On the possibility of an EleyRideal mechanism for ammonia synthesis on Mn6N5+x (x = 1)-(111) surfaces

Recently we reported an Eley–Rideal/Mars–van Krevelen mechanism for ammonia synthesis on cobalt molybdenum nitride (Co3Mo3N). In this mechanism hydrogenation of activated dinitrogen occurs directly from the gas phase in a low barrier step forming a hydrazinylidene intermediate QNNH2. In this paper we study whether such a mechanism of ammonia synthesis could occur on the (111) surface of another metal nitride, Mn6N5+x (x = 1), as this would explain the low-T ammonia synthesis activity of Co3Mo3N. We find that although N2 adsorbs more strongly than H2 on the (111) surface, having also examined the (110) and the (100) surface, N2 is not significantly activated when adsorbed in an end-on configuration. The hydrogenation reactions via an Eley–Rideal mechanism are all high barrier processes (4182 kJ mol ) and therefore an Eley–Rideal mechanism for ammonia synthesis is predicted to not occur on this material unless there are high temperatures. Our study indicates that the fact that an Eley–Rideal/Mars–van Krevelen mechanism occurs on Co3Mo3N is a result of the stronger activation of dinitrogen at nitrogen vacancies when dinitrogen is adsorbed in an end-on configuration.


Introduction
Metal nitrides, which are also called interstitial nitrides, have varying amounts of lattice nitrogen that occupies octahedral coordination sites, with the general formula MN y , with M = 3d metal and y o 1. 1 The structure that has received most attention is Z-Mn 3 N 2 2 which was found to be anti-ferromagnetic. 3 e-Mn 4 N 4 has the lowest percent nitrogen content, in which the atoms occupy a face-centered cubic (fcc) arrangement with interstitial nitrogen. The following in nitrogen content is z-Mn 2 N 0.86 5 (occasionally labelled as Mn 2 N 6 and Mn 5 N 2 7 ) which has a hexagonal close packed (hcp) structure. The manganese nitride with the largest nitrogen content is y-MnN 8 that has a slightly tetragonally distorted rocksalt phase (occasionally labelled as y-Mn 6 N 5+x 2 ). The manganese nitride phase studied here is y-Mn 6 N 5+x (for x = 1) which however did not contain any intrinsic nitrogen vacancies in the 3 Â 1 Â 1 unit cell and had therefore a 3 times smaller unit cell as shown in Fig. 1. This manganese nitride is refered to in this paper as y-Mn 6 N 5 . This manganese nitride has the advantage of having well defined low Miller index surfaces, which are depicted in Fig. 2.
Manganese nitrides have also been studied as a looping catalyst in ammonia synthesis 10,11 and for the reverse reaction, ammonia decomposition, by thermogravimetric analysis and neutron diffraction. 12 Mn 6 N 5+x and lithium imide (Li 2 NH) when combined result in a larger rate of ammonia decomposition than for either of the separate parts. 13 Additionally, CaNH can exert a strong synergistic effect on Mn 6 N 5+x leading to greatly enhanced catalytic activity for ammonia decomposition. 14 Manganese nitrides were also found to be an active and durable electrocatalyst in the oxygen evolution reaction (OER) from water under alkaline conditions. 15 Manganese nitrides can be synthesized by nitriding the metal with nitrogen or ammonia. 16 The rate of manganese nitride formation is higher at lower temperatures when ammonia instead of nitrogen is used as the source of lattice nitrogen, 17 which is a result of ammonia having a lower dissociation barrier than dinitrogen. Most of the manganese nitrides have been studied for their magnetic properties (e.g. e-Mn 4 N is ferromagnetic) however little is known about their activity as ammonia synthesis catalysts or nitrogen transfer reagents. There are only a few previous reports that mention a manganese nitride with the chemical formula y-Mn 6 N 5 . There is an electron diffraction study of the phase transition of this material from tetragonal to cubic at temperatures that exceed 440 AE 20 1C. The phase transition is attributed to magnetic reordering of the material rather than changes of the position of the atoms. 