Ethylidyne Formation from Ethylene over Pd(111): Alternative Routes

Aug 3, 2009 - Recently we presented a computational study on the conversion of ethylene to ethylidyne over Pd(111) via a plausible three-step mechanis...
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J. Phys. Chem. C 2009, 113, 15373–15379

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Ethylidyne Formation from Ethylene over Pd(111): Alternative Routes from a Density Functional Study Lyudmila V. Moskaleva, Hristiyan A. Aleksandrov,† Duygu Basaran, Zhi-Jian Zhao, and Notker Ro¨sch* Technische UniVersita¨t Mu¨nchen, Department Chemie and Catalysis Research Center, 85747 Garching, Germany ReceiVed: June 23, 2009

Recently we presented a computational study on the conversion of ethylene to ethylidyne over Pd(111) via a plausible three-step mechanism, ethylene f vinyl f ethylidene f ethylidyne. Here, using essentially the same periodic slab model density functional approach, we investigate two further possible routes, ethylene f vinyl f vinylidene f ethylidyne and ethylene f ethyl f ethylidene f ethylidyne. We systematically compared three coverages of the adsorbate, 1/3, 1/4, and 1/9. We show that the reaction pathway via vinylidene is also feasible on Pd(111). One is not able to judge solely from the potential energy landscape whether the route via ethylidene or that via vinylidene dominates the formation of ethylidyne; at low coverages, our results tend to favor slightly the latter mechanism. The mechanism via ethyl could be operative when a sufficient concentration of surface hydrogen is present. It features the lowest activation barrier for the rate-limiting second step, 81-88 kJ mol-1, but the activation energy for ethyl hydrogenation to ethane, 51 kJ mol-1, is still much lower; this suggests that ethyl should preferentially convert to ethane rather than to ethylidene. 1. Introduction The dehydrogenation of ethylene to ethylidyne over Pd(111) surface recently attracted renewed interest.1–5 It is well known that ethylidyne species (CH3C) are formed upon room-temperature adsorption of ethylene onto Pd(111)6 and other closepacked noble-metal surfaces.7–9 Ethylidyne moieties cover the metal surface during ethylene hydrogenation over Pd(111) and thus probably affect the sites available for ethylene adsorption and reaction with hydrogen.10 The complex mechanism of ethylidyne formation from adsorbed ethylene over Pd(111) is still under discussion; for an overview of pertinent experimental and computational results, see ref 3. Recently, we reported3 the results of DFT calculations on a three-step mechanism1 involving vinyl and ethylidene as intermediate species (Reactions a-e-d, Figure 1). For the first (and likely rate-limiting) reaction step, the H dissociation to form vinyl (Reaction a), we calculated a barrier of 46 kJ mol-1 with respect to gas-phase ethylene at 1/3 coverage. This result is substantially lower than the value of 89 kJ mol-1 calculated earlier.1 That discrepancy prompted a very recent experimental measurement of the activation energy,4 which yielded a value 49 ( 5 kJ mol-1, in excellent agreement with our theoretical prediction. (Note that such good agreement may, in part, be serendipitous because the theoretical result for coverage 1/9 is even lower, 10 kJ mol-1.) First-principles calculations utilizing cluster or slab models are often successful in assessing relative barrier heights of elementary reaction steps and help to identify plausible reaction pathways. As the intrinsic accuracy of theoretical binding energies has been estimated at 20-30 kJ mol-1,11 we do not expect quantitative accuracy for barrier heights calculated with current DFT methods. * To whom correspondence should be addressed. E-mail: roesch@ mytum.de. † Permanent address: Faculty of Chemistry, University of Sofia, Sofia, Bulgaria.

Figure 1. Reaction pathways of ethylene conversion to ethylidyne proposed in the literature over Pt group metals. Arrows pointing to the left, to the right, and vertically down indicate dehydrogenation steps, hydrogenation steps, and 1,2 H shift, respectively. Pathway a-e-d (Mechanism 1) was studied computationally in previous works, refs 1, 3, 5. Pathways a-f-g (Mechanism 2) and h-i-d (Mechanism 3) are addressed in the present work. Elementary Reactions f and g are characterized by TS1 and TS2, respectively. Reaction h is characterized by TS3 (from di-σ ethylene) and TS4 (from π ethylene). Reactions i and j are characterized by TS5 and TS6, respectively.

