Transformations of Ethylene on the Pd(111) Surface: A Density

J. Phys. Chem. C 2010, 114, 17683–17692

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Transformations of Ethylene on the Pd(111) Surface: A Density Functional Study Zhao-Xu Chen,*,†,‡ Hristiyan A. Aleksandrov,‡,§ Duygu Basaran,‡ and Notker Ro¨sch*,‡ Institute of Theoretical and Computational Chemistry, Key Laboratory of Mesoscopic Chemistry of MOE, School of Chemistry and Chemical Engineering, Nanjing UniVersity, Nanjing 210093, P.R. China, Department Chemie and Catalysis Research Center, Technische UniVersita¨t Mu¨nchen, 85747 Garching, Germany, and Faculty of Chemistry, UniVersity of Sofia, 1126 Sofia, Bulgaria ReceiVed: May 30, 2010; ReVised Manuscript ReceiVed: August 25, 2010

The chemistry of ethylene on group VIII metals is important for the petrochemical and polymer industries. Thus far, a complete first-principles-based conversion network of ethylene as a prototypical olefin system on metal surfaces is lacking. In this paper we present a comprehensive view on transformations of ethylene on Pd(111), based on density functional slab model calculations. Specifically, we characterized the thermodynamics and kinetics of C-H and C-C bond scission as well as H isomerization of a series of species C2Hx (x ) 0-4). Accordingly, dehydrogenation or hydrogenation processes are favored for most species, whereas reactions involving the scission or formation of the C-C bond feature high barriers. Ethynyl (CHC) likely is the precursor of C-C bond scission. Ethylidyne is found to be located in a basin of the potential energy surface, which allows one to rationalize relevant experimental observations. In addition, we note that one should be cautious when using information on the potential energy surface obtained with the unity-bond-index quadraticexponential-potential (UBI-QEP) method. 1. Introduction Ethylene has long served as prototypical model system for understanding the reforming and conversion of olefinic hydrocarbons over group VIII metal surfaces.1,2 Pd is a useful catalyst for hydrocarbon transformation, and many studies addressed the chemistry of ethylene over this metal.3 Experimentally it is found that ethylidyne (CH3C), ethynyl (CHC, also referred to as acetylidene or acetylide), and vinyl (CH2CH) moieties are formed when ethylene adsorbs onto Pd surfaces,4-9 indicating that C-H bond breaking occurs. C1Hx and C2Hx species are observed upon ethylene adsorption on palladium particles, supported on an oxidized tungsten foil at room temperature;10 these observations demonstrate that both C-H and C-C bond cleavage occur. Steps and other surface defects may favor C-C bond breaking, as shown for ethylene reactions on Ni.11 Indeed, the barrier of the reaction C2H4 f CH2 + CH2 is higher on Pd(111), 2.12 eV, than that on Pd(211), 1.69 eV.12 These computational results are consistent with the experimental observation that ethynyl (CHC) and vinyl (CH2CH) are formed at lower temperatures, while CH species appear on Pd(111) at elevated temperatures, as high as 400-500 K.4 On the other hand, C-H and C-C bonds break at room temperature over Pd particles where step edges are abundant.10 Theoretical approaches have also been applied to explore the adsorption and reactivity of ethylene as well as its derivatives.3,12-23 These calculations revealed that ethylene and resulting species interact with the substrate through carbon centers that tend to exhibit an sp3 hybridization. Dehydrogenation of ethylene to vinyl is the rate-limiting step of ethylene decomposition, and a lower coverage is favorable for this transformation.3,23 The thermodynamics of the C-C bond scission has been calculated * To whom correspondence should be addressed. E-mail: zxchen@ nju.edu.cn, [email protected]. † Nanjing University. ‡ Technische Universita¨t Mu¨nchen. § University of Sofia.

for the reaction CHC f CH + C,24 while computational studies on the kinetics of the C-C bond breaking have been reported for ethylene on Ni and Pd surfaces11,12 and for C2 hydrocarbons on Pt25 and Pd(111).12,26 While many computational investigations addressed the thermodynamics and kinetics of the breaking/ forming of C-H bonds on Pd surfaces, there are noticeably fewer first-principles studies of the C-C bond rupture/formation of ethylene and its derivatives. Surface and especially subsurface carbon atoms were recently shown to notably affect surface or catalytic reactions.27 For C2Hx compounds such carbon centers originate from C-C bond rupture.28 Detailed knowledge of C-C bond breaking and forming is required for a comprehensive understanding of ethylene transformations over metal surfaces as well as for controlling and optimizing the reaction conditions on metal catalysts. Therefore, a theoretical study of the C-C bond scission of ethylene and related species is crucial. However, there are other motivations for exploring these issues. For example, ethane hydrogenolysis on many group VIII metals generally is believed to follow the Sinfelt-Taylor mechanism29 that comprises several steps, among which C-C bond cleavage of C2Hx (x ) 0-5) is thought to be rate limiting. Species such as C2,30 CH2CH, CH2CH2,31 and C2H232 were proposed some time ago as precursors of C-C bond scission. However, reliable information is still lacking. The unity-bond-index quadraticexponential-potential (UBI-QEP) method was used to generate pertinent information.33,34 Yet, one may question the reliability of these results (and the corresponding conclusions) owing to the fact that they strongly depend on the parameters adopted. We will show that barriers and heats of reaction from UBIQEP calculations in some cases differ remarkably from our firstprinciples results; in addition, there seem to be consistency issues with this theoretical approach.33,34 To gain a panoramic view of ethylene transformations on Pd surfaces, we explored the thermodynamics and kinetics of C-H and C-C bond scission processes for the series C2Hx (x ) 0-4)

