Electrochemical ammonia production on molybdenum nitride nanoclusters

Theoretical investigations of electrochemical production of ammonia at ambient temperature and pressure on nitrogen covered molybdenum nanoparticles are presented. Density functional theory calculations are used in combination with the computational hydrogen electrode approach to calculate the free energy proﬁle for electrochemical protonation of N 2 and N adatoms on cuboctahedral Mo 13 nanoparticles. Pathways for electrochemical ammonia production via direct protonation of N adatoms and N 2 admolecules with an onset potential as low as -0.5 V and generally lower than -0.8 V on both a nitrogen covered or clean Mo nanoparticle. Calculations presented here show that nitrogen dissociation at either nitrogen vacancies on a nitrogen covered molybdenum particle or at a clean molybdenum particle is unlikely to occur at ambient conditions due to very high activation barriers of 1.8 eV. The calculations suggest that the nitrogen will be favored at the surface compared to hydrogen even at potentials of -0.8 V and the Faradaic losses due to HER should be low.


I. INTRODUCTION
Ammonia is a chemical compound of great interest and versatility, which is primarily used for making fertilizer; ultimately sustaining roughly one-third of the World's population.[1,2] In terms of reducing the carbon footprint, ammonia is interesting for a number of reasons.
Improving the sustainability of the already huge industrial catalytic production of ammonia, which is on the order of over 100 million metric tons annually and responsible for 1-2% of the global energy consumption would reduce cost of producing ammonia.Ammonia is also becoming increasingly interesting as a potential transportation fuel [3].As an energy carrier, ammonia has the benefit that it can be used in very energy e cient fuel cells, such as solid oxide fuel cells (SOFC) or a direct ammonia fuel cells (DAFC) [4].Furthermore, it has the interesting feature of not emitting CO 2 while having a high energy density that is comparable with traditional fossil fuels, both volumetric and gravimetric [3,5].A highly energy-e cient method for the synthesis of ammonia (NH 3 ) from molecular nitrogen (N 2 ) is therefore desirable.Currently, ammonia synthesis is achieved by the Haber-Bosch process, in which N 2 is initially dissociated and subsequently each nitrogen atom is protonated [6], i.e. the dissociative mechanism.The Haber-Bosch process is energy-intensive and centralized due to the required high temperature and pressure and it is associated with a high capital cost to construct the production plants.
The natural enzymatic process for ammonia production in Nitrogenase takes place by initially weakening the N-N bond through successive electrochemical protonation, until the dissociation barrier is low enough to break the N-N bond; this process is referred to as the associative mechanism [38].In this paper, we present a pathway for electrochemical reduction of nitrogen into ammonia on molybdenum nanoclusters, which could ultimately become sustainable through utilization of renewable electricity sources like windmills or solar cells.
We have previously identified Mo nanoclusters as a primary candidate for electrochemical production of NH 3 via the associative mechanism [39] and shown that at potentials relevant for NH 3 production, nitrogen will adsorb preferentially over hydrogen [35], thereby minimizing the traditional Faradaic losses due to the competing HER [37].These findings render nitrogen covered Mo nanoclusters as a prime candidate for electrochemical ammonia production.
In this paper, we investigate nitride formation and reduction on molybdenum nanoclusters as well as the competing hydrogen adsorption process.The potentials required for ammonia production through direct protonation of adsorbed nitrogen adatoms and molecules through the associative mechanism are presented.The dissociation barrier for N 2 molecules at various nitrogen coverages will also be presented.

