A DF-vdW study of the CH4 adsorption on different Ni surfaces

Abstract A systematic density functional (DF) theory based study of methane (CH 4 ) adsorption on the three lowest-index Miller Ni surfaces plus two stepped Ni surfaces is presented. A standard GGA type functional (PBE) has been used to compute the total energy and the van der Waals (vdW) contribution included to properly described the weak molecular interaction of CH 4 with the Ni metal surfaces. The surfaces are represented by a periodic supercell approach and several sites and molecular orientations have been explored with one, two and three H atoms pointing towards the surface. Although all adsorption energy values are small, taking into account dispersion terms allows one to distinguish the effect of the surface structure on methane adsorption.


Introduction
Since some years ago the use of hydrogen as fuel have been suggested as a good alternative as energy source because its oxidation releases a high amount of energy and the gas emissions are inoffensive [1]. However, its synthesis is required [2,3] because there are not natural sources. Methane as hydrogen source is an excellent alternative because is present in natural deposits and it can be obtained as a product of degradation of biomass.
Among the different transition metals, Ni is the most typical catalyst for methane decomposition [5,29]. Hence it is not surprising to find that Ni has been extensively theoretically studied for methane dissociation catalysis. For instance, Density Functional (DF) methods employing different exchange-correlation functionals, in particular those within the Generalized Gradient Approximation (GGA), have been used to describe the methane adsorption on metallic surfaces [30,31]. However, this interaction is known to be weak and dominated by dispersion terms and, consequently, the GGA calculations do not reproduce this trend. In fact, using the revised version of the Perdew-Burke-Ernzerhof (rPBE) functional a value of 5 kJ mol -1 was predicted for the adsorption energy of CH 4 on Ni(111) [30]. A stronger adsorption (36 kJ mol -1 ) was found on a defective surface involving a Ni adatom [17]. Nevertheless the weak interaction of CH 4 with metallic surfaces using GGA functionals hinders a more detailed analysis of different molecular configurations or site structures and the differentiation among diverse types of surfaces becomes difficult.
To contribute to the better understanding of the interaction of CH 4 with different types of Ni surfaces, here we report a systematic theoretical study of the adsorption of this molecule on a variety of well-defined surfaces models and using a GGA-based functional which includes a description of the van der Waals (vdW) forces. We will show that this type of approach describes very well the weak interaction between methane and Ni, with results close to the experimental ones. Moreover, to analyze the effect of coordinatively unsaturated sites, we considered the interaction of CH 4 with the lowest-index Miller Ni surfaces (111), (110), and (100) and the two stepped surfaces, the (533) and the (577).

Surface Models and Computational Details
Methane adsorption on pristine (111), (110), and (100) Ni surfaces, and on stepped Ni(533) and Ni(577) surfaces has been studied using density functional calculations either neglecting or including dispersion terms (see below) carried out on periodic slab models and making use of the VASP code [32,33]. In order to decouple the effect of dispersion on the interaction of methane with the Ni surfaces and on the Ni substrate itself, the slab models were constructed using the PBE Slab models consisting of at least three metallic layers have been constructed. A vacuum region with a width larger than five metallic layers (12 Å) has been placed in the normal direction to the surface to avoid interaction between the repeated slabs. A (2×2) supercell has been used for Ni(100), a (3×2) was used for Ni(110), a (3×3) for Ni(111), a (3×1) for Ni(533) and finally, a (2×1) supercell was used for Ni(577) surface ( Figure 1). In all cases the structures include eight to nine surface metal atoms leading to a similar coverage in all the studied surfaces. Note that stepped models result from the combination of lowest-index Miller surfaces: the Ni(533) surface is a combination of (111) terraces with steps with an arrangement of a (100) plane and, in the Ni(577) case, the (111) terraces combine with (110) steps.
The interaction of methane on the different surface models has been studied by placing the corresponding species just on one side of the slab, the first metallic layer of the slab was relaxed in response to the presence of the CH 4 molecule and the rest, two atomic layers were fixed at theirs atomic positions. All calculations included a dipole correction as implemented in VASP. Three different CH 4 orientations were considered with one, two, or three H atoms pointing towards to the metallic surface.
The exploration of the preferred adsorption sites has been carried out by means of total energy DF theory based calculations and subsequent geometry optimization employing the optPBE functional approach due to . In this method a 4 modified exchange implementation of the vdW-DF is used whereas other proposals exist as described in a recent review [40]. However, the performance of the different functionals including dispersion terms is still to be fully assessed and a considerable amount of work has been devoted to the interaction of benzene with metal surfaces which is taken as a benchmark system [41]. Interestingly, optPBE provides a good agreement between average experimental adsorption energy and calculated valued for benzene on various metallic surfaces [42,43] even if the experimental measures need also to be taken into account with caution. It is also rewarding to see that for this reference system, results predicted by optPBE agree with the, in principle, more sophisticated but not yet broadly used, DFT-VDw surf method [41,44] and with more accurate calculations such as those obtained from the random phase approximation [41] which, in turn, are in agreement with calorimetric measurements [41]. Moroever, optPBe has been extensively used to study the interaction of water with metallic surfaces providing quite satisfactory results [45]. Therefore, it is expected that, even if a direct comparison to experiment is not possible here which make it difficult to estimate error bars in the calculated properties, the general trends will be correctly described which is the main goal of the present study. A 3×3×1 Monkhorst-Pack k-points grid was used to sample the Brillouin zone of the surface unit cell [49]. All employed parameters were tested using tighter values, yet changes were not significant. Due to the magnetic nature of Ni the polarized spin formalism has always been used except obviously for the gas phase CH 4 molecule.
Harmonic vibrational frequencies have been obtained from the Hessian matrix constructed by finite differences of each molecule nucleus displaced in the three spatial coordinates by 0.01 Å and used to properly characterize the final optimized structures as true minima in the potential energy surface. For these structures, the adsorption energy was calculated the following equation; where E ads is the adsorption energy, !" ! /!"# is the energy of the methane molecule interacting with the metallic surface, !"# is the corresponding energy of the bare surface, 5 and !" ! is the energy of the isolated molecule. Note that, within this definition, the more positive the adsorption energy, the stronger the bond to the surface. The adsorption energy was subsequently corrected for the Zero Point Energy (ZPE) and the resulting values are denoted as E ZPE .
In order to provide results comparable to the experiments, the desorption temperature was calculated using the Redhead method, based on the Arrehenius equation: where, r des is the desorption rate constant, A is the preexponential factor, T is the desorption temperature, R the gas constant and E ZPE is the desorption energy of methane corrected by ZPE. The rate constant and the pre-exponential factor are considered constants with standard values of 1·10 6 and 1·10 10 , respectively. Note, however, that the reported desorption temperatures should be taken as a gross estimation.
The CH 4 adsorption on the different metallic surfaces was studied assuming that the incoming molecule adsorbs at a given site of the surface, either top, bridge, three-or fourfold sites on low-index surfaces, and additionally at steps, terraces, or edge sites of stepped surfaces. All possible sites on each surface were explored depending of the atomic arrangement of the surfaces.