10.1021/jp104949w  2010 American Chemical Society Published on Web 09/22/2010

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using density functional slab model calculations. In this work, we provide, for the first time, a complete set of pertinent information on the transformations of ethylene over Pd(111). The paper is organized as follows. In section 2, we describe our models and the computational method. In section 3, we describe the transition state structures and activation energies of each elementary reaction step. Then we discuss C-H and C-C bond breaking and their implications on transformations of ethylene. Finally, we offer some conclusions in section 4. 2. Models and Computational Details The calculations were carried out with the plane-wave-based Vienna ab initio simulation package (VASP)35,36 using the generalized-gradient approximation (GGA) in the form of the exchange-correlation functional PW91,37 where appropriate in spin-polarized fashion. The interaction between atomic cores and electrons was described by the projector augmented wave (PAW) method.38,39 For integration over the Brillouin zone, we used the k-point sampling scheme of Monkhorst and Pack;40 we invoked a generalized Gaussian smearing technique41 (with a default width of 0.15 eV) to accelerate convergence and extrapolated the results to 0 K. The surface was modeled by a four-layer slab with a (3 × 3) surface unit cell where the two “top” layers were allowed to relax whereas the “bottom” two layers were fixed at the theoretical Pd-Pd distance of 280 pm.42 The vacuum spacing was always larger than 1 nm. All calculations were carried out using a 5 × 5 × 1 k-point grid. We adopted an energy cutoff of 400 eV throughout; according to test calculations for ethylidyne on Pd(111), this value guarantees convergence of binding energies to better than 0.5 kJ mol-1. 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 is the total energy of the adsorbate in the gas phase (ground state), and Esub is the total energy of the clean substrate where the top two layers were relaxed. Thus, a positive value of BE implies a favorable process during which energy is released. The search for stationary points of the potential energy surface (local equilibrium structures, transition states) was carried on until the force acting on each atom was less than 2 × 10-4 eV/pm. We located transition states (TSs) of reactions using the nudged elastic band method43,44 or the dimer method.45 With a normal-mode analysis, we verified for each TS that there is exactly one mode with an imaginary frequency that indicates the relevant bond breaking or formation. We refrained from correcting reaction energies and barriers for zero-point energies to allow a direct comparison of the present results to related works of our group;3,23,46 our calculations show that such corrections will reduce barriers of C-H bond breaking by 10-15 kJ/mol and barriers of C-C scission by 5-8 kJ/mol. 3. Results The adsorption of H and most CHx (x ) 0-3) and C2Hx (x ) 0-4) species on Pd(111) has previously been explored by computational methods.3,26,47 These studies revealed that these carbon-containing moieties bind to a Pd(111) surface through carbon atoms that are in a tetrahedral configuration. To be concise, we provide a description of the adsorption complexes of the species studied as Supporting Information; see Table S1. Here, we focus on C-H and C-C bond-breaking reactions involved in ethylene transformation over Pd(111); see Tables 1 and 2 as well as Figures 1 and 2.

Chen et al. 3.1. C-H Bond Scission. In the following, we will discuss in detail elementary C-H bond-breaking reactions as illustrated in Figure 1. Pertinent structural parameters of optimized initial states (IS), transition states (TS), and final states (FS) are provided in Table 1. The corresponding reaction energies and barrier heights are summarized in Table 3 and Figure 3. CH2CH2 f CH2CH + H. Recently, we revisited the threestep mechanism of ethylene conversion to ethylidyne on Pd(111).3 In that work, we examined the reactions CH2CH2 f CH2CH f CH3CH f CH3C. Here, we briefly describe the ethylene dehydrogenation step and refer the reader to that paper for other steps.3 C-H bond scission of ethylene is believed to start from the di-σ complex.48 The C-H distance, initially at 110 pm (Figure 1a), elongates to 174 pm in the TS (Table 1); the dissociating H atom is essentially on top of a Pd atom (Figure 1b), ending up in the FS at a hollow site with a H-Pd bond length of ∼180 pm (Figure 1c). Such H-Pd distances are typical also for all other FS structures where C2Hx species and H are coadsorbed. After the TS, the C center originally bound to the dissociating H moves toward a bridge site in the FS, yielding an η1η2(C,C) configuration of CH2CH. The reaction heat was calculated at 5 kJ/mol (for adsorbates at formally infinite separation). The corresponding activation barrier was at 99 kJ/mol (Table 3); a previous RPBE study12 determined the barrier to be ∼20 kJ/mol higher. CH2CH f CHCH + H. Dehydrogenation of vinyl may proceed along two routes, yielding either acetylene or vinylidene as product. Here, we first address the route to acetylene which, according to the UBI-QEP approach, is kinetically more favorable, by 66 kJ/mol, than the path to vinylidene.33 Figure 1d shows the IS of this reaction which begins with an elongation of the breaking C-H bond, induced by the H atom moving toward a neighboring fcc site. Concomitantly the carbon center of that CH2 moiety moves to a bridge position. The C-H distance of the TS is 160 pm (Figure 1e, Table 1). In the FS, the product acetylene adsorbs in η2η2(C,C) fashion (Figure 1f). Correspondingly, the C-C bond shortens from 138 to 136 pm (Figure 1e and 1f; Table 1). This reaction is calculated to be exothermic, by -17 kJ/mol, while the barrier is determined at 76 kJ/mol (Table 3). Both the barrier and the reaction heat show that vinyl dehydrogenates more favorably than ethylene. CH2CH f CH2C + H. The dehydrogenation pathway of vinyl to vinylidene starts from an IS (Figure 1d) where H abstraction occurs via elongation of the C1-H bond (Figure 1g).49 In the TS, this distance extends to 166 pm (Table 1). Concomitantly, the C-C bond shrinks from 145 pm in the IS to 139 pm in the TS (Table 1). C1-H bond scission enhances the bonding capability of the C1 center with the substrate, as shown by reduced C1-Pd distances in the TS (by 1, 6, and 55 pm; Table 1). At the reaction barrier, the dissociating H center is on top of a Pd atom, with H-Pd ) 160 pm (Figure 1g; Table 1). The product vinylidene exhibits an η3(C1)η1(C2) structure50 (Figure 1h). The reaction releases 33 kJ/mol (Table 3). The computed barrier is 57 kJ/mol. This value is 19 kJ/mol lower than the one for forming acetylene from vinyl, at variance with prediction of the UBI-QEP approach.33 CH2C f CHC + H. Vinylidene may further dehydrogenate to ethynyl, CHC. The initial η3η1(C,C) structure (Figure 1i) features the three C1-Pd bonds, 196-206 pm (Table 1). The C2-H bond increases from 109 to 172 pm in the TS (Table 1; Figure 1j). Concomitantly, the (hydrogen-rich) C2 center changes from η1 to η2, the three C2-Pd distances shorten to 216, 217, and 271 pm (Table 1), while the C1 atom moves only slightly and retains its η3 status. In the FS (Figure 1k), the C2-H

Transformations of Ethylene on the Pd(111) Surface

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TABLE 1: Optimized Structural Parameters (pm) for the Initial State (IS), Transition State (TS), and Final State (FS) of C-H Bond-Breaking Reactions of Various C2Hx species (x ) 0-4)a CH2CH2 f CH2CH + H

CH2CH f CHCH + H

CH2CH f CH2C + H

CH2C f CHC + H

CH3C f CH2C + H

CHCH f CHC + H

CHC f CC + H

a

parameter

IS

TS

FS

C-C C-H C1-Pd C2-Pd H-Pd C-C C-H C1-Pd C2-Pd H-Pd C-C C-H C1-Pd C2-Pd H-Pd C-C C-H C1-Pd C2-Pd H-Pd C-C C-H C1-Pd C2-Pd H-Pd C-C C-H C1-Pd C2-Pd H-Pd C-C C-H C1-Pd C2-Pd H-Pd

