DFT Study on the Complex Reaction Networks in the Conversion of

Apr 15, 2009 - FIN-40014 JyVäskylä, Finland. ReceiVed: NoVember 17, 2008; ReVised Manuscript ReceiVed: March 5, 2009. Adsorption and conversion of ...
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J. Phys. Chem. C 2009, 113, 8278–8286

DFT Study on the Complex Reaction Networks in the Conversion of Ethylene to Ethylidyne on Flat and Stepped Pd J. Andersin,† N. Lopez,‡ and K. Honkala*,†,§ Department of Chemistry, Nanoscience Center, P.O. Box 35, UniVersity of JyVa¨skyla¨, FIN-40014 JyVa¨skyla¨, Finland, Institute of Chemical Research of Catalonia (ICIQ), AVgda. Paisos Catalans, 16, 43007 Tarragona, Spain, and Department of Physics, Nanoscience Center, P.O. Box 35, UniVersity of JyVa¨skyla¨, FIN-40014 JyVa¨skyla¨, Finland ReceiVed: NoVember 17, 2008; ReVised Manuscript ReceiVed: March 5, 2009

Adsorption and conversion of ethylene to ethylidyne on flat (111) and stepped Pd surfaces have been studied with the aim to unravel the complex chemistry of small organic molecules on Pd. These processes are crucial to understanding many experimental observations on Pd catalysts involved in selective hydrogenations, steam reforming, polymerization, and several other chemical processes. Our results provide a view on the complex chemistry of olefins on the surface, where several competitive processes take place simultaneously and where a hierarchy among different bond activations can be established. For Pd, the C-H bonds of the olefins are the most labile on the surface, followed by C-C and last isomerization processes. From the picture above not always the most straightforward reaction mechanism is necessarily the one taking place on the surface. Scrambling of H atoms on the organic moieties is the most effective way to generate certain (even long lasting) isomers on the surfaces. Introduction Understanding ethylene adsorption and reactivity on transition metal surfaces is of importance because it forms a prototype to study many aspects related to reactivity of olefins. In fact, the interaction of ethylene with metal surfaces can lead to different processes like ethylene hydrogenation, decomposition, and polymerization, and the selectivity for each of these processes depends on the nature of the metals and the working conditions.1-6 Interesting features are typically adsorption properties of different species and catalytical hydrogenation and dehydrogenation reactions as well as the C-C bond cleavage. Ethylene is an important intermediate in many industrially relevant processes like in acetylene hydrogenation and the synthesis of vinyl acetate which both proceed over Pd catalysts.6 The adsorption of ethylene has been extensively studied experimentally over single-crystal metal surfaces7-9 and oxidesupported metal particles.10-13 NEXAFS,14 HREELS,15,16 and RAIRS17,18 studies suggest that ethylene is di-σ- or π-bonded on Pd(111) at low temperature. On Pd(100) and Pd(110) surfaces both di-σ- and π-bonded ethylene species are observed in EELS studies.19,20 DFT (density functional theory) calculations indicate that di-σ-bonded species are more stable than π-bonded16,21-24 and calculated adsorption energies vary from -0.64 to -0.87 eV depending on the computational setup. From UHV TPD experiments, the adsorption energy has been estimated to be -0.56 eV at 0.05 ML coverage.25 On small Pd particles and PdAu alloys ethylene is mainly π-bonded at low temperature, whereas on larger particles also di-σ-bonded species are present according to IRAS studies.10,12,26 Ethylene hydrogenation over supported Pd particles has been reported to be independent of * To whom correspondence should be addressed. † Department of Chemistry,University of Jyva¨skyla¨. ‡ Institute of Chemical Research of Catalonia. § Department of Physics, University of Jyva¨skyla¨.

the particle size,11 and over Pd single crystal surfaces, it is claimed to be structure insensitive under most reaction conditions.8 Upon heating ethylene is observed to dehydrogenate, and different intermediates are observed on a Pd surface depending on the symmetry and reaction conditions: ethynyl on Pd(110), vinyl on Pd(100), and ethylidyne on Pd(111).15,19,27 Ethylidyne is spectroscopically identified to bond in a 3-fold site with molecular axis perpendicular to the surface.28 LEED and EELS analysis confirm the formation of the ordered (3 × 3-R30°) overlayer on Pd(111)29,30 with preferred adsorption on a 3-fold hollow site.31 TPD experiments give activation energy for ethylidyne formation of 0.95 eV.18 RAIRS and TPD experiments show that ethylene adsorbs also on a ethylidyne covered Pd surface.32 In recent thermal desorption experiments, no conversion from ethylene to ethylidyne is observed upon heating from 100 to 300 K but observed changes in spectra are, with the help of the DFT calculations, assigned to a change of adsorption site from di-σ to π bonded. If ethylene adsorption is done at room temperature an ethylidyne (CCH3) state is populated.16,30 Up to 350 K ethylidyne is a predominant surface species. At temperatures beyond that ethylidyne decomposes to CCH and CH species, and eventually to C atoms, which can migrate to subsurface sites.16,30,33 The presence of ethylidyne does not affect the surface chemistry except that it slightly reduces the saturation coverage of ethylene.16,18,32,34 However, there exists increasing amount of evidence that the decomposition products, at least carbon atoms, play important role in several surface events taking place on Pd. A recent in situ X-ray photoelectron spectroscopy study showed the importance of the formation of subsurface carbon in the selective hydrogenation of 1-pentyne and the oxidation of ethylene over Pd based catalysts.35 The spectroscopical study by Teschner et al. indicates that the population of the subsurface sites of Pd either by H or C govern the alkyne hydrogenation process.1 There is also experimental data declaring the significance of the formation of near-surface

10.1021/jp8100877 CCC: $40.75  2009 American Chemical Society Published on Web 04/15/2009

Conversion of Ethylene to Ethylidyne

J. Phys. Chem. C, Vol. 113, No. 19, 2009 8279 dyne but probably via vinyl,39 since the rate of vinylidene hydrogenation is substantially low.43 In this work we focus on the adsorption and conversion of ethylene to ethylidyne on flat and stepped Pd surfaces. Steps are found to dominate ethylene decomposition on Ni44 and Cu45 surfaces and on Pt clusters.46 We also investigate the C-C bond breaking from the C2H4 level since on a Ni(211) it is shown to compete with the dehydrogenation.44 The paper is organized as follows. We start with describing the computational method. Then, the adsorption of ethylene and ethylidyne and various intermediates, including ethyl, vinyl, ethylidene is discussed in detail. After that we focus on activation barriers and transition state geometries for different possible reaction paths and compare the pathways on flat and stepped surfaces. Computational Methods

