Chemisorption and Transformation of CHx Fragments (x = 0−3) on a

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J. Phys. Chem. B 1998, 102, 1578-1585

Chemisorption and Transformation of CHx Fragments (x ) 0-3) on a Pd(111) Surface: A Periodic Density Functional Study J.-F. Paul† and P. Sautet* Institut de Recherches sur la Catalyse, CNRS, 2 AV A. Einstein, 69626 Villeurbanne Cedex, and Laboratoire de Chimie the´ orique, Ecole Normale Supe´ rieure, 69364 Lyon Cedex 07, France ReceiVed: October 13, 1997; In Final Form: December 15, 1997

The chemisorption of CHx (x ) 0-3) fragments on a Pd(111) surface has been studied with density functional periodic calculations. The binding energy decreases strongly as the number of H atoms increases, and the fragment tends to restore its tetravalency on the surface: carbon prefers a hollow site, the CH fragment is also in a hollow site, the CH2 is preferentially in a bridge, and the CH3 is on top of a Pd atom. On the surface the C-H bond cleavages are weakly endothermic, and the most stable surface species is CH3. Dehydrogenation to carbon is however possible through bimolecular reactions with simultaneous formation of CH4.

1. Introduction The stability of hydrocarbon molecules and fragments on metal surfaces is of great importance for the understanding of several catalytic elementary steps.1 The reforming of CH4 is, for example, a major catalytic reaction that goes through different carbonaceous species as intermediates, but the nature of these hydrocarbon fragments on the surface is still under debate. The second reaction of the traditional indirect conversion route of methane is the Fischer-Tropsch process where, on the contrary, new valuable hydrocarbon chains are produced from carbonaceous species on the surface. This capability of metal catalyst to cleave C-H bonds and also to create C-C and C-H bonds is singular. The activation of the C-H bond of methane or other saturated hydrocarbons on transition metal surfaces has also been the subject of recent interest in order to define new direct routes for the conversion of natural gas via the nonoxidative homologation of methane. The dissociative adsorption of methane on metals is an activated reaction, very slow at moderate temperatures. Although methane transformation is usually done on metals such as Co or Ni, it was suggested that Pd may also be an effective catalyst for partial oxidation of methane. Wang et al. have dissociately chemisorbed methane on a stepped Pd(679) surface at a pressure of 1 Torr and at surface temperatures higher than 400 K, with the formation of surface carbon and hydrogen species.2 Comparable results were obtained by Solymosi et al. on supported Pd clusters.3 Dissociation appeared above 473 K, when C2H6 and H2 were observed in the gas phase. Ethane was supposed to come from surface coupling of CH3 fragments, although surface CH3 and other CHx species could not be identified from IR, supposedly because of their very short lifetimes. Only surface carbon was obtained. On Ni(111), Ceyer et al. reported the existence of CH3 and CH fragments from methane dissociation.4 CH, CH2, and CH3 fragments are well-known as ligands in organometallic complexes, and this knowledge can be partially * Corresponding author. Email: [email protected]. † Present address: Laboratoire de catalyse he ´ te´roge`ne et homoge`ne, Universite´ des Sciences et Techniques de Lille, 59655 Villeneuve d’Ascq Cedex, France. Email: [email protected].