145 110 212, 292, 335 212, 290, 335 324, 335, 470 145 110 203, 203, 265 208, 287, 288 261, 318, 379 145 110 203, 203, 265 208, 287, 288

145 174 207, 210, 264 208, 292, 295 159, 300, 332 138 160 200, 215, 290 205, 231, 279 163, 242, 287 139 166 197, 202, 210 224, 307, 317 160, 307, 310 138 172 195, 202, 207 216, 217, 271 159, 280, 287 141 173 195, 195, 208 230 162 137 176 197, 201, 207 210, 216, 258 159, 326, 330 134 181 200, 214, 214 197, 212, 212 158, 345, 346

145 273 203, 206, 261 207, 289, 292 176, 181, 188 136 303 202, 215, 281 200, 219, 283 178, 179, 187 138 296 196, 198, 204 228, 309, 310 178, 179, 187 136 322 197, 198, 208 212, 215, 256 179, 180, 184 138 284 196, 196, 208 234, 306, 309 176, 178, 187 137 363 196, 201, 207 209, 217, 260 179, 179, 186 135 306 197, 211, 214 199, 211, 215 177, 180, 185

139 109 196, 196, 206 227, 308, 309 149 110 197, 197, 198 304, 307, 310 137 109 200, 217, 281 200, 217, 281 305, 499, 513 137 109 197, 201, 201 212, 229, 230 265, 404, 468

C1 refers to the carbon center with less (or no) H atoms attached.

distance has increased to 322 pm and the C2-Pd bonds have shrunk appreciably, to 212 and 215 pm. The product ethynyl adsorbs basically in a η2η3(C,C) structure in which the two carbon centers anchor at adjacent hollow sites. The activation barrier is calculated at 138 kJ/mol, while the reaction is endothermic by 40 kJ/mol (Table 3). CH3C f CH2C + H. Figure 1l, 1m, and 1n illustrates the dehydrogenation of CH3C to CH2C. Initially CH3C is at a hollow site with C-Pd ) 197 pm (Table 1, Figure 1l). The reaction begins by a tilting of the C-C bond toward the surface, which reduces the H-Pd distance to 162 pm in the TS (Figure 1m). There, C2-H is elongated to 173 pm while center C2 is at a top site with C2-Pd ) 230 pm (Table 1). Beyond the TS, the C-C bond continues to tilt. In the FS (Figure 1n), center C1 is roughly at a hollow position. This reaction is endothermic by 35 kJ/mol and has to overcome a barrier of 120 kJ/mol (Table 3). CHCH f CHC + H. The dehydrogenation of acetylene, bound in η2η2(C,C) fashion (Figure 1o), begins with a C-H elongation where the dissociating H passes via a top position to an fcc site. In the TS, the C centers are essentially at hollow sites with C-H ) 176 pm while H resides at an off-top position (Figure 1p; Table 1). The C-C axis changed from parallel to the substrate surface in the IS to a tilted orientation in the TS. The product, ethynyl, exhibits a η3η2(C,C) structure (Figure 1q). The barrier of this reaction is calculated at 119 kJ/mol, 43 kJ/mol higher than the dehydrogenation of CH2CH to acetylene (Table 3). This larger barrier reflects the fact that C-H bonds

of CHCH on average are stronger than those of CH2CH. The dehydrogenation of acetylene is endothermic by 24 kJ/mol (Table 3), which is also unfavorable compared to the dehydrogenation of CH2CH. CHC f CC + H. The dehydrogenation of η3η3(C,C)-bound ethynyl proceeds via an elongation of the C-H distance, where the H center moves toward a site on top of a Pd atom. The C-H distance increases from 109 pm in the IS (Figure 1r; Table 1) to 181 pm in the TS (Figure 1s; Table 1), where the H center is again located beyond the top position. The C-C bond of the TS, 134 pm, has shrunk 3 pm from the IS. After the TS, the H atom moves to a hollow site and the resulting carbon dimer forms a η3η3 (C,C) adsorption structure (Figure 1t). The reaction is endothermic by 59 kJ/mol (Table 3). The corresponding barrier, 154 kJ/mol, is the highest among all C-H bond-breaking reactions studied here, rendering this reaction the most unfavorable one. Inspection of Table 3 reveals consistent trends: from CH2CH to CHCH to CHC, both the barriers and the heats of the dehydrogenation increase, reflecting the increasing strength of the C-H bonding with decreasing H content. 3.2. C-C Bond Scission. Next, we will discuss the elementary C-C bond-breaking reactions (Figure 2). Table 2 provides key parameters of the optimized IS, TS, and FS structures. The corresponding reaction energies and barrier heights are summarized in Table 3 and Figure 3. CH2CH2 f CH2 + CH2. C-C scission in ethylene starts from the π complex at a top site (Figure 2a). During dissociation the CH2 groups move toward different bridge sites adjacent to

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TABLE 2: Optimized Structural Parameters (pm) for the Initial State (IS), Transition State (TS), and Final State (FS) of the C-C Bond-Breaking Reactions of Various C2Hx Species (x ) 0-4)a CH2CH2 f CH2 + CH2

CH2CH f CH2 + CH

CHCH f CH + CH

CHC f CH + C

CC f C + C CH3CH f CH3 + CH

CH3C f CH3 + C

CH2C f CH2 + C

a

parameter

IS

TS

FS

C-C C-H C1-Pd C2-Pd C-C C-H C1-Pd C2-Pd C-C C-H C1-Pd C2-Pd C-C C-H C1-Pd C2-Pd C-C C1-Pd C2-Pd C-C C-H C1-Pd C2-Pd C-C C-H C1-Pd C2-Pd C-C C-H C1-Pd C2-Pd

140 109 221, 320, 320 220, 322, 323 145 110 203, 203, 265 208, 287, 288 137 109 200, 217, 281 200, 217, 281 137 109 197, 201, 201 212, 229, 230 135 198, 213, 213 199, 211, 211 150 111 203, 203, 300 302, 306, 309 149 110 197, 197, 198 304, 307, 310 139 109 196, 196, 206 227, 308, 309

204 110 208, 212, 312 209, 213, 321 197 110 199, 202, 205 203, 219, 279 199 110 197, 201, 206 192, 197, 264 193 110 190, 196, 200 196, 202, 224 194 190, 199, 204 190, 198, 204 206 113 196, 196, 217 236, 291, 291 216 109 187, 187, 190 221, 347, 349 206 109 190, 192, 193 203, 219, 290

