Methane Capture at Room Temperature: Adsorption on cubic δ-MoC and orthorhombic β-Mo2C Molybdenum Carbides (001) Surfaces

Based on periodic Density Functional Theory (DFT) calculations, carried out using a standard generalized gradient approximation type exchange-correlation functional including or not a van der Waals dispersive forces, the ability of the cubic δ-MoC(001) surface to capture methane at room temperature is suggested. Adsorption on the orthorhombic β-Mo2C(001) surfaces, with two possible terminations, has been also considered and, in each case, several molecular orientations have been tested with one, two, or three hydrogen atoms pointing towards the surface on all high-symmetry adsorption sites. The DFT results indicate that the δ-MoC(001) surface shows a better affinity towards CH4 than β-Mo2C(001). The calculated adsorption energy values on δMoC(001) surface are larger, and hence better, than on other methane capturing materials such as metal organic frameworks. Besides, the theoretical desorption temperature values estimated from the Redhead equation indicate that methane would desorbs at 330 K when adsorbed on the δ-MoC(001) surface, whereas this temperature is lower than 150 K when the adsorption involves β-Mo2C(001). Despite of this, adsorbed methane presents a very similar structure compared to the isolated molecule, due to a weak molecular interaction between the adsorbate and the surface. Therefore, the activation of methane molecule is not observed, so these surfaces are, in principle, not recommended as possible methane dry reforming catalysts.


Introduction
The rather stringent terms of the Kyoto protocol have triggered that the governments of many countries have committed to reduce the emission of greenhouse effect gases. In spite of this, the predictions indicate that these emissions will continue increasing up to 2040 1 with devastating consequences in the so-called global climate growing since the landmark work of Levy and Boudart 25 highlighting the similar catalytic properties of tungsten carbide and platinum for a variety of reactions, which make them ideal replacements to Pt-group based catalysts. Not surprisingly, the number of articles on these compounds has greatly increased in the recent years due to their important physical, chemical, and catalytic properties. 26 Many experimental and theoretical investigations have explored the catalytic capability of several TMCs for a broad range of reactions. [27][28][29][30][31] One of the TMCs that has generated more interest in the latest times is Titanium Carbide (TiC). Rodríguez et al.
have shown that TiC(001) is an excellent catalyst to dissociate H 2 molecule 32,33 and to oxidize CO. 34 Also, it has been found that TiC can be an excellent support, since it is able to enhance the electronic structure of Au and Cu metal nanoparticles supported onto, 35 thus displaying a superior catalytic power with respect the isolated metal nanoparticles. Au/TiC(001) and Cu/TiC(001) are excellent catalysts for the hydrogenation of olefins, the hydrodesulfurization of thiophene, and the adsorption and decomposition of SO 2 . [36][37][38][39][40] However, one must point out that TiC is a cumbersome support to be used in practical applications due to the difficulty of anchoring metallic nanoparticles on the TiC surface on working conditions. Alternative materials are δ-MoC and β-Mo 2 C because they are much more active and do not require special conditions for their synthesis.