transferred to the case of a metallic surface.5 CH2, for example, is especially stable when bridging two metals atoms in a complex, indicative of its proclivity to occupy bridge sites on a surface. However, direct information for the structure and binding energy of these fragments on an extended metal surface is rather scarce. Methyl was characterized on Ni(111) and Pd(100) surfaces. On Pd(111), it was created by decomposition of methanol.6,7 The methyl fragments were only present in a small amount and were found to be thermally stable up to a temperature of 440 K. This contrasts with the results obtained from CH3I decomposition on Pd(100), where the produced CH3 fragments evolved at temperatures lower than 250 K.8,9 The dominant reaction mode is the decompostion to carbon and selfhydrogenation into CH4. There was no spectral evidence of the CH2 and CH species, indicative of a further rapid decomposition.10 On Ni(111), methyl begins breaking at 220 K, in parallel with methane formation.11 The dominant mechanism for CH4 production involves a bimolecular reaction between hydrocarbon fragment groups. There is no direct experimental information on the bonding geometry of a CH3 group on a metal surface. The binding energy of methyl on a metal surface is approximately 1.3 eV, as underlined from a comparison of the existing Pt, Ni, Cu, and Fe values.5 There are few examples of CH2 isolation and characterization on metal surfaces.5 Morever, the decomposition of this precursor usually takes place at very low temperatures. A characteristic photoemission signal was obtained for adsorbed CH2 on Pd(100) from the decompostion of CH2I2, although a significant proportion of it dimerized into C2H4 even at 90 K. The formation of methane, indicative of self-hydrogenation, also occurred at a temperature of 180 K.12 CH was obtained on Pd(111) by the 400 K decompostion of acetylene and characterized by HREELS.13 This CH fragment appeared to be stable up to temperatures of 500 K. CH species have also been obtained by hydrogenation of carbon adsorbed on Pt(111) and shown to dissociate again in C and H at an elevated temperature of 510 K.14 The evolution of the binding energy when removing H atoms and the implication of d electrons in the fragment-surface bond are two important issues. The mobility of the species on the

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Chemisorption and Transformation of CHx Fragments surface is also relevant information for catalytic processes. There is also little information on the thermodynamics of CH bond cleavage on the surface. Quantum chemistry is a technique of choice in order to address these structural and energetic problems. The chemisorption of CHx fragments has been studied by extended Hu¨ckel type methods on Ni(111), Rh(111),15,16 and Pt(111).17,18 In all cases, the hydrocarbon fragments show a configuration that optimizes hybridation and tends to complete carbon tetravalency: CH3 is on a top site, CH2 favors a 2-fold site, and CH and C are in 3-fold sites. The case of Ni(111) was later adressed by first-principle calculations, the surface being modeled by a cluster. Siegbahn et al. performed MRCCI calculations with clusters of typical size 1020 atoms.19 Methyl was found to adsorb on a 3-fold hollow site, with a binding energy of 2.2-2.4 eV and a good agreement with experiment for the C-H stretching vibrational frequency. Other fragments were only considered on the hollow site of a Ni3 cluster, yielding binding energies of 3.8 eV for CH2 and 5.2 eV for CH.20 An exothermicity of 0.3 eV was found for the formation of CH2 from CH and H on Ni(111). Yang and Whitten used an embedded cluster approach with ab initio valence CI calculations.21 All fragments are found to be most strongly chemisorbed in the 3-fold hollow site, with binding energies of 3.13 eV (CH), 2.91 eV (CH2), and 1.68 eV (CH3). Surface formation of CH2 (from CH and H) is found to be 1.45 eV exothermic, and formation of CH3 (from CH2 and H) is calculated 0.57 eV exothermic. Burghgraef et al. have studied the same problem with GGA-DFT calculations on clusters of 7 or 13 Ni atoms.22 In contrast with the previous ab initio studies, CH3 is found to be on the top site (0.66 eV), while CH2 (2.99 eV), CH (5.58 eV), and C (5.81 eV) are in the hollow site. The formation of CH3 from CH2 and H is exothermic by 0.4 eV, but formation of CH2 from CH and H is endothermic by 0.63 eV, and this also differs from the previous CI calculations. This study also underlines a nonnegligible influence of the selected cluster size on the calculated energies and frequencies. Therefore, the theoretical studies on Ni(111) give significant differences in preferred binding sites, chemisorption energies, and surface transformation energies for CHx species. To our knowledge there is only one calculation dealing with Pd, with the reactivity of methane on a Pd2 cluster.23 This model is, however, too small to compare with a Pd surface. To get some insight in the structure and stability of these organic fragments on a Pd surface, the chemisorption of CHx (x ) 0-3) molecules on Pd(111) has been studied with density functional periodic calculations. To our knowledge the chemisorption of CHx species on a metal surface has not been previously studied with first-principle slab calculations. The infinite nature of the metallic surface is better taken into account compared to a cluster model, and a nonzero coverage of adsorbates is considered. Recent developments of these periodic firstprinciple calculations, such as GGA approximation, indeed allow an accurate description of binding sites and binding energies as illustrated in the case of CO on Cu(100).24 The calculation method and the model used to describe the Pd(111) surface with the various adsorbates will be presented in section 2. The chemisorption of CHx fragments will be detailed in section 3, with a discussion of the relative stability of these species on the surface in section 4. 2. Method and Model All the calculations performed in this study have been made using the Amsterdam density functional code for the periodic structures (ADF-Band).25 This program calculates the electronic