Figure 1 shows the complex reaction network and the various species involved in the transformation of ethylene to ethylidyne. In continuation of our previous investigation,3 we report here a computational study of two alternative routes for ethylene-toethylidyne transformation via vinylidene (CH2C) or ethyl (CH3CH2). Calculations predict both pathways to feature barrier heights that are comparable to the previously favored route over vinyl and ethylidene. The route via ethyl could become increasingly important in the presence of coadsorbed hydrogen, but competitive ethyl hydrogenation to ethane is shown to have

10.1021/jp905888v CCC: $40.75  2009 American Chemical Society Published on Web 08/03/2009

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a lower activation barrier. Furthermore, we studied coverage effects on the adsorption energies of potential intermediates and on the barrier heights of various elementary steps. 2. Models and Computational Details We applied the same computational strategy as in our preceding work.3 We performed slab-model calculations on the basis of density functional theory (DFT) with the plane-wave based Vienna ab initio simulation package (VASP).12,13 We used the generalized-gradient approximation (GGA) in the form of the exchange-correlation functional PW91.14 The interaction between atomic cores and electrons was described by the projector augmented wave (PAW) method.15,16 The Brillouin zone was sampled using a Monkhorst-Pack17 mesh of 5 × 5 × 1 k points in the structure optimizations of this study; subsequently, the energies were refined in single-point fashion employing a k point grid of 7 × 7 × 1. The valence wave functions were expanded in a plane-wave basis with cutoff energy 400 eV, which according to our test calculations for ethylidyne on Pd(111), guarantees convergence of binding energies to better than 0.5 kJ mol-1.3 We performed structural optimizations by relaxing the positions of all atoms until the force on each atom was less than 2 × 10-4 eV/pm. We modeled the ideal Pd(111) surface by periodic five-layer slabs repeated in a supercell geometry with at least 1 nm vacuum spacing between them. The three “bottom” layers of a slab were kept fixed at the theoretical bulk-terminated geometry (Pd-Pd ) 280 pm) and the two upper layers of Pd atoms were allowed to relax during geometry optimizations, together with the adsorbate. The adsorbates were bound to one side of the slab model. We used three different unit cells, (3 × 3)R30°, (2 × 2), and (3 × 3), corresponding to surface coverages 1/3, 1/4, and 1/9, respectively. We located transition states only at the lowest and highest coverages, 1/9 and 1/3. The binding energy (BE) of an adsorbate was determined from BE ) Ead + Esub - Ead/sub where Ead/sub is the total energy of the slab model, covered with the adsorbate in the optimized geometry; Ead and Esub are the total energies of the adsorbate in the gas phase (ground state) and of the clean substrate, respectively. Calculations on gas-phase hydrocarbon species with open shells were carried out in spin-polarized fashion. With the above definition, positive values of BE imply a release of energy or a favorable interaction. Transition states (TSs) for the reactions were determined by applying the nudged elastic band (NEB) method18,19 with eight images of the system forming a discretization of the path between the fixed end points. A calculation of harmonic frequencies for the optimized transition state structures yielded only a single imaginary frequency in each case. 3. Results and Discussion Several experimental studies investigated ethylene adsorption on Pd(111) and indicated the formation of ethylidyne around room temperature,2,6,20 but the detailed mechanism of the conversion remains in question. No intermediates have been detected on the surface, suggesting that the first step in the conversion is likely to be rate-limiting. Figure 1 summarizes viable routes, most of which had been suggested for the analogous reaction on Pt(111).1,21–24 Note that the direct twostep isomerization pathways a-b and c-d were dismissed earlier due to very high barriers of 1,2-H-shift reactions.3,5 Recently we reinvestigated3 a three-step pathway of ethylene dehydrogenation over Pd(111), proposed earlier.1 It involves an initial rate-limiting dehydrogenation to vinyl and subsequently pro-

Figure 2. Reaction energy profile (kJ mol-1) of vinyl conversion to ethylidyne over Pd(111) at various coverages: 1/3 (black), 1/4 (red), and 1/9 (green). The route via vinylidene (e-d) is compared to the route via ethylidene (f-g, ref 3). Energies are calculated with respect to vinyl or vinyl and coadsorbed H.