Figure 1. Elementary reaction steps for the ethylene decomposition to ethylidyne on the surface including C-C bond breaking, hydrogenation, dehydrogenation, and isomerization reactions. Carbon atoms are colored blue, hydrogen atoms white and palladium atoms brown.

carbon for vinyl acetate synthesis36,37 and selective oxidation of ethylene38 on Pd catalysts. To produce ethylidyne from ethylene one hydrogen atom must be abstracted from the molecule and one hydrogen atom must migrate from one carbon to another one. There are several possible pathways for the conversion and they include various intermediates like, for instance, ethyl, vinyl or ethylidene and processes like hydrogenation, dehydrogenation and isomerization. The complex reaction network is summarized in Figure 1. Note that, we do not investigate the full decomposition path of ethylene to adsorbed C and H atoms but focus on ethylene conversion to ethylidyne, the most common intermediate for the Pd(111) surface, for which three different reaction paths are put forward. One possible reaction path involves ethylene dehydrogenation to vinyl, which is not, however, detected experimentally during the conversion.15,28 Vinyl can be grafted on the surface by exposing Pd(111) to vinyl iodine, which breaks into iodine and the hydrocarbon fragment. Reflection/adsorption infrared measurements show that adsorbed vinyl species convert into ethylidyne moieties at temperatures as low as 160 K.39 Vinyl can either isomerize to ethylidyne or hydrogenate to ethylidene, which dehydrogenates to ethylidyne. Isomerization of vinyl to ethylidyne was first suggested for the probable reaction pathway on Pt(111)40 but later IRAS experiments indicate that ethylidyne formation from vinyl goes via ethylene.41 Pallassana et al. performed DFT calculations for the conversion pathway from ethylene to ethylidyne via vinyl and ethylidene on Pd(111), and found the activation barriers of 1.57, 0.87, and 0.78 eV for sequential dehydrogenation, hydrogenation and dehydrogenation steps. Vinyl dehydrogenation to acetylene and conversion to ethylidyne via this route is unlikely since at UHV conditions, and in the absence of hydrogen, acetylene converts to vinylidene, which decomposes to carbon and hydrogen at ∼480 K.42 In the presence of hydrogen acetylene converts to ethylene or ethyli-

DFT calculations were carried out with the DACAPO code,47 where Kohn-Sham equations are solved selfconsistently using the RPBE48 GGA (generalized gradient approximation) to describe exchange and correlation effects. In some cases we also mention the PW91 GGA energies in order to compare our results to those presented in the literature. The plane wave basis was restricted by a kinetic energy cutoff of 25 Ry, and the core electrons of the atoms were treated with Vanderbilt ultrasoft pseudopotentials.49 We modeled the flat Pd(111) surface with a four-layer slab and a (3 × 2) unit cell and the stepped Pd(211) surface with a four-layer slab and a (2 × 1) unit cell. Both models correspond to 1/6 monolayer coverage for an adsorbate. The periodic images were separated by 10 Å of vacuum to minimize the interactions between the successive metal slabs. The Brillouin zone was sampled at 16 Monkhorst-Pack k-points. The two bottom metal layers were fixed to their ideal bulk positions while all the other atoms were relaxed until the residual force was below 0.05 eV/Å. Transition states for the reactions were determined by applying the nudged elastic band method (NEB),50 the adaptive nudged elastic band method (ANEB)51 and a constraint method, where either a C-C or C-H distance was fixed and the remaining degrees of freedom were relaxed. For the found transition states harmonic frequencies were calculated. Only a single imaginary frequency was obtained in each case, and the visualization of the vibration mode showed that it is along the reaction coordinate. Adsorption energies for some C2Hn (n ) 3-5) species are calculated relative to an ethylene molecule in gas phase infinitely far away from the surface. For C2Hn (n ) 3,4) species the adsorption energy, Eads, is

Eads ) Etot + (4 - n)EH+slab - ((5 - n)Eslab + EC2H4(g)) where Etot is the total energy of the adsorbate and the slab and EH+slab is the total energy of the H atom and the slab. Eslab refers to the energy of the clean slab, and EC2H4(g) is the energy of the gas-phase ethylene. For a exothermic (endothermic) reaction adsorption energy is negative (positive). For methylene the adsorption energy is calculated from the formula Eads ) Etot (Eslab + 1/2EC2H4(g)). The adsorption energy of H is given relative to the gas phase H2. The adsorption energy is a strong function of the reference state, that is in this case ethylene. We note that the direct comparison to previous calculations is not always possible if reference states differ.

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TABLE 1: Calculated Adsorption Energies for the Chemisorbed Species on Pd(111)a adsorbate/ state

formula

site

figure

adsorption energy [eV] RPBE (PW91)

ethylene/di-σ ethylene/π methylene/C2 vinyl/C1C2 ethylidyne/C3 ethylidene/C2 ethyl/C1

CH2CH2 CH2CH2 CH2 CH2CH CCH3 CHCH3 CH2CH3

bridge top bridge fcc/bridge fcc bridge top

2a 2b 3a 3b 3c 3d 3e

-0.36 (-0.96) -0.27 (-0.81) 0.45 (0.10) 0.02 (-0.75) -0.70 (-1.40) -0.02 (-0.60) -0.04 (-1.21)

a The C1-3 notation stands for the configuration in which the carbon forms 1-3 bonds to the palladium surface. (If only one carbon appears in the adsorption mode notation, the other carbon does not form bond(s) to the surface atoms.)

TABLE 2: Calculated Adsorption Energies for the Chemisorbed Species on Pd(211)a adsorbate/ state

formula

site

figure

adsorption energy [eV] RPBE (PW91)

ethylene/di-σ ethylene/π ethylene/π-90° methylene/C3 vinyl/C1 ethylidyne/C3 ethylidene/C2 ethyl/C1

CH2CH2 CH2CH2 CH2CH2 CH2 CH2CH CCH3 CHCH3 CH2CH3

bridge top top bridge bridge hcp bridge top

2c 2d 2e 3f 3g 3h 3i 3j

-0.69 (-1.23) -0.60 (-1.11) -0.59 (-1.06) 0.18 (-0.13) -0.22 (-0.86) -0.50 (-1.12) -0.40 (-0.89) -0.61 (-1.65)

a The C1-3 notation stands for the configuration in which the carbon forms 1-3 bonds to the palladium surface. (If only one carbon appears in the adsorption mode notation, the other carbon does not form bond(s) to the surface atoms.)