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Figure 1. Schematic for the x3 × x3 structure of C atoms on a Pd(111) surface.

structure for periodic systems in one, two, or three dimensions within density functional theory. The electron wave functions are developed on a basis set of numerical atomic orbitals (NAOs) and of Slater type orbitals (STOs). For the core of the atoms (in this case Pd and C), a frozen core approximation is used to reduce the size of the basis set. A characteristic of this program is to perform numerical integrations for all the matrix elements.26 The accuracy of the integration in real space and the sampling of the Brillouin zone for the integration accuracy in k-space are the two major numerical parameters in the calculation. The calculation of the density has been performed at the local density approximation (LDA) level, with the Vosko, Wilk, and Nusair parametrization,27 and nonlocal gradient corrections (generalized gradient approximation, GGA) introduced by Perdew and Wang28 (PW91) or by Becke29 for the exchange energy and Perdew30 for the correlation (BP86) have been applied for the calculation of the total energy. The Pd atom is modeled by a frozen core only up to the 3d orbital. Each orbital in the valence shell (4s, 4p, 4d, 5s) is represented by a double basis including a NAO and a STO. A 5p STO hybridization function has also been considered. The hydrogen and the carbon atom are represented with a similar double-ζ basis set, including a NAO and a STO, with additional p or d polarization functions. On a more technical field, all the calculations are performed with an integration accuracy greater than 10-4 and at least 15 k-points in the reduced Brillouin zone for all the 2D cells. These calculations are already accurate, and tests with higher accuracy parameters show a very small deviation of the energy and optimal geometry. With such periodic calculations, the surface is described by a two-dimensional slab and the adsorbate structure is also periodic on one side of the slab. A x3 × x3 structure has been considered that corresponds to a coverage of 1/3 (Figure 1). The adsorbate separation of 4.8 Å is large enough to avoid significant contact between them, although interactions through the surface are likely. The preferred adsorption site and geometry, the associated binding energy, and electronic structure have been determined for all cases (the adsorbate geometry was optimized for all low-energy binding sites). The geometry of the surface was kept frozen to the experimental bulk structure. A two-layer slab of Pd(111) was used for the geometry optimization, and the binding energy for the most stable geometries was recalculated on a three-layer slab in order to test convergence with slab thickness. We showed in the case of hydrogen adsorption that a reasonable convergence of the binding energies is already obtained with a 2-3-layer thick slab.31 The GGA Perdew-Wang 91 functional was considered for these structural optimizations, but the binding energy of these optima are also given with the GGA Becke-Perdew 86 functional.

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Paul and Sautet

Figure 2. Optimal structures and binding energies (eV) for CHx species on a Pd(111) surface with a GGA PW91 functional. Top (T), bridge (B), and hollow (H) sites have been examined, and the surface is described by a two-layer slab. The Pd-C bond lengths (Å) are given in italics.

TABLE 1: Electronic Populations and Charges electronic population C CH CH2a CH3

charge

C 2s

C 2px

C 2py

C 2pz

H

CHxb

Pd

1.85 1.58 1.45 1.34

0.83 0.87 1.235 1.24

0.83 0.87 0.86 1.24

0.91 1.24 1.14 0.80

0.54 0.64 0.66

-0.54 -0.24 -0.08 +0.35

+0.20 +0.16 +0.12 -0.01

a CH is in the xz-plane. b A difference of ca. 0.1e can be noted 2 compared to the sum of electronic populations, due to the contribution of d orbitals on C.

