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Mechanism of the Ethylene Conversion to Ethylidyne on Rh(111): A Density Functional Investigation Ming Li,† Wenyue Guo,*,† Ruibin Jiang,† Lianming Zhao,† Xiaoqing Lu,§ Houyu Zhu,† Dianling Fu,† and Honghong Shan*,‡ College of Physics Science and Technology, China UniVersity of Petroleum, Dongying, Shandong 257061, P.R. China, State Key Laboratory for HeaVy Oil Processing, China UniVersity of Petroleum, Dongying, Shandong 257061, P.R. China, and Department of Physics and Materials Science, City UniVersity of Hong Kong, Hong Kong SAR, People’s Republic of China ReceiVed: February 1, 2010; ReVised Manuscript ReceiVed: March 9, 2010
The conversion of ethylene to ethylidyne on Rh(111) is examined using self-consistent periodic density function theory. The adsorptions of the reactants, intermediates, and products involved as well as the thermodynamics and kinetics of the conversion are characterized. Ethylene could form two adsorption configurations designated as di-σ and π adsorptions on Rh(111); ethyl, vinyl, vinylidene, ethylidyne, and ethylidene prefer the saturated sp3 configuration of both carbon atoms with the lost H atoms replaced by the metal atoms. The three-step conversion path on Rh(111), i.e., ethylene f vinyl f vinylidene f ethylidyne, is the most feasible, in which the vinylidene hydrogenation is the rate-limiting step. The pathway through ethylidene intermediate, ethylene f vinyl f ethylidene f ethylidyne, is impractical because it has a conversion rate at least 104 times lower than the most favorable path at the real reaction conditions. The mechanism via ethyl intermediate, ethylene f ethyl f ethylidene f ethylidyne, is impossible because of the high dehydrogenation barrier of ethyl to ethylidene as well as the low barriers for the conversions of ethyl to ethane and/or ethylene. Conversion involving direct isomerizations is also unlikely to be important due to the very high energy barriers involved. 1. Introduction Ethylene is an important intermediate in many industrially relevant processes like acetylene hydrogenation and functionalized olefins (e.g., vinyl acetate) synthesis.1 Understanding the chemistry of ethylene on transition metal surfaces has attracted much attention because it presents a prototype to study many aspects related to the reactivity of olefins and serves as a benchmark for the study of more complex reactions involving higher alkenes and aromatics. In fact, ethylene on metal surfaces could result in various processes like hydrogenation, decomposition, and polymerization; the selectivity for each of these processes depends on not only the nature of the metals but also the working conditions.2-4 Adsorption properties of ethylene over single-crystal metal surfaces and oxide-supported metal particles have been extensively studied both experimentally5-10 and theoretically.11-13 The thermal activation of ethylene at room temperature has been reported to yield the thermodynamically more stable ethylidyne, CH3C, on a large number of metal surfaces, including Pt(111),4 Pd(111),14 Rh(111),15 Rh(100),16 Ir(111),17 and Ru(0001).18 The analogous formation of larger alkylidynes from alkenes has also been reported.19 In this paper, we are primarily interested in the ethylene-to-ethylidyne conversion on Rh(111) because the supported Rh catalysts that show good performances in alcohol steam reforming reactions suffer from coke deposition induced by the ethylene byproducts,20 and alkylidyne has been suggested * Corrsponding authors. E-mail:
[email protected] and shanhh@ upc.edu.cn. Telephone: 86-546-839-6634. Fax: 86-546-839-7511. † College of Physics Science and Technology, China University of Petroleum. ‡ State Key Laboratory for Heavy Oil Processing, China University of Petroleum. § City University of Hong Kong.
