DFT-D 3 Study of Molecular N 2 and H 2 Activation on Co 3 Mo 3 N Surfaces

Cobalt molybdenum nitride (Co3Mo3N) is one of the most active catalysts for ammonia synthesis, although the atomistic details of the reaction mechanism are currently unknown. We present a dispersioncorrected (D3) DFT study of the adsorption and activation of molecular nitrogen and hydrogen on Co3Mo3N-(111) surfaces to identify possible activation sites for ammonia synthesis. H2 was found to adsorb both molecularly on the Mo3N framework and dissociatively on Co8 clusters or Mo3 clusters that were exposed due to N-vacancies. We find that there are two possible activation sites for N2 where both N2 and H2 can coadsorb. The first is a Mo3 triangular cluster that resides at 3f nitrogen vacancies, and the second is a surface cavity where N2 is activated by a Co8 cluster, the second being a more efficient activation site. N2 was found to adsorb in three adsorption configurations: side-on, end-on, and an unusual tilt end-on (155°) configuration, and the existence of these three adsorption configurations is explained via MP2 calculations and the sphere-in-contact model.


INTRODUCTION
Co 3 Mo 3 N when synthesized using the procedure patented by Topsøe 1 is known to be active for ammonia synthesis at 400°C and elevated pressures using a 3:1, H 2 :N 2 mixture. 2,3 Indeed, Co 3 Mo 3 N when doped with Cs is one of the most active catalysts for ammonia synthesis, 2,4 with turnover-frequencies (TOF) that are remarkably high compared to graphitesupported Ru and Fe−K 2 O−Al 2 O 3 , the two catalysts currently used industrially for large scale ammonia synthesis. 2−8 Linear quantitative structure−property relationships (QSPR) between the dissociation energy of N 2 and its adsorption energy on Co 3 Mo 3 N were derived via periodic planewave DFT calculations 5,9 and the barrier for N 2 -dissociation was found to be the rate-determining step (RDS). It has been previously suggested that ammonia synthesis may proceed via Mars−van Krevelen (MvK) chemistry and that lattice nitrogen may act in nitrogen transfer, 10 which was also confirmed by isotopicexchange studies that showed that the lattice-N in Co 3 Mo 3 N is exchangeable at elevated temperatures. 11 The chemistry of N 2 / H 2 with Co 3 Mo 3 N has been previously studied via two experiments, which showed that such materials can be used as reagents to produce ammonia, consuming nitrogen that originates from the bulk of these materials. 12 These experiments confirm the gas phase nitrogen exchangeability with lattice-N based on powder XRD and isotopic studies. 11 They also showed that the Co 3 Mo 3 N can be regenerated from a less nitrogen-rich phase (i.e., Co 6 Mo 6 N) via a 700°C reaction with N 2 /H 2 or even N 2 , whereas the reverse reaction was obtained by changing the feedstream to Ar/H 2 . We have recently shown via DFT calculations that the mechanism can also proceed via MvK type surface chemistry at low temperatures as there is a large number of nitrogen vacancies (∼10 13 cm −2 ), which can activate N 2 by weakening of the triple bond. 13 N-vacancies were also found to participate in the mechanism for the electrochemical reduction of ammonia on VN and ZrN 14 and in the two-step solar-energy driven ammonia synthesis on metal nitrides. 15,16 Here, we extend the earlier study by investigating the adsorption at every possible site compared to the adsorption of molecular hydrogen.
The rest of the paper has the following structure: first we establish the calculation parameters that reproduce well the electronic structure of Fe x Co (3−x) Mo 3 N, where x = 0, 1, 2 and 3; next we describe the method for generating slabs of Co 3 Mo 3 N-(111) surfaces and apply the calculation parameters to address the question of hydrogen and nitrogen adsorption and activation on Co 3 Mo 3 N with and without defects. Finally we explain the various bonding configurations of N 2 via molecular orbital (MO) calculations and the sphere-in-contact model.