For the energy values, the most severe origins of errors are related to the limited slab thickness (∼0.1 eV) and to intrinsic errors from the exchange-correlation functional (see Discussion). From our experience, differences below 0.1 eV in relatiVe energies should not be considered too seriously. Reference energies for the free fragments were calculated with the same periodic calculations and with an identical basis set. A cubic box of size 20 Å was selected. Tests with molecular calculations showed no significant differences. Fragment geometries were optimized. CH was calculated in a doublet state (C-H ) 1.09 Å), CH2 is a triplet (C-H ) 1.085 Å, H-C-H ) 135 °), CH3 is a doublet (C-H ) 1.085 Å, D3h planar geometry), and CH4 is tetrahedral closed-shell (C-H ) 1.097 Å). 3. Chemisorption of CHx Fragments The PW91 binding energies for the various fragments are summarized in Figure 2, and electronic populations and charges are shown in Table 1. (a) Carbon. As for hydrogen,31 the most stable situation for the carbon atom on the Pd(111) surface is the hollow site, but with a much stronger binding energy (6.4 eV). Fcc and hcp hollow sites give a very similar binding energy and optimum geometry. A short Pd-C bond length (1.9 Å) is found. The bridge site is significantly less stable (+0.7 eV), and the Pd-C bond length is shorter compared to the hollow, as expected from the reduced coordination of the C atom. The atop site is very

Figure 3. Density of states projected on the C 2s and 2p orbitals (a), on a surface Pd atom in interaction with the adsorbate (b), and Pd-C COOP curve (c) for C in a fcc hollow site.

unfavorable (+2.6 eV). The lowest surface diffusion pathway through a bridge site between two hollow sites yields a rather high diffusion barrier (0.7 eV), and therefore, in contrast with the case of hydrogen, the mobility of carbon on the surface is found to be rather low. This high diffusion barrier is directly related to the strong binding energy. For the hollow site, an electron transfer occurs from the surface toward the adatom: from a qualitative Mu¨lliken analysis, C has a significant negative charge (fcc, -0.54; hcp, -0.6). Compared to the atom s2p2 configuration, the 2s orbital is slightly depopulated (1.85e), while the p orbitals (mainly pz) take an important part in the bonding and the associated charge transfer increases their total electronic population to 2.57e. An additional 0.1e population comes from d polarization orbitals and underlines a nonnegligible role of those orbitals in the interaction. This negative charge on the carbon is almost balanced by the positive charge of the 3 Pd neighbors (+0.20), the second layer Pd atoms being almost neutral. The density of states projected on the surface Pd atom and on the s and p orbitals of the C atom are given in Figure 3, the energy being referenced to the Fermi level. For the surface Pd atom, the d band is clearly located between -5 and 0 eV, but compared to the bare surface three sharp peaks appear below.

