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J. Phys. Chem. C 2009, 113, 2512–2520
Ethylene Conversion to Ethylidyne over Pd(111): Revisiting the Mechanism with First-Principles Calculations Lyudmila V. Moskaleva,† Zhao-Xu Chen,†,‡ Hristiyan A. Aleksandrov,†,§ Amjad Basha Mohammed,† Qiao Sun,†,⊥ and Notker Ro¨sch*,† Department Chemie and Catalysis Research Center, Technische UniVersita¨t Mu¨nchen, 85747 Garching, Germany, and 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 ReceiVed: September 16, 2008; ReVised Manuscript ReceiVed: December 14, 2008
On Pd(111), thermal activation of ethylene has been reported to yield ethylidyne. Using more approximate models, a plausible three-step mechanism, ethylene f vinyl f ethylidene f ethylidyne, was recently proposed for this process on the basis of DFT calculations. We employed more elaborate computational models and characterized the thermodynamics and kinetics of the mechanism of ethylene conversion to ethylidyne on Pd(111). We carried out density functional slab-model studies for three coverages of the adsorbate, 1/3, 1/4, and 1/9. The resulting refined potential energy landscape turned out to differ notably from that reported previously: our calculated barriers for the various elementary steps are significantly lower than those of previous studies, and we determined the overall process to be exothermic, in contrast to earlier computational results. We show that the three-step mechanism is thermodynamically and kinetically feasible on Pd(111), with the dehydrogenation of ethylene to vinyl being the rate-limiting step at all coverages considered. Direct conversion of ethylene to ethylidene is unlikely due to a very high barrier. Coverage effects have been found important. At high coverage, the rate-limiting first reaction barrier is ∼50 kJ mol-1 above the desorption energy of ethylene, whereas at low coverages the two energies become comparable. 1. Introduction One of the primary goals of contemporary research in heterogeneous catalysis is to attain comprehensive understanding of reaction mechanisms on surfaces at the molecular level.1 With recent advances in computational methodology and increased expertise, first-principle calculations utilizing cluster or slab models have become a powerful means that contributes to the solution of many questions concerning a detailed microscopic picture of reactions over transition metal catalysts.2-4 It is no surprise that the chemistry of ethylene on group VIII metal surfaces attracted much interest because this simplest unsaturated hydrocarbon can serve as a benchmark for studying more complex reactions of higher alkenes as well as aromatics. Adsorption properties of ethylene on these metals have been characterized in many experiments, e.g., refs 5-9 (for the work until 1998, see earlier reviews10-12), and several theoretical studies.8,9,13-18 The latter studies were carried out mainly in connection to ethylene hydrogenation on these metals, which has long served as a classical model process for studying the industrially important hydrogenation of olefins.19 The thermal activation of ethylene to around room temperature has been reported to yield the thermodynamically more stable ethylidyne, CH3-C≡, on quite a number of surfaces, including Pt(111)20,21 and Pd(111).22 The analogous formation of larger alkylidynes from alkenes has been observed as well.23,24 However, the * To whom correspondence should be addressed. † Technische Universita¨t Mu¨nchen. ‡ Nanjing University. § Permanent address: Faculty of Chemistry, University of Sofia, Sofia, Bulgaria. ⊥ Present address: Australian Institute of Bioengineering and Nanotechnology, The University of Queensland, Australia.
complex mechanism of this reaction, which must involve dehydrogenation and H migration, could not be unambiguously elucidated. Current interest in ethylene dehydrogenation has been triggered on one hand by attempts to connect this reaction to the synthesis of functionalized olefins, such as vinyl chloride or vinyl acetate,25 and on the other hand by the possible role of alkylidynes in catalytic hydrogenation-dehydrogenation and hydrocarbon-reforming reactions.26,27 Ethylidyne species, which cover the catalyst surface during ethylene hydrogenation, have been suggested26,27 to act as transfer agents for atomic hydrogen from the surface to the olefin adsorbed in the second layer. Yet, subsequent studies did not confirm this proposition.28 We note in passing that ethylidyne decomposes at higher temperatures by undergoing C-C bond scission to release CHx fragments on the metal surface.22b Thus, alkylidynes could be precursors to C-C bond breaking during industrially important catalytic reforming of larger hydrocarbons. Several intermediates, including ethyl, vinyl, and ethylidene, were proposed for ethylene-to-ethylidyne conversion, but none of them was detected experimentally.22,29 Recent kinetic studies of Zaera et al. on Pt(111), 30,31 supported by infrared-visible sum frequency generation experiments32 as well as Cs+ reactive ion scattering,33 suggested that dehydrogenation of ethylene likely involves an isomerization to ethylidene, CH3-CH), while vinyl intermediate as precursor of ethylidyne was ruled out because vinyl species were shown to convert back to ethylene before producing ethylidyne on Pt(111).29 On Pd(111), the conversion of ethylene to ethylidyne could likely involve the same intermediates as on Pt(111); however, different relative barrier heights might lead to a lowest-energy path of different topology. For instance, Tysoe et al. observed34 that vinyl fragments on Pd(111) rapidly convert to ethylidyne
10.1021/jp8082562 CCC: $40.75 2009 American Chemical Society Published on Web 01/21/2009
Ethylene Conversion to Ethylidyne over Pd(111) at temperatures as low as 160 K, whereas on Pt(111) this reaction proceeds only around 300 K.29 Yet, ethylene is known to convert to ethylidyne more slowly on Pd(111) than on Pt(111).35 Recently, a density functional (DF) study15c explored a plausible pathway of ethylene dehydrogenation over Pd(111) involving both vinyl and ethylidene intermediates. However, due to computational expense, that study was done at a relatively approximate level (especially with respect to the location of transition state structures) and only in the limit of high coverage. The current work is aimed at revisiting the pathway for ethyleneto-ethylidyne conversion proposed in that preceding work,15c using more elaborate models and a more precise method for locating transition states. We will show that our refined potential energy landscape differs significantly from that reported earlier,15c with implications on the reaction kinetics. In addition, we conclusively rule out an alternative pathway involving the direct isomerization of ethylene to ethylidene, as proposed for this reaction on Pt(111).31 Furthermore, we studied coverage effects on the adsorption energies of potential intermediates and on the barrier heights. The paper is organized as follows. In section 2, we describe our models and the computational method. In section 3, first we briefly summarize the mechanisms proposed in the literature for ethylene-to-ethylidyne conversion on close-packed surfaces of group VIII metals. Then, for Pd(111), we discuss the adsorption of ethylene, ethylidyne, and intermediates involved in the three-step mechanism considered in this work. Subsequently, we describe the transition state structures and the activation energies of each elementary reaction step, and we discuss the reaction kinetics for various coverages. We will show that our theoretical results map important aspects of the existing experimental evidence for ethylene decomposition on Pd(111) and Pt(111). 