COMPUTATIONAL METHODS
2.1. Methodology. Spin-polarized periodic planewave calculations have been performed with the VASP 5.3.5 17,18 code using the revPBE 19 and a 650 eV cutoff for the planewave expansion. A detailed description of the computational methodology for the planewave calculations can be found in ref 13, in which it was found that among various GGA and hybrid-GGA XC functionals, the revPBE yields accurate (to within 1%) bond dissociation enthalpies for N 2 (g). Here, we further test how well this functional can perform in modeling correctly the electronic structure in a homologous series Fe (3−x) Co x Mo 3 N, (x = 0, 1, 2, 3), via reproducing the lattice parameters when compared to powder neutron-diffraction (PND) data. The adsorption energy was taken in its simplest form, as the energetic difference between the total energies of the bound state of the surface−adsorbate complex from that of the surface slab and the isolated molecules, the latter in a 20 Å periodic unit cell, given by where X = N, H. The adsorption energy was also corrected for the dispersion correction using two approaches via the DFT-D3 method as implemented in VASP. 20 The first (ΔE ads,D3relax ) was to fully relax the cluster-adsorbate system, the surface and the adsorbate separately. The second was by performing a single point energy calculation with the D3-correction at the minimum energy structure obtained from an optimization without the correction (ΔE ads,D3static ). We find that the latter can lead to large errors with respect to the adsorption energies of hydrogen, which was overestimated by 35% in some cases and have therefore applied the former approach. Molecular calculations for the electronic structure of N 2 were performed within restricted density functional theory (DFT) implemented in the Gaussian09 code (rev D.01). 21 The basis set used was the correlation-consistent polarized valence double-ζ abbreviated as cc-pVDZ. 22 Stationary states were confirmed by the absence of imaginary frequencies in the vibrational analysis. The convergence criteria for the maximum forces and the root-mean-square (RMS) forces were less than 0.01 eV/Å and 0.001 eV/Å, respectively.
2.2. Choice of XC-Functional for Fe x Co (3-x) Mo 3 N. We find that the choice of exchange-correlation (XC) functional is critical when addressing the chemistry of N 2 /H 2 with Fe x Co (3−x) Mo 3 N, where x = 0, 1, 2, and 3. Although it has been shown for solids that hybrid XC functionals HSE03 23 (HSE06 24 ) and PBE0 give better results for calculating lattice parameters, bulk moduli and more importantly formation enthalpies, for cobalt and iron molybdenum nitrides and their alloys; we note that the revPBE functional, which is computationally far less demanding than PBE0 and HSE03/ 06 can yield an accurate description of the electronic structure of the material under study. Furthermore, it does not overestimate the bandgap by overestimation of the exchange splitting known for the hybrid functional PBE0. 23 It has been suggested that the HSE06 functional greatly improves the computer time and resource requirements mostly due the faster convergence of the total energy with respect to k-point mesh, as the bare unscreened exchange operator requires a 12 × 12 × 12 mesh equivalent to a 6 × 6 × 6 mesh for the HSE06 functional. 23 However, we found that the latter underestimates by 38 kJ/mol the bond dissociation enthalpy of N 2 (g), Δ 0K H(N−N). Therefore, we have tested the remaining XCfunctionals commonly used for solids, PBE, PW91, revPBE, and PBEsol with respect to their accuracies in predicting the lattice constant of Fe x Co (3-x) Mo 3 N, where x = 0, 1, 2, and 3 (see Table  1). These alloys contain also iron which makes possible the testing of the computational methodology on other elements for which crystallographic data are available. 25−27 Our calculations are based on full optimization of unit cell dimensions and atom positions and the reported meanaverage-percent-error (MAPE) value, which indicates to within which percentage the experimental values, are reproduced. The calculated values were compared to two sets of experimental lattice constants: the first comprised solely of PND data obtained at 4.2K (Exp 1 ) and the second based on combined XRD and temperature-dependent magnetic susceptibility measurements (Exp 2 ). In both sets, we obtained the same trend with respect to the average-MAPE calculated at each functional, which was found to be PBE < revPBE ≈ PW91 < PBEsol. In particular, according to Table 1, an average MAPE of 0.30−0.36% was found for PBE: both revPBE and PW91 gave values of about 0.5−0.6% and PBEsol gave higher average MAPE, of the order of 2%. The results show that with the use of a planewave code the lattice parameter can be estimated very well both with the PBE and the revPBE functional, which are also computationally less expensive than some of the hybrid GGA functionals tested.