Results Adsorption of Ethylene, and Hydrocarbon Fragments on Pd(111) and Pd(211). Before discussing ethylene conversion to ethylidyne on flat and stepped Pd surfaces we focus on the adsorption of ethylene and the possible intermediates of the conversion process. Table 1 presents the adsorption energies and configurations for ethylene and its derivatives on Pd(111), and Table 2 gives the corresponding values on Pd(211). The derivatives include methylene (CH2), vinyl (CHCH2), ethyl (CH2CH3), ethylidene (CHCH3), and ethylidyne (CCH3) species. For each adsorbate various different optimized geometries are calculated and the most stable geometries can be found from Figures 2 and 3. Consistent with several earlier studies,16,21,23,52 we find ethylene to bind strongest on di-σ- and π-bonded sites on the Pd(111) surface. According to our calculations it prefers the di-σ-site with an adsorption energy of -0.36 eV over the π-bonded site, which is 0.1 eV less stable. Adsorption energies for di-σ-bonded ethylene given in literature were calculated with PW91 GGA and range from -0.64 to -0.86 eV at 0.25 ML coverage. Our nonself-consistent PW91 adsorption energy is -0.96 eV being slightly larger than those reported earlier. Presumably, the difference is mainly due to the lower adsorbate coverage in our calculations, which leads to the weaker adsorbate-adsorbate repulsion. The optimized C-C bond length is 1.44 Å on the di-σ and 1.39 Å on the π site. The former agrees well the value 1.43 Å obtained from the NEXAFS studies.14 Also on the Pd(211) surface ethylene slightly favors the diσ-site over the π-bonded site, and the adsorption energies are

Figure 2. Calculated adsorption geometries for ethylene on the Pd(111) and Pd(211) surfaces: (a) di-σ mode Pd(111) (b) π-bound Pd(111), (c) di-σ mode Pd(211) (d) π-bound Pd(211), and (e) π-90°-bound Pd(211). The color coding is the same as in Figure 1.

-0.69 eV (PW91: -1.23 eV) and -0.60 eV, respectively. Our calculated value agrees well with the measured one, which is -0.56 eV.25 In addition, we examined the geometry, where ethylene is perpendicular to the step edge and one methylene group is at the top of the Pd atom and the other one hangs over the step, for more details see Figure 2e. This geometry is energetically degenerate to the π-bonded one. The C-C bond lengths at different configurations are 1.43, 1.40, and 1.39 Å for di-σ-π- and perpendicular-π-bonded ethylene molecules, respectively. Watwe et al. reported53 the ethylene adsorption energy at the di-σ-site on the Pt(211) at 0.25 ML coverage to be -1.78 eV (PW91) which is more than 0.5 eV lower than the value on Pd(211). Decreasing the ethylene coverage to 1/6 ML would most probably lead even stronger adsorption on Pt(211) since, in general, ethylene-ethylene interaction is repulsive. On the Ni(211) surface ethylene prefers the π-bonded site with the adsorption energy -0.76 eV,44 that is close to adsorption energy on Pd(211). The numbers indicate that ethylene adsorption energy on the group 10 stepped metal surfaces goes as Ebind(Pt(211)) > Ebind(Ni(211)) > Ebind(Pd(211)). On the (111) surface the order of the adsorption energies on nickel and palladium is inverse. From the comparison of adsorption energies on flat and stepped Pd surfaces we conclude that steps stabilize ethylene adsorption by 0.3 eV. On the Ni surface the stabilization is twice that, 0.6 eV, and on Pt surface it is 0.7 eV. Figure 3 shows the optimized structures for ethyl, ethylidene, ethylidyne, vinyl, and methylene. In general, C2Hn species favor adsorption sites, where a carbon atom can satisfy its tetravalency by forming the adequate number of bonds to the metal atoms.54 The structural isomer of ethylene, ethylidene (CHCH3), binds weakly on a bridge site on Pd(111), see Figure 3d), with the adsorption energy of -0.02 eV, which is considerably smaller than that of ethylene. On Pd(211) ethylidene binds with the adsorption energy of -0.40 eV at the bridge site, see Figure 3i. On both surfaces the C-C bond length is 1.50 Å that is 0.06 Å longer than calculated for ethylene. The PW91-calculated adsorption energies range from -0.4 eV (1/4 ML)16 to -0.6 eV (1/9 ML)52 on Pd(111). Our PW91 value is -0.6 eV at 1/6 ML. From the structural isomers containing three hydrogen atoms, ethylidyne, (CCH3), binds stronger to the Pd(111) surface than vinyl, CHCH2, their adsorption energies are -0.70 and +0.02 eV, respectively. On the Pd(211) the corresponding adsorption

Conversion of Ethylene to Ethylidyne

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Figure 3. Most stable adsorbate geometries for (a and f) methyl, (b and g) vinyl, (c and h) ethylidyne, (d and i) ethylidene, and (i and j) ethyl on the Pd(111) (top) and the Pd(211) (bottom) surfaces. The color coding is the same as in Figure 1.