18 Another report which addresses the magnetic transition in more detail is a neutron diffraction study of both Z-Mn 3 N 2 and y-Mn 6 N 5 . 9 The potential use of metal nitrides in ammonia synthesis as catalysts or as reagents has attracted considerable recent interest. 19 Directly relevant to this is the use of Mg 3 N 2 as a nitrogen transfer reagent in the Paal-Knorr pyrrole reaction. 20 We have recently reported this material to be an efficient nitrogen transfer reagent especially when doped with lithium. 11 The discovery of catalysts or reagents that can synthesize ammonia at lower temperature for small-scale production is highly desirable for in situ and ''on demand'' production of ammonia. 11 However to use a catalyst in a decentralised plant, exact knowledge of the reaction mechanism and kinetic models is necessary. Currently the mechanism of ammonia synthesis is not known on manganese nitrides, whether it follows a conventional Langmuir-Hinshelwood mechanism such as the one observed on the iron or ruthenium 21 ammonia synthesis catalysts or an Eley-Rideal/Mars-van Krevelen mechanism such as the one we recently found on cobalt molybdenum nitride (Co 3 Mo 3 N). 22,23 Furthermore, the details of the adsorption and activation of molecular nitrogen and hydrogen are not known and whether hydrogen poisons the surface of the catalyst as the adsorption energy of H 2 usually exceeds that of N 2 , as we have recently calculated on other metal nitrides. 24,25 In this DFT study we have calculated the adsorption and activation of N 2 and H 2 on various low Miller index surfaces of y-Mn 6 N 5 . We found the surface of this material that will adsorb N 2 favourably instead of H 2 . We then calculated the complete pathway for ammonia synthesis via an Eley-Rideal mechanism. The results are then discussed in reference to another metal nitride, Co 3 Mo 3 N, that has previously exhibited the possibility of an Eley-Rideal/Mars-van Krevelen mechanism for ammonia synthesis.

Computational methods
We have generated a slab model of the various surfaces of y-Mn 6 N 5 based on the structure reported in a neutron diffraction study. 9 The surfaces were modelled via slabs about 1 nm in width that had a 20 Å vacuum gap, for which the surface structure is shown in Fig. 2. All DFT calculations were periodic G-point 26 spin-polarised performed with the VASP 5.4.1 code. 27,28 Exchange and correlation (XC) effects were evaluated within the generalized gradient approximation (GGA) using the revised Perdew-Burke-Ernzerhof (revPBE) XC-functional. 29 We used the projector augmented-wave (PAW) method 30,31 to represent core states, 1s for N and H and 1s to 3p for Mn. The cut-off energy for the plane wave expansion was set to 600 eV for periodic bulk and slab calculations. Geometry optimizations were performed with a residual force threshold of 0.01 eV Å À1 using the conjugate-gradient algorithm whereas the convergence criterion for electronic relaxation was set to 10 À4 eV.
In a previous computational study we have tested the bond dissociation enthalpy (BDE) of N 2 with the use of various XC functionals, the % error for revPBE was found to be the lowest among various GGA and hybrid GGA functionals. In particular, we found that the % error was for revPBE = 0. 23 Therefore, we have combined this XC functional with pairwise additive correction for van der Waals (VdW) interactions via the D3 method, 32 denoted as revPBE-D3, with which all subsequent calculations have been performed to yield more accurate barrier heights according to the calculated BDE of the N-N bond and the inclusion of VdW interactions.
For the bulk unit cell, convergence of the energetic and magnetic properties was observed for a 5 Â 5 Â 5 Monkhorst-Pack grid (MP-grid). The convergence plots are given as supporting information Fig. S1 and S2 (ESI †). A similar or slightly larger grid density (so that the grid obtains numbers to the nearest integer) was used for the slab calculations, for consistency. A G-point centred MP k-point grid was used with a grid density of 3 Â 3 Â 1, 2 Â 2 Â 1, 2 Â 2 Â 1 and 3 Â 2 Â 1 for the (100), (111), (111) 0 and (110) surface of y-Mn 6 N 5 , respectively, shown in Fig. 2.