In an earlier account of bond dissociation enthalpy (BDE) of N 2 with the use of various XC functional, the % error for the revPBE was found to be the lowest among various GGA and hybrid GGA functionals. 13 In particular, we found that the % error was for revPBE = 0.2 < B3LYP = 1.7 < PBE0 = 3.5 < HSE06 = 4.1 < PBE = 4.9 < PW91 = 7.0. Therefore, all subsequent calculations have been performed with the revPBE functional, which can yield more accurate barrier heights according to the calculated BDE of the NN bond.

RESULTS AND DISCUSSION
3.1. Surface Models of Co 3 Mo 3 N. We have modeled the surface of Co 3 Mo 3 N using a 2 × 2 supercell slab with trigonal symmetry belonging to the space group P3̅ m1 (164), where a = b = 7.7972 Å, c = 30 Å, α = β = 90°, and γ = 120°. This was generated from a cubic unit cell with the η-carbide Fe 3 W 3 C structure belonging to the space group Fd3̅ m (227), where a = The Journal of Physical Chemistry C Article b = c = 11.0270 Å and α = β = γ = 90°. 29 We note that the (111) surface of the cubic unit cell (Fd3̅ m) is the (001) surface of the trigonal unit cell (P3̅ m1), which was further studied as it has the highest density of Co 8 clusters embedded in a molybdenum nitride (Mo 3 N) framework. In the case of a bifunctional mechanism, this surface would have the largest density of active sites. For the rest of the paper, we refer to this "(111)-surface" simply as "surface". Note that the actual 2 × 2 supercell used for these periodic slab calculations was shifted by a/2 and along a and by b/2 along b and had a nitrogen vacancy at the position indicated by a yellow circle in Figure 1. The slabs were generated by applying a scanning algorithm to scan the bulk in 0.1 Å increments and generate centro-symmetric slabs of thickness <1 nm for computational efficiency. A top view of these slabs along the c direction is shown in Figure 1 that shows the composition of six distinct surfaces generated, of which four had surface nitrogen (i.e., B, C, E, and F) and two had only a MoCo exposed phase (i.e., A and D) with subsurface nitrogen. The subsurface nitrogen is a 6-fold bound nitrogen (6f) to Mo atoms, whereas surfaces C, D, and F had entirely 3f nitrogens, and one surface (B) had 5f nitrogens. The nitrogen vacancy formation energies (VFE) and concentrations have been previously calculated, and the latter was found to be on the order of 10 13 per cm 2 at ambient conditions. 13 We have Note that only four out of the six surface compositions expose surface nitrogen (i.e., 5f or 3f). Two surfaces only have subsurface nitrogen (i.e., 6f). The Journal of Physical Chemistry C Article evaluated the surface composition in these slabs and found that it significantly differs among these thin films. It is interesting to note that the surface with the highest surface nitrogen concentration, C had a very low composition of nitrogen based on the normalized stoichiometric coefficient (s.c.) of nitrogen, having set the s.c. of cobalt to 1. These compositions were found to be A = CoMo 0.9 N 2.1 , For example surface A, which had a complete absence of exposed surface nitrogens, had the highest stoichiometric coefficient for nitrogen (i.e., N 2.1 ). This suggests that the exact surface composition of very thin layers of this material may have to be evaluated by topographic techniques, e.g., via scanning probe microscopies that are currently absent in the literature. In an earlier DFT study 13 with the same methodology used here, we proposed that surface C is the most active surface for Mars−van Krevelen type chemistry for ammonia synthesis. This choice was based on two kinetic factors and an energetic factor: (i) the density of sites that can activate N 2 (i.e., N-vacancies), (ii) which surface had the most exothermic adsorption energies for N 2 adsorption, and (iii) the surface formation energies (E S F ), which were calculated for the four surface compositions that had exposed surface nitrogen. As the calculation of surface stabilities is not possible for Co 3 Mo 3 N, we continue with surface C for calculating the coadsorption of N 2 /H 2 on Co 3 Mo 3 N.