2. Models and Computational Details The calculations were carried out with the plane-wave-based Vienna ab initio simulation package (VASP)36,37 using the generalized-gradient approximation (GGA) in the form of the exchange-correlation functional PW91.38 The interaction between atomic cores and electrons was described by the projector augmented wave (PAW) method.39,40 For the integrations over the Brillouin zone, we used the k point sampling scheme of Monkhorst and Pack,41 and we invoked a generalized Gaussian smearing technique42 (with the default smearing width of 0.2 eV) to accelerate convergence. The structure optimizations of this study were carried out with a 5 × 5 × 1 k point grid; subsequently, we refined the energies in single-point fashion employing a k point grid of 7 × 7 × 1. We adopted an energy cutoff of 400 eV throughout, which, according to our test calculations for ethylidyne on Pd(111), guarantees convergence of binding energies to better than 0.5 kJ mol-1. In structure optimizations, all atomic coordinates were optimized until the force acting on each atom became less than 2 × 10-4 eV/pm. An infinitely extended, ideal Pd(111) surface was modeled by five-layer slabs with the adsorbates bound to the surface layer of one side. Periodically repeated slabs were separated by a vacuum spacing of at least 1 nm to minimize spurious interactions. The three “bottom” layers of a slab were kept fixed at the theoretical bulk-terminated geometry (Pd-Pd ) 280 pm), and the two upper layers of Pd atoms were allowed to relax during geometry optimizations, together with the adsorbate. We used three different unit cells, (3 × 3)R30°, (2 × 2), and (3 × 3), to represent the surface coverages 1/3, 1/4, and 1/9, respectively. We located transition states only at the lowest and highest coverages, 1/9 and 1/3.
J. Phys. Chem. C, Vol. 113, No. 6, 2009 2513 SCHEME 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 and Esub are the total energies of the adsorbate in the gas phase (ground state) and of the clean substrate, respectively. Where appropriate, calculations were carried out in spin-polarized fashion. With the above definition, positive values of BE imply a release of energy or a favorable interaction. We located transition states (TSs) of reactions using the nudged elastic band (NEB) method43,44 with eight images of the system forming a discretization of the path between the fixed end points. With a normal-mode analysis, we verified for each TS that there is exactly one imaginary frequency. A comment is due concerning the main differences between the current model and that used in an earlier computational study of the same system.15c Here, we employed slab models of five layers, whereas three-layer slabs were used in the aforementioned work. That earlier calculation used pseudopotentials, whereas we invoked the PAW method. Most importantly, we located TSs using the NEB method and converged geometries to within a tolerance of 2 × 10-4 eV/pm for forces; the latter convergence threshold is a factor of 10 smaller than that used previously.15c Finally, in addition to the high coverage of 1/3, we also considered two lower coverages, 1/4 and 1/9, to examine coverage effects on the reaction energetics. 3. Results and Discussion It has long been established that the adsorption of ethylene on close-packed (111) surfaces of Pt or Pd around room temperature results in the formation of a strongly bound species identified as ethylidyne, CH3-C≡.20-22 The conversion of ethylene to ethylidyne was more extensively studied on Pt29-32,45,46 than on Pd,8,22 and certain progress in unraveling the reaction mechanism on Pt was achieved. However, complete understanding of this reaction on either metal is lacking. Obviously, the transformation comprises at least two steps: C-H bond breaking and H shift from one C atom to the other. Consistent with this simple logic, either dehydrogenation should occur first, forming a vinyl species (reaction a in Scheme 1) and then a hydrogen shift takes place (reaction b in Scheme 1), or, alternatively, the order of these elementary steps is reversed (reactions c and d of Scheme 1). Of course, more complex and less direct pathways can also be envisioned, such as a-e-d (Scheme 1) and others, e.g., paths involving vinylidene (CH2dC))47 or ethyl (CH3CH2-).48 However, the latter two pathways are considered unlikely because ethyl readily undergoes β-H elimination on Pt(111) and vinylidene transforms to ethylene at temperatures as low as 170 K.27 For a more detailed overview of all proposed mechanisms, see ref 49. On the basis of their kinetic studies on Pt(111),29 Zaera et al. argued against the mechanism a-b because they observed vinyl converting back to ethylene before ethylidyne was formed, i.e.,
2514 J. Phys. Chem. C, Vol. 113, No. 6, 2009 the activation energy of the latter process must be much higher. Instead, they favored ethylidene as the likely precursor to ethylidyne along the two-step pathway c-d.31 Ethylidene moieties on Pt(111) were shown to convert into surface-bound ethylidyne already at temperatures as low as 150 K;46 recently, further evidence supporting ethylidene as a reaction intermediate was reported.33 Nevertheless, the main argument against the twostep pathway c-d remains the result of a temperatureprogrammed desorption (TPD) study,45 which suggested that the H atom involved in the first (rate-limiting) step is the same that desorbs around 300 K, thus favoring vinyl formation, reaction a of Scheme 1. A tentative explanation of that result assumed29 a fast ethylene-ethylidene preequilibrium (implying kc . kd, k-c . kd) prior to the formation of ethylidyne. Yet, this hypothesis can be questioned from a view of an apparently very low barrier for reaction d; the latter reaction takes place at 150 K,46 whereas both forward and reverse barriers of reaction c are expected to be rather high. For