as the precursor of C-C bond-breaking which releases CHx fragments at high temperatures during industrially important catalytic reforming processes.21 On Rh(111), experiments showed that ethylene is adsorbed molecularly at low temperatures, and the CdC bond is significantly weakened by the donation and back-donation of electrons between the ethylene π and π* orbitals and the surface metals.22 Tight binding approach predicted that ethylene binds at 2-fold bridge site with the CdC bond parallel to a Rh-Rh bond on clean Rh(111).23 At high temperatures, ethylene dehydrogenates into ethylidyne and efforts have been made to determine the adsorption structure of ethylidyne.24,25 In contrast to the structural studies, the knowledge of the ethylene conversion mechanism is still far away. The ethyl intermediate was first proposed by Somorjai et al. in the ethylene-to-ethylidyne conversion on the basis of the calculated activation energies for several possible mechanisms on Pt(111) and Rh(111).26 However, experimental evidence for ethyl decomposition was in direct contrast to this proposal since ethyl would dehydrogenate to ethylene rather than ethylidene on Pt(111).27 The formation of vinyl intermediate during the ethylene-to-ethylidyne conversion was first suggested on the basis of the temperature programmed desorption (TPD) results of CD2CDH on Pt(111).28 The strongest evidence for the vinyl intermediate on Rh(111) comes from a temperature programmed static secondary ion mass spectrometry (TPSSIMS) study of the ethylene-to-ethylidyne conversion;29 self-hydrogenation of ethylene was excluded.30 Despite these investigations, the mechanism of ethyleneto-ethylidyne conversion on Rh(111) is still not unambiguously elucidated. First-principles calculations utilizing slab models are often successful in assessing relative barrier heights of elementary steps and identifying plausible reaction pathways. However, to
10.1021/jp100970c 2010 American Chemical Society Published on Web 04/14/2010
Ethylene Conversion to Ethylidyne
Figure 1. Network for the conversion of ethylene to ethylidyne on the Pt-group metals proposed in ref 29. The elementary reactions steps contain hydrogenation (H), isomerization (I), and dehydrogenation (D).
our knowledge, there are no any theoretical works related to the ethylene-to-ethylidyne conversion on single Rh(111) surface. In this paper, we present a complete periodic density functional theory (DFT) investigation of the ethylene-to-ethylidyne conversion via dehydrogenation, hydrogenation, and isomerization on Rh(111). The conversion network is shown in Figure 1.29 2. Computational Details The calculations were performed in the framework of DFT with the program package DMol3 in Materials Studio of Accelrys Inc.31-33 using the generalized gradient approximation (GGA) in the form of exchange-correlation functional PW91.34,35 To take the relativity effect into account, the density functional semicore pseudopotential (DSPP)36 method was employed for the Rh atoms, whereas the carbon and hydrogen atoms were treated with an all-electron basis set. The valence electron functions were expanded into a set of numerical atomic orbitals by a double-numerical basis with polarization functions (DNP). A Fermi smearing of 0.005 hartree and a real-space cutoff of 4.5 Å were used to improve the computational performance. All computations were performed with spin-polarization. The low coveraged Rh(111) surface was modeled with a three-layer slab with four rhodium atoms per layer representing a p(2 × 2) unit cell, and a (3 × 3)R30° three-layer slab unit cell was used to model the relatively high surface coverage where is needed; a vacuum region of 12 Å thickness was used to separate the surface from its periodic image in the direction along the surface normal. A single adsorbate was allowed to adsorb on one side of the unit cells, corresponding to the surface coverages of 1/4 and 1/3 ML. The reciprocal space was sampled with a (6 × 6 × 1) k-point grid generated automatically using the Monkhorst-Pack method.37 Full-geometry optimization was performed for all relevant adsorbates and the uppermost two layers without symmetry restriction, while the bottom layer Rh atoms were fixed at the bulk-truncated positions at the experimentally determined lattice constant of 3.804 Å. The tolerances of energy, gradient, and displacement convergence were 1 × 10-5 hartree, 2 × 10-3 hartree/Å, and 5 × 10-3 Å, respectively. The adsorption energy ∆Eads of an adsorbate on Rh(111) was calculated using the equation