H 2 Adsorption and Activation on Co 3 Mo 3 N.
Various phases of atomically adsorbed hydrogen have been observed via scanning-tunnelling microscopy (STM) on Co nanoparticles grown on Cu(111). 30 In a recent DFT study, the adsorption energy of H 2 was found to be roughly proportional to the surface energy in the following order Co(100) > Co(110) > Co(111). 31 The nitrogen vacancy-induced heterogeneity of the surface, offers H 2 an additional degree of complexity with respect to the availability of adsorption sites. In this study, we have studied the adsorption of H 2 at 8 symmetry unique sites of the C surface of Co 3 Mo 3 N shown in Figure 2, with a nitrogen vacancy shown by the yellow circle in Figure 1. This surface is expected to yield a better representation of the actual surface of the catalyst, which we have previously shown to have a large number of nitrogen vacancies (∼10 13 cm −2 ) even at ambient temperature. The adsorption energy of H 2 was found to be roughly proportional to the percentage of H−H activation defined as the percentage lengthening of the H−H bond, when adsorbed side-on at every adsorption site with an adsorption angle of a(M−H−H) = 72°−87°. In this adsorption configuration, the adsorbate−surface bonding is interpreted as an interaction between the filled 1σ MO of H 2 with empty πstates of the metal and π-back-donation into the antibonding orbital of H 2 . Interestingly an end-on adsorption could not be found in agreement with H 2 adsorption studies on rhodium clusters. 32 H 2 can absorb either molecularly or dissociatively (see Scheme 1) at five distinct adsorption sites after optimization of 8 symmetry unique adsorption sites, which are shown in Figure   2. The molecular adsorption occurred mostly on the MoN 3 framework, where it was bound through the Mo atoms (see Table 2). Dissociative adsorption occurred on exposed Co atoms that belong to the Co 8 clusters or Mo 3 clusters that were exposed due to N-vacancies.
The adsorption energies without (ΔE H2 ) and with (ΔE H2,relax-D3, ΔE H2,static-D3 ) the inclusion of dispersion interactions via the DFT-D3 method and the optimized structure of the adsorbates (i.e., r (H−H) , r (M-H) , a (M−H-H) ) are presented in Table 2. We have also calculated % activation, defined as the percent increase of the H−H bond length during adsorption. It may seem at some point surprising that the addition of the D3 correction can shift the adsorption energy endo-or exothermically; however, for the static calculation, it always adds to a more exothermic adsorption energy, which is what is expected.
The various adsorption sites found had the following characteristics: site 1 the hydrogen was adsorbed side-on to a molybdenum atom that was adjacent to a nitrogen-vacancy site (N vac ) with an adsorption energy of −67 kJ/mol but with only a small activation of the H−H bond.
Site 2 was found to dissociatively chemisorb H 2 , where it was bound to a molybdenum atom at a nitrogen vacancy site. This site had the largest % activation (i.e., 41%) for molecular hydrogen; sites 3−5 in which hydrogen was adsorbed on a molybdenum atom on the MoN 3 framework with a moderate adsorption energy of −30 to −68 kJ/mol due to the less metallic character of the MoN 3 framework. The strongest adsorption energy for H 2 was found on sites 6−7, which corresponds to a corner atom of the Co 8 nanoclusters denoted as Co 8-top , with adsorption energy of −127 and −110 kJ/mol, respectively. At these sites, the H−H bond was also found to be considerably activated (i.e., 23−24%). These results indicate that the Co 8 clusters will be saturated with molecular hydrogen at low temperatures under conditions where both N 2 /H 2 are available in the feedstream. Interestingly we find that at site 8, H 2 will generally not adsorb at low-T based on the D3corrected adsorption energy of just 21 kJ/mol, and it is the only site on the Co 3 Mo 3 N surface that will not be occupied by hydrogen when it is coadsorbed with N 2 . Therefore, we consider site 8 as free under conditions of competitive adsorption with N 2 at low temperatures (e.g., T < 200°C).