A. DFT calculations
The calculations were carried out with density functional theory (DFT) calculations [40,41] using the RPBE exchange correlation functional [42] along with the projector augmented wave method [43,44] as implemented in the GPAW code [45][46][47].A grid of (3,3) for the finite di↵erence stencils have been used together with a grid spacing of 0.18 Å, at least 20 free bands above the Fermi level and a Monkhorst-Pack [48] k-point sampling of 2⇥2⇥2.A 7 Å vacuum layer around the nanocluster has been applied.When solving the electronic density self-consistently, the convergence criteria have been chosen such that the changes were  10 5 eV for the energy and 10 4 electrons per valence electron for the density.In all calculations, a Fermi smearing of 10 4 eV has been used.The atomic simulation environment ASE [49] was used to set up the atomic structure of these systems.All structural (and atomic) relaxations of the adsorbates (N, H, NH, etc.) attached on the Mo 13 N x nanocluster were carried out using the BFGS and FIRE [50] optimizers within ASE.In the determination of transition states and activation barriers the nudged elastic band (NEB) method [51][52][53] has been used with a spring constant of 1 eV/ Å2 .To precisely determine the transition state configuration and the corresponding minimum energy pathway between initial and final states, the climbing image method [53] was used as the final step in the NEB calculations.
B. The Mo 13 N x cluster The system of interest is the cuboctahedral molybdenum particle containing 13 atoms.
The clean molybdenum structure is shown in Fig. 1a.It has a molybdenum atom as the center and a shell of 12 molybdenum atoms [54][55][56].The particle was allowed to relax to find its optimum lattice constant and is through the whole study allowed to fully relax in all directions.The Mo 13 particle is of particular interest because it is highly undercoordinated and molybdenum binds nitrogen stronger than hydrogen; hence giving rise to a nitrogen coverage on the nanocluster.
There are two relevant adsorption sites on the molybdenum particle surface.The first adsorption site is the three-fold hollow site with three nearest metal neighbors, marked with 1, and the second adsorption site is a four-fold hollow site with four closest metal neighbors, marked with 2. Two images for the filling of the nitrogen skin are shown in 1b) (half-filled skin) and 1c) (filled skin).the four-fold hollow site is marked with 2. In the filled nitrogen skin, the four-fold hollow adsorption sites have changed into a bridge site and is now marked 3 on c), while the geometry is kept for the adsorbed nitrogen atoms in the original three-fold hollow sites (marked with 4).
In the case of a full nitrogen skin, two types of bonding exists for the nitrogen adatoms.
One is the three-fold hollow site, e.g., the atom marked 3 in Fig. 1c.The other adsorption sites is a bridge site with two molybdenum atoms (marked 4 in Fig. 1c).In the process of filling the nitrogen skin, the adsorption sites change from a four-fold hollow site to a bridge site; the change will be discussed further in a later section.

C. Reaction pathways
In the process of describing the production of ammonia electrochemically, it is convenient to model the anode reaction as the source of electrons and protons.The electrons are transported to the cathode side through an external circuit, while the protons are introduced into the proton-conducting electrolyte keeping up the equilibrium while di↵using to the cathode.At the cathode, nitrogen will react with protons and electrons in one of two reactions to form ammonia.At the catalytic active site the reaction for the nitrogen admolecule is and for the nitrogen adatom In this study, formation of ammonia through these pathways has been investigated at different nitrogen coverages.The reduction processes on the molybdenum cluster has been simulated using the Heyrovski-type [57] reaction for both the protonation of nitrogen adatoms and nitrogen admolecules; the Heyrovski-type mechanisms is a process where the proton is directly attached to an adatom or admolecule from the electrolyte and the electron comes from the surface and merges with the proton to create a hydrogen atom bonded to the molecule.In this study, the adsorbed species of nitrogen adatoms or nitrogen admolecules are directly protonated and the following species are created on the surface; NH x or N 2 H x (x={0,1,2,3}).In principle, a Tafel-type reaction also exists, but it requires the reaction barriers for the hydrogenation steps [34,58] and will therefore require a higher temperature to drive the process forward.This is due to the fact, that the Tafel-type reaction [59] requires that the proton and electron to first merge on the surface to form a hydrogen adatom, and then the hydrogen adatom reacts with the adsorbed species of NH x or N 2 H x (x={0,1,2,3}).
The calculated reaction pathways for the electrochemical ammonia production is presented below.First, the reaction pathway of direct protonation of the nitrogen adatoms on the surface is considered.Here, a nitrogen adatom is directly protonated and after successive protonations, the formed ammonia is released from the surface.This process removes nitrogen atoms from the surface and would therefore require a regeneration of the nitrogen adatoms on the surface to retain the skin.Therefore, this presented pathway below does not describe the full catalytic cycle; only the nitride reduction.
Regeneration of the nitride will have to happen through N 2 dissociation on the surface.
This reaction is a heterogeneous reaction and will require low activation barriers to allow for preferential nitride regeneration over ammonia production.
Next, the associative Heyrovski mechanism is considered, where a nitrogen molecule is directly protonated until it splits into two molecules in the form of NH x species that later form gaseous ammonia.In the equations below, information from the calculations have been used, where the addition of the fourth H to the molecule N 2 H 3 * weakens the internal N-N bond su ciently such that the molecule readily dissociates into NH x species on the surface.
The reaction steps described above are either purely electrochemical or thermal steps and together they describe the full catalytic cycle of the MoN x particle for ammonia synthesis.