In the last years, MoC and Mo 2 C have been used for studying synthetic and reactive aspects associated to environmental processes. [41][42][43] It is worth pointing out that here we follow the notation convention defined by the Joint Committee on Power Diffraction Standards (JCPDS) data files, 44 in which hexagonal and orthorhombic Mo 2 C are denoted α-Mo 2 C and β-Mo 2 C, respectively. Note, however, that some authors in the literature refer to orthorhombic Mo 2 C as α-Mo 2 C, 45-47 following an early definition by Christensen. 48 Very recently, orthorhombic β-Mo 2 C(001)-Mo terminated surface (bulk space group: Pbcn) 49 has been proposed for CO 2 dissociation and the subsequent conversion to methanol (CO 2 + 3H 2 → CH 3 OH + H 2 O). 50,51 Furthermore, β-Mo 2 C(001)-C terminated surface and cubic δ-MoC(001) can activate the C-O bonds. In the field of CH 4 adsorption, Tominaga et al. have theoretically predicted 52 that CH 4 is dissociated on hexagonal α-Mo 2 C (bulk space group: P3m1), 49 although the authors missed in defining this surface as β and not α, as happened as well with the experimental studies carried out by Oshikawa et al. 53 Thereby, taking into account these appealing results, the interaction between CH 4 and cubic and orthorhombic molybdenum carbides (001) surfaces is put under light, to see whether one could propose these materials as methane dry reforming catalysts. In different experimental thermodynamic studies it has been determined that, in order to attain high syngas yields, methane dry reforming requires reaction temperatures higher than 600 K, although carbon deposition is produced during the reaction. 18,54 Noble metals as Pt, Rh, and Ru are highly active towards dry reforming reaction and they are more resistant to carbon formation than other transition metal catalysts. However, they are seldom used due to their exceedingly high cost. Despite of these impairments, interesting results were published, in which Mo carbides are extremely active catalysts for the dry reforming, partial oxidation, and steam reforming of methane, with an activity comparable to noble metal catalysts. 55,56 For all the above-mentioned reasons, and the excellent results obtained by Tominaga et al.,52 a theoretical study about the adsorption of CH 4 on clean molybdenum carbides (001) surfaces seems necessary and has been undertaken. In this first study, we intend to analyse the methane capture on cubic and orthorhombic molybdenum carbide (001) pristine surfaces. Note that by so we disregard other possible effects, such as the the promotion by means of adsorbed metal alkalis, 57 or the effect of surface defects, as found to be matter of interest in the catalytic activity of a surface, as found, for example, in similar compounds such titanium nitride. 58,59 These aspects, which can come to be important, are however out of the scope of the present study, and matter of future work.
The structure of the adsorbed CH 4 is determined exploring whether catalysts based on Mo n C(001) surfaces are able to activate, and eventually break, the C-H bond.
The calculations provide a well-detailed panel about the geometry and energy of methane adsorption on these surfaces. Besides, the Density of States (DOS), Electron Localization Function (ELF), and Charge Density Difference (CDD) plots were investigated in pertinent cases to complete the adsorption framework. This information allows determining the type of adsorption and predicting the role that these surfaces can play in methane reformation. Moreover desorption temperatures have been calculated in order to ascertain the material capability for capturing methane.

Computational details
Periodic Density Functional Theory (DFT) calculations were carried out using the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional 60 within the Generalized Gradient Approximation (GGA), as implemented in VASP 5.3.3 code. 61 In the applied methodology, the electronic density of the valence electrons is expanded in a plane-wave basis set and the effect caused by the core electrons on those in the valence region is described by the Projected Augmented Wave (PAW) method of Blöch, 62 as implemented by Kresse and Joubert. 63 A cutoff kinetic energy of 415 eV was used together with a 5×5×1 mesh of k-points, selected by means of the Monkhorst-Pack scheme to carry out the numerical integrations in the Brillouin zone. 64 These values were optimized in a previous work on these surfaces and were found to provide highlyaccurate results. 65 Surface slab models with four layers have been constructed by repetition of four 12.12×10.46×14.75 Å for β-Mo 2 C. 65 The Newton-Raphson algorithm was employed for the atomic structure optimization together with a convergence criterion of 0.01 eV Å -1 for the forces acting on relaxed atoms. The electronic relaxation convergence criterion was set to 10 -5 eV.
Because of its predictable weak interaction, the study of methane adsorption requires a correct description of the van der Waals interactions that raise from the electron density dynamic fluctuation, and that can play a key role in such a process. In order to consider this type of interaction, the D2 correction of Grimme 66 was used, as implemented in VASP code.
The adsorption energy (E ads ) has been calculated as: where E !" ! /!"# is the energy of the CH 4 adsorbed on the surface, E !" ! is the energy of an isolated molecule, and E !"# is the energy of the clean relaxed MoC or Mo 2 C surface.