∆Eads ) Eads + ERh(111) - Eads/Rh(111) where Eads is the total energy of the adsorbate, ERh(111) is the total energy of the clean Rh(111) slab, and Eads/Rh(111) is the total energy of the adsorbate on Rh(111). By this definition, a positive ∆Eads implies a stable adsorption. Transition state (TS) searches were performed at the same theoretical level with the complete LST/QST method.38 In this method, the linear synchronous transit (LST) maximization was performed, followed by an energy minimization in directions
J. Phys. Chem. C, Vol. 114, No. 18, 2010 8441 conjugating to the reaction pathway to obtain an approximated TS. The approximated TS was used to perform quadratic synchronous transit (QST) maximization and then another conjugated gradient minimization was performed. The cycle was repeated until a stationary point was located. Each TS structure was characterized by a vibrational analysis with exactly one imaginary frequency. The reaction energy (∆H) and energy barrier (Ea) of a step on Rh(111) were calculated based on the following formulas:
∆H ) EFS - EIS and
Ea ) ETS - EIS where EIS, ETS, and EFS are the total energies of the initial state (IS), TS, and final state (FS), respectively. Rate constant k and pre-exponential A0 were estimated using conventional transition state theory39
k)
kBT q* -Ea/RT 0 ) A0e-Ea/RT e h q
where kB is the Boltzmann constant, R is the gas constant, h is the Planck’s constant, and E0a and Ea are activation energies with and without zero-point-energy (ZPE) corrections. T is temperature, which was selected as 190 and 300 K, corresponding to the conversion temperature of vinyl to ethylidyne29 and the initial temperature of ethylidyne decomposition,30 respectively. q and q* are the partition functions at the IS and TS, respectively. At a given temperature T, the pre-exponential factor A0 was determined by partition functions of adsorbed species containing neither translation nor rotation contributions, and the electronic contribution was unity as the electronic energy level difference is usually on the order of 1 eV.40 The remaining vibrational contributions were calculated in harmonic approximation.40 3. Results In this section, we discuss the adsorption of various intermediates involved in the ethylene-to-ethylidyne conversion; then we focus on the TS structure, activation barrier, and reaction energy of each elementary step to gather a general view of the conversion. 3.1. Adsorbed Intermediates. As shown in Figure 1, the conversion of ethylene to ethylidyne may involve C-H bondforming (hydrogenation), C-H bond-breaking (dehydrogenation), and 1,2-H shift (isomerization) steps through various intermediates of C2Hx. Here, we focus on the adsorption of all the possible intermediates. Table 1 presents energies and configurations for the adsorptions of ethylene and its derivates on Rh(111); and the optimized structures are shown in Figure 2. Ethylene. Consistent with the previous studies,41 we find that ethylene could bind to Rh(111) via two different modes designated as di-σ and π adsorptions (see Figure 2). In the di-σ mode, both C atoms of ethylene are substantially rehybridized (sp2 f sp3) via forming σ bonds with adjacent metal atoms in the η1η1 fashion at bridge site, whereas in the π adsorption the adsorbate coordinates to only one metal atom via a π donor bond at top site. The adsorption energies are calculated to be 0.97 (di-σ) and 0.95 (π) eV. The optimized C-C bond lengths are 1.45 (di-σ) and 1.40 (π) Å, or 0.13 and 0.08 Å stretched
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TABLE 1: Adsorption Sites, Adsorption Configurations, Adsorption Energies (eV), and Structural Parameters (Å and °) for Intermediates Involved in the Conversion of Ethylene to Ethylidyne on Rh(111) species
site
CH2CH2* top bridge CH3C* fcc hcp CH2CH* top fcc hcp CH2C* fcc hcp CH3CH* bridge CH3CH2* top CH3CH3* bridge H* top bridge fcc hcp
mode ∆Eads π di-σ η3 η3 η1 η1 η2 η1 η2 η 1 η3 η1 η3 η2 η1 η1 η2 η3 η3
0.95 0.97 5.52 5.67 2.43 2.88 2.95 4.22 4.32 4.20 1.73 0.31 2.55 2.74 2.79 2.77
dCRh 2.17, 2.13, 1.98, 1.99, 1.98 2.11; 2.09; 2.25; 2.28; 2.03, 2.08 3.51,
2.17 2.13 2.01, 2.01 1.99, 1.99
dCC anglesa
1.40 1.45 1.47 1.47 1.33 2.06, 2.06 1.45 2.05, 2.07 1.44 1.92, 2.03, 2.12 1.38 1.97, 1.97, 2.08 1.38 2.03 1.49 1.50 3.57 1.50
90 90 3 2 55 74 74 49 46 26 61 89
a Values are angles between the surface normal and the C-C axis in the corresponding species.