D. Electrochemical modelling
With DFT it is possible to calculate the reaction energy, E, for each of the reaction intermediates described above in the direct protonation of nitrogen adatoms and nitrogen admolecules following the Heyrovski type protonation process.This reaction energy is calculated with respect to the gas phase molecules of hydrogen and nitrogen and the right corresponding Mo 13 N x nanocluster: where E M 13 Na NxHy is the total energy of the combined system of the Mo 13 N a and the adsorbed N x H y adsorbates, E Mo 13 Na is the total energy of the system containing only the Mo 13 N a nanocluster, while E N 2 (g) and E H 2 (g) are the calculated gas-phase energies of nitrogen and hydrogen molecules, respectively.
The reaction energies provides information about the catalytic properties for ammonia formation.However, for a thorough understanding, free energy corrections for each reaction intermediate needs to be determined and included in the analysis.The expression of the free energy relative to the gas phase of molecular nitrogen and hydrogen is where E ZPE and S are the reaction zero point energy and reaction entropy, respectively.
The corrections for the zero point energy and entropy have been taken from a previous study [39], where the harmonic approximation was applied, the vibrational frequencies calculated for the reaction intermediates studied in this work and the corrections (ZPE and S) [60,61] at ambient conditions.
In addition to the entropy and zero point energy corrections, an applied potential driving the electrochemical reaction will influence the free energy for the reactions.To include the e↵ect of an applied potential, the computational hydrogen electrode [62] has been employed, which has previously been very successful in describing a number of electrochemical reactions, including the trends in oxygen [63][64][65] and nitrogen [35,39] and CO 2 reduction.[66] The procedure of the computational standard hydrogen electrode is briefly outlined below.
The standard hydrogen electrode (SHE) is chosen as the reference potential.The chemical potential (the free energy per H) of H + + e is related to that of an applied potential of U = 0 V relative to the SHE and a partial pressure of 1 bar of H 2 in the gas phase at 298 K and pH = 0, the reaction free energy of eq. 1 is equal to the net reaction of eq.4a -4c and eq.7a -7f at an electrode.
The next step is to incorporate the e↵ects of an applied potential in all reactions involving an electron transfer and for the protons the pH.The free energy shift for a part reaction involving n electrons is -neU and hence the change in free energy reads where the pH value is set to zero.For pH values di↵erent from 0, the correction to the free energy of H + -ions, there is a correction to the entropy arising from the concentration dependence and gives a shift of G(pH presented in the present study are for a pH value of 0.
To drive the electrochemical reaction forward, the reaction should be exergonic, i.e. the change in free energy for each part reaction described in eq.4a -4c and eq.7a -7f has to be exothermic.From eq. 10, it is evident that the applied potential can be tuned such that the reaction steps involving a proton transfer can be made exothermic and the specific applied potential ensuring this criteria is denoted the "onset" potential.As an example, the onset potential for part reaction 4b is determined in the following way: The next step is to apply a potential such that each forward reaction has negative free energy change and the onset potential is defined when G dis,2 = 0.The onset potential for each part reaction can then be calculated as: Applying the potential U ensures that the reaction occurs spontaneously, as long as the protonation barrier is low.