Chemisorption and Transformation of CHx Fragments The lowest peak is mainly centered on the C 2s orbital, and the mixing is small with the Pd atoms because of the large energy gap between that orbital and those of Pd. The second and third peaks are centered on (px, py) and pz orbitals, respectively, and they show a good mixing with the surface Pd atoms since these levels are very close to the Pd d band. The contribution of the surface Pd atoms to these split-off states is mainly from the d orbitals. The C orbitals are predominantly present in these three split-off states that are localized at the surface (their amplitude on second-layer Pd atoms is negligible), while the weight of the C atom in the d band region is small. This is confirmed by the crystal orbital overlap population (COOP) plot that indicates the bond population as a function of energy. The bonding regions for the carbon-Pd interaction (positive values) are located on the two peaks just below the d band (Figure 3). In the d band region, the COOP is small and changes sign so that the overall contribution of the d-band region to the total overlap population (integration up to the Fermi level) is negligible. Eighty-five percent of the C-Pd overlap population comes from the interaction between d orbitals of Pd and p orbitals of C. This especially underlines the great implication of pd d electrons in the bonding with C. The d bandwidth of Pd is here correctly described by the calculations, and this is an important ingredient for an accurate representation of surface chemisorption properties. (b) CH. The CH fragment, for which the C-H bond was kept vertical in the calculations, is also preferably in a hollow site, both hollow sites giving a very similar binding energy. The most stable one is the hcp site, the fcc being only 0.06 eV less stable. The optimal Pd-C bond lengths are also very comparable for these hollow sites (hcp, 1.97 Å; fcc, 1.99 Å). Again, compared to the hollow site, the bridge site is rather less stable (+0.57 eV), and the top site is very unstable (+2.57 eV). The presence of the C-H bond decreases the Pd-C ones compared to the case of C chemisorption, but this effect is rather small and the binding energies of all sites are reduced by 0.40.6 eV. The CH bond is only slightly elongated compared to the gas-phase fragment (1.11 Å). The barrier for the adsorbate surface diffusion between hollow sites is 0.57 eV. The fragment still has a negative charge on the surface (-0.2), and this charge is then significantly reduced compared to that of the carbon atom. The density of states projected on the first-layer Pd atom and on the C s and p orbitals is shown in Figure 4. Compared to C, the low-lying 2s peak is still present, together with the two other sharp peaks below the d band. The main differences are the energy lowering of the pz peak due to its interaction with H and its weaker mixing with the Pd atoms. This pz peak is moved below the px, py ones, and its participation in the Pd-C bond is reduced as seen from the COOP curve. The pz orbital is now involved in the interaction with H, and its capability to interact with the metal is reduced. This is the main origin of the adsorbate-surface interaction weakening. The electronic population of px and py orbitals is not significantly modified compared to C, the charge modification of the fragment being associated to the σ (s, pz, H) orbital framework. (c) CH2. The trend to decrease binding energy with additional H atoms on C continues for CH2, but the binding energy variation is now stronger. This energy destabilization is more important for the high coordination sites: the range of binding energies among various sites is reduced, and this even results in a change of the preferred binding mode, from hollow to bridge. No tilt of the CH2 C2 axis has been found from the calculation. Two bridge site geometries have been tested, with a tetrahedral or planar arrangement around C, the former being

J. Phys. Chem. B, Vol. 102, No. 9, 1998 1581

Figure 4. Density of states projected on the C 2s and 2p orbitals (a), on a surface Pd atom in interaction with the adsorbate (b), and Pd-C COOP curve (c) for CH in a hcp hollow site.

much more stable. The optimum H-C-H angle for this tetrahedral configuration is 113°. This angle is close to the optimum for the free CH2 fragment in the singlet state (110°), while the most stable triplet state has an angle of 135°. The CH bond distance was not optimized because of the low symmetry of the site and was kept to 1.10 Å. For CH2 however, the hollow site is only 0.14 eV higher in energy than the bridge. In contrast with C and CH, this implies a very easy surface diffusion for the fragment. The adsorbate geometry for the hollow site is similar to that for the bridge site (H-C-H ) 112°), and there is no significant difference between the fcc and the hcp site. The rotational orientation of CH2 at the 3-fold site was also examined, and a barrier of only 0.01 eV was found. The projected density of states (DOS) for CH2 in the most stable bridge site is shown in Figure 5. The peaks for px, py, and pz orbitals of C are now completely separated, due to the symmetry lowering, while the 2s peak is only slightly stabilized. The most stabilized p peak corresponds to the py orbital, which interacts strongly with the H atoms, and then comes the less perturbed pz orbital. The px orbital is not interacting with the hydrogen, and it is located right at the bottom of the d band. The overlap population is again located at the energies corresponding to these molecular-orbital-like peaks, with about equal

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Paul and Sautet TABLE 2: Binding Energy Difference (eV) between the Two-Layer and the Three-Layer Slabs for the CHx Fragments

Figure 5. Density of states projected on the C 2s and 2p orbitals (a), on a surface Pd atom in interaction with the adsorbate (b), and Pd-C COOP curve (c) for CH2 in a bridge site.