from the gas-phase value (1.32 Å), consistent with the previous HREELS results.26 Ethylidyne. Ethylidyne is a stable surface species formed at around room temperature on the hexagonally close-packed surfaces of the group VIII 4d and 5d transition metals. The structure of ethylidyne has been extensively studied on the (111) surfaces of Pt,42,43 Rh,24,25,44,45 Pd,46,47 Ir,17 and Ru(0001)48 and has been characterized as the upright adsorption at 3-fold sites. Our calculations confirm the configurations on Rh(111) with the binding energies of 5.67 (hcp) and 5.52 (fcc) eV (see Figure 2), in agreement with the UBI-QEP value (5.46 eV).49 The C-C bond is tilted by 2° with the length of 1.47 Å, consistent with the values of 2.5° and 1.48 ( 0.04 Å determined in the LEED experiment.25 Vinyl. According to our calculations, vinyl prefers to adsorb directly over the 3-fold sites on Rh(111) in the parallel η1η2 fashion entailing the sp3 configuration at each C atom (see Figure 2). The calculated binding energies are 2.95 and 2.88 eV for the hcp and fcc adsorptions, respectively. In the hcp adsorption, the C-C bond length is 1.44 Å or 0.14 Å elongated from the gas-phase value (1.30 Å). Also, we find that vinyl forms the ethylene-type structure and gains the energy of 2.43 eV at top site, the C-C bond (d ) 1.33 Å) is 55° tilted from the surface normal (see Figure 2). Vinylidene. As shown in Figure 2, vinylidene on Rh(111) prefers the η1η3 mode at 3-fold sites to complete its valence configuration at each C atom. The adsorption energies are calculated to be 4.32 (hcp) and 4.22 (fcc) eV. In the hcp adsorption, the respective C-Rh bonds are 2.28 Å long in the η1 end and 1.97, 1.97, and 2.08 Å long in the η3 end; the C-C bond is 0.09 Å stretched from the gas-phase bond (1.29 Å), and it is notably tilted (by 46°) allowing the overlap of the molecular π with the metal d orbitals as well as favoring the η1-σ and η3-σ bonds. Ethylidene. It can be imagined that ethylidene prefers bridge site to satisfy the valence requirement of the sp3-hybridized C center. This point is validated by our calculations. As shown in Figure 2, the C-C bond of the adsorbed ethylidene is tilted by 26° from the surface normal with the length of 1.49 Å, and the two C-Rh bond lengths are determined to be 2.03 Å. The calculated binding energy (4.20 eV) is consistent with the UBIQEP value (4.08 eV).49
Ethyl. Ethyl prefers the top adsorption, in which, in order to form the ethane-like configuration, a surface metal atom replaces the lost hydrogen atom in the radical at the C-Rh distance of 2.08 Å (see Figure 2). The binding energy is calculated to be 1.73 eV, consistent with the value of methyl on Rh(111) (1.84 eV).50 Ethane. Ethane prefers parallel adsorption at bridge site on Rh(111) (see Figure 2). The binding energy is calculated to be 0.31 eV, in good agreement with the previous theoretical result (0.30 eV).49 This relatively weak adsorption is consistent with the large C-Rh distance (3.51 and 3.57 Å), suggesting the facility for ethane desorption. Atomic Hydrogen. The H atom prefers the highly coordinated 3-fold sites, consistent with the previous experimental and theoretical results.51,52 The binding energies are calculated to be 2.79 (fcc) and 2.77 (hcp) eV. Further investigation of other adsorption sites shows no obvious change in the binding energies (2.55 (top) and 2.74 (bridge) eV), indicating the significant mobility of the adsorbed H,53 favoring the hydrogenation and dehydrogenation of intermediates on the surface. 3.2. Pathways for Ethylene to Ethylidyne Conversion. In this section, we present the structural and energetic details of the reaction profiles given in Figure 1. The corresponding reaction paths comprise various elementary steps of dehydrogenation, hydrogenation, and isomerization. Configurations of the TS’s involved in the elementary steps are shown in Figure 3. Table 2 lists the calculated thermodynamic and kinetic parameters for all the steps together with the rate constants at 190 and 300 K for some competitive steps. 