The initial charge density was obtained by superposition of atomic charges. Initial adsorption configurations were such that the distance between the adsorbate and the nearest surface site was set to 2 Å in an end-on configuration for N 2 and H 2 . This adsorption configuration was found to also result in end-on and tilt adsorbed adsorbates. The various adsorption sites were every symmetry unique surface site shown in Fig. 2. This resulted in 4, 4, 3 and 3 symmetry unique adsorption sites for the (110), (100), (111) 0 and (111) surface, respectively. The adsorption energy was taken as the total difference between the energy of the fully relaxed bound state of the surface-adsorbate complex and that of the fully relaxed surface slab and the isolated molecules, given by: where X = N, H. Dispersion corrections were included via the DFT-D3 method as implemented in VASP. 32 Activation barriers were calculated with the nudged elastic band (NEB) method having five images for each barrier as implemented in VASP. 33 The effective magnetic moment per Mn atom in the optimised bulk structure of y-Mn 6 N 5 was found to be 3.95 m B , which was in good agreement with the experimentally measured value which ranges between 3.3 and 3.8 m B . 9 Furthermore, the optimised structure of the bulk unit cell was found to converge to the lattice parameters determined by neutron diffraction (a = b = 4.2193(1) Å, c = 4.1287(1) Å, and a = b = g = 901), 9 when the initial structure was the neutron diffraction crystal structure, for cutoff energies of the plane wave expansion greater than 500 eV. When the plane wave expansion had a cutoff smaller than 500 eV, these lattice parameters were severly underestimated.
We have studied an Eley-Rideal mechanism for ammonia synthesis on y-Mn 6 N 5 but without the missing N in the 3 Â 1 Â 1 unit cell. This reduces the size of the unit cell considerably to the 1 Â 1 Â 1 unit cell shown in Fig. 1, which is a face-centred cubic arrangement of Mn atoms with N atoms octahedrally coordinated. This unit cell has a chemical formula Mn 4 N 4 (or MnN) in which lower Miller index surfaces are shown in Fig. 2. Although our calculations for simplicity were done on Mn 4 N 4 , we refer to it as y-Mn 6 N 5 .

Adsorption and activation of N 2 and H 2
The adsorption of N 2 was investigated on every atop, bridge and hollow adsorption site of the (111), (111) 0 , (110) and (100) surfaces of y-Mn 6 N 5 as depicted in Fig. 2. The dispersioncorrected adsorption energy and the percent activation of the N-N bond are shown in Fig. 3a. The adsorption energy was found to be between À5 kJ mol À1 and À43 kJ mol À1 , which is weak, indicating physisorption except for the (111) surface where a value of À120 kJ mol À1 was calculated. This adsorption energy is unusually large for dinitrogen and it clearly suggests chemisorption. Although this adsorption energy is very large, the percent activation of the N-N bond is less than 4%. This is much lower than the activation of end-on adsorbed N 2 on Co 3 Mo 3 N at nitrogen vacancies where 11% activation was found. However, it is comparable to the activation of N 2 found on another metal nitride, Ta 3 N 5 , which was less than 3%. 24 Therefore, the adsorption and activation of N 2 on this metal nitride is molecular in the absence of nitrogen vacancies. It is intriguing that among the various metal nitrides studied computationally thus far, the (111) surface of y-Mn 6 N 5 is the only surface where the adsorption energy of N 2 exceeds that of H 2 ; we will return to this point later.
We have studied the adsorption of H 2 on all low Miller index surfaces of y-Mn 6 N 5 . The adsorption of H 2 was found to be molecular with an adsorption energy that ranged between À79 kJ mol À1 and À87 kJ mol À1 . This adsorption energy is rather large for molecular hydrogen and identical in strength with the value calculated on other metal nitrides such as Ta 3 N 5 where it was found to be between À81 kJ mol À1 and À87 kJ mol À1 .