III. RESULTS AND DISCUSSION
A. Stability of the nitrogen skin 1.The energetics of the nitrogen and hydrogen skins In the investigation of the nitrogen coverage on the cuboctahedral structure, the first sites of interest for nitrogen adsorption are the three-fold hollow sites, marked with 1 in Fig. 1a.These sites are known to adsorb nitrogen most strongly [32,39].
The addition of nitrogen adatoms to the molybdenum nanoparticle has been carried out adding the nitrogen adatoms to three-fold hollow sites.For the first additions of nitrogen adatoms the particle changes shape to optimize the adsorption of nitrogen adatoms.For the fifth nitrogen addition, the adsorption in the three-fold hollow site again follow the cuboctahedral shape.The adsorption free energies of the first eight nitrogen atoms are shown in Fig. 2, (dark filled line), where 0 is the free energy of the clean Mo 13 nanocluster and the respective number of 1/2N 2 in gas phase.The graph shows that the adsorption free energies are strongest for the first additions and are then reduced when more nitrogen are added to the surface.The average binding energy for the nitrogen adatoms is presented with a dotted dark line in Fig. 2. The higher the nitrogen coverage, the smaller the structural changes.
The adsorption of hydrogen on the cuboctahedral molybdenum nanoparticle is carried out by adding hydrogen to the three fold hollow sites.In Fig. 2, the adsorption free energy of hydrogen is plotted with a pale red color and forms almost a straight line.There is no observed restructuring of the nanocluster.

The Nitrogen skin under reaction conditions
With respect to coverage, the competition between nitrogen (dark filled line) and hydrogen (the light dashed line) at an applied potential of -0.8 V in Fig. 2 shows that nitrogen will be preferred on the surface with overpotential as high as -0.8 V with respect to SHE.
Overpotential of up to -0.8 V have previously been shown to be su cient for the production of ammonia on a Mo model system surface [39].
The results for molybdenum nanocluster covered with either nitrogen or hydrogen shows that it is indeed interesting to investigate the production of ammonia on this nitrogen skinned molybdenum particles because the particle should preferentially have nitrogen on the surface under reaction conditions.The stronger nitrogen bonds compared to hydrogen should subsequently result in reduced Faradaic losses due to lower hydrogen evolution on the molybdenum nanocluster under reaction conditions for ammonia production.The next step is to determine the electrochemical properties of the Mo 13 N x nanoparticle with respect to the direct protonation of nitrogen adatoms or the associative pathway from an adsorbed N 2 molecule at nitrogen vacancy sites.

Direct protonation of the nitrogen skin
Our calculations show that a nitrogen skin is stable with respect to hydrogen.The first thing to investigate in the determination of the electrochemical properties of the molybdenum nanocluster is thus the direct protonation of the nitrogen skin.The filled skin has two nitrogen adsorption sites, the three-fold hollow site and the bridge site.Calculations performed on the filled skin are shown in Fig. 3 where the onset potential is the potential required to make each part reaction exothermic.The figure shows that the onset potential is close to -0.5 V for ammonia production with respect to SHE for both nitrogen adsorption sites.The geometry of the reaction intermediates for each of the reaction pathways is presented in Fig. 3.The geometries of NH are either a bridge site or a three-fold hollow site.For both NH 2 species it is a bridge site, where the geometry of the NH 2 in the three-fold hollow pathway has been moved from the three-fold hollow site to a bridge site during the relaxation of the system.The most stable adsorption site of NH 3 for both studied reaction pathways is the on top sites.A comprehensive electronic charge analysis of the preferred protonation sites has not been performed due to the large associated variations in the geometrical relaxations of the small nanoclusters, but the observations of the adsorption geometries are in good agreement with observed geometries for NH x adsorption structures presented in literature [32,35,39,67].
For the further direct protonation of the Mo 13 N x nanoclusters, similar onset potentials for reduction of the nitrogen skin are observed.For structures with high nitrogen coverage, the lowest onset potentials are on the order of -0.6 V to -0.8 V, see Fig. 1   The minimum energy path for the N 2 dissociation on the Mo 13 N 10 can be seen in Fig.

4.
Here, the initial and final state configuration together with the transition state is shown.
The barrier for the splitting of N 2 is found to be 1.72 eV, indicating that splitting of N 2 is not possible on an almost filled nitrogen skin on the molybdenum particle.