3.2.1. ConWersion Wia Initial Isomerization. This pathway involves isomerization of ethylene to ethylidene and subsequent methylidyne H abstraction to form ethylidyne. In the first step, both the adsorption modes of ethylene are taken as the initial states (ISs), and the final state (FS) is taken to be the bridge adsorbed ethylidene. For the di-σ ethylene, the H migration starts with torsion of both methylenes. In TS1-1a (see Figure 3), the C-C bond length decreases to 1.43 Å (1.45 Å in the IS); and the breaking C-H bond is elongated to 1.30 Å. Although this process is only 0.14 eV endothermic, the energy barrier is calculated to be as high as 2.15 eV. Similarly, TS1-1b for the isomerization from the π bound ethylene also has the relative torsion of the methylene groups and the stretching of the C-H bond; this process also accounts for a high energy barrier (2.27 eV) and a low reaction energy (0.11 eV). The high activation barriers of these two isomerization paths can be explained by the fact that the shifting H at the TSs does not touch the surface, i.e., the reactions are not surface mediated. Note that analogous TS structures have also been found for ethylene isomerization on Pd(111),54 Fe(100),55 and Pt(110).56 For the dehydrogenation of ethylidene, the turn of the C-C axis of the bridge adsorbed ethylidene toward the surface normal lowers the HR atom sufficiently such that it could interact with adjacent Rh atom. In TS1-2 (see Figure 3), the C-HR bond is weakened and nearly ruptured as reflected by its length (1.52 Å), the C atom sits at the 3-fold fcc site and the HR atom at the adjacent top site. This process is expected to be almost spontaneous due to the very low barrier (0.11 eV) and the high exothermicity (0.66 eV). Obviously, in spite of the very low barrier of the dehydrogenation step, the very high barriers for the first step suggest conversion via initial isomerization is unlikely to be important. 3.2.2. ConWersion Wia Initial Dehydrogenation. Dehydrogenation of Ethylene to Vinyl. On Rh(111), ethylene dehydrogenation was believed to start with the di-σ adsorption.30 Indeed, the di-σ adsorption of ethylene is slightly more stable than the
Ethylene Conversion to Ethylidyne
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Figure 2. Most stable adsorption configurations of intermediates involved in the ethylene-to-ethylidyne conversion on Rh(111).
π-adsorption. Therefore, we take the di-σ ethylene as the IS of the ethylene dehydrogenation. In the FS, the vinyl species is at its most stable state (hcp-η1η2), and the released H atom is placed at adjacent fcc site. Like the situation of Pd(111),57 the initial C-H bond scission proceeds via a three-center TS, C-Rh-H, in a concerted manner in which the C-H bond breaks and the H-Rh bond forms simultaneously. In TS2-1 (see Figure 3), the involved C atom sits at bridge site, sharing a Rh atom with the atomic H at top site; the C-H and Rh-H distances are 1.61 and 1.55 Å. This step is almost thermoneutral (0.02 eV endothermic) affording an energy barrier of 0.52 eV. Reactions of Vinyl to Ethylidyne. As shown in Figure 1, the vinyl species may transform to ethylidyne via three possible routes: direct isomerization, hydrogenation/dehydrogenation via ethylidene, and/or dehydrogenation/hydrogenation through vinylidene. In the following, we exam all of these possibilities one by one. (a) Isomerization Channel (Channel I). Vinyl isomerization to ethylidyne on Rh(111) experiences a rather high barrier (1.62 eV), though it is exothermic by 0.60 eV. This process involves the stretching vibration of the η1-C-Rh bond in the η1η2 adsorbed vinyl so that the methylidyne H could be close to the methylene C, which is also not metal mediated. Correspondingly, in TS2-2a (see Figure 3), the C-C bond shortened by 0.03 Å is tilted by 40° compared to 74° in the IS; the breaking C-H bond is elongated to 1.26 Å (1.08 Å in the IS) and the distance between the shifting H and the methylene C is 1.45 Å. These facts manifest a developing bonding interaction between the methylene C and the shifting H. (b) Hydrogenation/Dehydrogenation Channel (Channel II). For the hydrogenation step, we take the vinyl species at its favorable hcp site and the atomic H at the adjacent fcc site as the IS, and ethylidene at the bridge site as the FS. The hydrogenation of vinyl proceeds by a concerted breaking of both the metal-H and metal-C bonds and the formation of the C-H