ceeds via an ethylidene intermediate (pathway a-e-d, Figure 1). The reaction profile calculated by us corroborated that route as plausible as it comprises notably lower barriers for critical reaction steps as compared to that earlier study. This reaction route is also supported by the experimental evidence that vinyl adsorbed on Pd(111) readily converts to ethylidyne at temperatures as low as 160 K.25 A recent kinetic study yielded an apparent activation barrier for the overall reaction with respect to gas-phase ethylene in good agreement with our calculated value.4 However, there are two other possible routes, a-f-g and h-id, which were discussed by some authors on the basis of indirect experimental evidence for Pt(111),21–23,26 but could not be entirely excluded on either metal. We will address them in the following. 3.1. Conversion via Vinyl and Vinylidene. The route a-f-g (Figure 1) differs only in the second and third elementary steps from the route over ethylidene, a-e-d, described in detail in our previous work.3 Thus, we will focus on the two last elementary steps, the dehydrogenation of vinyl to vinylidene (CH2C) and the addition of hydrogen to vinylidene forming ethylidyne. Figure 2 compares the reaction profiles of the two pathways from adsorbed vinyl, e-d (left panel) and f-g (right panel). Because in most cases the surface coverage was found not to affect significantly the structures, we will mainly refer to the results obtained for low surface coverage, 1/9; the data at higher coverages are summarized in Table 1. In contrast, the effect of increasing surface coverage on the reaction energetics is in many cases substantial and will be discussed. 3.1.1. Dehydrogenation of Vinyl to Vinylidene. In the reactant state, the vinyl species is most favorably bound in a η1η2 mode over a 3-fold fcc site on Pd(111).1,3 The C-C bond of adsorbed vinyl, 144-145 pm, is close to that of di-σ ethylene,3 while the C-Pd bonds are 4-9 pm shorter than in the latter system (Tables 1 and 2). The dehydrogenation product vinylidene is bound in a η1η3 mode over an fcc hollow site. Its C-C axis is notably tilted from the surface normal, which allows overlap between molecular π orbitals and surface d-orbitals. Increased repulsive interactions at high coverages affect the amount of this tilting in a very sensitive fashion. The shortest C-Pd distance between the carbon atom of the CH2 group and the surface is calculated at 1/9 coverage, 227 pm; it elongates to 241 pm at 1/3 coverage. In the presence of a coadsorbed

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TABLE 1: Optimized Geometriesa (pm) and Energy Characteristics (kJ mol-1) of Intermediates and Transition States for the Transformation of Vinyl to Ethylidyne at Various Coverages, θ vinyl TS1f vinylidene + Hg TS2f ethylidyne

θ

C-C

C-Hb

H-Pdb

1/3 1/4 1/9 1/3 1/9 1/3 1/4 1/9 1/3 1/9 1/3 1/4 1/9

144 145 145 138 139 135 138 138 141 141 149 149 149

110 110 110 170 166 278 282 296 173 173 110 110 110

266 264 262 159 160 179, 180, 181 178, 184, 184 178, 179, 187 165 162 307 330 326

C-Pdc 204, 204, 203, 197, 197, 199, 197, 196, 197, 195, 197, 198, 197,

205, 204, 203, 202, 202, 200, 197, 198, 197, 195, 197, 198, 198,

209 208 208 210, 210, 209, 208, 204, 207, 208, 197 199 198

236 224 270 232 228 239 230

Ereld

BEe

0 0 0 62 57 0 -13 -21 70 57 -63 -58 -63

251 267 274 378h 381h 394h 533 540 553

a A-B, distance between atoms A and B. b Distance that breaks/forms during a reaction. c The two (three) C-Pd distances of a higher coordinated C atom are listed first for vinyl, TS1, vinylidene, and TS2. See also Figure 3. d Relative energy with respect to vinyl adsorbed on Pd(111). e Binding energy (BE) of an adsorbate (see text). f TS1 and TS2 refer to elementary Reactions f and g, respectively (Figure 1). g The hydrogen atom is coadsorbed unless stated otherwise. h Without coadsorbed hydrogen.

Figure 3. Structures of the transition states (left column) and the corresponding product states (right column) of the elementary reactions f and g (Figure 1) at 1/9 coverage. Selected distances in pm.