example, our calculated barrier for reaction c on Pd(111) is ∼200 kJ mol-1 (see below); on Pt that barrier is unlikely to be much lower. Thus, both direct pathways on Pt(111), a-b and c-d, can be disputed. Early theoretical studies on the mechanism of ethene-toethylidyne conversion on Pt(111), as summarized in ref 50, were carried out more than one decade ago and, therefore, generally were limited to less accurate methods. A DFT study50 using a Pt8 cluster model favored the two-step pathway a-b and vinyl as the likely intermediate. However, that and other computational studies only estimated the reaction energetics50 but did not touch reaction barriers; hence, they have not been able to discount conclusively either ethylidene or vinyl as reaction intermediate. Recently, a DF study51 considered dehydrogenation and isomerization of propylene on Pt(111); dehydrogenation of propylene to propylidyne was found thermodynamically favorable. From simulated vibrational spectra, two possible intermediates were proposed,51 propylidene and 1-propenyl; yet again, no reaction barriers were reported. Knowledge regarding the mechanism of ethylidyne formation on Pd surfaces gained from experiments is even less definitive than in the case of Pt. Several studies indicated the formation of ethylidyne after room temperature adsorption of ethylene on Pd(111),5a,8,22,55 but there were no attempts to explore the detailed mechanism of conversion. As in the case of Pt, no intermediates could be detected on Pd(111) in any of these experiments indicating that the first elementary step in the transformation of ethylene to ethylidyne should be rate-limiting. In a DF slabmodel study, Neurock et al.15c determined adsorption energies of several potential reaction intermediates; on the basis of energetic considerations, they suggested the reaction pathway a-e-d as plausible. Interestingly, this mechanism almost fits the experimental observations collected for the reaction kinetics on Pt(111). Namely, dehydrogenation was suggested as first step by a TPD study,45 and ethylidene was identified as direct precursor of ethylidyne.31,46 Only the notion that vinyl converts back to ethylene at lower energy than it reacts to form ethylidyne29 is in conflict with the pathway a-e-d. The results of our calculations presented below suggest that on Pd(111) these two barriers are of comparable heights at all coverages scrutinized. Thus, over Pd(111) the pathway a-e-d appears plausible according to the results to be described in the following. We note parenthetically that on Rh(111) C-H bond rupture and formation of a vinyl intermediate was experimentally identified as the initial step in the decomposition of ethylene.49 The above-mentioned study of Neurock et al.,15c however, furnished a reaction energy profile that is qualitatively quite
Moskaleva et al.
Figure 1. Reaction energy profile (kJ mol-1) of ethylene conversion to ethylidyne over Pd(111) at 1/3 coverage, comparing results of the present study (lower curve, black line) to those of ref 15c (upper curve, gray line). Energies are calculated with respect to ethylene in the gas phase and clean Pd(111); atomic hydrogen is coadsorbed.
different (Figure 1). In fact, that earlier reaction energy diagram may be questioned on several terms. For one, the net reaction energy, 34 kJ mol-1, for the conversion of adsorbed ethylene to coadsorbed ethylidyne and hydrogen (computed for a coverage of 1/3), indicates an endothermic process, whereas the reaction is expected to be exothermic, as ethylidyne on Pt-group (111) surfaces was found to be thermodynamically more stable than adsorbed ethylene.22 Of course, that gain in free energy might be at least partially due to entropy. Also, a repulsive interaction of ethylidyne and coadsorbed hydrogen may unfavorably have affected the reaction energy in that earlier study;15c still, the fact that the transformation energy of adsorbed ethylene was calculated to be positive raises concern. Moreover, a preceding paper15a of that group reported a reaction energy of -10 kJ mol-1 for the conversion of ethylene to ethylidyne + H on Pd(111), for a coverage of 1/4; however, the coverage seen in the corresponding figures is not clear. There are indications in later publications15b,d,e that the coverage used in most calculations of ref 15a was in fact 1/3. References 15a and 15c report the adsorption energy of ethylene as 62 kJ mol-1 at 1/4 coverage, whereas more recent publications by the same group15e with very similar models assign the value 62 kJ mol-1 to coverage 1/3 and list a value of 82 kJ mol-1 for coverage 1/4. Clarification appears to be appropriate. Therefore, we were motivated to recalculate the intermediates and TSs along the whole reaction path using the same density functional and the same coverage, 1/3, as in ref 15c, but with more refined models (thicker slabs, denser k point mesh, finer convergence criteria). We obtained a qualitatively and quantitatively strikingly different result, see Figure 1. Many pertinent energies differ by 30-50 kJ mol-1, the largest difference (for TS3) reaching 80 kJ mol-1, an amount that cannot be simply attributed to differences in the computational models. To make the current reinvestigation more general, we carried out additional calculations for lower surface coverages, 1/4 and 1/9. The change of the potential energy landscape with coverage may have important implications for the reaction kinetics. Incidentally, Zaera et al.46 proposed that on Pt(111) the ratelimiting step in the transformation of ethylene to ethylidyne likely changes at increased ethylene coverage. Throughout this work, we will systematically compare the results of our calculations at different adsorbate coverage. 3.1. Adsorption Complexes of H and C2Hx (x ) 3, 4) Species on Pd(111). Ethylene. Depending on the surface geometry and the presence of coadsorbates, two adsorption modes have been identified for ethylene bound to group VIII
Ethylene Conversion to Ethylidyne over Pd(111)
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TABLE 1: Calculated Structural Parameters (pm), Selected Vibrational Frequencies (meV), and Adsorption Energies (kJ mol-1) for Ethylene Adsorbed on Pd(111) in Di-σ or π Modes at Different Surface Coverages θa π complex
di-σ complex θ
1/3
1/4
C-C C-Pd freq.g
b
144 213b
145 ; 144 ; 144 ; 145 ; exp. 142 ( 9 212b; 214c; 213d; exp. 196 ( 5f
Eads
71b; 65c
83b; 78c; 80d; 80e
b
c
d
e
f
1/9
1/4
145 212b 372 (363) νC-H 178 (177) νC-C 137 (136) δCH2 109 (108) ωCH2 46 νPd-C 90b
140 ; 139 ; 140 ; exp. 145 ( 10 221b; 221c; exp. 228 ( 12f
140b 220b
64b; 60c; 63d; 63e
78b
b
b
c
d
1/9 f
a Also shown are experimental values where available. b This work. c Reference 15d. d Reference 16. e Reference 8. f Reference 5d; coverage ∼0.25 ML. g Experimental values in parentheses; ref 8.
