mechanism of ammonia synthesis on Fe(211) and Fe3 clusters was elucidated theoretically very recently [6,7].Since ammonia is produced globally in vast amounts, currently represents about 50% of the product used by humans, and requires about 2% of the global energy use, it is desirable to find catalysts to synthesize it in a more sustainable way.Therefore, metal nitrides that can operate at lower temperatures and pressures have been suggested as alternatives to the iron catalyst.There is also a ruthenium-supported graphite catalyst that is used in small-scale industrial plants for ammonia synthesis that operates at more moderate temperatures (200-300 °C) [8].In this catalyst, an -N2H intermediate was found to be important and it was discovered that the reaction mechanism is associative [9].
When we started investigating the mechanism of ammonia synthesis on cobalt molybdenum nitride, only a handful of previous studies had computationally studied this and assumed that the surface intermediates are -N and -H [10] and that an L-H mechanism operates [11].Other kinetic studies have applied Brønsted-Evans-Polanyi (BEP) relationships that correlated the dissociation barrier to the adsorption energy of N2 [10,12].We have set out to understand the mechanism of ammonia synthesis on cobalt molybdenum nitride (Co3Mo3N), which is known to be a more active catalyst for ammonia synthesis than the iron catalysts, especially when doped with caesium [10,11,13,14].For Co3Mo3N metal support, interactions with crystalline MgO support have been found to be beneficial for the activity of this catalyst [15].The optimum feedstock composition was investigated using ammonia synthesis rate measurements [16].For this catalyst, we found that there are two competing mechanism in which ammonia is synthesised in: (1) via the conventional Langmuir-Hinshelwood (L-H) mechanism, and (2) via an Eley-Rideal/Mars-van Krevelen (E-R) mechanism [17,18].Following this study, we modelled the reaction mechanism for ammonia synthesis on tantalum nitride (Ta3N5) [19], manganese nitride (Mn6N5) [20], and iron molybdenum nitride (Fe3Mo3N) [21], but generally found lower activity than the Co3Mo3N catalyst.There have also been studies by other groups concerning the mechanism of the ammonia synthesis reaction on metal nitrides.For example, Younes Abghoui and Egill Skúlason, who investigated Zr, Nb, Cr, and V mononitrides [22,23] for the electrochemical reduction in ammonia and in a two-step solar-energy driven ammonia synthesis on metal nitrides, found nitrogen vacancies to be important catalytic centres [24,25].Furthermore, in the study of the electrochemical synthesis of ammonia on group III-VII transition metal nitrides, NbN was found to be suitable [26].The Co3Mo3N catalyst, when doped with Cs, was found to produce H2 from ammonia via a decomposition pathway [27].Furthermore, spatially resolved Co3Mo3N particles on SBA-15 were found to have enhanced catalytic activity by Said Laassiri and co-workers [28].Recently, enhanced nitrogen activation was observed in the electrochemical synthesis of ammonia over a composite Co3Mo3N and La0.6Sr0.4Co0.2Fe0.8O3perovskite cathode [29].
For the first time, the different mechanisms that are happening on chemically related materials are studied with respect to ammonia synthesis.The computational process of elucidating a reaction mechanism is tedious and is attempted for one material/catalyst at the time.However, in this study, by combining the results of a series of papers on related materials (i.e., metal nitrides), we show that we can rank them in terms of activity on the basis of the activation barrier of the rate-determining step.This study should inspire other computational chemists to try ranking materials based on catalytic activity of the potential energy diagram for the reaction.