299 110 201, 205, 239 199, 205, 283 386 110 195, 195, 196 201, 202, 266 307 110 194, 195, 202 193, 195, 202 316 110 186, 187, 196 193, 194, 203 320 186, 187, 198 186, 187, 198 365 110 195, 195, 196 205, 368, 368 368 109 186, 187, 187 205, 360, 364 372 109 187, 187, 189 201, 202, 285

C1 refers to the carbon center with less (or no) H atoms attached.

the top position. The C-C distance of the TS (Figure 2b), 204 pm, is 64 pm longer than in the IS (Figure 2a, Table 2). The shortest C-Pd distance decreases from initially ∼220 to ∼208 pm in the TS (Table 2). Beyond the TS, each CH2 group moves to a bridge site (Figure 2c), reaching a tetrahedral coordination of the C center. The reaction is calculated endothermic by 87 kJ/mol, featuring an activation barrier of 163 kJ/mol (Table 3). Both characteristics are more unfavorable than the corresponding quantities of the dehydrogenation process: the barrier is 64 kJ/ mol higher and the heat of reaction is 82 kJ/mol more endothermic. Thus, ethylene over Pd(111) is expected to undergo preferentially dehydrogenation. Previous RPBE calculations12 obtained a barrier of 204 kJ/mol, 40 kJ/mol higher than our value. The UBI-QEP estimates are 134 kJ/mol for the barrier and 96 kJ/mol for the heat of reaction.34 Another UBI study33 reported a slightly higher barrier, 152 kJ/mol, which is closer to our result. CH2CH f CH2 + CH. Vinyl decomposition via C-C breaking starts from a η2η1(C,C) configuration (Figure 1d). The bond scission begins with the CH moiety moving toward a hollow site while the CH2 part approaches a bridge site. In the TS (Figure 2d), the C-C bond, 197 pm, is 52 pm longer than in the IS (Figure 1d, Table 2). The CH2 group has essentially reached the bridge site, while the three distances C1-Pd (199, 202, 205 pm) indicate that the CH group has almost arrived at the hollow site. Beyond the TS, the resulting CH and CH2 moieties move on and finally settle at the hollow and the bridge sites, respectively (Figure 2e). This reaction barrier is calculated at 134 kJ/mol and the heat of reaction at 19 kJ/mol (Table 3). This barrier of C-C scission is 58 kJ/mol higher than the barrier to form acetylene via C-H bond breaking (Table 3), again

showing the latter type of reaction to be preferred. The UBIQEP method33 predicted a much lower barrier for the C-C scission, only 53 kJ/mol, and a large exothermicity, -95 kJ/ mol. Both results differ markedly from ours. CHCH f CH + CH. Acetylene binds to the surface in the η2η2(C,C) fashion (Figure 1o). C-C bond scission starts with one CH group moving to an hcp site, which elongates the C-C distance and pulls the other CH group slightly away from the bridge site to an fcc position. In the TS (Figure 2f), the C-C distance has increased to 199 pm from 137 pm in the IS (Table 2). One CH group is basically located at the bridge site, while the other CH moiety is at a pseudo hollow site with C-Pd distances of ∼200 pm. In the FS (Figure 2g), the two CH groups are at adjacent hollow sites with C-C ) 307 pm (Table 2). For this step we calculated a barrier of 142 kJ/mol and a heat of reaction of -27 kJ/mol (Table 3). Previous UBI-QEP studies predicted values of 15534 and 185 kJ/mol33 for the barrier of C-C bond breaking of acetylene. It is worth pointing out that our result for the barrier of C-C scission of CHCH is only 23 kJ/mol higher than the barrier of the corresponding C-H breaking. C-C bond breaking of acetylene is thermodynamically favored over its dehydrogenation (Table 3). CHC f CH + C. The stable adsorption complex of CHC features an η3η3(C,C) configuration (Figure 1r). The C-C scission starts by displacing the CH group from the fcc site toward the adjacent hcp position whereby the C-C distance stretches from 137 pm in the IS to 193 pm in the TS (Table 2). In the TS, the CH group and the other C atom are at bridge positions (Figure 2h). As shown by the C1-Pd distances, 190, 196, and 200 pm (Table 2), the C center still interacts with three metal atoms because the metal surface is distorted. Beyond the



Figure 1. Structures of initial, transition, and final states of C-H bond-breaking reactions on Pd(111). Selected interatomic distances are given in pm. CH2CH2 f CH2CH + H: (a) initial state, (b) transition state, (c) final state. CH2CH f CHCH + H: (d) initial state, (e) transition state, (f) final state. CH2CH f CH2C + H: (d) initial state, (g) transition state, (h) final state. CH2C f CHC + H: (i) initial state, (j) transition state, (k) final state. CH3C f CH2C + H: (l) initial state, (m) transition state, (n) final state. CHCH f CHC + H: (o) initial state, (p) transition state, (q) final state. CCH f CC + H: (r) initial state, (s) transition state, (t) final state.

TS, the CH group and the C moiety move to hcp sites (Figure 2i). The C-C bond rupture is calculated to be exothermic, by 27 kJ/mol, with a barrier of 138 kJ/mol (Table 3). This barrier is 16 kJ/mol lower than that the dehydrogenation barrier of CHC. More importantly, this step is also thermodynamically much favorable, by 86 kJ/mol, than the C-H bond breaking (Table 3). Thus, our calculated kinetic and thermodynamic results show that CHC decomposes preferentially through C-C cleavage. CC f C + C. The dehydrogenation of CHC produces a carbon dimer which can only react via C-C bond breaking. The decomposition of C2 starts from an η3η3(C,C) configuration

with C-C ) 135 pm (Figure 2j, Table 2). The two carbon centers share two Pd atoms (Figure 2j). The dissociation begins with one carbon center being displaced toward a hollow site. In the TS, the two carbon centers are located at bridge sites with C-C ) 194 pm and C-Pd distances in the range of 190-204 pm (Figure 2k; Table 2). Past the TS the carbon centers move to hollow positions (Figure 2l). We calculated this reaction to be exothermic by 61 kJ/mol (when both C atoms are at infinite separation, Table 3); the corresponding barrier is 121 kJ/mol. This barrier is the lowest one among all C-C scission steps investigated in the present study, while the reaction

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Figure 2. Structures of initial, transition and final states of C-C bond-breaking reactions on Pd(111). Selected interatomic distances are given in pm. CH2CH2 f CH2 + CH2: (a) initial state, (b) transition state, (c) final state. CH2CH f CH2 + CH: initial state given in Figure 1d, (d) transition state, (e) final state. CHCH f CH + CH: initial state given in Figure 1o, (f) transition state, (g) final state. CCH f C + CH: initial state given in Figure 1r, (h) transition state, (i) final state. CC f C + C: (j) initial state, (k) transition state, (l) final state. CH3CH f CH3 + CH: (m) initial state, (n) transition state, (o) final state. CH3C f CH3 + C: initial state given in Figure 1l, (p) transition state, (q) final state. CH2C f CH2 + C: initial state given in Figure 1i, (r) transition state, (s) final state.