H, the sterical hindrance causes further elongation of that distance, to 270 pm at 1/3 coverage (Table 1). In contrast, the C-C bond length decreases only slightly from 138 to 135 pm as the coverage increases from 1/9 to 1/3. We calculated binding energies of 378-394 kJ mol-1 for adsorbed vinylidene, where the interaction increases with decreasing coverage (Table 1). Our binding energy for 1/3 coverage, 378 kJ mol-1, is in good agreement with an earlier theoretical result, 363 kJ mol-1.1 The H atom, released during dehydrogenation, was placed at the fcc site near the η3 C atom of adsorbed vinylidene (Figure 3). In the corresponding transition state, denoted as TS1 (Table 1, Figure 3), the C-H bond breaks and simultaneously the H-Pd bond forms. Concurrently, the reacting C atom is forming a third C-Pd bond at a 3-fold hollow site, whereas the other C atom moves upward and the corresponding C-Pd distance increases to 224 pm (Table 1). As mentioned above, this weakened bond is also preserved in the final state, and the bond length at 1/9 coverage, 228 pm (Table 1), is close to the C-Pd distance of π-adsorbed ethylene, 221-222 pm (Table 2).3 In the transition state the C-H distance is elongated by 56 pm, to 166 pm, whereas the H-Pd distance decreases to 160 pm, characteristic of an H atom bound at an atop site (Table 1).27 The activation energy of H dissociation from vinyl at a coverage 1/9 was calculated as low as 57 kJ mol-1 (Table 1,

Figure 2), 20 kJ mol-1 below the barrier for H addition to vinyl to form ethylidene (Reaction e, Figure 1) at the same coverage.3 In contrast, at coverage 1/3, the barrier for ethylidene formation, 52 kJ mol-1, is 10 kJ mol-1 below the barrier for dehydrogenation (Figure 2). Thus, the barrier heights for elementary Reactions e and f are comparable. At lower coverages, the dehydrogenation of vinyl (to vinylidene) may even be expected to be more favorable than its hydrogenation (to ethylidene) if one considers the difference in the barrier heights and the dependence of the latter process on the availability of H on the surface. Recall that the barrier for the vinyl reaction back to ethylene (reverse Reaction a, Figure 1) was calculated almost equal to that of Reaction e at both coverages 1/3 and 1/9; thus, reverse Reaction a is also a competing reaction channel for adsorbed vinyl species. 3.1.2. Hydrogenation of Vinylidene to Ethylidyne. As just stated, in the initial state, vinylidene is bound in a η1η3 mode above a 3-fold fcc site. The reacting atomic hydrogen was placed at a neighboring 3-fold site, in front of the C atom of the CH2 group. The initial state of elementary Reaction g (Figure 1) differs from the final state of Reaction f (Figure 1) by the position of the coadsorbed H atom. The latter intermediate is 7 kJ mol-1 more stable at coverage 1/9. However, in view of the high mobility of H on the surface, one may assume fast diffusion and skip the H migration step. We calculated reaction energies and barrier heights with respect to the energetically slightly lower lying final state of Reaction f. The product of hydrogenation, ethylidyne, is known to occupy high-coordinated 3-fold fcc sites.6,28 In TS2 (Figure 3), bonds C-Pd and H-Pd are being broken, while the C-H bond is being created. The three H-Pd distances in the reactant are not equal, the bond directed to vinylidene being the longest. This H-Pd bond decreases from 187 pm in the reactant to 162 pm in TS2 (Table 1) as the H atom moves over a top site toward the C atom. The other two H-Pd bonds stretch to 249 and 274 pm. The C-H distance in TS2 decreases to 173 pm, manifesting a developing bonding interaction (Table 1). The breaking C-Pd bond in TS2, 230 pm, remains rather short, thus facilitating the approach of the H atom, whereas it breaks completely in the final state and the methyl group moves upward. The C-C bond significantly elongates during hydrogenation, from 138 pm in the surface bound vinylidene to 149 pm in ethylidyne (Table 1).

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TABLE 2: Optimized Geometriesa (pm) and Energy Characteristics (kJ mol-1) of Intermediates and Transition States for Ethyl Transformation to Ethylidene at Various Coverages, θ di-σ ethylene + He TS3g TS4g ethyl π ethylene + He TS5g ethylidene + He

θ

C-C

C-Hb

1/3 1/4 1/9 1/3 1/9 1/3 1/9 1/3 1/4 1/9 1/3 1/4 1/9 1/3 1/9 1/3 1/4 1/9

144 144 144 146 148 143 144 151 151 151 139 139 139 152 151 151 150 150

274 271 283 152 153 147 143 110 110 110 262 316 314 159 167 291 296 308

H-Pdb 175, 176, 177, 173, 166, 180, 182, 262 289 282 173, 178, 179, 165, 160, 176, 182, 180,