Results and Discussion
Before discussing the results of the CH 4 adsorption, let us briefly analyze the isolated molecule case: The calculated bond distance of C-H is 1.095 Å, in excellent agreement with the measured value of 1.086 Å [50]. Regarding the vibrational frequencies, four normal modes (ν 1 , ν 2 , ν 3 , and ν 4 ) with A 1 , E, F 2 , and F 2 symmetry, respectively. The However such a small elongation must be treated with caution, and it is not unexpected since it is fully consistent with the weak character of the interaction.
For the most stable, less active Ni(111) and more studied surface [6,17], initial and final adsorption sites, calculated adsorption energy values, vibrational frequencies, and geometric parameters are summarized in Table 1, while a sketch of the most stable adsorption site is presented in Figure 2. From the values encompassed on  (110) and Ni(100) surfaces, whose results are found in Tables 2 and 3, respectively, and the most stable conformations are depicted in Figure 2. On both surfaces the adsorption energy is 2-3 times increased with respect to that obtained for the densely-packed Ni (111)  The defective surfaces are presumably more active and in the case of the Ni (533) surface this statement is partially true ( Table 4). The adsorption energy values are larger than on the Ni(111), but similar to those of Ni(100) which is not surprising since the Ni(533) surface has steps with an atomic arrangement similar to those Ni atoms in the Ni(100) surface. Therefore, the calculated adsorption energy values for these two surfaces are similar although the value for Ni(533) is slightly increased by ~2 kJ mol -1 , a finding easily explained in terms of the lower coordination of the Ni atoms at the steps, and also by the fact that the strongest adsorption situation on this stepped surface corresponds to an step edge line ( Figure 2). However, as in the cases discussed above, there is still a high variety of easily reachable conformations. Here it is important to point out that results in Tables 1 to 5 include the initial and final configuration from the geometry optimizations. In some cases more than one initial starting point converge to the same final structure but, because of the convergence thresholds, the final structures may display some very small numerical differences. These could have been removed but keeping them allows one to have an idea of the numerical accuracy and, at the same time, provides information about the final state for each initial configuration.
In the particular case of the Ni(577) surface, the situation is similar to that of the above-explained cases. Here the adsorption energies are comparable to those of the Ni(100) and Ni (533) surfaces with similar estimated desorption temperatures so that the adsorption can be still considered physisorption. As discussed for Ni(533), the preferred adsorption sites are located at the step edge line, with many possible accessible conformations, Figure 2 displays a sketch of the most stable one. The enhanced activity seems to join the stability of (111) terraces with the higher-activity of low-coordinated atoms at the (110) steps. One can perhaps argue that this is related to the higher activity of Ni nanoparticles, containing a significant number of low-coordinated sites.
The analysis of the vibrational frequencies reported in Tables 1 to 5  shifted by more than 100 cm -1 with respect to free molecule, suggesting the proclivity of this state for eventually contributing to breaking the C-H bond. Interestingly, the Ni (577) surface displays a completely different behavior which is not unexpected in the view of the 8 larger interaction with methane. Here, the ν 1 mode is reduced by ~30 cm -1 , but the other vibrations are blue shifted, the ν 2 mode by ~30 cm -1 and ν 3 and ν 4 by 60 cm -1 .

Conclusions
The interaction methane with several Ni surfaces has been studied by periodic density functional calculations explicitly including dispersion terms. The interaction is always weak and can be safely classified as physisorption. Nevertheless, including dispersion terms have important qualitative consequence since it permits to distinguish the different surfaces. Hence, the interaction of methane with these surfaces decrease in the order Ni (577)