energy is the most exothermic one. The UBI-QEP method classifies this process as barrier free with a huge exothermicity of 682 kJ/mol.33 CH3CH f CH3 + CH. CH3CH moieties may be formed from ethylene via a two-step indirect H-shift reaction: (i) ethylene dehydrogenation to vinyl and (ii) hydrogenation of vinyl to ethylidene.3 The shift process has essentially equal kinetic and thermodynamic parameters as those for ethylene dehydrogenation.3 Direct H-shift reactions typically have high barriers, ∼200 kJ/mol.3 In the scheme shown in Figure 3 the results of H-shift

reactions refer to a two-step process where an H atom first dissociates onto the surface and then recombines with the newly formed species. In the IS of the reaction CH3CH f CH3 + CH the CH group is at a bridge site and the CH3 group is located above a hollow position (Figure 2m). The C-C scission is induced by displacing the CH group toward a hollow site and the CH3 moiety to a top site; concomitantly, the C-C bonding is weakened and the interaction of the CH and the CH3 groups with the substrate enhanced. In the TS, the CH and the CH3 groups are approximately at a bridge and a top site, respectively



TABLE 3: Activation Barriers Ea and Heats of Reaction Er (in kJ/mol) for Various C-H and C-C Bond Scission Reactionsa C-H

b

C-Cb

CH2CH2f CH2CH + H CH2CH f CHCH + H CH2CH f CH2C + H CH2C f CHC + H CH3C f CH2C + H CHCH f CHC + H CHC f CC + H CH2CH2 f CH2 + CH2 CH2CH f CH2 + CH CHCH f CH + CH CHC f CH + C CC f C + C CH3CH f CH3 + CH CH3C f CH3 + C CH2C f CH2 + C

Ea

Er

E r′

99 76 57 138 120 119 154 163 134 142 138 121 151 194 187

25 -11 -21 46 42 31 72 101 29 19 25 1 6 117 89

5 -17 -33 40 35 24 59 87 19 -27 -27 -61 0 116 76

a Ea ) E(TS) - E(IS); Er ) E(FS) - E(IS), where E(IS), E(TS), and E(FS) refer to the total energies of the initial, transition, and final states, respectively. Er is the heat of the reaction when the product fragments are coadsorbed; Er′ is the corresponding energy when the product species are formally at infinite separation. Negative values of Er and Er′ represent exothermic reactions. Corrections for zero-point vibrational energies are not included. b Bond that breaks during the reaction.

Figure 3. Reaction barriers and reaction energies (first and second values, respectively; in kJ/mol) for various C-H and C-C bondbreaking reactions of ethylene and related species C2Hx (x ) 0-4) over a Pd(111) surface. Light blue values indicate the corresponding UBIQEP results from ref 34.

(Figure 2n), with C-C ) 206 pm (Table 2). When the system moves from the TS to the FS, the CH group diffuses toward a hollow site. In the FS (Figure 2o), CH3 and CH are located at the top and hollow sites, respectively, with C-C ) 365 pm (Table 2). This step basically is a thermo-neutral reaction with a barrier of 151 kJ/mol (Table 3). CH3C f CH3 + C. Ethylidyne, CH3C, adsorbs via the C1 center in η3(C) fashion (Figure 1l). The three C1-Pd bonds have very similar lengths, 197-198 pm (Table 2). The C-C bond, 149 pm, is perpendicular to the metal surface. In the reaction, the methyl group tilts closer to the surface and the C-C distance elongates. In the TS, center C1 stays at the original hollow site with all C1-Pd bonds shortened by 8-10 pm (Table 2). The CH3 group is roughly at a top site, with

C2-Pd ) 221 pm and C-C ) 216 pm (Figure 2p; Table 2). The reaction proceeds by CH3 moving to a top site and the C2-Pd distance further decreasing by 16 pm (Figure 2q) while the C1 center remains almost fixed; in the FS, C-C ) 368 pm (Table 2). For this C-C bond to cleave, the system has to overcome the highest barrier calculated in this work, 194 kJ/ mol, with the largest endothermicity, 116 kJ/mol (Table 3). Thus, this step is most unlikely. The calculated values for the barrier and the heat of reaction are in striking contrast to those predicted by the UBI-QEP method: 36 and -83 kJ/mol, respectively, casting severe doubts on this latter approach. CH2C f CH2 + C. Vinylidene CH2C adsorbs in an η3η1(C,C) mode (Figure 1i). C-C bond scission begins with the CH2 moiety moving to a neighboring bridge site, while the C center remains at the original hollow site. In the TS, the two C2-Pd distances of the CH2 group are 203 and 219 pm, with C-C ) 206 pm (Figure 2r; Table 2). In the FS, the two C centers are separated by 372 pm, while the CH2 and the C moieties occupy a bridge and a hollow position, respectively (Figure 2s). The process features a barrier of 187 kJ/mol and a heat of reaction of 76 kJ/mol (Table 3), indicating that C-C bond breaking of vinylidene is very unfavorable. 4. Discussion 4.1. Transformations of Ethylene on the Pd(111). Thus far, we described the structures, kinetics, and thermodynamics of C-C and C-H bond scission for a series of species derived from ethylene. To reach a panoramic view of ethylene transformations over Pd surfaces, we collected the energetics of each step for all species C2Hx (x ) 0-4, Figure 3). Calculated heats of reaction are given as second values (products formally at infinite separation) and the corresponding activation barriers as first values (without zero-point correction). We note the general trend that the barriers of C-C bond breaking decrease with increasing degree of dehydrogenation, while the barriers of C-H scission tend to increase. In the following we analyze the transformation of each species by comparing the feasibility of C-H and C-C bond scission. CH2CH2 and CH3CH. C-C bond scission of ethylene is calculated to be very unfavorable as shown by a substantial barrier of 163 kJ/mol and a large endothermicity of 87 kJ/mol. In contrast, dehydrogenation to vinyl or transformation into ethylidene through indirect H shift obviously is quite favorable. In view of the uncertainties of the computational method, the barrier for the dehydrogenation of ethylene to vinyl, 99 kJ/mol, is comparable to the binding energy of ethylene on Pd(111), 94 kJ/mol. Therefore, such transformations of ethylene on the surface are expected to occur, besides desorption. According to the calculated barrier and heat of reaction, ethylidene is unlikely to undergo C-C bond breaking to form a CH3 and a CH group, again because of a high barrier, 151 kJ/mol. Rather, ethylidene preferentially will dehydrogenate to ethylidyne where a remarkably low barrier of only 25 kJ/mol has to be overcome. The formation of CH2CH by abstracting a hydrogen from the methyl group is less favorable than the route to CH3C. From the calculated information shown in Figure 3, formation of CH2CH and CH3C is very likely upon adsorption of ethylene on Pd(111) surface. CH2CH and CH3C. Vinyl CH2CH can undergo four types of reactions: (i) C-C bond breaking to CH2 and CH, (ii) indirect H shift to ethylidyne CH3C, (iii) dehydrogenation to either acetylene CHCH or vinylidene CH2C, and (iv) hydrogenation to ethylene CH2CH2 or ethylidene (CH3CH) (Figure 3). C-C bond breaking to C1Hx fragments is unfavorable owing to the rather high barrier of 134 kJ/mol. The barrier (53 kJ/mol)