contribution of each of them. The CH2 fragment is almost neutral, but the neighboring Pd atoms are still positively charged. This comes from the fact that occupied d states on Pd are destabilized above the Fermi level by interaction with the adsorbate. Electronic charge is then transferred from these orbitals toward low-lying vacant states of the surface that act as electron reservoirs.32 (d) CH3. The C3 axis of CH3 was kept vertical in the optimizations. The various sites show very close binding energies, with a quasi degenerate chemisorption situation. At the GGA level, the top site is favored but is only less than 0.1 eV more stable than the hollow site chemisorption. In contrast, the hollow case is slightly more stable at the LDA level. This underlines the importance of a precise treatment of electronic correlation in order to correctly describe this small energy difference. It is, however, clear that the diffusion of CH3 on the Pd(111) surface is very fast. The GGA top site optimal structure shows an out-of-plane bending of the H atoms of 18°, very close to the 19° bending in the associated CH4 structure, and a CH bond distance of 1.10 Å. The rotation around the Pd-C bond is almost free with a less than 0.01 eV barrier. Among hollow sites, the fcc one is 0.1 eV more stable than the hcp one. The Pd-C distance is strongly elongated compared

C

CH

CH2

CH3

0.2

0.03

0.04

0.01

to the top site (2.38 Å compared to 2.05 Å), while the H outof-plane bending angle is increased to 21°. An important difference with the more dehydrogenated fragments is that CH3 acts as an electron donor with a net charge of +0.35. This is due to the fact that the px and py orbitals are now participating in the C-H bonding pairs and are no longer available for accepting electrons (this was the case for only one of them for the CH2 fragment). The projected density of states for the top site is shown in Figure 6. Only one split-off state is present and mostly corresponds to the C 2s orbital. However, a marked peak can be noticed at the bottom of the d band, and it is associated with a mixing between the πCH3 orbitals (px and py orbitals) and the Pd surface atoms. The σ (pz) orbital is diluted in the metal band due to its adequate energy position and its strong interaction with the surface. Part of this orbital is above the Fermi level and is not populated (the pz electronic population is 0.83). From this participation of the pz orbital to the d band, it follows that a much more significant contribution of the d band levels to the Pd-C overlap population is obtained. Bonding and antibonding character energy regions are observed, but the overall effect of these d band states is repulsive and destabilizes the Pd-C bond. (e) Discussion. All the previous results were obtained with two-layer slabs. One important question is whether they can be representative of the behavior of a real surface. To test convergence with slab thickness, the energies of the optimal geometries were recalculated with three-layer slabs, and the binding energy differences for all fragments are indicated in Table 2. This clearly proves that even with somewhat thin layers, a good energy convergence is obtained, especially for the hydrogenated species. The largest difference is obtained for C (which is associated to the strongest electron transfer), but this is also the largest binding energy and the relative change is only 3%. Another important point is the choice of the exchange correlation functional. The energies for the optimal geometries have been calculated with the GGA BP86 functional and are presented in Figure 7. The general picture is very similar, compared to the PW91 results of Figure 1. All level orders are conserved, the binding energies being decreased by 0.1-0.2 eV. Things are different for the LDA results, where a wellknown strong overbinding is found, ranging from 1 to 1.4 eV additional binding energy. The order of sites is reversed for the CH3 case, the hollow site being more stable than the bridge, itself more stable than the top. Therefore, the results presented are not modified, as long as a GGA functional is selected. For a given site the Pd-C bond length increases with the number of H atoms on C, while it decreases when the metallic coordination is reduced from 3 to 1, and this is consistent with a bond-order conservation principle. Both effects compensate, and the Pd-C distance only shows a small increase between C (1.9 Å) and CH3 (2.05 Å). The order in chemisorption energy is the following, where H has been taken from ref 31

Eads(CH3) < Eads(H) < Eads(CH2) < Eads(CH) < Eads(C) and this is in general agreement with all cluster calculations on Ni(111). Concerning binding sites for CHx species, the simple

Chemisorption and Transformation of CHx Fragments

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Figure 7. Binding energies (eV) for CHx species on a Pd(111) surface with a GGA BP86 functional. Top (T), bridge (B), and hollow (H) sites have been examined with the optimal geometries of Figure 2 on a two-layer slab.