3.3. N 2 Adsorption and Activation on Co 3 Mo 3 N. The adsorption of N 2 over a range of surfaces has been studied using various surface analytical probes extensively. Both physisorbed and chemisorbed states are identified using a combination of electron spectroscopy and thermal desorption techniques. 33 According to this report and earlier LEED experiments, N 2 can chemisorb side-on and end-on on the surfaces of certain metals (e.g., Ni, Fe, Ru, and W). In this study, we find that apart from these two adsorption configurations, N 2 can also adsorb in a tilt end-on configuration on Co 3 Mo 3 N shown in Scheme 2. This is a well-defined adsorption configuration with a tilt angle equal to 155°in which the dihedral d(Co−Mo−N−N) of this bond is found to be 0°.
Angle resolved photoemission spectra have identified two phases of N 2 adsorbed to Fe(111) surfaces (γ-phase and αphase). In the first, N 2 is adsorbed perpendicularly, and in the latter in a strongly inclined configuration, where N 2 was described to form two covalent bonds with Fe atoms. 34 A c(2 × 2)-N/Fe(100) structure was found to form on Fe(111) and Fe(110) surfaces, whereas two side-on (α and α′) and two endon (β and γ) adsorbed states have been found via periodic DFT calculations for molecular N 2 adsorption on Fe(111). 35 Two

Scheme 1. Simplified Schematic Showing (a) Molecular and (b) Dissociative Adsorption of H 2 on Co 3 Mo 3 N Surfaces
The Journal of Physical Chemistry C Article adsorption configurations for molecular nitrogen have been previously identified as side-on and end-on, based on an extensive collection of surface analytical studies. 33,36 Side-on and end-on adsorbed configurations for N 2 , when it is adsorbed to nickel surfaces have also been found, where the end-on adsorption occurs either through a single surface atom on Ni(110) surfaces or in a tilt end-on configuration through two surface atoms on Ni(110) surfaces. 37 An end-on adsorbed configuration of N 2 as well as CO, which is isoelectronic, was found via X-ray emission spectroscopy (XES) and DFT calculations on Ni(100). 38 An end-on adsorbed configuration for N 2 has been found on cobalt clusters of the form Co n (N 2 ) + , where n = 8−17 using infrared photon dissociation (IRPD) spectroscopy and DFT calculations of the stretching frequency of the N−N bond. 39 On the surface of Co 3 Mo 3 N (i.e., surface C), we have identified three adsorption configurations for N 2 , which are shown in Scheme 2. For the eight adsorption sites, we placed N 2 either side-on or end-on at every site shown in Figure 3 and let it optimize without any restrictions. The adsorption energies for N 2 without (ΔE N2 ) and with (ΔE H2,relax-D3 ) the inclusion of dispersion interactions via the DFT-D3 method and the optimized structure of the adsorbates (i.e., r (H−H) , r (M-H) , a (M−H-H) ) are presented in Table 3. The side-on configurations stayed either side-on or became a tilt end-on configuration during relaxation. This change in adsorption configurations was not observed for the end-on configuration, which remained endon even after relaxation. This indicates that there is barrier for the end-on to side-on transformation. Adsorption at some sites would activate nitrogen, but dissociation such as in the case of H 2 was not observed, in accord with the large bond dissociation enthalpy of N 2 (i.e., 946 kJ/mol).
The various adsorption sites found had the following characteristics: site 1 the nitrogen was adsorbed in a tilt endon configuration to a molybdenum atom that was adjacent to a nitrogen-vacancy site (N vac ) with an adsorption energy of −59 kJ/mol but with only a small activation of the N−N bond. Site Table 2 Table 2 contained only one adsorbed nitrogen per 2 × 2 unit cell.