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estimated with the UBI-QEP method34 and the corresponding heat of reaction (-95 kJ/mol) differ notably from our DF results. Another study using the UBI-QEP approach33 reported a barrier of 121 kJ/mol, close to our result. Hydrogenation of vinyl to CH3CH or CH2CH2 needs to overcome a barrier of ∼100 kJ/ mol. The latter is simply a reverse reaction of ethylene dehydrogenation. Indirect H shift to CH3C has a barrier of 78 kJ/mol, which is quite a bit lower than the barriers of hydrogenation and C-C bond breaking. Two dehydrogenation products exist for vinyl: acetylene, CHCH, and vinylidene, CH2C. The UBI-QEP approach predicts the barriers of vinyl transformations to acetylene and vinylidene to be 2 and 67 kJ/ mol,33 respectively, indicating the formation of acetylene to be preferred over that of vinylidene. However, we calculated the barriers in reverse order: 76 kJ/mol to CHCH and 57 kJ/mol to CH2C. Although our barrier to acetylene is 74 kJ/mol higher than the corresponding UBI-QEP result, it is much lower than our barrier of C-C scission, 134 kJ/mol (Figure 3). According to our results, dehydrogenation to CH2C is the most feasible transformation. This finding is consistent with the experimental observation that acetylene forms vinylidene species on Pd(111) at room temperature.51,52 Previously C230 and CH2CH and CH2CH231 were suggested as precursors of C-C bond breaking in ethane hydrogenolysis. According to the present results, CH2CH2 will preferably dehydrogenate to vinyl, which further dehydrogenates to vinylidene, rather than to undertake the C-C bond breaking. Thus, CH2CH and CH2CH2 are unlikely the precursors. As just pointed out, ethylidyne CH3C can be produced by dehydrogenating CH3CH. Its transformation to C and CH3 via C-C breaking needs to overcome a barrier of at least 194 kJ/ mol (Figure 3), indicating that C-C bond cleavage of CH3C is very unlikely. Further dehydrogenation of CH3C to CH2C is an endothermic process. The UBI-QEP method estimated a barrier of 90 kJ/mol for this process.33 We calculated an even higher barrier, 120 kJ/mol. Figure 3 shows that all steps leading to the formation of CH3C are exothermic. Hence, ethylidyne is at the bottom of a basin of the potential energy surface; thus, it is a stable species and should be easy to observe. This conclusion seems consistent with all experiments we are aware of.4,53 CH2C, CHCH, and CHC. As shown above, vinylidene CH2C is the most favorable product of vinyl. It may undergo transformation via five routes: hydrogenation to (i) vinyl or (ii) ethylidyne, (iii) isomerization to CHCH, (iv) dehydrogenation to CHC, and (v) decomposition to CH2 and C by C-C bond breaking (Figure 3). C-C bond scission is the most difficult reaction among these pathways, as the barrier to overcome is calculated at 187 kJ/mol. Next in line are the barriers of dehydrogenation to CHC, 138 kJ/mol, and of the indirect H shift to CHCH, 134 kJ/mol. Although the hydrogenation of vinylidene to CH3C is calculated to have a similar barrier, 85 kJ/mol, as hydrogenation to CH2CH, 90 kJ/mol, the former reaction is thermodynamically more favored (Figure 3). Acetylene can be formed through dehydrogenation of vinyl, as shown above. Breaking its C-C bond requires overcoming a barrier of 142 kJ/mol, which is somewhat higher than the barrier of C-H scission, 119 kJ/mol. The latter reaction leads to ethynyl (CHC), indicating that dehydrogenation is favored also for acetylene. Indirect H shift to CH2C is calculated to have an effective barrier of the same height as dehydrogenation. The reverse process of acetylene to CH2CH is characterized by a notably lower barrier, 93 kJ/mol. Thus, kinetically hydrogenation is preferred for CHCH. Acetylene will react on the surface

Chen et al. rather than desorb, because its binding energy at the surface, 203 kJ/mol, is significantly larger than the barriers just mentioned. When there is sufficient hydrogen available on the surface, recombination of CHC to CH2C or CHCH can be expected. The barriers for the two processes are similar, ∼100 kJ/mol, and both processes are slightly exothermic, by 40 and 24 kJ/ mol, respectively. The dehydrogenation of ethynyl to C2 has a barrier of 154 kJ/mol, which is 16 kJ/mol higher than that of the C-C bond breaking. In addition, C-C scission of CHC is thermodynamically more favorable by 86 kJ/mol than its dehydrogenation. Dehydrogenation of CHC yields a carbon dimer. The decomposition of C2 to C1 on Pd(111) is exothermic by 61 kJ/ mol. The corresponding barrier, 121 kJ/mol, is the lowest of any C-C bond scission step explored in this work. For this reaction, the UBI-QEP method predicted no barrier and an exothermicity of -683 kJ/mol.34 In summary, our calculations predict CHC and CC as precursors of the formation of C1 species. CHC is more likely as the dehydrogenation of CHC to CC requires overcoming a barrier of 154 kJ/mol, thus breaking this C-C bond is both kinetically and thermodynamically more favorable (Figure 3). Experiments on Pt(111)54 also found that CH3C finally decomposes to hydrogen-containing CHx species, which at temperatures above 500 K are converted to hydrogen-free Cx species. This experimental result implies that the precursors of C-C bond scission are hydrogen-containing C2Hx species, not hydrogen-free CC species. The surface chemistry of Pd is similar to that of Pt;46,55 hence, the experimental results indirectly substantiate our theoretical results.54 Experimental studies9 show that ethylene on Pd(111) converts to ethylidyne at ∼300 K and after further heating ethylidyne decomposes to C1 species at ∼425 K, yielding hydrogen. Our computational results show that direct C-C bond scission, CH3C f CH3 + C, is not likely, due to the very high barrier, 194 kJ/mol, and the large endothermicity, 116 kJ/mol. Two other more complex reaction schemes seem to be more plausible: (i) CH3C f CH2C f CHC f CH + C and (ii) CH3C f CH2C f CHCH f CH + CH. The highest barrier along the first chain of reactions is 138 kJ/mol and 142 kJ/mol along the latter. If ethylene is heated rapidly to 400 K, other pathways (not only those involving ethylidyne) may be involved, e.g., CH2CH2 f CH2CH f CH2C f CHC f CH + C and CH2CH2 f CH2CH f CHCH f CHC f CH + C. In all cases it seems that the most favorable final steps should be CH2C f CHC f CH + C. This finding is in good agreement with previous experiments, which also found the formation of CHC species during ethylidyne decomposition on Pd(111)8,56 and Pt(111).57,58 Looking back at this reaction network, it is interesting to probe the correlation between reaction barriers and reaction energies. As often occurs for similar reactions, one finds a linear relationship for the C-H and C-C bond scission steps with correlation coefficients of 0.99 and 0.90, respectively (see Figure S1 of the Supporting Information). Such a Brønsted-EvansPolanyi relation was previously found, not only for the C-H bond breaking but also for the O-H bond cleavage.59 4.2. Comparison with UBI-QEP Results. Finally, we would like to comment on the unity-bond-index quadratic-exponentialpotential (UBI-QEP) approach. Zeigarnik et al.34 estimated barriers and heats of reaction of C-C bond scission for a number of species. Comparison with the present results reveals that for CH2CH2 and CHCH on Pd(111) the UBI-QEP-estimated barriers for C-C breaking are relatively close (within 30 kJ/mol) to