energies are -0.50 eV (ethylidyne) and -0.22 eV (vinyl). The optimized geometries for both surfaces are given in Figure 3. On Pd(111) ethylidyne sits on a fcc-hollow position with a molecular axis along the surface normal, and has the C-C bond length 1.49 Å. Sock et al. report adsorption energy of -1.2 eV at 1/4 ML, and Moskaleva et al. report -1.32 eV at 1/9 ML coverage. We obtain -1.4 eV at 1/6 ML coverage and with nonself-consistent PW91 GGA. For the vinyl species the most stable adsorption mode is C1C2 (see Figure 3) for both surfaces. The notation stands for the configuration where the carbon atom with two hydrogens forms one bond to the palladium surface whereas the carbon with one hydrogen forms two bonds to the surface. (If only one carbon appears in the adsorption mode notation, the other carbon does not form bond(s) to surface atoms.) In this study, we assume that ethyl formation takes place via self-hydrogenation, and thus the adsorption energy of ethyl is calculated with respect to two ethylene molecules in gas-phase, and to be precise the ethyl adsorption energy includes vinyl adsorption energy. The preferred adsorption site over Pd(111) is on the top of a Pd atom with adsorption energy -0.02 eV. The adsorption geometry resembles that of ethyl on Pt(111), except that there the methyl group points toward the adjacent Pt atom,53 and here it is toward the hollow site, see Figure 3e. The optimized adsorption geometry of ethyl over Pd(211) is also at a top site, see Figure 3j, and the adsorption energy equals to -0.61 eV. We find that the outcome of the C-C bond breaking of ethylene, a methylene, sits on a bridge site on both surfaces. The adsorption is endothermic with respect to gas-phase ethylene. On a Ni surface methyl binds to a hollow (bridge) site on a Ni(111) (Ni(211)) surface and the corresponding adsorption energies are +0.29 and -0.05 eV, respectively.44 Upon ethylene dehydrogenation we have hydrogen adsorption on the surface. The hydrogen atom prefers a fcc hollow site on Pd(111) in agreement with previous calculations.55,56 Rahman et al. studied H adsorption on Pd(211) and found a hcp site on the terrace to be slightly better than a hcp site right behind the step.57 From the five best structures given in ref 57, we found that the most stable one is a hcp hollow behind the step. The hydrogen adsorption energies are -0.44 and -0.36 eV on Pd(111) and Pd(211) surfaces. Note, that since the hydrogen may readily diffuse from steps onto the terrace sites, this would result in even larger binding energies for C2H3 + H isomers on the Pd(211) compared to the Pd(111).

In general, a step site strengthens the adsorption but there are two exceptions among the adsorbates studied here, ethylidyne and hydrogen. They both bind stronger on the flat than the stepped surface. Some variation is seen for H adsorption, where the three H-Pd distances are 1.82 Å on Pd(111) but on Pd(211) the site is distorted and H-Pd distances range from 1.81 to 1.86 Å. The more detailed analysis shows that the anomaly in ethylidyne adsorption can not be explained with geometrical effects: on both surfaces the C-C bond length is 1.49 Å and the C-Pd distances are 2.0 Å. By calculating CCH3 adsorption energy with respect to a gas-phase CCH3 radical the hydrogen adsorption energy is ruled out, in which case 0.1 eV stronger binding is found to the terrace than to the step. The d-band center analysis shows that the d-band of the Pd edge atoms is 0.15 eV higher in energy than that of the terrace atoms. This supports the fact that ethylidyne and hydrogen should bind stronger on the stepped than on the flat Pd surface, particularly since both of them bind to two step edge atoms. Increasing the cutoff energy and the number of k-points did not change the picture: H and CCH3 still bind more weakly on the step. Ethylene Conversion to Ethylidyne on Pd(111) and Pd(211) Surfaces. There exist several suggestions for the overall reaction pathways for ethylene decomposition on transition metal surfaces, see for example refs 40, 58, and 59. Those consist of elementary reactions including dehydrogenation, hydrogenation and isomerization (1,2-H-shift). We studied also the energetics involved in ethylene direct decomposition to methylene species. The reaction steps are represented in Figure 1, from which the numbering of the reaction steps used in the text is also taken. The first stage of the ethylene decomposition on Pd is presumably one of the following; ethylene goes through C-C bond breaking (step 1, Figure 1), ethylene dehydrogenates to vinyl (step 2), an isomerization, where ethylene converts to ethylidene (step 3), or ethylene hydrogenates to form ethyl species (step 4). Note that, the fourth step requires the presence of hydrogen on the surface. Here, we assume that the hydrogen is obtained from ethylene dehydrogenation. The energetics involved in these reactions as well as in the possible subsequent reactions are discussed in the following subsections. Ethylene C-C Bond CleaWage. From the metastable π-site ethylene decomposition to two methylenes leads to activation barriers of 2.12 and 1.69 eV on flat and stepped surfaces, respectively. At the step edge the transition state is oriented parallel to the step as on the Ni step, where the corresponding

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Figure 4. Optimized transition state geometries for (a and f) ethylene dehydrogenation to vinyl, (b and g) vinyl hydrogenation to ethylidene, (c and h) ethylene hydrogenation to ethyl, (d and i) ethyl dehydrogenation to ethylidene, and (e and j) ethylidene dehydrogenation to ethylidyne on the Pd(111) (top) and the Pd(211) (bottom) surfaces. The color coding is the same as in Figure 1.

activation barriers are 1.35 and 0.96 eV. Over 1 eV higher barriers are obtained from the most stable adsorption site, di-σ, and from π-90°. Note that, the difference in the stabilities of adsorption sites is only 0.1 eV on both surfaces. The steps decrease the activation barrier by 0.4 eV for both Pd and Ni. On the Ni step sites the ethylene decomposition to methylene competes with the dehydrogenation reaction.44 Relatively high activation energies even on the step indicate that similar behavior might not be seen on the Pd surface, but we will return to this later. Isomerization of Ethylene (H2CdCH2) to Ethylidene (HC-CH3) and Vinyl (HCdCH2) to Ethylidyne (C-CH3). Ethylidyne formation from ethylene has been proposed to involve isomerization on Pt. The hypothesis is supported by RAIRS and TPD experiments for trideuterioethylene adsorption on Pt(111).40 Although no experimental evidence exists, the isomerization might be important on Pd as well. Our calculations, however, indicate that the isomerization to ethylidene is unlikely since the activation barriers of the 1,2-H-shift from ethylene to ethylidene (step 3) and from vinyl to ethylidene (step 7) are relatively high. It should be noted that our discussion on the structure and energy of the transition states of the 1,2-Hshift remains preliminary. This is because pinpointing of the transition state was challenging due to its unusual structure: at the transition state the shifting hydrogen does not touch a surface i.e. the H-shift reaction resembles a gas-phase process, and thus the transition state is not surface mediated. Similar kind of transition state structures as ours were found for ethylene isomerization on Pd(111),21 Fe(100),60 and Pt(110)61 surfaces. Anghel et al. report the transition state energy for ethylene isomerization to ethylidene to be 2.31 eV on Pt(110). For Pd(111) and Fe(100) surfaces no estimates for transition state energies are given.21,60 Our transition state energies are of same order of magnitude as the one given by Anghel et al. Our results do not indicate isomerization as a likely step in ethylidyne formation, yet our results are not conclusive. Dehydrogenation of Ethylene to Vinyl. Due to the relatively high activation barriers of ethylene decomposition to methylene and isomerization, it is more likely that disproportionation takes place. Adsorbed ethylene can dehydrogenate to vinyl via C-H bond breaking. Note that, dehydrogenation of hydrocarbon requires an empty surface site to accommodate the hydrogen released. This is hindered at high coverages. Since the difference in ethylene adsorption energies on di-σ and π sites over both surfaces is small, we have calculated the