In contrast to what was observed on Co 3 Mo 3 N surfaces, we do not observe dissociative adsorption of hydrogen when nitrogen vacancies are not present and the adsorption of H 2 is molecular on every symmetry unique adsorption site of the (111), (111) 0 , (110) and (100) surfaces of y-Mn 6 N 5 . This indicates that there is a barrier for the dissociative chemisorption of H 2 on y-Mn 6 N 5 , however the dissociative chemisorption of H 2 at N-vacancies was not considered. In total 15 adsorption sites were investigated and these corresponded to every atop, bridge and hollow site on the three low Miller index surfaces of y-Mn 6 N 5 . The adsorption energy of H 2 and the percent activation of the H-H bond are plotted in Fig. 3b. The activation of the H-H bond is also very constant for these adsorption configurations, which was found to be between 1.3% and 1.7%. The most prevalent adsorption configuration of H 2 was the end-on adsorption although a tilt was also frequent and one side-on configuration was also found.
If we address the question of competitive adsorption of N 2 and H 2 on the various low Miller index surfaces of y-Mn 6 N 5 , certain conclusions can be drawn based on these adsorption data. These conclusions are relevant to surfaces of this material that completely lack intrinsic nitrogen vacancies. (i) All surfaces apart from the (111) surface would have mostly hydrogen adsorbed to them, (ii) only the (111) surface would activate the N-N bond significantly, (iii) no activation of the H-H bond is observed when H 2 is adsorbed molecularly, and (iv) there is a barrier for the dissociative adsorption of H 2 . For the above four reasons we have modelled the ammonia synthesis mechanism on the (111) surface and only considered hydrogenation reactions via an Eley-Rideal type mechanism. We were primarily interested if an Eley-Rideal mechanism is possible on this manganese nitride, as we have seen on another metal nitride, Co 3 Mo 3 N. 22 We note that a potential Langmuir-Hinshelwood mechanism and the participation of intrinsic nitrogen vacancies in the mechanism are not considered in this study and will be the topic of a subsequent study.

Mechanism of ammonia synthesis on h-Mn 6 N 5
There are only a few studies of the ammonia synthesis mechanism via DFT on metal surfaces, nanoclusters and in organometallic complexes. Most of the early computational studies are focused on understanding the adsorption, activation and dissociation of N 2 on the Ru(0001) surface where it was found to occur primarily at steps rather than planar terraces with an activation barrier of 0.5 eV. 34 These findings were in agreement with earlier experimental studies by Ertl and co-workers who found through variabletemperature temperature programmed desorption (TPD) measurements the dissociation activation barriers of 0.3 eV 35 and 0.6 eV 36 on Ru/MgO. The effect of promoters such as Na and Cs was attributed to an electrostatic interaction that lowers the dissociation activation barrier on Ru(0001). 37 A partial study of the ammonia synthesis mechanism by Hu et al. 38 revealed that the hydrogenation steps of nitrogen can be as high in barrier as the N-N dissociation steps. Logadóttir and Nørskov 21 studied the ammonia synthesis mechanism on Ru(0001) surfaces at steps and at terraces. The influence of an electric field on DE for the dissociation of N 2 and the formation of NNH was studied on Ru surfaces (i.e. (0001) and (10% 11)) and found to increase and decrease, respectively. 39 Moreover, the barrier for NNH formation was found to decrease with the application of an electric field. There are few theoretical studies of electrochemical ammonia synthesis on metal nanoclusters 40 and surfaces 10,41,42 at ambient temperature and pressure. Abghoui and Skúlasson 43 studied a Mars-van Krevelen mechanism for electrochemical ammonia synthesis on the (100) facet of VN and the (110) facet of RuN. The same authors showed that H-assisted N 2 activation is significantly more facile than direct N 2 dissociation on transition metal nitrides (TMNs). 