Transformations of Ethylene on the Pd(111) Surface our first-principles results (Figure 3). However, for the adsorbed radicaloid species CH3CH, CH3C, CH2CH, CHC, and CC, the UBI-QEP barriers are remarkably lower than the present values. The largest difference, 131 kJ/mol, has to be noted for the barrier of C-C scission of CHC into CH and C. For the C-C bond scission of CH2CH and CHCH, a later UBI-QEP study33 reported 121 and 185 kJ/mol, respectively, compared to previous 53 and 155 kJ/mol.34,60 The UBI-QEP barriers for C-H bond cleavage, 2 kJ/mol for CH2CH to CHCH and 102 kJ/mol for CH3CH to CH3C, also differ by more than 70 kJ/mol from the present density functional results. For these latter reactions, the heats of reaction estimated with the UBI-QEP method also differ notably from our first-principles results. Overall, one concludes from this comparison that UBI-QEP techniques have to be used with due caution. 5. Conclusions We presented a comprehensive systematic first-principles study on possible transformation pathways of ethylene over Pd(111) surface. We demonstrate that for kinetic reasons most species will preferentially undergo C-H bond scission rather than C-C bond breaking. The barriers of C-H scission tend to decrease with the increasing H content in the C2Hx species (x ) 0-4), while the barriers of C-C scission increase concomitantly. Finally, for CHC, C-C bond breaking is more favorable than C-H cleavage, both kinetically and thermodynamically. Thus, this species likely is the precursor of C1containing species that are formed from ethylene over Pd(111). However, the lowest barrier for C-C bond breaking, among all systems studied here, was calculated for CC. The barriers of C-H scission range from 57 to 154 kJ/mol, exhibiting a propensity to increase with H content of the species; the barriers for breaking C-C bonds range from 121 to 194 kJ/mol. The calculated heats of reaction vary greatly: from -21 to 72 kJ/ mol for C-H cleavage and from 1 to 117 kJ/mol for C-C bond breaking. The calculated energetic profile shows that CH3C is the most stable species. Our results indicate that direct C-C bond scission, CH3C f CH3 + C, is not likely while at higher temperature the decomposition of CH3C may involve the channel CH3C f CH2C f CHC f CH + C. We also found a linear relationship between the barriers of the C-H and C-C bond scission steps and the corresponding reaction energies. Finally, comparison of our density functional results to those of UBI-QEP calculations revealed that UBI-QEP results can differ greatly from the corresponding first-principles values. Acknowledgment. Z.X.C. is grateful to the Alexander von Humboldt Foundation for funding a renewed research stay. H.A.A. thanks the Bulgarian National Science Fund (National Center of Advanced Materials UNION). This work was supported by Deutsche Forschungsgemeinschaft and Fonds der Chemischen Industrie (Germany). We also thank LeibnizRechenzentrum München for a generous allotment of computer time. Supporting Information Available: Description of the adsorption complexes of H, CHx (x ) 0-3), and C2Hx species (x ) 0-4) on Pd(111); table with adsorption modes and binding energies for various species relevant to ethylene transformations on Pd(111) surfaces; linear relationship between calculated reaction energies and activation barriers for C-H and C-C bond scission steps; Cartesian coordinates of all optimized structures of the clean surface Pd(111) surface as well as all reactants, transition states, and products of Tables 1 and 2. This material is available free of charge via the Internet at http://pubs.acs.org.