dehydrogenation pathways from both initial sites. From the slightly more stable di-σ site calculations give the activation barriers of 1.25 eV (1.12 eV) on Pd(111) (Pd(211)). The reaction path is very similar on both surfaces: in addition to activation the C-H bond one C atom migrates toward a bridge position. This can be seen from the optimized transition state geometries given in Figure 4, which resemble the most stable adsorption sites of the vinyl.62 On Pd(211) the methylene end tilts away from the surface plane. Note that, transition state energies given with respect to gas-phase ethylene are lower on the step. It means that steps are more effective to dehydrogenate ethylene than the terrace sites. Our calculations indicate that a π-site acts as a precursor to dehydrogenation but it is not directly active. This is because the dehydrogenation from the π-site leads to a reaction pathway, where ethylene first diffuses to a di-σ site from which it dehydrogenates as described above. Pallassana et al. reported 1.56 eV62 and Moskaleva et al. 1.21 eV for activation barrier on Pd(111). The agreement with the latter one is very good whereas somewhat larger value of Pallasana et al. is mainly due to the different computational set up. The activation barrier for dehydrogenation on Pd(111) is 0.45 eV lower than the barrier calculated for the C-C bond breaking on the step. The energy difference is 0.56 eV, if dehydrogenation takes place on the step. Thus, we can conclude that unlike on the Ni surface, where the C-C bond breaking on the step begins to compete with the dehydrogenation, no such competition is seen on Pd. On Pd ethylene has to proceed via one or several dehydrogenation step(s) before a C-C bond breaks. AlternatiWe Routes for Vinyl-Ethylidyne Decomposition. From vinyl we have various possible reaction pathways to ethylidyne. If we rule out the direct conversion via a 1,2-Hshift due to the high activation barrier, one is left with three alternative reaction paths (numbering from Figure 1): (i) hydrogenation to ethylidene (step 6) followed by dehydrogenation to ethylidyne (step 10), (ii) dehydrogenation to vinylidene (step 8) followed by hydrogenation to ethylidyne (step 14), (iii) dehydrogenation to acetylene (step 9) followed by either direct isomerization to vinylidene (step 11) or dehydrogenation to acetylidene (step 12) and hydrogenation (step 13) to vinylidene, which hydrogenates to ethylidyne (step 14). The hydrogenationdehydrogenation steps are closely related to the Horiuti-Polanyi mechanism.63 We can eliminate paths (ii) and (iii), which contain the dehydrogenation of vinyl to C2H2 species. The decision is based on experiments, which indicate that vinylidene does not convert

Conversion of Ethylene to Ethylidyne directly to ethylidyne but rather reacts with adsorbed hydrogen to form vinyl which rapidly converts to ethylidyne on Pd(111).39 Thus, we can focus on the pathway containing steps 6 and 10 (Figure 1), where vinyl first hydrogenates to ethylidene and then dehydrogenates to ethylidyne. At the beginning vinyl sits on its most favorable adsorption site with the methylene end over the Pd atom and the methylidyne end at the bridge position and the H atom resides in the neighboring hcp (bridge) site on Pd(111) (Pd(211)). Along with the simultaneous breaking of H-Pd and C-Pd bond, the C-H bond develops. The methylidyne end stays on a bridge site during the hydrogenation while the C-C axis tilts toward the surface normal. The optimized transition state geometries for both surfaces are presented in Figure 4, panels b and g. Our activation barrier on Pd(111) is 0.90 eV, which is close to values reported earlier.21,52 On Pd(211) the activation barrier is 0.86 eV. The last step in the ethylidyne formation is ethylidene dehydrogenation to ethylidyne. Note that, this step is included to the reaction pathway suggested to proceed via ethyl species, which is described in the next section. On both surfaces ethylidene sits on a bridge with methyl group tilted toward the hollow site, and the dehydrogenation proceeds on the similar manner as described by Pallassana.21 The C-C axis tilts toward the surface normal and brings the R-H close to the metal surface thus initiating a R-H-metal interaction leading to dehydrogenation. Simultaneously R-carbon migrates toward the hollow site. The activation barriers are 0.34 eV on Pd(111) and 0.77 eV on Pd(211). Again, on Pd(111) our activation barrier agrees very well with that in ref 52 and Pallassana et al. obtained 0.77 eV for C-H bond activation to form ethylidyne on Pd(111). The discrepancy in our and their barrier heights might be due to the slightly different computational setup and the fact that in ref 21 the transition state geometries were searched using cluster calculations whereas our results are based on self-consistent periodic slab calculations. Moskaleva et al. report the barrier height of 0.25 eV for ethylidene dehydrogenation to ethylidyne, very much in agreement with our result.52 Ethylene Hydrogenation to Ethyl and Dehydrogenation to Ethylidyne. In principle, ethylene conversion to ethylidyne could proceed via ethyl and ethylidene species, see Figure 1 reaction steps 4, 5, and 10. However, this reaction path requires that we have hydrogen on the surface. Here, we assume that the needed hydrogen is obtained from dehydrogenated ethylene, thus ethylene self-hydrogenates to ethyl. We are aware that the possibility of this pathway depends sensitively on the amount of hydrogen present, and we also note that self-hydrogenation can lead to ethane species. However, the amount of ethane produced via self-hydrogenation is negligibly small compared to the case, where hydrogen is coadsorbed on a surface.13 Sum frequency generation experiments indicate that while ethylene mainly binds to a di-σ-site, the π-bonded species might be important for hydrogenation activity on Pt.64 Neurock and co-workers have found, using DFT calculations, that at low coverage ethylene hydrogenation to ethyl takes place from the di-σ site whereas at high coverage they found a lower barrier from the π-site.65 The corresponding activation barriers are 0.90 and 0.37 eV, respectively. Like in the case of ethylene dehydrogenation, the ethylene hydrogenation pathways are calculated from both di-σ and π initial states. The hydrogenation of π-bound ethylene leads first to the diffusion of ethylene to a di-σ. We found that hydrogenation from di-σ site gives activation barriers: 0.94 eV on Pd(111) in a nice agreement with the earlier calculations, and 0.84 eV