Within this definition, the more negative the E ads value, the stronger the adsorption.
where ∆ is the CDD, !!! is the electron density of the CH 4 on the surface, ! is that of the surface after the adsorption but without the adsorbate, and ! is that of CH 4 in the adsorption geometry without the substrate. The values used to represent the isosurfaces vary between 0.01 and 0.001 a.u.
The CH 4 vibrational frequencies changes induced by adsorption have been also determined through the construction and diagonalization of the Hessian matrix, constructed by independent displacements of atoms by 0.03 Å.
where R is the ideal gases constant, T d is the desorption temperature, A is the preexponential factor, and E b is the desorption activation energy including Zero Point Energy (ZPE) correction which is calculated by Formula 4,  Figure 3. In the case of C termination, there exist two geometries degenerated in energy, with two or three hydrogen atoms pointing to the surface (Figure 3a and 3b), respectively, whereas in the case of Mo termination (Figure 3c), a distinct situation appears; when vdW correction is not included in the calculations, only a quarter of the tested geometries reach the most stable physisorbed state. The rest tend to reach other minima with adsorption energies of -0.03 eV at best and likely to be artefacts rather than physically meaningful structures. Nevertheless, when vdW correction is included, the majority of the tested geometries reach the most favourable adsorption geometry. This issue was not featured on C termination, yet another effect was noticeable; once vdW dispersion is turned on, the CH 4 -surface distance can be reduced by ~1 Å in selected cases. Despite of this proximity to the surface, the molecular structure is not varied, i.e. the approach is carried out in a rigid fashion. Because of all these reasons, a proper vdW correction is necessary so as to study the methane adsorption on these surfaces, both from the structural and the energetic aspects. This fact is justified by the vdW contribution to the adsorption energy (85% on average). Curiously these results do not keep the trend encountered for CO 2 adsorption on these molybdenum carbide surfaces. 50 This is because here the effect of Grimme correction on the calculations only affects the energy adsorption value, without modification of the adsorbate structure.
The vibrational frequencies of the different configurations were calculated and are shown in Table 3. Most of vibrational frequencies decrease, probably due to a slightly weakening of C-H bonds. This is especially interesting in the case of β(Mo)-H 2 (tMo) for the two highest energy vibration modes (T 2 and A 1 ), whose frequency values shift considerably, by more than 250 cm - Overall, as a first approximation, one would not advise the use of any termination of β-Mo 2 C(001) surface as a catalyst for methane dry reforming, since these surfaces are not able to activate the C-H CH 4 bond when adsorbing it. Note that a more solid argument would require a methane dehydrogenation reaction profile, as previously carried out on Pt an Cu surfaces. 72,73 However, such study is out of the scope of the present research, and matter of future work, although, according to the desorption temperature estimates shown in Table 2, these surfaces would adsorb CH 4 but only at than δ-H 2 (tMo) and δ-H 3 (tMo). One could suggest that this result is again influenced by the charge transfer. In general terms though, the adsorption of methane does not perturb the electronic structure of δ-MoC.

Conclusions
An extensive theoretical study of the adsorption of CH 4 on cubic δ-MoC and orthorhombic β-Mo 2 C (001) surfaces -the last one with C and Mo terminationscarried out at DFT level using the PBE functional has been presented. A van der Waals correction has been included to ascertain whether dispersive forces represent a key ingredient which has to be taken into account to properly describe these. Interestingly shown that these surfaces efficiently activate CO 2 , they do not constitute possible candidates for methane dry reforming catalysts.
The most striking prediction of the present work is that methane can remain adsorbed on δ-MoC(001) at room temperature. Besides, the predicted temperature desorption values are larger than those corresponding to other methane capture materials such as MOFs which makes δ-MoC(001) may be a potential candidate for methane capture.