metal surfaces at low temperature (typically below 200 K),10 designated as di-σ- and π-adsorbed ethylene. The former is attached to two metal atoms in η1η1 fashion (via two σ bonds) at a “bridge” site. The π-bonded species is thought to coordinate to only one metal atom via a π donor bond (“atop” site). Accordingly, ethylene in the di-σ mode is expected to be substantially rehybridized (from C sp2 to almost sp3), whereas the π-bonded form remains rather close to the structure in the gas phase. Recent experimental studies provided evidence that ethylene adsorbs in a di-σ bonding state on clean Pd(111)5,6 but converts to a more weakly adsorbed π-bonded species on a hydrogen- or oxygen-precovered Pd(111) surface.5b,c,8 Similarly, on Pt(111), the di-σ mode has been found most favorable.52,53 Several theoretical studies8,13,15,16 compared the adsorption of di-σ- and π-bonded ethylene on Pd surfaces using (2 × 2) or (3 × 3) unit cells, which correspond to coverages 1/4 and 1/3, respectively, Table 1. All of these calculations were done with the PW91 functional using slab models of 3-4 metal layers. A recent study15d reported adsorption energies of 65 and 78 kJ mol-1 from calculations on di-σ-adsorbed ethylene with 1/3 and 1/4 coverage, respectively. These values are consistent with the values of 71 and 83 kJ mol-1 as obtained in the present study for the di-σ-adsorbed ethylene at 1/3 and 1/4 coverage, respectively (Table 1). The systematic difference of ∼5 kJ mol-1 has to be attributed to the fact that we used a slab model with more metal layers (five layers). At the low coverage of 1/9, the adsorption energy of di-σ ethylene increases further, to 90 kJ mol-1 (Table 1). We calculated π-bonded ethylene only at low coverages of 1/4 and 1/9 because this type of adsorption complex is not of primary interest to the present work. Adsorption energies at these two coverages were 64 and 78 kJ mol-1, respectively, i.e., 19 and 12 kJ mol-1 less than those of di-σ-bound ethylene at the corresponding coverages (Table 1). Similar energy differences between the two adsorption modes, 17-18 kJ mol-1, had been obtained in other theoretical studies on Pd(111) at 1/4 coverage, Table 1.8,15d,16 Likewise, on Pt(111) at surface coverages 1/8-1/2, di-σ-bound ethylene was found to be favored over the π-bonded complex by 14-16 kJ mol-1.13 Thus, computational studies corroborate the experimentally observed energetic preference of di-σ-bound ethylene; however, the difference between the two modes is rather small and could be compensated for by an entropic term not included in the theoretical values. It has been suggested15a that at low surface coverage π-adsorbed ethylene possesses one extra degree of freedom for rotation about the C2V axis normal to the surface. As that degree of freedom features a very low barrier, this can lead to a change in the value of T∆S of nearly 30-40 kJ mol-1 at room temperature,15a so that the order of preference might even be reversed.
Likely, both di-σ and π-ethylene coexist on the surface, whereas their ratio varies strongly with temperature and coverage as well as other experimental parameters. In fact, no general agreement existed until recently regarding the preferred binding mode of ethylene on clean Pd(111). For instance, early results54,55 from high-resolution electron energy loss spectroscopy were interpreted in favor of π-bonded ethylene.The experimental activation energy to ethylene desorption, 54 kJ mol-1,55 and 68 kJ mol-1,5b estimated from low-coverage TPD experiments at ultrahigh vacuum conditions, might be an average over di-σ and π-ethylene. Nevertheless, theoretical adsorption energies for both adsorption modes at low coverage are significantly higher. Actually, the experimental values may hold some uncertainty as they were derived from a rather oversimplified Arrhenius model with assumed preexponential factors.56 The structures of adsorbed ethylene from published calculations and those of the present work (collected in Table 1) agree within 1-2 pm. In contrast to the adsorption energies, no sizable coverage dependence of the C-C and C-Pd distances can be observed. As expected from simple bond-order considerations, the C-C bond shortens by 5 pm on going from the di-σ- to the π-bonded ethylene. The calculated geometry of di-σ-bonded ethylene agrees well with the structure derived from LEED at 80 K.5d The latter experiments predicted an ethylene species bonded at short bridges on the surface with a C-C bond length of (142 ( 9) pm and a C-Pd distance of (196 ( 5) pm, although the latter value is somewhat shorter than the corresponding theoretical values, 212-214 pm (Table 1). The structure of π-bonded ethylene has also been measured in the same work on hydrogen-covered Pd(111).5d The C-C bond length of (145 ( 10) pm and the C-Pd distance of (228 ( 12) pm (Table 1) agree with theoretical results (139-140 and 220-221 pm, respectively) within the experimental error bars. Vibrational frequencies of di-σ- and π-bonded ethylene on Pd(111) have previously been calculated and compared with experimental data.8 Therefore, we skip the discussion of the vibrational analysis here, but note that most of our calculated frequencies at 1/9 coverage (Table 1) agree within 1 meV with the theoretical values for 1/4 coverage.8 Ethylidyne. Early LEED studies22 identified the dominant surface species formed by ethylene on Pd(111) at room temperature as ethylidyne (CH3-C≡), bonded with its C-C axis perpendicular to the metal surface. Such an orientation is indicative of adsorption at high-coordinated hollow sites, as typically found on other (111) surfaces.57 Recent studies suggested58 that the stable site for ethylidyne on Pd(111) is identical to that on Pt(111),59 i.e., the fcc threefold hollow site. In the present work, fcc hollow sites are only slightly more favorable than hcp sites, by 3-6 kJ mol-1. Using a Pd19 cluster
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TABLE 2: Optimized Geometriesa (pm) and Energetic Characteristics (kJ mol-1) of Intermediates and Transition States for Ethylene Dehydrogenation to Ethylidyne at Varied Coverage θ ethylene TS1 vinyl + Hf TS2 ethylidene TS3 ethylidyne + Hf
θ
C-C
C-Hb
H-Pdb