J. Phys. Chem. C, Vol. 113, No. 19, 2009 8283 on Pd(211). Again, the reaction paths are similar on both surfaces. During the development of the C-H bond, the breaking of C-metal and H-metal bond takes place and a methyl group moves away from the surface and the methylene end moves over the Pd atom. The best transition state geometries for the hydrogenation are illustrated in Figure 4, panels c and h. It is possible that ethyl undergoes two dehydrogenation steps on the way to ethylidyne. First, ethyl dehydrogenates to ethylidene and then to ethylidyne. To put it differently first R carbon loses one hydrogen and then the other one. The simultaneous loss of both hydrogens has not been discussed in accordance with the sequential processes described by Horiuti and Polanyi.63 The calculated activation barriers for the first dehydrogenation step from ethyl to ethylidene are 0.96 and 0.67 eV on Pd(111) and Pd(211), respectively. The optimized transition state geometries are given in Figure 4, panels d and i. On the step the abstraction of the hydrogen takes place along the step and the methyl end hangs over the step. The final step, the dehydrogenation of ethylidene, is already discussed above in the context of the reaction path proceeding via vinyl. Discussion The discussion of various reaction steps is summarized in Figure 5, which gives a detailed one-dimensional potential energy surface for ethylene conversion to ethylidyne. The zero of energy is given with respect to gas phase ethylene on left side of the figure. First, we adsorb two ethylene molecules on the surface. In the case of the Pd step we place one reactive molecule at a time on the step while the other hydrocarbon (not involved into a particular reaction step) is stored on a terrace. We assume that a diffusion of molecules on the surface happens readily with a barrier lower than the those of elementary reactions.66 Various reaction steps including C-C bond breaking (at the level of ethylene), dehydrogenation and hydrogenation follow to the right. In general, step sites strengthen the adsorption the only exceptions being H and ethylidyne. Also transition state energies are mainly lower on the step than on the terrace sites, and thus the reactions proceed more effectively on steps. On both surfaces the formation of ethylidyne is exothermic. DFT calculations suggest that ethylene decomposition to methylene does not compete with dehydrogenation. Steps do lower the activation barrier of the C-C bond breaking but it is nonetheless 1.69 eV on the step, while the dehydrogenation barriers are 1.25 eV on the Pd(111) and 1.13 eV on Pd(211). In ethylidyne formation we discuss in detail two possible reactions pathways: one via vinyl and ethylidene to ethylidyne and one via ethyl and ethylidene to ethylidyne. The latter step requires atomic hydrogen to proceed. Here, we assume that the hydrogen is obtained from dehydrogenation of ethylene. The comparison of the dehydrogenation and hydrogenation barriers of ethylene shows that on both surfaces activation barriers for ethylidyne formation via ethyl are lower than via vinyl. One should keep in mind that although the reaction pathway via ethyl has lower barriers, thus indicating to be more probable one, it is in this case limited by the presence H atoms. Our results are in good agreement with experimental observations. The measured binding energy of ethylene at low coverage is about -0.56 eV and our theoretical values are -0.36 and -0.69 eV for the (111) and (211) surfaces. Experimentally ethylidyne appears with a reaction barrier of 0.95 eV.18 From our reaction profiles, the first C-H bond breaking is the rate limiting step of the dissociation process on both surfaces and our barrier is 1.25-1.13 eV without considering the zero-point

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Figure 5. Potential energy diagram for ethylene decomposition on Pd(111) and Pd(211) surfaces. Black (green) line represents the adsorption energies of the different hydro-carbon species on Pd(111) (Pd(211)). Numbering is the same as in Figure 1. Transition state energies for C-C bond breaking, dehydrogenation and hydrogenation reactions are illustrated with blue, red, and green lines, respectively. The solid line refers to a Pd(111) and the dashed line to the Pd(211) surface. The zero of energy is ethylene far way from the clean surface. We assume that we have a reservoir of molecules on the terrace; i.e., those molecules or fragments that are not involved to a particular reaction step sit on a terrace.

TABLE 3: Reaction Energies, ∆E, and Activation Barriers, Eact, Both in eV for All of the Computed Reactions step ∆E (111) Eact (111) ∆E (211) Eact (211) 2 H2CCH2* + * T HCCH2* + H* H2CCH3* + * T -4 H2CCH2* + H* 5 H2CCH3* + * T HCCH3* + H* HCCH3* + * T -6 HCCH2* + H* HCCH3* +* T 10 CCH3* + H* Figure 6. Brønsted-Evans-Polanyi type of relationship for the dehydrogenation steps of ethylene on Pd. The data point numbering corresponds the one used in the text and given in Figure 1 for the reactions. Black (red) circles stand for terrace (step) reactions.

vibrational energy that, according to our calculations, accounts for almost 0.2 eV, thus very much in agreement with the experimental results. Moreover, the vinyl species is not detected in the experiments.15,28 This could be explained by the smaller barriers found for all the rest hydrogenation-dehydrogenation steps that lead to ethylidyne. Our calculations indicate also why ethylidyne seems to be a long-lasting species since the C-C bond splitting appears very high in energy. Although the decomposition of ethylidyne will be the subject of further investigations, we can anticipate that the C-C dissociation for this system will show a comparable energy to that calculated for ethylene while geometric factors explain the difficulties to cleavage the C-H bond, thus this is compatible with the high temperature needed for the decomposition of this intermediate. Finally, Figure 6 and Table 3 compile and summarize all the energies from the dehydrogenation steps given in the set of equations at the end of this section. Dehydrogenation steps of ethylene related structures are found to follow a BrønstedEvans-Polanyi67,68 type of relationship with the reaction energy. Note, that so far BEP lines have been made mainly for simple molecules (mostly C1 or alkanes) whereas here it is applied for larger molecules, different degrees of insat-