differences for the fragments are large, and this is attributed to a decrease of the participation of carbon p orbitals in the adsorbate-surface bond when going from C to CH3. A bond energy per surface metal atom involved can be calculated for the optimal sites and only shows a small variation between C (2.13 eV) and CH3 (1.71 eV). 4. Transformation of CHx Fragments From this study of the chemisorption of CHx fragments on Pd(111), it is possible to analyze the enthalpies of the surface CH bond cleavage reactions: Figure 6. Density of states projected on the C 2s and 2p orbitals (a), on a surface Pd atom in interaction with the adsorbate (b), and Pd-C COOP curve (c) for CH3 in a top site.

picture that emerges from our calculations is that the surface metal coordination of the CHx fragments tends to restore the tetravalency of carbon in agreement with the picture of bonding between CHx and a metal surface drawn from previous extended Hu¨ckel calculations on Pt and Rh.15-17 This contrasts, however, with the results of ab initio cluster calculations where all species were found on the hollow site for Ni(111).19-21 The DFT calculations on Ni(111) agree for the top site for CH3 but suggest a hollow site for CH2. It should be noted, however, that the hollow site in our calculations is less stable by only 0.07 eV for CH3 and 0.14 eV for CH2. In these circumstances, it is not clear what is the true importance of a precise binding-site determination for chemical reactivity purposes. The mobility of the various surface species certainly has important implications for reactivity. A clear order emerges from the calculations with a monotonic decrease of the mobility from the most mobile CH3 to the immobile C atoms. This trend is identical with that obtained in ref 22. Comparison of actual binding energy values is more difficult because of the different metal, method, or model for the surface. The value for CH3 is very close to that obtained by Yang and Whitten21 and within 15-25% error from the 1.3 eV experimental estimate,5 while the large values for CH and C are more in line with the DFT results of Burghgraef et al.22 The chemisorption energy

CH4 T CH3a + Ha T CH2a + 2Ha T CHa + 3Ha T Ca + 4Ha This evaluation was performed here by combining the chemisorption energies of the CHx fragments with that obtained from an independent calculation of a hydrogen atom on Pd(111), without considering coverage and co-adsorption effects. This can therefore only be considered as a qualitative approach, but already allows an enlightening of thermodynamic trends. It can first be recalled that these C-H bond scissions are strongly endothermic in the gas phase with, for example, an experimental value of +4.52 eV for the first C-H cleavage (the calculated endothermicity is +4.76 eV). On the surface, the enthalpy change for breaking the successive C-H bonds is still mostly unfavorable but the endothermicity is much reduced (Figure 8). Among all surface species, CH3 has the lowest energy. On the other hand, CH2 does not appear to be a very stable entity, with both hydrogenation to CH3 and dehydrogenation to CH being favorable. This CH fragment itself appears like a local minimum with reasonable stability, the transformation to carbon being significantly endothermic. It must be noticed that this stability trend is completely different from the chemisorption energy one, since C-H and Pd-H bonds are also taken into account in the energy balance. As shown in Figure 8, both GGA functionals give a very similar picture, the PW91 functional showing a 0.11 eV smaller endothermicity for the first CH bond cleavage. How-

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Paul and Sautet fragments. Another remark is that in the proposed mechanisms for chain growth on the surface, CH2 intermediates are often used as building blocks. From the calculation, they do not seem to be very stable, and it is suggested that mechanisms involving CH or CH3 units should be considered. However, Figure 8 and eqs 1-3 only show the energetics, and an evaluation of the energy barriers between these states would certainly be important to address kinetics effects. 5. Conclusion

Figure 8. Energy variation due to successive C-H bond cleavages on a Pd(111) surface obtained from combination of separated CHx and H adsorption calculations. Results with the BP86 and PW91 nonlocal exchange correlation functionals are given, as well as with the LDA approach.

ever, the profile drawn from a LDA approach is completely different, each CH bond scission being on the contrary strongly exothermic. This is related with cumulated overbinding errors, the number of adsorbate species increasing by one at each step. The GGA energy profile is similar to that obtained with GGADFT calculations on Ni clusters,22 but differs from the ab initio results where the formation of surface CH2 (from CH and H) is found to be exothermic by 1.45 19 or 0.3 eV.21 The profile of Figure 8 seems to disagree with the high pressure experiments, where methane shows indeed a low sticking on a Pd surface, but where the fraction chemisorbed evolves to dehydrogenated species (presumably to carbon), without showing any strong population of CH3 molecules.2,3 It is not possible to understand this point with reactions involving only one CHx fragment, and bimolecular reactions need to be considered.