44 Michalsky and Steinfeld 45 explored the possibility of a solar-driven ammonia synthesis cycle where the Fe doping of manganese nitrides was found to increase the number of nitrogen vacancies. Michalsky and Peterson 10 also studied the possibility of low-pressure ammonia synthesis for energy storage through chemical looping of metal nitrides. There are also a few DFT studies of the enzymatic ammonia synthesis mechanism. Rod and Nørskov 46 studied the ammonia synthesis mechanism on the FeMo cofactor in nitrogenases and found that the reaction is an associative mechanism in which end-on nitrogen adsorbed to the Fe of the cluster undergoes stepwise hydrogenation, forming first hydrazine, which after further hydrogenation forms ammonia. An associative mechanism for ammonia synthesis was studied on mono-and dinuclear molybdenum complexes and cubane-type metal-sulfido clusters. 47 More recently an associative ammonia synthesis mechanism has been studied on singly dispersed bimetallic catalyst Rh 1 Co 3 /CoO(011) 48 similar to how the biological fixation of N 2 occurs by nitrogenases in plants. 49 The basic characteristic of View Article Online these ammonia synthesis mechanisms is that N 2 is hydrogenated by H + which causes gradual weakening and dissociation of the NRN bond. 50,51 There is only our previous study of an Eley-Rideal/Mars-van Krevelen mechanism on Co 3 Mo 3 N which we have shown to proceed efficiently by nitrogen activation in an end-on configuration at nitrogen vacancies. 22 The question that arises is whether an Eley-Rideal mechanism also exist on other metal nitrides? We have therefore modelled a complete pathway for ammonia synthesis via an Eley-Rideal mechanism. The reaction mechanism was modelled on the (111) surface of y-Mn 6 N 5 , which we found adsorbs nitrogen in an end-on configuration. The elementary reaction steps of the mechanism are shown in Scheme 1. The mechanism is an associative mechanism where the hydrogenation of N 2 causes gradual weakening of the NRN bond and the formation of ammonia. The reaction mechanism is depicted in Fig. 4 for which a brief description is given next. Two N 2 adsorb end-on on two manganese atoms that are separated by a nearest neighbour manganese atom (steps B and C). H 2 was then fixed by one of its atoms at a 3 Å separation from the terminal nitrogen of adsorbed N 2 (step E). The reason for this is that H 2 has an exothermic interaction with adsorbed N 2 , and therefore this increases the reaction barrier for its reaction forming diazanylidene, QNNH 2 . Here a clear distinction has to be made with respect to an Eley-Rideal mechanism occurring at high pressure and at ambient pressure. For the first the adsorption step of H 2 could be ignored as the H 2 coming from the gas phase has high enough velocity that it would not allow any structural perturbation of the adsorbate at the adsorption site, before the bimolecular collision and reaction. So at high pressure this phenomenon would decrease the barrier for hydrogenation by an amount equal to the exothermicity of the adsorption step. Based on this rational higher pressures would act favourably on the barriers of the hydrogenation steps via an Eley-Rideal mechanism. In step F H 2 adsorbs again at a 3 Å distance from the terminal nitrogen of the second adsorbed N 2 . A second diazanylidene is formed upon hydrogenation (step G). Two diazanylidene adsobates then react with an incoming molecular hydrogen (step H), forming two diazanes, -NNH 3 (step I). This elementary reaction step although it appears to be trimolecular is in fact bimolecular, as the two diazanylidene molecules are bound to the same substrate. In steps J and K the diazanes decompose forming two ammonia molecules and leaving nitride groups on the surface. H 2 adsorbs to the first nitride group (step L) forming an azanylium, 4NH 2 (step M). H 2 then adsorbs to the second nitride group (step N) and a second azanylium group forms (step O). The two azanylium groups are aligned in such a way that they can stereochemically interact favourably with a H 2 coming from the gas phase (step P). There are other alignments of the azanylium group that were higher in energy and therefore not considered in the mechanism. This reaction forms two surface adsorbed ammonia groups at positions that are separated by a Mn atom (step Q). The surface adsorbed ammonia desorbs from the manganese nitride surface (step R) and an adsorbate free surface is recovered so that a new catalytic cycle can be initiated.