H2CCH2* + * T 2CH2*

1

Dehydrogenation 0.38 1.25

0.47

1.13

-0.29

0.65

-0.29

0.55

0.05

0.96

0.06

0.67

0.04

0.94

0.18

1.04

-0.68

0.34

-0.10

0.77

C-C Splitting 1.16 2.12

0.96

1.69

uration and a complex reaction network. In fact, for the (111) surface geometry the activation energies and reaction energies follow a line remarkably well (square of the correlation coefficient R ) 0.999). The linear response for the (211) case is slightly lower (R ) 0.980) but still clearly demonstrates the existing correlation between the reactant/product geometries and the transition state geometries. Recently, it has been found that the manifestation of BEP relations for the surface reactions is a general electronic structure effect and the geometric effects are responsible for the scatter seen around the BEP line.69 Geometric effects are undoubtedly behind the “noise” what we see for the dehydrogenation reactions on the Pd(211): We have various transition states, as can be seen in Figure 4, each with a different geometry and bond length. For Pd(111) the linear fitting gives the correlation Eact ) 0.86∆E + 0.91 between the activation energy Eact and the reaction energy ∆E. For Pd(211) the equation is Eact ) 0.77∆E + 0.78. From these fits it should be possible to get a coarse estimation for the activation barriers when the corresponding reaction energy is known. Considering the challenges in determining the transition states for hydrogenation and dehydrogenation reactions, this kind of relation is most useful to estimate the activation barriers when reaction energy is known. However, it is worth noting

Conversion of Ethylene to Ethylidyne that the predictions made based on the fits are still rough estimates and should be refined to obtain more accurate values. Although the presence of two different lines for the BEP relationships suggest a certain degree of structure sensitivity for the present reaction the slopes are rather similar and the deviations in each point, in particular for the Pd(211) case, prevent us from doing a more complex analysis on this issue. We made a regression including all the points (both surfaces) and the BEP line looks pretty good (R ) 0.937). Therefore in the present case structure sensitivity cannot be derived from the presence of these two lines in the BEP correlations. However, it is important to notice though that for reaction (-6) and particularly for reaction (10) the reaction energy is very different for (111) and (211) surfaces therefore the main source of structure sensitivity for this reaction is not the different slope of the BEP-lines but the change in relative reaction energies (∆E) for reaction 10. Conclusions By means of density functional theory we have studied the reaction pathways for different processes involving the hydrogenation-dehydrogenation, decomposition and isomerization of organic moieties derived from ethylene on two Pd surfaces: (111) and (211). Our results show how under low coverage ethylene and its derivatives hydrogenation-dehydrogenations are the most likely processes on both surfaces. This differs from Ni for which a more pronounced step effect in terms of the selectivity for the activation of C-H or C-C processes was observed. In addition, isomerization processes are energetically very costly and thus are not likely to take place under relevant operation conditions. Instead moieties containing CH3 fragments are generated by indirect processes the most likely related to the scrambling of hydrogen atoms on the surface. Finally, the hydrogen related processes in ethylene decomposition on the surface, seem to follow the Brønsted-Evans-Polanyi type of behavior. The similar slope of the linear relationships seems to indicate that the reaction is not strongly dependent on the surface, however, differences in the reaction energies for particular steps might indicate some structure sensitivity. Acknowledgment. This work was financially supported by the Academy of Finland through project 118532. The computational resources were provided by the Nanoscience Center University of Jyva¨skyla¨ and the Finnish IT Center for Science (CSC). N.L. thanks MICINN project CTQ2006-00464/BQU and RES for support. References and Notes (1) Teschner, D.; Borsodi, J.; Wootsch, A.; Revay, Z.; Ha¨vecker, M.; Knop-Gericke, A.; Jackson, S. D.; Schlo¨gl, R. Science 2008, 320, 86. (2) Molnar, A.; Sarkany, A.; Varga, M. J. Mol. Catal. A 2001, 173, 185. (3) Ma, Z.; Zaera, F. Surf. Sci. Rep. 2006, 61, 229. (4) Segura, Y.; Lopez, N.; Perez-Ramirez, J. J. Cat. 2007, 247, 383. (5) Studt, F.; Abild-Pedersen, F.; Bligaard, T.; Sørensen, R. Z.; Christensen, C. H.; Nørskov, J. K. Science 2008, 320, 1320. (6) Bartholomew, C.; Farrauto, R. Fundamentals of industrial catalysis; Wiley: New York, 2006. (7) Somorjai, G. A. Introduction to Surface Chemistry and Catalysis; John Wiley & Sons Inc.: New York, 1994. (8) Masel, R. I. Principles of adsorption and reaction on solid surfaces; John Wiley & Sons: New York, 1996. (9) Zaera, F. Prog. Surf. Sci. 2001, 69, 1. (10) Frank, M.; Ba¨umer, M. Phys. Chem. Chem. Phys. 2000, 2, 3723. (11) Doyle, A. M.; Shaikhutdinov, S.; Freund, H. J. Angew. Chem. Int. 2005, 44, 629.