The associative mechanism
The direct protonation of N 2 admolecules has been thoroughly investigated on the almost filled nitrogen skin on the molybdenum cluster.Two di↵erent reaction pathways were studied 12 at two di↵erent nitrogen coverages.The higher nitrogen coverage (Mo 13 N 12 ) is presented here, while the lower nitrogen coverage case (Mo 13 N 10 ) can be seen in the supplementary material, the main results from both cases are the same.

FIG. 5.
Onset potentials for all part reactions for protonation of an adsorbed nitrogen molecule on the Mo 13 N 12 nanocluster.For the bridge site, the light dashed line, the onset potential is -0.75 V and for the three-fold site, the dark filled line, the onset potential is -0.6 V.
The Mo 13 N 12 -N 2 is the system with the highest nitrogen coverage that can adsorb a nitrogen molecule in a nitrogen vacancy site.The nitrogen molecule has two possible adsorption sites, one is a three-fold hollow site and the other is a bridge site.The vacancy site barely adsorbs the N 2 molecule; the reaction free energy for adsorption is -0.07 eV with the threefold hollow site as the most stable one.The reason for the weak adsorption of the nitrogen molecules is a steric hindrance caused by the nearby adsorbed nitrogen atoms Fig. 5 shows the onset potentials for driving the protonation of N 2 .For both nitrogen pathways, the most endothermic reaction step is the first protonation.Here, the onset potential is around -0.6 V for the three-fold hollow site, marked by the dark filled line, and -0.75 V for the bridge site, marked by the light dashed line.For the pathway taking place on the bridge site, only the first three protonation steps are shown, since the onset potential for the pathway in the three-fold hollow site is lower.During the fourth protonation of N 2 H 3 at the three-fold hollow site, the molecule prefers to dissociate into two NH 2 molecules.The protonation and splitting of the N-N bond is strongly exothermic, where the reaction free energy of this step is 1 eV downhill.It was possible to find a semi-stable N 2 H 4 configuration, but the creation of this reaction intermediate on the surface is 0.9 eV uphill.The associative mechanism was also examined on a more reduced cluster (Mo 13 N 10 ).The adsorption energy of the nitrogen molecule is stronger, -1.2 eV, and the onset potentials for the individual part reactions for ammonia formation are presented in Fig. 2 in the ESI where an onset potential of -0.6 V in the best case.
With onset potentials of less than -0.8 V for all protonation processes, both the direct protonation of surface nitrogen and the associative pathways for N 2 , shows that the protonation of nitrogen adatoms and admolecules into ammonia is possible.

C. The hydrogen competition
With an adsorption energy of -0.06 eV for N 2 , in the case Mo 13 N 12 and a corresponding adsorption energy of hydrogen adatoms at -0.65 eV, the hydrogen adatoms will preferential bind to the nitrogen vacancy sites.Lower nitrogen coverage increases the adsorption energy of nitrogen molecules.It increase from -0.06 eV to -2.56 eV at the clean molybdenum particle, while the corresponding adsorption energies of hydrogen is almost constant, rising from -0.66 eV to -0.74 eV.The adsorption energies can be seen in table I.The studied at the high nitrogen coverage show that the hydrogenation of the nitrogen adatoms and admolecules is possible at reasonable overpotentials, but the dissociation is an issue with a huge activation barrier.This will lead to formation of ammonia from adsorbed nitrogen, but the nitrogen skin will be reduced under reaction conditions because the dissociation will not lead to a regeneration of the nitrogen skin.Furthermore, the adsorption of nitrogen molecules with respect to hydrogen adatoms is not preferential at high nitrogen coverage.
At a coverage of 10 nitrogen atoms, N 2 binds with -1.2 eV, compared to a hydrogen adsorption energy of ✓G H = -0.73eV (see table I).Fig. 2 in the ESI shows that the potential required for electrochemical ammonia production is -0.6 V.At this potential, the formation of H on the surface will have a reaction free energy of -1.33 eV, while the protonation of N2 will have a reaction free energy of only -0.4 eV.It is therefore expected that H will first cover the unoccupied nitrogen vacancy sites.When all sites are filled, the protonation of N 2 will proceed because the formation of H 2 (g) will be 0.13 eV uphill and at the potential required for electrochemical ammonia production all reaction steps for ammonia production will be exergonic.Adsorbate-adsorbate interactions may however lower, e.g., the free energy barrier for producing gas phase hydrogen at high coverage, but quantification would require a more detailed analysis.
Overall, this will lead to reduction of the nitrogen skin and hydrogen adsorption at high nitrogen coverage.On the other hand, adsorption energies at low nitrogen coverage show that nitrogen will be preferred over hydrogen at these conditions.