176, 180 181, 181 179, 186 187 217 187 188

175, 179, 181, 227, 282, 181, 184, 180,

183 182 182 252 303 184 184 186

C-Pd 215, 215, 212, 210, 210, 212, 213, 207 207 207 223, 222, 221, 208, 207, 204, 204, 202,

215 215 215 233 227 236 237

224 223 222 213 210 206 204 204

Erelc

BEd

0 0 0 64 85 75 90 1 13 28 15 7 11 89 109 28 26 29

71f 83f 90f

151 159 164 57f 64f 74f 338f 348f 357f

a A-B, distance between atoms A and B. b Distance that breaks/forms during a reaction. c Relative energy with respect to di-σ ethylene + H coadsorbed on Pd(111). d The BE of an adsorbate (see text). e The hydrogen atom is coadsorbed unless stated otherwise. f Without coadsorbed hydrogen. g TS3 and TS4 refer to the hydrogenation of di-σ and π ethylene, respectively (Reaction h in Figure 1); TS5 corresponds to Reaction i in Figure 1.

The associated activation barrier was calculated at 78 kJ mol-1 for coverage 1/9 (Figure 2). This value is ∼20 kJ mol-1 higher than the barrier of the preceding step, Reaction f, but is still well below the activation energy of the rate-controlling ethylene dehydrogenation, 100 kJ mol-1 at the same coverage.3 Vinylidene hydrogenation was calculated exothermic by 42-63 kJ mol-1, where the larger value corresponds to higher coverage (Figure 2). The forward and reverse hydrogenation barriers of vinylidene, back to vinyl and forward to ethylidyne, differ by 8 kJ mol-1 or less, manifesting that vinylidene intermediates on Pd(111) can indeed transform to ethylidyne. Note that this result is in contrast to the assumption reoccurring in the literature1,5,25 that vinylidene does not directly convert to ethylidyne but preferentially reacts back to vinyl, which in turn can react to form ethylidyne over the route e-d (Figure 1). 3.1.3. CoWerage Dependence of the Energy Landscape. The coverage dependence of the calculated reaction energy profile (Figure 2) is most significant for the vinylidene intermediate with coadsorbed hydrogen, where the effective coverage is twice as high as that of monoadsorbed species, vinyl and ethylidyne. Raising the coverage from 1/9 to 1/3 increases the repulsive interaction between coadsorbates and increases the (relative) energy of the intermediate vinylidene/H by 20 kJ mol-1. If one calculates the relative energy assuming “infinitely separated” vinylidene and hydrogen (by calculating reaction energies from gas-phase reaction energies and individual adsorption energies), the energy changes of both Reactions f and g become essentially independent of coverage. Concomitantly, with raising the energy of vinylidene/H intermediate at a coverage 1/3, the barrier for back reaction to vinyl (TS1) is lowered by 16 kJ mol-1, becoming 8 kJ mol-1 lower than the barrier of forward Reaction g (TS2). Nevertheless, such a difference is small, while the thermodynamics favors the formation of ethylidyne over exothermic Reaction g. Direct comparison of the two reaction landscapes of Routes e-d and f-g in Figure 2 suggests that both of them could operate at room temperature. Judged from barrier heights only, it seems that at the limit of low coverage the route via vinylidene is slightly more favorable (due to vinyl dehydrogenation exhibiting a barrier 20 kJ mol-1 lower than that for vinyl hydrogenation),