J. Phys. Chem. C, Vol. 113, No. 19, 2009 8285 (12) Shaikhutdinov, S.; Heemeier, M.; Lear, T.; Lennon, D.; Oldman, R. J.; Jackson, S. D.; Freund, H. J. J. Cat. 2001, 200, 330. (13) Freund, H. J. Cat. Today 2005, 100, 3. (14) Wang, L. P.; Tysoe, W. T.; Ormerod, R. M.; Lambert, R. M.; Hoffmann, H.; Zaera, F. J. Phys. Chem. 1990, 94, 4236. (15) Gates, J. A.; Kesmodel, L. L. Surf. Sci. 1982, 120, L461. (16) Sock, M.; Eichler, A.; Surnev, S.; Andersen, J.; Klo¨tzer, B.; Hayek, K.; Ramsey, M.; Netzer, F. Surf. Sci. 2003, 545, 122. (17) Stacchiola, D.; Burkholder, L.; Tysoe, W. T. Surf. Sci. 2002, 511, 215. (18) Stacchiola, D.; Calaza, F.; Zheng, T.; Tysoe, W. T. J. Mol. Catal. A 2005, 228, 35. (19) Stuve, E. M.; Madix, R. J.; Brundle, C. R. Surf. Sci. 152/ 1985, 153, 532. (20) Chesters, M.; McDougall, G.; Pemble, M.; Sheppard, N. Appl. Surf. Sci. 1985, 22, 369. (21) Pallassana, V.; Neurock, M.; Lusvardi, V. S.; Lerou, J. J.; Kragten, D. D.; van Santen, R. A. J. Phys. Chem. B 2002, 106, 1656. (22) Mittendorfer, F.; Thomazeau, C.; Raybaud, P.; Toulhoat, H. J. Phys. Chem. B 2003, 107, 12287. (23) Ge, Q.; Neurock, M. Chem. Phys. Lett. 2002, 358, 377. (24) Lopez, N.; Bridier, B.; Perez-Ramirez, J. J. Phys. Chem. C 2008, 112, 9346. (25) Tysoe, W. T.; Nyberg, G. L.; Lambert, R. M. J. Phys. Chem. 1984, 88, 1960. (26) Garcia-Mota, M.; Lopez, N. J. Am. Chem. Soc. 2008, 130, 14406. (27) Nishijima, M.; Yoshinobu, J.; Sekitani, J.; Onchi, M. J. Chem. Phys. 1989, 90, 5114. (28) Kesmodel, L.; Gates, J. Surf. Sci. 1981, 111, L747. (29) Nascente, P. A. P.; Hove, M. A.; Somorjai, G. A. Surf. Sci. 1991, 253, 167. (30) Gabasch, H.; Hayek, K.; Klo¨tzer, B.; Knop-Gericke, A.; Schlo¨gl, R. J. Phys. Chem. 2006, 110, 4947. (31) Stacchiola, D.; Kaltchev, M.; Wu, G.; Tysoe, W. T. Surf. Sci. 2000, 470, L32. (32) Stacchiola, D.; Tysoe, W. T. Surf. Sci. 2002, 513, L431. (33) Jungwirthova, I.; Kesmodel, L. L. J. Phys. Chem. B 2001, 105, 674. (34) Beebe, T. M.; Yayes, J. T. J. Am. Chem. Soc. 1986, 108, 663. (35) Vass, E.; Ha¨vecker, M.; Zafeiratos, S.; Teschner, D.; Knop-Gericke, A.; Schlögl, R. J. Phys.: Condens. Matter 2008, 20, 184016. (36) Han, Y.-F.; Kumar, D.; Sivadinarayana, C.; Clearfield, A.; Goodman, D. Cat. Lett. 2004, 94, 131. (37) Bowker, M.; Morgan, C. Cat. Lett. 2004, 98, 67. (38) Unterberger, W.; Gabasch, H.; Hayek, K.; Klo¨tzer, B. Cat. Lett. 2005, 104, 1. (39) Azad, S.; Kaltchev, M.; Stacchiola, D.; Wu, G.; Tysoe, W. T. J. Phys. Chem. B 2000, 104, 3107. (40) Zaera, F.; French, C. R. J. Am. Chem. Soc. 1999, 121, 2236. (41) Zaera, F.; Bernstein, N. J. Am. Chem. Soc. 1994, 116, 4881. (42) Ormerod, R. M.; Lambert, R. M.; Hoffmann, H.; Zaera, F.; Wang, L. P.; Bennet, D. W.; Tysoe, W. J. Phys. Chem. 1994, 98, 2134. (43) Ormerod, R. M.; Lambert, R. M.; Bennett, D. W.; Tysoe, W. Surf. Sci. 1995, 330, 1. (44) Vang, R. T.; Honkala, K.; Dahl, S.; Schnadt, E. J.; Læsgaard, E.; Clausen, B. S.; Nørskov, J. K.; Besenbacher, F. Nat. Mat. 2005, 4, 160. (45) Kravchuk, T.; Vattuone, L.; van Burkholder, L.; Tysoe, W. T.; Rocca, M. J. Am. Chem. Soc. 2008, 130, 12552. (46) Bus, E.; Ramaker, D. E.; Bokhoven, J. A. J. Am. Chem. Soc. 2007, 129, 8094. (47) https://wiki.fysik.dtu.dk. (48) Hammer, B.; Hansen, L. B.; Nørskov, J. K. Phys. ReV. B 1999, 59, 7413. (49) Vanderbilt, D. Phys. ReV. B 1990, 41, 7892. (50) Jo´nsson, H.; Millis, G.; Jacobsen, K. W. In Classical ans Quantum Dynamics in Condensed Phase Simulations; Berne, B. J., Ciccotti, G., Coker D. F., Eds.; World Scientific: Singapore, 1998. (51) Maragakis, P.; Andreev, S. A.; Brumer, Y.; Reichman, D. R.; Kaxiras, E. J. Chem. Phys. 2002, 117, 4651. (52) Moskaleva, M.; Chen, Z. X.; Aleksandrov, H. A.; Mohammed, A. B.; Sun, Q.; Rösch, N. J. Phys. Chem. C 2009, 113, 2512. (53) Watwe, R. M.; Cortright, R. D.; Nørskov, J. K.; Dumesic, J. A. J. Phys. Chem. B 2000, 104, 2299. (54) Abild-Pedersen, F.; Greeley, J.; Studt, F.; Rossmeisl, J.; Munter, T. R.; Moses, P. G.; Sku´lason, E.; Bligaard, T.; Nørskov, J. K. Phys. ReV. Lett. 2007, 99, 016105. (55) Mitsui, T.; Rose, M. K.; Fomin, E.; Ogletree, D. E.; Salmeron, M. Nature (London) 2003, 422, 705. (56) Lopez, N.; Łodziana, Z.; Illas, F.; Salmeron, M. Phys. ReV. Lett. 2004, 93, 146103. (57) Hong, S.; Rahman, T. S. Phys. ReV. B 2007, 75, 155405. (58) White, J. M. Langmuir 1994, 10, 3946.

8286

J. Phys. Chem. C, Vol. 113, No. 19, 2009

(59) Borg, H. J.; van Hardevelt, R. M.; Niemantsverdriet, J. W. J. Chem. Soc., Faraday. Trans 1995, 91, 3679. (60) Lo, J. M. H.; Ziegler, T. J. Chem. Phys. 2007, 111, 13149. (61) Angel, A. T.; Wales, D. J.; Jenkins, S. J.; King, D. A. J. Chem. Phys. 2007, 126, 044710. (62) Pallassana, V.; Neurock, M. J. Catal. 2000, 191, 301. (63) Horiuti, I.; Polanyi, M. Trans. Faraday Soc. 1934, 30, 1164. (64) Cremer, P. S.; Su, X.; Shen, Y. R.; Somorjai, G. A. J. Am. Chem. Soc. 1996, 118, 2942.

Andersin et al. (65) Neurock, M.; van Santen, R. A. J. Phys. Chem. B 2000, 104, 11127. (66) Nilekar, A. U.; Greeley, J.; Mavrikakis, M. Angew. Chem., Int. Ed. 2006, 45, 42. (67) Brønsted, J. N. Chem. ReV. 1928, 5, 231. (68) Evans, M. G.; Polanyi, M. Trans. Faraday Soc. 1938, 34, 11. (69) Munter, T. R.; Bligaard, T.; Christensen, C. H.; Nørskov, J. K. Phys. Chem. Chem. Phys. 2008, 10, 5202.

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