C-Pdc
Ereld
1/3 1/4 1/9 1/3 1/9 1/3 1/4 1/9 1/3 1/9 1/3 1/4 1/9 1/3 1/9 1/3 1/4 1/9
144 145 145 144 145 144 145 145 146 147 150 150 150 150 150 149 149 149
110 110 110 184 175 260 295 272 158 162 111 111 111 136 129 283 282 298
250 254 254 158 162 175, 179, 181 180, 183, 183 175, 181, 188 171, 193 162, 241 234 252 232 182, 201, 214 185, 200, 226 183, 183, 183 179, 183, 184 179, 179, 188
213 212 212 207, 210, 211 207, 210, 209 204, 209, 211 204, 204, 209 202, 206, 207 204, 204, 224 202, 203, 220 202, 203 203, 203 202, 203 202, 204, 207 203, 205, 209 199, 199, 199 198, 199, 199 196, 197, 199
-71 -83 -90 46 10 -8 (-48) -51 (-63) -63 (-69) 44 14 -39 -49 -58 -11 -33 -84 (-114) -105 (-120) -127 (-133)
BEe 71 83 90 252g 267g 273g 338 348 357 533g 540g 553g
a A-B, distance between atoms A and B. b Distance that breaks/forms during a reaction. c The two C-Pd distances of the η2-bound C atom are listed first for TS1, vinyl, and TS2. See also Figure 2. d Relative energy with respect to ethylene in the gas phase and clean Pd(111). Values in parentheses are calculated in the limit of hydrogen at infinite separation from the coadsorbate. e The binding energy (BE) of an adsorbate is calculated according to BE ) Ead + Esub - Ead/sub, where Ead/sub is the total energy of the slab model, covered with the adsorbate in the optimized geometry, and Ead and Esub are the total energies of the adsorbate in the gas phase (ground state) and of the clean substrate, respectively. f The hydrogen atom is coadsorbed unless stated otherwise. g Without coadsorbed hydrogen.
model, Neurock and van Santen calculated a difference of similar magnitude, 17 kJ mol-1, and a diffusion barrier of 33 kJ mol-1.15a We calculated the binding energy of ethylidyne at the threefold fcc site on Pd(111) at 533-553 kJ mol-1 (Table 2), using the doublet state of ethylidyne in the gas phase as reference. The C-C bond length, 149 pm, turned out to be independent of the coverage. The C-Pd bond elongates from 196-197 to 199 pm as the coverage increases from 1/9 to 1/3 (Table 2); concomitantly, the calculated binding energy decreases slightly, by 20 kJ mol-1. Intermediates: Vinyl and Ethylidene. The intermediate vinyl (CH2dCH-) prefers to bind directly over a threefold fcc site of Pd(111), in η1η2 fashion, which entails an sp3 configuration at each carbon atom. We calculated binding energies of 252-273 kJ mol-1 for adsorbed vinyl, where the interaction increases with decreasing coverage (Table 2). The C-C bond of adsorbed vinyl, 144-145 pm, is close to that of di-σ ethylene, indicating about the same degree of rehybridization, while the C-Pd bond can be as short as 203-204 pm, i.e., 2-9 pm shorter than in adsorbed ethylene. Our results agree closely with earlier theoretical values.15c Ethylidene (CH3-CH)) prefers to bind at a bridge site on the surface to satisfy the valence requirement of an sp3hybridized carbon center. Its binding energy decreases from 357 to 338 kJ mol-1 as the coverage increases from 1/9 to 1/3 (Table 2). The C-C bond was calculated at 150 pm, consistent with pure single bond character; the two C-Pd distances were determined at 202-203 pm, independent of coverage. Coadsorbate: Atomic Hydrogen. H atoms adsorbed on Pd(111) prefer the highly coordinated fcc threefold hollow sites, as established by means of low-energy electron diffraction (LEED)60 and corroborated by theoretical studies61 including this work, although calculations give only small preference to fcc over hcp sites, at most 5 kJ mol-1.61,62 The barrier for H diffusion over Pd(111), calculated at ∼20 kJ mol-1,61 indicates significant mobility. Adsorption energies of H atoms on fcc sites obtained in the current study hardly decrease with coverage,
from 276 kJ mol-1 at 1/9 coverage to 274 kJ mol-1 at 1/3 coverage. In previous PW91 calculations with thinner slab models,15e H adsorption energies of 260 and 248 kJ mol-1 were obtained for 1/4 and 1/3 coverage, respectively. The energy for dissociative adsorption of molecular hydrogen (per H atom) calculated in this study ranges from 54 kJ mol-1 at 1/3 coverage to 56 kJ mol-1 at 1/9 coverage, somewhat above the experimental value, 43 kJ mol-1, from measurements of the work function.63 3.2. Three-Step Mechanism for Ethylene Conversion to Ethylidyne. Now, we will present structural and energetic details of the reaction profiles given in Figure 1. The corresponding reaction path comprises three elementary H dissociation/addition steps to be discussed below. We will mainly refer to the results obtained for a high surface coverage, 1/3. Because the surface coverage was found not to affect significantly the structures, we will not explicitly describe how the structures evolve along the reaction path at lower coverages; instead, we refer the reader to Table 2. In contrast, we will discuss the effect of decreasing surface coverage on the reaction energetics in a separate subsection. Dehydrogenation of Ethylene to Vinyl. Ethylene that converts to ethylidyne on Pd(111) is believed to be bound to the surface in a di-σ mode (whereas π-adsorbed ethylene was shown to be the active species for ethylene hydrogenation5b,15a). Thus, in accord with previous computational work,15c we took the more strongly bound di-σ mode of ethylene as initial reactant state. In the final state, the product vinyl species is most favorably bound in a η1η2 mode;15c the H atom, released during dehydrogenation, was placed at the neighboring fcc site (Figure 2). C-H bond activation proceeds via a three-center TS, C-Pd-H, where in a concerted motion the C-H bond breaks and the H-Pd bond forms. Simultaneously, the reacting C atom is forming a second C-Pd bond at a Pd-Pd bridge site. In TS1 (Table 2, Figure 2), the C-H distance is elongated by 74 pm, to 184 pm, whereas the H-Pd distance decreases to 158 pm, characteristic of an H atom bound at an atop site.61 As expected for a dissociation reaction, this TS is of fairly “late” nature, as
Ethylene Conversion to Ethylidyne over Pd(111)
Figure 2. Structures of the transition states (left column) and the corresponding product states (right column) of the three steps of ethylene conversion to ethylidyne at 1/3 coverage. Selected distances in pm.