whereas at high coverages the route over ethylidene is expected to become more important. 3.2. Conversion via Ethyl and Ethylidene. Another possible route of ethylidyne formation takes place via an initial hydrogenation of ethylene to ethyl, which subsequently dehydrogenates to ethylidene and ethylidyne, mechanism h-i-d (Figure 1). The first step requires the presence of a sufficient amount of hydrogen on the surface and thus could be operating, for example, during ethylene hydrogenation. We calculated the corresponding transition states, described below. The structural and energetic details of the reaction profiles are given in Table 2. We note that the last step of the overall transformation, Reaction d, was calculated earlier3 and is omitted here for clarity. In addition, we considered a competing process, ethyl hydrogenation to ethane. 3.2.1. Hydrogenation of Ethylene to Ethyl. Recent experimental studies using reflection absorption infrared spectroscopy,29 low-energy electron defraction,30 and high-resolution electron energy loss spectroscopy2 revealed that ethylene is adsorbed in di-σ fashion on clean Pd(111) at temperatures around 100 K, but the π-adsorbed complex occurs on hydrogenprecovered Pd(111).29 Density functional calculations predict the di-σ complex to be 10-19 kJ mol-1 stronger bound than π-adsorbed ethylene.2,3,5 TPD experiments estimated the difference in binding energies to be somewhat larger, ∼30 kJ mol-1.31 However, due to a larger entropy of the π-complex its relative stability is expected to increase with temperature. From our calculations we estimated T∆S at 10-12 kJ mol-1 at room temperature for the conversion from di-σ to π-adsorbed ethylene; thus, the difference in adsorption energies is compensated to some extent. π-adsorbed ethylene is believed to be the active species for ethylene hydrogenation because this adsorption geometry prevails on the H-covered surface. Also, due to its lower binding energy, the π-complex is expected to have a lower barrier for hydrogenation. We investigated hydrogenation pathways of ethylene from both di-σ and π-bonded initial states. In the final state, the ethyl species forms only a single C-Pd bond to satisfy the valence requirement of an sp3-hybridized carbon center, the C-C bond being oriented along a Pd-Pd bridge. The C-Pd distance, 207 pm, is 5 pm shorter than in

Ethylidyne Formation from Ethylene over Pd(111) the di-σ ethylene complex, close to the value of vinyl (Tables 1 and 2). The binding energy was calculated at 151-164 kJ mol-1, where the interaction increases with decreasing coverage (Table 2). These values agree well with an earlier computational result, 140 kJ mol-1, for 1/4 coverage.31 3.2.1.1. Hydrogenation of Di-σ Ethylene. The structure of the transition state (TS3) is rather similar to that of TS2 (Figures 3, 5); however, while moving toward the C atom, the reacting H atom passes through a structure intermediate between top and bridge coordination. The shorter of the two H-Pd bonds decreases from 186 pm in the reactant to 166 pm in TS3, whereas the other H-Pd bond increases from 177 pm in the reactant to 217 pm in TS3. The C-H distance in TS3 decreases to 153 pm, while the breaking C-Pd bond stretches from 215 to 227 pm. In the final state the methyl group moves away from the surface. A very similar TS geometry had been found in cluster model calculations.32 That study reported the barrier height of C-H bond activation of ethyl (reverse Reaction h) at 69 and 63 kJ mol-1 from cluster and slab model calculations, respectively. We determined comparable barrier heights for ethyl dehydrogenation to ethylene, 63 kJ mol-1 at coverage 1/3 and 57 kJ mol-1 at coverage 1/9. The barrier of the forward reaction, ethylene hydrogenation, was calculated substantially lower, 64 kJ mol-1 at coverage 1/3, than the barrier at coverage 1/9, 85 kJ mol-1. Our results are consistent with the barrier calculated earlier31 for the coverage 1/4, 72 kJ mol-1. A more recent density functional study5 reported a forward barrier of 91 kJ mol-1, which was calculated with respect to isolated ethylene and hydrogen surface fragments at a coverage 1/6. If we take the same reference state as used in that work (instead of coadsorbed ethylene and H atom as done above), we obtain activation barriers of 91 and 93 kJ mol-1 at coverages 1/3 and 1/9, respectively, in quantitative agreement with the earlier theoretical work.5 Hence, the coverage dependence of the forward barrier essentially is due to lateral interactions with coadsorbed H species, which become strongly repulsive as the coverage increases to 1/3. Of course, the value of the activation energy appropriate for comparison with experiments depends on the actual concentration of coadsorbed hydrogen in a particular experimental setup. For instance, if ethylene hydrogenation is considered, the coverages of H and ethylene have to be comparable; in that case, therefore, coadsorbed ethylene and H seem to be more appropriate as reference state. 3.2.1.2. Hydrogenation of π Ethylene. The hydrogenation of π-adsorbed species proceeds via a four-center transition state (TS4) that involves C and H atoms of a forming bond, as well as two Pd atoms (Figure 5). In TS4 the attacking H passes through a bridge-bound state with two H-Pd distances at 188 and 182 pm (Figure 3, Table 2) and inserts into the C-Pd bond. In TS4 the C-H distance of the forming bond is 143 pm, while the C-Pd bond stretches from 222 pm in the reactant state to 237 pm in the transition state. Earlier theoretical studies4,31 did not find a transition state for a direct hydrogenation of π ethylene at low coverages and concluded that ethylene first converts to a di-σ bound geometry. From a density functional study at high coverage 1/3, Neurock and van Santen predicted a significantly lower hydrogenation barrier for π ethylene, 36 kJ mol-1, than for di-σ ethylene, 72 kJ mol-1.31 That finding may be connected to the rather low adsorption energy calculated for the π-adsorbed species, only 27 kJ mol-1.31 We predict the adsorption energy of π ethylene at 57-74 kJ mol-1, depending on the coverage, while the experimental estimate is 50 kJ mol-1.30 The activation energy for hydrogenation of ethylene seems to correlate roughly with adsorption energy of ethylene. Thus, our calculated