Potential energy surface of reaction
In Fig. 5 we present the potential energy curve for the Eley-Rideal mechanism on y-Mn 6 N 5 -(111). The values of the activation energy barriers (E act ) and the reaction energies (DE react ) are tabulated in Table 1. We observe that the adsorption of N 2 to the (111) surface is exothermic by À122 kJ mol À1 (step B and C). This is followed by an exothermic adsorption of molecular H 2 of À76 kJ mol À1 (step D). The previous adsorption energies indicate that the surface will be entirely covered with end-on N 2 before the reaction of H 2 starts to occur. H 2 then reacts with the adsorbed N 2 in a high barrier process with an activation energy of 327 kJ mol À1 (step D to E). The adsorption of a second H 2 is only slightly exothermic by À17 kJ mol À1 . The next hydrogenation barrier is 478 kJ mol À1 high which is considerably higher than the first hydrogenation barrier which could be due to stereochemical repulsion between the diazanylidene and the incoming H 2 . Here the adsorption of H 2 to the two diazanylidenes is slightly exothermic by À20 kJ mol À1 . The third hydrogenation barrier of this H 2 that forms two diazanes is much smaller (182 kJ mol À1 ) compared to the barrier of N 2 hydrogenation to NNH 2 . The decomposition of the diazane into ammonia and a nitride is slightly endothermic by 11 kJ mol À1 for the first ammonia (step J) and 67 kJ mol À1 for the second ammonia (step K). The adsorption of the fourth H 2 to the nitride was found to be again exothermic by À78 kJ mol À1 (step L) with a high hydrogenation barrier of 265 kJ mol À1 (step L to M) in order to form azanylium. This was followed by the adsorption of the fifth H 2 , which was again found to be exothermic by À81 kJ mol À1 (step N).
Interestingly, the hydrogenation of the nitride into an azanylium that had an adjacent azanylium (step N to O) had a barrier of only 2 kJ mol À1 . We note that this elementary View Article Online reaction step may be a low energy pathway for the hydrogenation of surface nitrides in metal nitrides that have 3-fold bound nitrogen which is relevant to the formation of nitrogen vacancies on manganese nitrides on surfaces such as (111) 0 shown in Fig. 2. The adsorption of the sixth H 2 becomes endothermic by 26 kJ mol À1 (step P). The subsequent barrier for hydrogenation is 137 kJ mol À1 which forms two ammonia molecules adsorbed to the surface. The desorption of these ammonia from the surface is highly endothermic, with DE of 103 kJ mol À1 (step R) and 267 kJ mol À1 , respectively, for the desorption of the first and second ammonia. From the above potential energy surface of the reaction it is apparent that the mechanism does not proceed at low temperatures via Eley-Rideal chemistry although it is possible at high T. The hydrogenation barriers, apart from the 5th hydrogenation barrier, are high and therefore other mechanisms should be examined, such as Langmuir-Hinshelwood mechanisms or other pathways that occur at nitrogen vacancies. It is intriguing though that an Eley-Rideal mechanism for the hydrogenation of surface activated nitrogen exists on Co 3 Mo 3 N, which could be the underlying reason for the known enhanced activity of this tertiary metal nitride.

Conclusions
The adsorption and activation of N 2 and H 2 was studied on every low Miller index surface of Mn 6 N 5+x (x = 1). The adsorption of N 2 was molecular in the absence of nitrogen vacancies with adsorption energies of À5 kJ mol À1 to À43 kJ mol À1 . Only the (111) surface was found to activate N 2 , 4%, with a large exothermic adsorption energy (À120 kJ mol À1 ). This surface would inhibit the poisoning of the surface by H 2 which was found to bind strongly (À79 kJ mol À1 to À87 kJ mol À1 ) in a molecular form in the absence of nitrogen vacancies to all surfaces of Mn 6 N 5+x (x = 1). The complete reaction Eley-Rideal reaction pathway was modelled on the (111) surface of Mn 6 N 5+x (x = 1). It shows that an Eley-Rideal mechanism, in contrast with what was found on Co 3 Mo 3 N, would only proceed at high temperatures. This suggests that other mechanisms such as Langmuir-Hinshelwood or mechanisms that invoke nitrogen vacancies should be the focus of future studies of mechanistic pathways.

Conflicts of interest
There are no conflicts to declare.