Materials and Methods
All calculations were completed with the plane-wave code VASP 4 and VASP 5 [30,31].The unit cell of each metal nitride was optimised by changing the lattice vectors and atomic positions, and then that unit cell was used to generate the slab.All DFT calculations were Γ-point [32] spin-polarised calculations within the generalized gradient approximation (GGA) using the revised Perdew-Burke-Ernzerhof (revPBE) exchange-correlation (XC) functional [33], with the projector augmented-wave (PAW) method [34,35] used to represent core states.The force threshold on the geometry optimisations was 0.02 eV Å −1 and the convergence criterion for electronic relaxation was 10 −4 eV.The plane-wave cutoff was set to 800 eV and the k-point convergence was achieved for the 4 × 4 × 1 Monkhorst-Pack grid for the Ta3N5.The plane-wave cutoff was set to 600 eV for the Mn6N5 system with a k-point grid of 2 × 2 × 1.The cutoff energy for the Co3Mo3N and Fe3Mo3N system was set to 650 eV using a 4 × 4 × 1 k-point grid.
Grimme's dispersion corrections were included via the zero-damping DFT-D3 correction method [36], in which the following dispersion energy correction is added to the Kohn-Sham energies, where  6, and  8, denote the averaged (isotropic) 6th and 8th order dispersion coefficients for atom pair ij and   is the internuclear distance between atoms i and j, respectively. 6 and  8 are the functional-dependent scaling factors.The Nudged Elastic Band (NEB) method was used to calculate activation barriers [37] using five images to map out the barrier.

Cobalt Molybdenum Nitride (Co3Mo3N)
The Eley-Rideal/Mars-van Krevelen mechanism is shown in Figure 1a.The active side for the catalytic cycle is a nitrogen vacancy on the molybdenum nitride framework.Molecular nitrogen chemisorbs at the N-vacancies in an end-on configuration and then molecular hydrogen chemisorbs dissociatively onto the molecular nitrogen, forming a diazene intermediate.Following this, another molecular hydrogen from the gas phase physisorbs molecularly at an adjacent molybdenum nitride centre, as shown in C′.The molecular physisorbed hydrogen then reacts with the diazene intermediate, forming a hydrazine intermediate and an atomically chemisorbed H as shown in D′.The hydrazine intermediate dissociates, forming the first stoichiometric ammonia in a low barrier process, leaving behind on the surface of the catalyst a nitrate and atomic hydrogen, as shown in E′.The atomic hydrogen then moves to the nitride forming -NH.Subsequently, another molecular hydrogen physisorbs at the molybdenum nitride framework where it reacts with the -NH forming -NH2, as shown in H′.Following this, the atomic hydrogen from the molybdenum nitride framework reacts with -NH2 forming -NH3 as shown in I′.This ammonia molecule desorbs from a catalyst in a high barrier process, indicating that the catalyst surface may be covered with ammonia after a few catalytic cycles.[18] with permission.
The Langmuir-Hinshelwood mechanism is shown in Figure 1b.The active site for this mechanism can be found at the interface of the cobalt clusters and the molybdenum nitride framework.In this mechanism, molecular nitrogen adsorbs side-on at the active site and is significantly activated (i.e., 21%), as shown in A. The activated nitrogen undergoes dissociation and forms two bridged N-species, as shown in B. Then, H2 chemisorbs dissociatively on the cobalt cluster, as shown in C. H then reacts with the bridged-N species, forming a >N-H intermediate, as shown in D, which moves to a hollow position at the Mo3 site.Another H reacts with N-H forming >NH2 at a bridge site of the cobalt cluster, as shown in E. In F, another H2 adsorbs dissociatively on the cobalt cluster.In G, the 3fbound-N to the Mo3 hollow moves due to surface diffusion to the adjacent Co-Mo2 hollow, while displacing NH3 chemisorbs on the Co8 cluster.In H, 3f-bound-N at Co-Mo2 hollow moves to the adjacent bridge position at Co8, reacting with H and forming an >NH intermediate.In J, H2 adsorbs dissociatively on the cobalt cluster, forming in K a >NH2 intermediate.In L, a third H atom reacts with >NH2, forming >NH3, which then desorbs from the active site of the L-H mechanism, as shown in M.
In Figure 2, we compare the Langmuir-Hinshelwood (L-H) with the Eley-Rideal/Mars-van Krevelen (E-R) mechanism and we can observe that all barriers for the hydrogenation steps in the L-H mechanism are larger than the E-R mechanism.This gives a clear indication that the E-R mechanism of cobalt molybdenum nitride is a kinetically faster mechanism and will be the main mechanism for ammonia synthesis over Co3Mo3N.