D. Low nitrogen coverage
From the study of the N 2 dissociation, the direct protonation of the nitrogen skin, the protonation of N 2 and the competing adsorption of hydrogen, we find that the skin will most likely not be completely filled with nitrogen.Even at low nitrogen coverages the onset potential for the direct protonation is still less than -0.6 V, see Fig 3 in the ESI.Nitrogen adatoms on the surface for any given nitrogen coverage will be protonated into ammonia at potentials lower than -0.6 V.In the following, the dissociation and reduction of N 2 molecules are carried out on a clean molybdenum surface with either N 2 or two N adatoms adsorbed.
As see in table I, N 2 adsorbs with 2.5 eV while two nitrogen atoms adsorb with 4 eV.In comparison the hydrogen binding energy is only -0.74 eV and with an applied potential of -0.8 V the hydrogen is bonded -1.54  The dissociation of nitrogen molecules is a crucial reaction step.The free energy of the N 2 and 2N on the surface gives rise to a very exothermic splitting of N 2 .According to the Brøndsted-Evans-Polanyi [68] relations one would expect a lower activation barrier.This is not the case, the activation barrier for this system is still around 1.8 eV and will be rate limiting at room temperature, see Fig. S4 in the ESI.

Associative mechanism
Two routes for the associative pathways are presented in Fig. 6.The first route is pathway 1, which is a process where first one of the nitrogen atoms is directly protonated until ammonia is formed and then continues with protonation of the second nitrogen until formation of ammonia is achieved.This results in a splitting of the nitrogen bond at the third addition of a hydrogen atom (the 3 rd protonation coordinate).The second part of the first route is protonation of the second nitrogen atom.The crucial step is the last protonation of the NH 2 to NH 3 , where an onset potential of -0.6 V is required.This route presents a pathway for formation of the nitrogen skin, but the onset potentials for the nitrogen adatom (4 th and 5 th protonation coordinate) is positive and hence should occur instantaneously at reaction conditions and therefore a nitrogen build up is most likely not happen.N-N bond where NH and NH 3 are formed on the surface.The issues for this route are both the formation of NH 2 -NH and the formation of NH 3 .These steps require an onset potential of -0.7 V and -0.45 V, respectively.The graph shows that the fourth protonation step, where the N-N breaking occurs, is very exothermic.

E. Desorption of ammonia
One issue that has not been illustrated with the use of the onset potential for the presented pathways of ammonia formation is desorption of ammonia from the surface.In this study the very reactive metal molybdenum is being studied and according to literature and the Sabatier principle the best catalysts are the ones that have just the 'right' reactivity.Too reactive metals have issue of getting products of the surface and too weak metals will have issues in the formation of the products.Two nitrogen coverages have been chosen to illustrate desorption of ammonia from the molybdenum nanocluster.One case is the high coverage of nitrogen (the Mo 13 N 10 cluster) and the other case a low coverage of nitrogen (the Mo 13 cluster).In both cases the molybdenum nanoclusters have two ammonia molecules adsorbed.The di↵erent ways of desorbing the two ammonia molecules were studied.The reference system for calculating the desorption energy of ammonia is the free ammonia particle and the respective ammonia molecule(s) in gas phase.
In the case of high nitrogen coverage the energy for desorption of ammonia from the surface is as low as 0.38 eV and in the worst-case scenario it is 0.51 eV.These desorption barriers will not be a major issue under ambient reaction conditions.Desorption of ammonia will be slightly hindered, but not the end that it will lower the activity of the catalyst by many orders of magnitude.
In the other case, the low nitrogen coverage, the values of the desorption energy of ammonia are in the best case 0.16 eV and in the worst case 0.40 eV.These are low thermodynamic barriers for desorption of ammonia from the surface.These calculations indicate that the electrochemical production of ammonia should not be thermally hindered.