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Figure 4. Reaction energy profile (kJ mol-1) of ethylene conversion to ethylidene via ethyl (h-i) over Pd(111) at various coverages: (black) 1/3, (red) 1/4, and (green) 1/9. Energies are calculated with respect to di-σ ethylene with coadsorbed H on Pd(111).

activation barriers for H addition to π-bound ethylene (60 and 79 kJ mol-1 at coverages 1/3 and 1/9, respectively) are only slightly lower than those of di-σ ethylene; see also Figure 4. The coverage-dependent barrier heights for the reverse reaction (ethyl dehydrogenation to form π ethylene) are even 5-10 kJ mol-1 above the corresponding barrier heights for the formation of di-σ ethylene. 3.2.2. Dehydrogenation of Ethyl to Ethylidene. Ethyl dehydrogenates to ethylidene via TS5 (Figure 5), which is a 3-center TS, C-Pd-H, and very similar to TS1 in its reactive part. The C-H distance is elongated to 167 pm, whereas the H-Pd distance decreases to 160 pm, as the H atom moves over a top site toward a neighboring 3-fold site. Concomitantly, the reactive C center creates a second C-Pd bond, 210 pm, at a Pd-Pd bridge site. The activation energy for ethyl dehydrogenation to ethylidene was calculated at 81-88 kJ mol-1 (Table 2, Figure 4), essentially independent of coverage. We note the very good agreement with the value previously reported for 1/6 coverage, 93 kJ mol-1.5 Also, the reaction energy obtained earlier, 5 kJ mol-1,5 agrees quite well with the present results, 13 kJ mol-1 at coverage 1/4 and 1 kJ mol-1 at coverage 1/9 (Figure 4). 3.2.3. Hydrogenation of Ethyl to Ethane. The second hydrogenation step of ethylene (Reaction j, Figure 1) leads to ethane, which is only weakly physisorbed at the surface (Table 3, Figure 5). In the 4-center TS6 (Figure 5), the reacting H atom approaches the surface-bound CH2 group at a bridge site. The H-Pd distances of TS6 are 191 and 169 pm. The C-Pd distance of TS6, 222 pm, is 13 pm longer than the corresponding bond of the reacting ethyl species, whereas the C-H distance decreases to 159 pm (Table 3). The TS structure is qualitatively similar to that obtained earlier in cluster-model calculations,31 but several pertinent distances differ by as much as 10 pm. The present calculations yield an activation barrier for ethyl hydrogenation to ethane of only 51 kJ mol-1 at both coverages considered, i.e. Twenty kJ mol-1 below the value previously determined,31 whereas the reaction energy, -28 to -37 kJ mol-1, becomes more negative with increasing coverage. According to our calculations, the hydrogenation barrier of ethyl is lower than the activation barrier of ethylene hydrogenation (Reaction h, Figure 1), in good agreement with recent experimental results30,33 which suggested the first step of ethylene hydrogenation likely to be rate-limiting. 3.2.4. Can Ethylidyne Be Formed Via Ethyl Intermediate? Figure 4 compares the calculated reaction energy profiles for the conversion of ethylene to ethylidene via ethyl over Pd(111) for three different coverages. At both high and low coverages

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Moskaleva et al. kJ mol-1, i.e., 30-37 kJ mol-1 less than the activation energy of ethyl dehydrogenation to ethylidene (Reaction i). Accordingly, one expects that ethyl, when it is formed, preferentially and irreversibly undergoes hydrogenation to ethane, rather than dehydrogenation to ethylidene and ethylidyne. We would like to emphasize that the discussed route via ethyl as intermediate requires a significant H concentration to be present on the surface, e.g., when the surface is precovered by H prior to exposure to ethylene.33 The amount of hydrogen released during ethylene dehydrogenation is not sufficient due to fast desorption at room temperature. 4. Conclusions

Figure 5. Structures of the transition states (left column) and the corresponding product states (right column) of the elementary reactions h, i, and j (Figure 1) at 1/9 coverage. Selected distances in pm.