is evident from the rather long C-H distance, 184 pm, and the rather short C-Pd distance, 210 pm, close to the 204 pm of the C-Pd bond of the adsorbed vinyl. Another peculiarity of TS1 is the short H-Pd distance of 158 pm which is even shorter than in the final state, 179 pm, where H arrives at a threefold fcc site. The activation energy of H dissociation from ethylene at a coverage 1/3 was calculated at 117 kJ mol-1 (Table 2, Figure 1), 34 kJ mol-1 below the barrier previously reported for the same coverage.15b,c The result of that earlier computational study seems overestimated, likely as a consequence of the less rigorous procedure for locating TS structures used in that work. For example, inspection of details of the TS1 geometry shows that the H-Pd distance in the latter study, 174 pm, is 16 pm larger than in the present work. The reaction energy, 73 kJ mol-1, obtained earlier,15b,c agrees reasonably well with the present result, 63 kJ mol-1 (Figure 1). The product state comprises vinyl and a coadsorbed H atom. At a formal coverage as high as 1/3, the coadsorption of an H atom further increases the actual coverage to 2/3. The repulsive interactions between coadsorbates significantly raise the total energy of the product state. This becomes evident if one calculates the reaction energy assuming “infinitely separated” vinyl and hydrogen, each at coverage 1/3. (For that purpose, reaction energies are calculated from gasphase reaction energies and individual adsorption energies.) In that case the reaction is only 23 kJ mol-1 endothermic. Thus, the effect of coadsorption at this coverage is as large as 40 kJ mol-1! Vinyl Hydrogenation to Ethylidene. As already noted, in the reactant state, vinyl is bound in a η1η2 mode above a threefold fcc site. The attacking atomic hydrogen was placed at a neighboring threefold site, in front of the C atom of the CH2 group (Figure 2). Thus, the initial state of elementary reaction e (Scheme 1) differs from the final state of reaction a (Scheme 1) by the position of the coadsorbed H atom. However, these two states were calculated isoenergetic, and the high mobility
J. Phys. Chem. C, Vol. 113, No. 6, 2009 2517 of H on the surface, referred to above, allows one to skip the H migration step in our three-step mechanism and to assume fast diffusion. The product of hydrogenation, ethylidene, was found to preferentially bind to a bridge site.15c In the three-center TS2 (Figure 2), bonds C-Pd and H-Pd are being broken, while the C-H bond is being created. The H-Pd distance decreases from 181 pm in the reactant to 171 pm in TS2, as the H atom moves over a top site toward the C atom. The C-Pd distance in TS2, 224 pm, is 13 pm longer than the corresponding bond of the reacting vinyl species, whereas the C-H distance decreases to 158 pm, indicating an incipient bonding interaction. The C-C bond slightly elongates during the reaction, from 144 pm in the surface-bound vinyl to 150 pm in ethylidene (Table 2). Vinyl hydrogenation at coverage 1/3 features an activation barrier of only 52 kJ mol-1 (Figure 1), 32 kJ mol-1 below the value previously determined.15c We calculated the reaction to be exothermic by 31 kJ mol-1, 14 kJ mol-1 beyond the previous result (Figure 1).15c Our values for the two hydrogenation barriers of vinyl, back to ethylene (54 kJ mol-1) and forward to ethylidene (52 kJ mol-1), are very similar, manifesting that vinyl intermediates on Pd(111) can indeed transform to ethylidene and subsequently to ethylidyne. This is in contrast to the situation on Pt(111) where vinyl preferentially reacts back to ethylene according to the experiments of Zaera et al.29 Dehydrogenation of Ethylidene to Ethylidyne. The initial state of the third elementary step (reaction d, Scheme 1) coincides with the final state of reaction e (Scheme 1). At the beginning of the reaction, the C atom of the CH group is displaced toward the threefold hollow site. At the same time the CH3 group moves upward, so that the C-C axis bends toward the surface normal. The dissociating H atom of the CH group starts to interact with the two Pd atoms of the bridge site at which ethylidene is initially bound. This, in turn, weakens the C-H bond as shown by its elongation from 111 pm in the reactant state to 136 pm in TS3 (Table 2, Figure 2). Different from TS1 and TS2, where the reacting H atom migrates over a top site, in TS3 the dissociating H atom passes through a bridgebound state with two H-Pd distances at 182 and 201 pm, and ends up at a neighboring fcc site. In the product state, both the ethylidyne moiety and the coadsorbed H atom occupy adjacent threefold fcc hollow sites. The activation barrier calculated for ethylidene dehydrogenation at 1/3 coverage is as low as 28 kJ mol-1! This should be contrasted with the value of 75 kJ mol-1 obtained in the previous theoretical work.15c The TS3 structure reported therein, although qualitatively similar to ours, differs notably in critical distances. In particular, the C-H distance of the dissociating hydrogen is 13 pm longer, and one of the H-Pd distances, 200 pm, is 14 pm shorter;15c this may be due to a loose convergence threshold for the forces; see above. The low barrier for this last transformation is particularly remarkable. It allows us to conclude that the dehydrogenation of ethylidene should be fast and irreversible. The reaction is exothermic by 45 kJ mol-1. On Pt(111) ethylidene can readily transform to ethylidyne already at 150 K.46 Our results predict a similarly facile reaction on Pd(111). CoWerage-Dependent Reaction Mechanism. Figure 3 compares the reaction energy profiles as calculated for the conversion of ethylene to ethylidyne over Pd(111) for three different coverages. Not unexpectedly, the overall reaction, sketched above in terms of a three-step mechanism, is determined to be exothermic. Even at the high surface coverage of 1/3, the overall process is 13 kJ mol-1 exothermic. In the limit of low coverage
2518 J. Phys. Chem. C, Vol. 113, No. 6, 2009
Figure 3. Reaction energy profile (kJ mol-1) of ethylene conversion to ethylidyne over Pd(111) at various coverages: (a) 1/3, (b) 1/4, and (c) 1/9. Energies are calculated with respect to ethylene in the gas phase and clean Pd(111); atomic hydrogen is coadsorbed (see text).