J. Phys. Chem. C, Vol. 114, No. 41, 2010 17691 References and Notes (1) Ponec, V.; Bond, G. C. Catalysis by Metals and Alloys; Elsevier: Amsterdam, 1995. (2) Bond, G. C. Metal-Catalysed Reactions of Hydrocarbons; Springer: New York, 2005. (3) Moskaleva, L. V.; Chen, Z.-X.; Aleksandrov, H. A.; Mohammed, A. B.; Sun, Q.; Ro¨sch, N. J. Phys. Chem. C 2009, 113, 2512, and references therein. (4) Gates, J. A.; Kesmodel, L. L. Surf. Sci. 1983, 124, 68. (5) Nishijima, M.; Yoshinobu, J.; Sekitani, T.; Onchi, M. J. Chem. Phys. 1989, 90, 5114. (6) Stuve, E. M.; Madix, R. J.; Brundle, C. R. Surf. Sci. 1985, 152153, 532. (7) Beebe, T. P.; Yates, J. T., Jr. J. Am. Chem. Soc. 1986, 108, 663. (8) Gabasch, H.; Hayek, K.; Klo¨tzer, B.; Knop-Gericke, A.; Schlo¨gl, R. J. Phys. Chem. B 2006, 110, 4947. (9) Stacchiola, D.; Kaltchev, M.; Wu, G.; Tysoe, W. T. Surf. Sci. 2000, 470, L32. (10) Jirka, I.; Plsˇek, J.; Vondraéèk, M.; Sˇutara, F.; Matolıń, V.; Cha´b, V.; Prince, K. C. Surf. Sci. 2007, 601, 3114. (11) Vang, R. T.; Honkala, K.; Dahl, S.; Vestergaard, E. K.; Schnadt, J.; Lægsgaard, E.; Clausen, B. S.; Nørskov, J. K.; Besenbacher, F. Surf. Sci. 2006, 600, 66. (12) Andersin, J.; Lopez, N.; Honkala, K. J. Phys. Chem. C 2009, 113, 8278. (13) Goda, A. M.; Barteau, M. A.; Chen, J. G. J. Phys. Chem. B 2006, 110, 11823. (14) Medlin, J. W.; Allendorf, M. D. J. Phys. Chem. B 2003, 107, 217. (15) Kua, J.; Faglioni, F.; Goddard III, W. A. J. Am. Chem. Soc. 2000, 122, 2309. (16) Paul, J.-F.; Sautet, P. J. Phys. Chem. 1998, 102, 1578. (17) Ge, Q.; Neurock, M. Chem. Phys. Lett. 2002, 358, 377. (18) Brown, W. A.; Kose, R.; King, D. A. Chem. ReV. 1998, 98, 797. (19) Pallassana, V.; Neurock, M. J. Catal. 2000, 191, 301. (20) Mei, D. H.; Sheth, P. A.; Neurock, M.; Smith, C. M. J. Catal. 2006, 242, 1. (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) Neurock, M.; van Santen, R. A. J. Phys. Chem. B 2000, 104, 11127. (23) Moskaleva, L. V.; Aleksandrov, H. A.; Basaran, D.; Zhao, Z.-J.; Ro¨sch, N. J. Phys. Chem. C 2009, 113, 15373. (24) Sheth, P. A.; Neurock, M.; Smith, C. M. J. Phys. Chem. B 2005, 109, 12449. (25) Ramchandra, M. W.; Randy, D. C.; Norskov, J. K.; Dumesic, J. A. J. Phys. Chem. B 2000, 104, 2299. (26) Kozlov, S. M.; Yudanov, I. V.; Aleksandrov, H. A.; Ro¨sch, N. Phys. Chem. Chem. Phys. 2009, 11, 10955. (27) Teschner, D.; Borsodi, J.; Wootsch, A.; Re´vay, Z.; Ha¨vecker, M.; Knop-Gericke, A.; Jackson, S. D.; Schlo¨gl, R. Science 2008, 320, 86. (28) Yudanov, I. V.; Matveev, A. V.; Neyman, K. M.; Ro¨sch, N. J. Am. Chem. Soc. 2009, 130, 9342. (29) Sinfelt, J. H. AdV. Catal. 1973, 23, 91. (30) Sinfelt, J. H. J. Catal. 1972, 27, 468. (31) Goddard, S. A.; Amiridis, M. D.; Rekoske, J. E.; Cardona-Martinez, N.; Dumesic, J. A. J. Catal. 1989, 117, 155. (32) Ko, E. I.; Garten, R. L. J. Catal. 1981, 68, 233. (33) Zeigarnik, A. V.; Shustorovich, E. Russ. J. Phys. Chem. B 2007, 1, 330. (34) Zeigarnik, A. V.; Valde´s-Pe´rez, R. E.; Myatkovskaya, O. N. J. Phys. Chem. B 2000, 104, 10578. (35) Kresse, G.; Hafner, J. Phys. ReV. B 1994, 49, 14251. (36) Kresse, G.; Furthmu¨ller, J. Comput. Mater. Sci. 1996, 6, 15. (37) Perdew, J. P.; Wang, Y. Phys. ReV. B 1992, 45, 13244. (38) Blo¨chl, P. E. Phys. ReV. B 1994, 50, 17953. (39) Kresse, G.; Joubert, D. Phys. ReV. B 1999, 59, 1758. (40) Monkhorst, H. J.; Pack, J. D. Phys. ReV. B 1976, 13, 5188. (41) Methfessel, M.; Paxton, A. T. Phys. ReV. B 1989, 40, 3616. (42) Chen, Z.-X.; Neyman, K. M.; Gordienko, A. B.; Ro¨sch, N. Phys. ReV. B 2002, 68, 075417. (43) Mills, G.; Jońsson, H.; Schenter, G. K. Surf. Sci. 1995, 324, 305. (44) Jońsson, H.; Mills, G.; Jacobsen, K. W. In Classical and Quantum Dynamics in Condensed Phase Simulations; Berne, B. J., Ciccotti, G., Coker, D. F., Eds.; World Scientific: Singapore, 1998; p 385. (45) Henkelman, G.; Jońsson, H. J. Chem. Phys. 1999, 111, 7010. (46) Zhao, Z.-J.; Moskaleva, L. V.; Aleksandrov, H. A.; Basaran, D.; Ro¨sch, N. J. Phys. Chem. C 2010, 114, 12190. (47) Chen, Z.-X.; Neyman, K. M.; Lim, K. H.; Ro¨sch, N. Langmuir 2004, 20, 8068. (48) Sheppard, N.; De La Cruz, C. AdV. Catal. 1998, 42, 181. (49) In this work, C1 refers to the carbon center with less or no H atoms attached and C2 refers to the other carbon center.

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(50) In the following we will use short-hand notations like η3η1(C,C) instead of η3(C1)η1(C2), etc. (51) Stacchiola, D.; Calaza, F.; Zheng, T.; Tysoe, W. T. J. Mol. Catal. A: Chem. 2005, 228, 35. (52) Ormerod, R. M.; Lambert, R. M.; Hoffmann, H.; Zaera, F.; Wang, L. P.; Bennett, D. W.; Tysoe, W. T. J. Phys. Chem. 1994, 98, 2134. (53) Azad, S.; Kaltchev, M.; Stacchiola, D.; Wu, G.; Tysoe, W. T. J. Phys. Chem. B 2000, 104, 3107. (54) Lee, A. F.; Wilson, K. J. Vac. Sci. Technol. A 2003, 21, 563. (55) Desai, S. K.; Neurock, M.; Kourtakis, M. J. Phys. Chem. B 2002, 106, 2559.

Chen et al. (56) Jungwirthova´, I.; Kesmodel, L. L. J. Phys. Chem. B 2001, 105, 674. (57) Deng, R.; Herceg, E.; Trenary, M. Surf. Sci. 2004, 573, 310. (58) Deng, R.; Herceg, E.; Trenary, M. J. Am. Chem. Soc. 2005, 127, 17628. (59) Michaelides, A.; Liu, Z. P.; Zhang, C. J.; Alavi, A.; King, D. A.; Hu, P. J. Am. Chem. Soc. 2003, 125, 3704. (60) Different binding energies likely have been adopted for related species in that earlier work: ref 34.

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Transformations of Ethylene on the Pd(111) Surface: A Density

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