. Adsorption Energy (ΔE) of H 2 Adsorbed to C Surface of Co 3 Mo 3 N; H−H Bond Length (r(H−H)), M−N Bond Length (r(M−H)); Tilt Angle (a(M−H−H)), Adsorption Site Composition and % Elongation for
The Journal of Physical Chemistry C Article 2 was found to activate N 2 , where it was bound end-on at the 3fold hollow generated by the nitrogen vacancy. This site had the second largest % activation (i.e., 11%) for molecular nitrogen. Site 3 N 2 was adsorbed in an end-on configuration on the Mo 3 N framework with a weak adsorption energy (1.5 kJ/ mol) due to the less metallic character of the Mo 3 N framework. . This % activation is even larger than the activation that we have found at 5f sites on surface B, which was 19%, in a previous study. 13 Although the adsorption energy at this site maybe positive, if we take into account the entropy change for adsorption at 300 K, which is −TΔS= −58 kJ/mol, the adsorption free energy becomes −17 kJ/mol. To summarize, two activation sites for N 2 have been found (i) the first at nitrogen vacancies on the Mo 3 N framework (i.e., site 2) and (ii) the second at surface cavities where it activated on a Co atom at the 16d Wyckoff sites Co 8 (i.e., site 8, Co 8-side ). The existence of two activation sides for nitrogen clearly suggests that there may be more than one ammonia synthesis mechanism occurring on Co 3 Mo 3 N catalysts. In the following section, we explain based on molecular orbital (MO) diagrams why these three adsorption configurations where found, based on the energy and spatial distribution of the frontier orbitals. 3.4. Interpretation of the Three N 2 Adsorption Configurations on Co 3 Mo 3 N. It is intriguing that there are three different low-coverage adsorption configurations for N 2 on the surface of Co 3 Mo 3 N, which suggests that there are three different adsorbate−surface bonding interactions. We have calculated with MP2/cc-pVTZ the molecular orbitals (MOs) of N 2 in order to tentatively offer an interpretation of the three adsorption configurations found. The eigenvalues and eigenfunctions of these calculations are shown in Figure 4, which show that the ordering for the highest-occupiedmolecular-orbitals (HOMO: 1π u ), which has a π-symmetry is separated by only 0.7 eV from an MO with σ-symmetry (HOMO−1: 3σ g ). Both these orbitals are expected to undergo bonding interactions. Because these MOs have their lobes pointing along directions perpendicular to the molecular axis (90°) of N 2 and along the molecular axis (180°), therefore bonding interactions are expected along these directions. Furthermore, these MOs are not expected to take any charge from the metal atoms, but could possibly donate electron density in the form of π-donation and σ-donation, respectively. Morokuma 40 in an energy decomposition analysis (EDA) of the bonding in (CO) 4 Fe−CO and (CO) 4 Fe−N 2 revealed equaly strong contributions from σ-donation and π-backdonation, results which however may differ for cobalt dimers in which a very strong M−M interaction is present. 41 The lowest-unoccupied-molecular-orbital (LUMO: 1π* g ) has a degenarate pair of orbitals and is expected to accept electron density from filled d-states of the metal through the πback-donation mechanism. 42 The symmetry of the highest occupied-molecular-orbital (LUMO: 1π u ) is identical to that of CO(g), although there the lobes of the antibonding orbital are somewhat stronger on the carbon atom. 43 We have previously shown that carbon monoxide (CO) adsorbs on various d 7 , d 8 , and d 9 metal nanoclusters in a primarily end-on configuration 44,45 at an angle of a(M−C-O) = 180°. The existence of the end-on configuration was explained by a mechanism in which the filled d-states of the metal (that have π-symmetry) donate electron density into the empty antibonding state of CO and where the filled HOMO of CO which has σ-symmetry and resembles the HOMO−1 of N 2 , undergoes mostly σ-repulsion. This was in agreement with previous theoretical 43, 46 and X-ray   The Journal of Physical Chemistry C Article emission spectroscopy (XES) studies. 