TABLE 3: Optimized Geometriesa (pm) and Energy Characteristics (kJ mol-1) of Intermediates and Transition States for Ethyl Hydrogenation to Ethane at Various Coverages, θ θ ethyl + H

e

TS6g ethane

1/3 1/4 1/9 1/3 1/9 1/3 1/4 1/9

C-C C-Hb 151 151 151 151 151 153 153 152

258 259 256 162 159 111 110 112

H-Pdb 178, 178, 176, 170, 169, 249 291 226

178, 180 179, 184 177, 187 187 191

C-Pd Erelc 209 209 209 222 222 342 384 335

BEd

0 151f 0 159f 0 164f 51 51 -37 7 -31 7 -28 8

a A-B, distance between atoms A and B. b Distance that breaks/ forms during a reaction. c Relative energy with respect to ethyl + H coadsorbed on Pd(111). d The BE of an adsorbate (see text). e The hydrogen atom is coadsorbed unless stated otherwise. f Without coadsorbed hydrogen. g TS6 corresponds to Reaction j in Figure 1.

the barrier heights for elementary Reactions h and i (Figure 1) are lower than the activation barrier of ethylene dehydrogenation to vinyl (Reaction a), 100-117 kJ mol-1,3 and from that point the mechanism of ethylidyne formation via ethyl may be plausible if a sufficient concentration of coadsorbed H atoms is present on the surface. On the other hand, one should not forget about the competing hydrogenation of ethyl to ethane. According to our calculations, the barrier for the latter process is only 51

In continuation of our recent study on the mechanism of ethylene conversion to ethylidyne via vinyl and ethylidene (Mechanism 1),3 we now investigated two alternative mechanisms, via vinyl and vinylidene (Mechanism 2) and via ethyl and ethylidene (Mechanism 3) by means of periodic slab model density functional calculations. We compared three surface coverages, 1/3, 1/4, and 1/9. Our previous study showed that Mechanism 1, with the highest activation barrier, 100-117 kJ mol-1 for the dehydrogenation of ethylene to vinyl, is a conceivable reaction pathway. On the basis of the reaction energies and barrier heights calculated in the present work Mechanism 2, which involves the same first (and likely rate-limiting) step, followed by dehydrogenation to vinylidene and rehydrogenation to ethylidyne, appears to be equally plausible. At coverage 1/9, the activation energy of H dissociation from vinyl, 57 kJ mol-1 (Mechanism 2) is 20 kJ mol-1 below the barrier of H addition to vinyl to form ethylidene (Mechanism 1); the latter elementary reaction depends on the availability of H on the surface. Therefore, at low and intermediate coverages the dehydrogenation of vinyl to vinylidene according to Mechanism 2 may even be expected to be more favorable than Mechanism 1. Kinetic modeling may provide further clarification which of the two mechanisms prevails at particular experimental conditions.34,35 Mechanism 3 involves H atom addition to ethylene as initial step and thus requires notable concentrations of surface hydrogen. The present analysis revealed that the barrier heights of the three elementary reactions of Mechanism 3 (at most 88 kJ mol-1) are lower than the rate-limiting barriers of Mechanisms 1 and 2. At variance with earlier theoretical studies, we find that the activation energy of π-ethylene hydrogenation is only slightly lower than that for H addition to di-σ ethylene. Nevertheless, we conclude that Mechanism 3 is unlikely due to even lower activation energy, only 51 kJ mol-1, for ethyl hydrogenation to ethane. The latter reaction is also thermodynamically more favorable than ethyl dehydrogenation to ethylidene and irreversible due to ethane desorption. The competition between these two parallel reaction channels will, of course, depend on the H coverage; therefore, once again kinetic modeling may be useful to verify our qualitative reasoning. Acknowledgment. This work was supported by Deutsche Forschungsgemeinschaft and Fonds der Chemischen Industrie (Germany). H.A.A. is grateful for support by the National Center of Advanced Materials UNION and the Bulgarian National Science Fund (contract VUH-17/05). References and Notes (1) Pallassana, V.; Neurock, M.; Lusvardi, V. S.; Lerou, J. J.; Kragten, D. D.; Van Santen, R. A. J. Phys. Chem. B 2002, 106, 1656.

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