The chemisorption of CHx (x ) 0-3) on a Pd(111) surface has been analyzed with density functional periodic calculations. The carbon atom prefers a hollow site, the CH fragment is also in a hollow site, the CH2 is preferentially in a bridge, and the CH3 is on top of a Pd atom, in simple agreement with the free valence. The binding energy decreases strongly from C to CH3. Successive surface dehydrogenation of the molecule and fragments is still significantly endothermic, and the most stable species are CH and CH3 in agreement with the HREELS study on Ni(111).4 If the fist step from CH4 to CH3 is excluded, an exothermic dehydrogenation pathway can be obtained from bimolecular reactions with simultaneous formation of CH4. The stability of CH3 deserves a special comment, considering the recent debate in the litterature. An isolated CH3 species would be very stable, since dehydrogenation to CH2 is endothermic. However, transformation is possible if two CH3 molecules meet. When created from methanol, CH3 is only present in small amount on the surface, together with oxygenate species. This might hinder CH3 mobility and make the bimolecular reaction very improbable. On the contrary, decomposition of CH3I yields a high coverage of methyl species, which would easily transform from bimolecular reactions. The apparently contradictory experimental observations could therefore be reconciled. From these calculations, accurate energetic stabilities can be determined for the organic fragments, on a realistic model of the surface, which is an important point for the analysis of the catalytic elementary steps.

2CH3 f CH4 + CH2

∆E ) -0.04 eV (PW91) or -0.12 eV (BP86) (1)

Acknowledgment. The authors thank IDRIS at CNRS for the attribution of CPU time (Project No. 970016).

CH3 + CH f CH4 + C

∆E ) +0.08 eV (PW91) -0.02 eV (BP86)

References and Notes

or (2)

In both reactions, the driving force to dehydrogenate CH3 or CH is taken from the formation of CH4 from another CH3 fragment, and the net result is exothermic or almost thermoneutral. The net effect of these reactions is a transfer of hydrogen from one species to the other. The global reaction

4CH3 f 3CH4 + C

∆E ) -0.33 eV (PW91) or -0.62 eV (BP86) (3)

is exothermic. The high mobility of CH3 fragments can also be an important factor for the occurrence of such bimolecular reactions. Dehydrogenation of CH3 is therefore necessarily accompanied by the formation of CH4 as evidenced by experiments. The key point for the catalytic reactions is that the energy variations between all surface species are small, and, depending on the experimental conditions, the surface can be used to cleave or to form C-H bonds. The system is very balanced, easy to displace either toward the dehydrogenated or hydrogenated

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Chemisorption and Transformation of CHx Fragments (18) Zheng, C.; Apeloig, Y.; Hoffmann, R. J. Am. Chem. Soc. 1988, 110, 749. (19) Schu¨le, J.; Siegbahn, P. E. M.; Wahlgren, U. J. Chem. Phys. 1988, 89, 6982. (20) Siegbahn, P. E. M.; Panas, I. Surf. Sci. 1990, 240, 37. (21) Yang, H.; Whitten, Y. L. Surf. Sci. 1991, 255, 193. (22) Burghgraef, H.; Jansen, A. P. J.; van Santen, R. A. Surf. Sci. 1995, 324, 345. (23) Blomberg, M. R. A.; Siegbahn, P. E. M.; Svensson, M. J. Phys. Chem. 1992, 96, 5783. (24) Philipsen, P. H. T.; Tevelde, B.; Baerends, E. J. Chem. Phys. Lett. 1994, 226, 583.

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