IV. CONCLUSIONS
Our theoretical study of the nitrogen covered molybdenum nanoparticle at ambient temperature and pressure indicate that these particles have potential for creating ammonia with low onset potential both at low and high nitrogen coverage.Faradaic losses due to the competing HER are reduced compared to other model systems presented in the literature.
On the molybdenum nanoparticles nitrogen should be favored on the surface with applied potentials as high as -0.8 V.
At high nitrogen coverage, the pathways for creating ammonia are both the direct protonation of the nitrogen adatoms from the nitrogen coverage on the molybdenum nanoparticle and the protonation of an adsorbed nitrogen molecule adsorbed in the created nitrogen vacancy.The required onset potentials for both reaction pathways are on the order of -0.7 V to -0.5 V.The competition between hydrogen adatoms and nitrogen admolecules will be an issue at high nitrogen coverage, where hydrogen is preferred.
At low nitrogen coverage, the associative mechanism should require onset potentials of -0.6 V. Nitrogen admolecules are preferred at these conditions compared to hydrogen adatoms.
The dissociation of nitrogen at both low and high nitrogen coverage have very high activation barriers of around 1.8 eV, e↵ectively blocking the dissociative mechanism at ambient conditions.
Desorption energies of ammonia from the surface is varying from 0.1 eV to 0.5 eV.These desorption barriers should not make the ammonia production on the molybdenum thermally hindered at ambient conditions and room temperature.
The present study shows that molybdenum nanoclusters are promising electrocatalysts for ammonia production.Nitrogen molecules are found to bind preferentially over hydrogen on certain partially and fully reduced nitrogen skins on molybdenum nanoclusters at the potentials needed for electrochemical ammonia production through the associative mechanism.

3 FIG. 1 .
FIG. 1. a) The clean Mo 13 nanocluster.b) the Mo 13 N 7 nanocluster after adsorption of seven nitrogen atoms (the dark atoms).c) the Mo 13 N 14 with a filled nitrogen skin.The clean cuboctahedral nanoparticle, a), has two special adsorption sites, where the three-fold hollow is marked with 1 and

9 FIG. 2 .
FIG.2.The free energy for covering the Mo13 cuboctahedral nanoparticle with either nitrogen or hydrogen.The filled dark line shows the filling of the nitrogen skin and the dark dotted line shows the average free energy of binding nitrogen to the surface.The light colored line shows the free energy of adsorbing hydrogen, while the dashed light colored line shows the free energy of adsorbed hydrogen with an external applied potential of -0.8 V.

10 PageFIG. 3 .
FIG.3.The onset potential for each protonation reaction of a nitrogen adatom originating from the Mo 13 N 14 nanocluster structure.The onset potential for the three-fold site, dark filled line, and the bridge site, light dashed line, are close to -0.5 V.

2. N 2 dissociationFIG. 4 .
FIG. 4.The dissociation of N 2 on the Mo 13 N 10 nanocluster calculated using the nudged elastic band method.The initial state of adsorbed N 2 , marked with a, the transition state is marked with b and the final state is marked c.

FIG. 6 . 16 Page
FIG.6.The onset potential of the protonation of the N 2 molecule on the 'clean' Mo 13 particle.

11 Page 11 of 25 Physical Chemistry Chemical Physics Physical Chemistry Chemical Physics Accepted Manuscript Open
in ESI.These calculations indicate that the nitrogen skin can be protonated to create ammonia and a nitrogen vacancy site at the surface.When a Mo 13 N x nanocluster adsorbs a nitrogen molecule, there are two pathways for the Access Article.Published on 02 October 2013.Downloaded on 03/10/2013 14:30:19.The nitrogen molecule can either go through the associative mechanism and create ammonia directly or dissociate into two nitrogen adatoms and hence regenerate the nitrogen skin.The dissociation will be discussed first.

TABLE I .
The most stable adsorption energies of nitrogen molecules and hydrogen adatoms at di↵erent nitrogen coverages.The last column presents the binding energy of hydrogen at an applied potential of -0.6 V, which is potential at what ammonia creation is possible.