Figure 2.
Relative energy diagram of Langmuir-Hinshelwood (red) and Eley-Rideal/Mars-van Krevelen (black) mechanism for ammonia synthesis on Co3Mo3N surfaces.Energies in reference with the empty surface with one nitrogen vacancy, 3H2(g), and N2(g), reproduced from Ref. [18] with permission.

Tantalum Nitride (Ta3N5)
The mechanism of ammonia synthesis on tantalum nitride starts again with a nitrogen vacancy, as shown in O of Figure 3. Molecular nitrogen chemisorbs at this N-vacancy in a side-on configuration.Subsequently, molecular hydrogen chemisorbs in a side-on configuration at an adjacent tantalum centre, as shown in B. Another molecular hydrogen from the gas phase chemisorbs at the other tantalum centre of the catalytic site, as shown in C. The molecularly chemisorbed hydrogen then dissociates and reacts with the chemisorbed nitrogen, forming initially NN-H, as shown in D. This step has a barrier of 50 kJ/mol, which is a relatively moderate barrier for hydrogenation.In a subsequent step, another molecular hydrogen dissociates, reacting with NN-H and forming H-NN-H, as shown in E. The H-NN-H species then moves to the adjacent tantalum site, forming in the process an ammonia molecule, as shown in F. This intermediate generates the first stoichiometric ammonia in a rather high barrier step (F→G).In the following step, molecular hydrogen chemisorbs on the tantalum atom that does not have any preadsorbed hydrogen, as shown in H.This molecular hydrogen then dissociates, forming a -NH species, as shown in I. Subsequently, the atomic chemisorbed hydrogen from the nearby tantalum sites hydrogenates the -NH, forming initially >NH2, as shown in J. Then the >NH2 reacts with -H, forming ammonia that is adsorbed to the tantalum atom, as shown in K.The ammonia desorbs form the catalytic site in a high barrier process, indicating that the catalytic site may be poisoned by adsorbed ammonia.The details of all the activation barriers are shown in Figure 4 and it generally appears that the tantalum nitride catalyst is less reactive than the Co3Mo3N catalyst.

Manganese Nitride (Mn6N5)
The mechanism of ammonia synthesis of manganese nitride starts again with nitrogen vacancies at the surface of the (111) surface.Molecular nitrogen chemisorbs in an endon configuration at these nitrogen vacancies and on the Mn atoms, as shown in Figure 5 in B and C. Molecular hydrogen that physisorbs on these N2 sites then reacts with them in a high barrier process, forming -NNH2.The same happens for the N2 adsorbed onto the Mn atoms, which also forms -NNH2.Subsequently, molecular hydrogen interacts with two -NNH2 species on the surface, simultaneously forming two ammonia molecules that are adsorbed on nitrogens of the manganese nitride framework.When these ammonia molecules desorb, which happens in two consecutive steps in a relatively low barrier process, all nitrogen vacancy sites on the surface of the catalyst are occupied.At this point, molecular hydrogen chemisorbs on the nitrogen of the manganese nitride framework, and in a moderate barrier process forms >NH2, as shown in M.This happens also for another nitrogen on the (111) surface of Mn6N5, forming a second >NH2 species, as shown in O.After this, molecular hydrogen interacts with two >NH2 species, forming two ammonia molecules that are chemisorbed on the Mn atoms, as shown in P.These ammonia molecules desorb in a relatively high-energy process, leaving the surface exposed to nitrogen vacancy sites that act as catalytic centres for the upcoming catalytic cycles.The differences of this mechanism from the one occurring on Co3Mo3N is that molecular hydrogen reacts in an Eley-Rideal type mechanism during the formation of ammonia, which, however, is found to be a high-barrier process on this catalyst.Therefore, this catalyst has the lowest activity for ammonia synthesis compared to the other metal nitrides in this study.The potential energy diagram for this reaction mechanism is depicted in Figure 6 and shows that the surface of the catalyst is poisoned by -NNH2 species and that increasing the concentration or partial pressure of hydrogen in the feedstream may have a positive effect on the kinetics of this reaction on Mn6N5.