(θ ) 1/9), the product side is favored by 37 kJ mol-1, whereas at the intermediate coverage (θ ) 1/4) the reaction is exothermic by 22 kJ mol-1. The less exothermic reaction at high coverage can be rationalized by repulsive lateral interactions of coadsorbed ethylidyne and hydrogen species in the product state. Because each of these fragments occupies a separate surface site, the formal coverage 1/3 translates into an actual coverage of 2/3 on the product side. For that situation, the repulsive interaction between coadsorbed ethylidyne and H amounts to 30 kJ mol-1. At lower coverages of 1/4 and 1/9, the energy of coadsorption also raises the product state, but only by 15 and 6 kJ mol-1, respectively (Table 2). At lower coverages, empty sites are available for hydrogen diffusion away from ethylidyne; hence, it is probably more correct to refer to the reaction energy calculated in the limit of infinitely separated coadsorbates (see above). In this scenario, the overall transformation of ethylene to ethylidyne is calculated exothermic by 43 kJ mol-1 for 1/3 and 1/9 coverages. Note that at high coverages some hydrogen and a significant fraction of ethylene (unless the surface is exposed to high pressures of C2H4) are expected to desorb from the surface, thus freeing up some space and bringing the energy of the products further down. When adsorbed on Pd particles at coverages ∼8%, ethylene was measured64 to liberate 145 kJ mol-1 of heat; this large release of energy was attributed to the formation of ethylidyne. In fact, this value agrees quite well with the overall heat of reaction, -133 kJ mol-1 at θ ) 1/9, as calculated in our work relative to ethylene in the gas phase (Table 2). From Figure 3 one notes that the overall reaction energy profile changes quite smoothly with increasing surface coverage. Relative energies of all intermediates and transition states increase with increasing coverage (due to repulsive lateral interactions between coadsorbed species), and the results for the intermediate coverage of 1/4 are always bracketed by those at 1/3 and 1/9 coverages. Hence, we refrained from calculating transition states at 1/4 coverage because they can be expected to fall inside the intervals given by the results for the lowest and the highest coverage considered. As initially thought for the reaction on Pt(111),29 the first elementary step, ethylene dehydrogenation to vinyl, is likely rate-limiting because the associated barrier is calculated to be significantly higher than those for the second and third steps. This first barrier amounts to 117 kJ mol-1 at 1/3 surface coverage and drops down to 100 kJ mol-1 at 1/9 coverage. TS1 is of fairly late character, hence more crowded at higher coverages, consistent with the coverage dependence of the calculated barrier. At 1/3 coverage, the barrier for ethylene
Moskaleva et al. desorption, 71 kJ mol-1 (Figure 3), is significantly lower than the barrier of dehydrogenation, but at 1/9 coverage both barriers become comparable, 90 and 100 kJ mol-1, respectively. This may rationalize why strongly dosed ethylene on Pd(111) at low temperatures desorbed completely upon heating to 450 K,8 whereas formation of ethylidyne was observed if the surface was exposed to 100 L ethylene at 300 K.8 In the latter case, dehydrogenation of ethylene competed with its desorption, and thermodynamically more favorable ethylidyne was thus formed up to the saturation coverage of 1/3. To explore the coverages of ethylene that might be expected for various experimentally relevant values of pressure and temperature, we constructed Langmuir isotherms on the basis of thermodynamic parameters calculated in this work (see the Supporting Information). We predict at 100 K the saturation coverage of ethylene to be already reached at pressures as low as 10-9 torr, whereas at 300 K the coverage is below 50% of saturation at pressures below 4 torr. However, one should treat these plots with due caution, considering that the intrinsic accuracy of theoretical binding energies is 20-30 kJ mol-1, 65and the resulting uncertainty of the equilibrium constant of adsorption is up to 4 orders of magnitude at 300 K. On Pt(111), vinyl as intermediate was discounted as possible precursor of the formation of ethylidyne because of the lower barrier for its back-reaction to adsorbed ethylene.29 At both coverages, 1/3 and 1/9, we determined the two reactions of vinyl, forward and backward, to have barriers of about equal heights. Thus, on Pd(111) at coverages lower than 1/9, ethylidene can be expected to be formed from vinyl despite the slight endothermicity of this process. The last barrier, for the dehydrogenation of ethylidene to ethylidyne, is very low, and the elementary reaction is exothermic by 45-69 kJ mol-1; hence, newly formed ethylidene species are expected to react immediately to ethylidyne, thus shifting the equilibrium of the preceding two steps to the right. A Comment on AlternatiWe Mechanisms. The three-step mechanism discussed above appears to be a conceivable scenario, and quite possibly it is the main one. However, other routes, such as the one via an ethyl intermediate, cannot be completely excluded. Both two-step mechanisms, a-b and c-d of Scheme 1, are unlikely because barriers for 1, 2 hydrogenshift (reactions b and c) are expected to be very high. Early theoretical studies suggested47,66 that 1, 2 hydrogen-shift reactions in adsorbed hydrocarbons have relatively high activation energies in comparison with hydrogenation and dehydrogenation reactions. Here, we calculated the activation barrier for the direct isomerization of adsorbed ethylene to ethylidene (reaction c in Scheme 1) to be ∼200 kJ mol-1 at 1/9 surface coverage, much higher than the rate-limiting barrier, 100-117 kJ mol-1, in the mechanism a-e-d presented above. 