47,48 CO adsorbed in a tilt configuration has been previously found on Ag n (n = 1 to 7), which was rationalized on the basis of better orbital overlap of tilt-CO with Ag n -HOMO of σ-symmetry and of the linear endon CO with Ag n -HOMO of π-symmetry. 49 Furthermore, a tilt-CO was also found as a results of CO−CO repulsions 50,51 or adsorption at 4-fold hollow sites. 52 There have been many computational studies of the doping, support and NP-size effects on CO adsorption on various metal and their oxides 53−59 and as elementary reaction steps in catalytic reactions. 60−62 In a recent combined DFT and experimental study of the catalytic CO oxidation using bimetallic M x Au 25−x SC 2 H 4 Ph clusters, where M = Cu, Au, Ag, the following trend Cu > Au > Ag was found and interpreted as a result of a stronger metal-CO interaction in metals with a smaller covalent radius. 40,41,63 Based on these earlier studies and the results found here, we rationalize that the π-backdonation of electron density into the LUMO of both N 2 and CO is expected to result in a linear end-on adsorption. 64 The tilt end-on adsorption configuration of N 2 on Co 3 Mo 3 N has not been previously reported and is shown in Scheme 2. This is a well-defined adsorption configuration with a tilt angle equal to 155°in which the dihedral d(Co−Mo−N−N) of this bond is found to be 0. In the following section, we provide evidence that there are two bonding interactions that take place based on the sphere-in-contact model. 65 We have taken literature values for the atomic radius of the elements participating in the bonding and drawn to scale a sphere-in-contact model of the tilt end-on adsorption configuration for N 2 on Co 3 Mo 3 N. This is depicted in Figure 5 From the optimized structures presented in Table 2, we find that the tilt angle ranges between 152 and 158°with an average value at 155°. We have used the sphere-in-contact model to provide an explanation of the bonding in the tilt end-on configuration. In this model, each element is represented by its atomic radius. The atomic radius of nitrogen we can estimate from our DFT calculations (N: 58.4 pm) based on the average bond length of N 2 for the tilt end-on configuration, in excellent agreement with the double bond atomic radius obtained by fitting a set of atomic radius data of various elements (60 pm). 66 For the atomic radius of molybdenum and cobalt, we used literature values of 190 and 152 pm, respectively. 67 If we draw the bonding via a sphere-in-contact model as shown in Figure 5, we find that for a tilt angle of 155°, the spheres are in perfect contact, which indicates the presence of covalent bonding interactions, and that there is bonding both from the 3σ g (HOMO−1) along the molecular axis of N 2 and the 1π u (HOMO) perpendicular to the molecular axis of N 2 . This orientation is such that it would additionally undergo interactions between filled d-states of the metal and antibonding 1π* g MO of N 2. The small percentage activation of the N−N bond indicates a potential bonding mechanism where π-back-donation and a tautochronous σand π-repulsion are present, which results in this unusual tilt end-on adsorbed configuration of N 2 .

■ CONCLUSIONS
We present a dispersion-corrected DFT study of the adsorption and activation of molecular nitrogen and hydrogen on cobalt molybdenum nitride (111) surfaces to identify possible activation sites for ammonia synthesis. H 2 was found to adsorb both molecularly on the Mo 3 N framework and dissociatively on Co 8 clusters or Mo 3 clusters that were exposed due to Nvacancies. N 2 was found to adsorb side-on, end-on, and in an unusual tilt end-on (155°) configuration, which is rationalized via MO diagrams and the sphere-in-contact model. We find that there are two possible activation sites for N 2 . The first is a Mo 3 triangular cluster that resides at 3f nitrogen vacancies and the second is a surface cavity where N 2 is activated by the inner tetrahedral atom of the Co 8 cluster, the second being a more efficient activation site and a particular activation sites exposed only in Co 3 Mo 3 N surfaces with a surface composition of