Iron Molybdenum Nitride (Fe3Mo3N)
The E-R mechanism of ammonia synthesis of iron molybdenum nitride is the same as the mechanism for cobalt molybdenum nitride.From the barriers of the reaction mechanism, as shown in Figure 7, it becomes clear that the Fe3Mo3N catalyst is less reactive than the Co3Mo3N catalyst for ammonia synthesis.In particular, all hydrogenation steps are high-barrier processes.However, the desorption of ammonia from the catalyst requires less energy compared to the hydrogenation steps.The barriers for the reaction pathway indicate that Fe3Mo3N is less reactive than Co3Mo3N for ammonia synthesis but more reactive than Ta3N5 and Mn6N5.The future of ammonia synthesis research using computational tools relies on the use of aspects coming from kinetics to rank catalytic materials based on their activity.This so far has been a tedious process which requires exact knowledge of the reaction mechanism and calculation of all the barriers for the reaction.Currently, we are not aware of another study where different reaction mechanism are considered for ammonia synthesis to rank catalytic materials.
Future directions of this research would be to study the mechanism of ammonia synthesis on other metal nitrides and attempt to find a mechanism that has a lower barrier for the RDS of cobalt molybdenum nitride.This would direct the way of computational screening of catalysts that at the moment is in its infancy.Also, finding softwares that can map out the mechanism of reactions using automated methods and methods that invoke machine learning is a possible direction.
There are definitely limitations and challenges for computational-only studies of reaction mechanisms.The first limitation is that DFT calculations have an accuracy of 1-2 kJ/mol, which can make a significant difference when we start talking about the rate and the activity of different materials.Also, in some cases, as has been shown for Co3Mo3N, the catalytic materials undergoes degradation, which will definitely affect the mechanism [39].Currently, taking into account various phases of the catalyst that are not the ones derived from X-ray crystallography is challenging and should be considered with care in future studies using computational tools.
The industrial use of catalyst for ammonia production is a long and slow process.For example, the Ru/Graphite catalyst was first studied computationally before it was used for small-scale ammonia synthesis production.Therefore, such ranking of catalytic materials is very advantageous as it can save time, resources, and funding from experimental efforts to improve these catalysts.It is without any doubt that the computational ranking of catalytic materials for ammonia synthesis will accelerate the discovery of new catalysts that are more active than the existing catalysts.We are therefore in the era that new experiments will be informed by computational studies of this kind more frequently.

Conclusions
We screened the activity of various metal nitrides using DFT calculations for the ammonia synthesis reaction.We found that the metal nitrides invoke nitrogen vacancies as catalytic sites for the ammonia synthesis reaction, but they proceed with different mechanisms.Co3Mo3N and Fe3Mo3N undergo an Eley-Rideal/Mars-van Krevelen mechanism that is associative.Ta3N5 undergoes a Langmuir-Hinshelwood mechanism for ammonia synthesis, which again happens at nitrogen vacancies.Mn6N5 undergoes an Eley-Rideal mechanism for ammonia synthesis, but the kinetics are not great because of the high barrier for the hydrogenation step of surface nitrogen.Following analysis of the activation energy barriers for the various mechanisms on metal nitrides, we find the following trend for the activity of these metal nitrides for ammonia synthesis: Co3Mo3N > Fe3Mo3N > Ta3N5 > Mn6N5.

Figure 3 .
Figure 3. Ammonia synthesis at nitrogen vacancies of the Ta3N5-(100) surface.The mechanism initiates at O with the adsorption of dinitrogen to a nitrogen vacancy.Figure reproduced with permission from Ref. [38].

Figure 5 .
Figure 5. Reaction mechanism for ammonia synthesis via an Eley-Rideal mechanism on θ-Mn6N5-(111) reproduced with permission from Ref. [20].Catalyst shown in black and intermediates shown in red.