4. Conclusions Using a DFT method, we carried out a periodic slab-model study to reexamine the three-step mechanism for the conversion of ethylene to ethylidyne on Pd(111). This mechanism was initially proposed by Neurock et al.15c The present calculations were carried out at a more accurate level, and the results differ significantly from those previously reported.15c We characterized computationally both the thermodynamics and the kinetics of these elementary processes. On the basis of the calculated energetics, we showed that indeed the three-step mechanism via vinyl and ethylidene is a conceivable reaction pathway, which fits currently available experimental observations for this system. Calculations predict the highest activation
Ethylene Conversion to Ethylidyne over Pd(111) barrier, 100-117 kJ mol-1 depending on coverage, for the initial step, the dehydrogenation of ethylene to vinyl, where the lower value corresponds to the low coverage of 1/9. The present results are 34-51 kJ mol-1 lower than the published value.15c We also calculated significantly lower activation barriers for the second and especially the third step than the values reported previously.15c We found coverage effects important for the reaction under study. We predict that at high surface coverages the barrier for ethylene desorption is significantly below the barrier for dehydrogenation; thus, most of ethylene is expected to desorb rather than convert to ethylidyne until the coverage becomes low enough for the situation to change. With lower coverage, the barrier of ethylene desorption increases and becomes comparable to that of dehydrogenation to ethylidyne. In this respect, we note that the formation of ethylidyne was also found to slow down with increasing coverage in a related study on Pt(111), but there this effect was differently rationalized.46 The reaction mechanism on Pt(111) does not have to be the same as elaborated here for Pd(111), but it is natural to expect qualitatively similar energetics of adsorption on these two surfaces. Zaera and colleagues discounted vinyl as ethylidyne precursor on Pt(111) and favor the two-step mechanism via ethylidene as intermediate.31 On the basis of the present work, one would expect a very high barrier for this first isomerization step. Therefore, further experimental and theoretical studies seem due to resolve this longstanding question. Finally, a general reminder in view of the idealized computational models used in all studies discussed above: Catalytic reactions are known to occur preferentially at defects of surfaces, such as step-edge sites.67 Thus, in connection to practically used catalysts, such as Pd black, the results of the present model study on flat surfaces may need to be adjusted. Acknowledgment. We thank Prof. J. A. Lercher for stimulating discussions and Dr. A. Genest for very valuable assistance with the calculations. Z.-X.C. is grateful to the Alexander von Humboldt Foundation for funding a renewed research stay. This work was supported by Deutsche Forschungsgemeinschaft and Fonds der Chemischen Industrie (Germany). Supporting Information Available: Cartesian coordinates of the atoms in the optimized structures of Table 2, Langmuir adsorption isotherms of ethylene on Pd(111). This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Chemisorption and Reactivity on Supported Clusters and Thin Films. Lambert, R. M., Pacchioni, G., Eds.; NATO AdVanced Study Institute, Series E, Vol. 331; Kluwer Publishing: Dordrecht, 1997. (2) Ge, Q.; Kose, R.; King, D. A. AdV. Catal. 2000, 43, 207. (3) Neyman, K. M.; Lim, K. H.; Chen, Z.-X.; Moskaleva, L. V.; Bayer, A.; Reindl, A.; Borgmann, D.; Denecke, R.; Steinru¨ck, H.-P.; Ro¨sch, N. Phys. Chem. Chem. Phys. 2007, 9, 3470. (4) Yudanov, I. V.; Matveev, A. V.; Neyman, K. M.; Ro¨sch, N. J. Am. Chem. Soc., in press. (5) (a) Kaltchev, M.; Thompson, A. W.; Tysoe, W. T. Surf. Sci. 1997, 391, 145. (b) Stacchiola, D.; Azad, S.; Burkholder, L.; Tysoe, W. T. J. Phys. Chem. B. 2001, 105, 11233. (c) Stacchiola, D.; Burkholder, L.; Tysoe, W. T. Surf. Sci. 2002, 511, 215. (d) Zheng, T.; Stacchiola, D.; Poon, H. C.; Saldin, D. K.; Tysoe, W. T. Surf. Sci. 2004, 564, 71. (6) Shaikhutdinov, S.; Frank, M.; Ba¨umer, M.; Jackson, S. D.; Oldman, R. J.; Hemminger, J. C.; Freund, H. J. Catal. Lett. 2002, 80, 115. (7) Ofner, H.; Zaera, F. J. Am. Chem. Soc. 2002, 124, 10982. (8) Sock, M.; Eichler, A.; Surnev, S.; Andersen, J. N.; Klo¨tzer, B.; Hayek, K.; Ramsey, M. G.; Netzer, F. P. Surf. Sci. 2003, 545, 122. (9) (a) Vang, R. T.; Honkala, K.; Dahl, S.; Vestergaard, E. K.; Schnadt, J.; Lægsgaard, E.; Clausen, B. S.; Nørskov, J. K.; Besenbacher, F. Nat.
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