bond. Again, a three-centered TS (TS2-2b; see Figure 3) is involved, in which, as the atomic H moves over the top site (dCH ) 1.56 Å), the H-Rh distance decreases to 1.58 Å from 1.83 Å (IS); the C-Rh distance (2.21 Å) stretches 0.1 Å from that in the IS. During the process, the C-C bond is elongated, from 1.44 Å in vinyl to 1.47 Å in ethylidene. This hydrogenation process is endothermic by 0.14 eV, and the relevant activation barrier is 0.59 eV. The subsequent dehydrogenation of ethylidene to ethylidyne has been discussed above. (c) Dehydrogenation/Hydrogenation Channel (Channel III). For the dehydrogenation of vinyl, we take the most favorable η1η2 vinyl over hcp site as the IS, and the coadsorbed vinylidene (hcp-η1η3) and H (at fcc site near the η3 end of vinylidene) as the FS. As shown in Figure 3, in TS2-2c, methylidyne H has been shifted to the adjacent top site with the C-H and Rh-H distances of 1.53 and 1.60 Å, respectively; the involved C atom sits at the 3-fold hollow site forming the third C-Rh bond, while the other C atom is uplifted. This step is exothermic by 0.26 eV with an activation barrier of 0.21 eV. For the hydrogenation of vinylidene, the IS is selected as vinylidene (η1η3) at hcp site and the atomic hydrogen at the fcc site adjacent to the methylene C of vinylidene. In TS2-2d (see Figure 3), the H atom is at the top site sharing the Rh atom with the methylene C and the C-H distance is decreased to 1.58 Å (2.71 Å in the IS), manifesting a developing bonding interaction; the methylene C-surface distance is 2.12 Å, changing slightly from the value in the IS (2.11 Å). This process is featured by the significant stretch of the C-C bond, from 1.38 Å in the IS to 1.42 Å in the TS and last to 1.47 Å in the FS. The activation barrier is calculated to be 0.66 eV, and the reaction energy is -0.30 eV. 3.2.3. ConWersion Wia Initial Hydrogenation. Hydrogenation of Ethylene to Ethyl. Recent experimental studies indicated that ethylene is π-adsorbed on hydrogen-precovered Rh(111),58 so π-adsorbed ethylene is believed to be the active species for
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Figure 3. Structures for transition states involved in the ethylene-to-ethylidyne conversion on Rh(111).
ethylene hydrogenation. Here, we investigated the hydrogenation pathways from both di-σ- and π-adsorbed ethylene. (a) Hydrogenation of Di-σ Ethylene. In this step, we take the coadsorbed di-σ ethylene and H (fcc) as the IS, and the top adsorbed ethyl as the FS. While moving toward the C end, the attacking atomic H passes through a bridge site, with the H-Rh bonds of 1.69 and 1.88 Å long in the TS (TS3-1a; see Figure 3). The barrier is calculated to be 0.63 eV, and the reaction energy is only 0.02 eV. The reverse reaction (ethyl dehydrogenation to di-σ ethylene) accounts for a nearly comparable barrier (0.61 eV). (b) Hydrogenation of π-Adsorbed Ethylene. This hydrogenation step proceeds via a four-center TS (TS3-1b) that involves C, H, and two Rh atoms, in which the atomic H sits at bridge site, bonding to two Rh atoms (dRhH ) 1.84 and 1.96 Å) and one C atom (dCH ) 1.33 Å); and the C-Rh bond is weakened for the formation of the four-center structure (dRhC ) 2.33 (TS) vs 2.17 (IS) Å). The activation barrier is calculated to be 0.57 eV, which is slightly lower than that of the di-σ ethylene hydrogenation. Also, the reverse reaction accounts for an energy barrier of 0.59 eV. Dehydrogenation of Ethyl to Ethylidene. This C-H bond scission process involves a C-H bond activation by the Rh atom anchored by the methylene C, such that in the TS (TS3-2a), the involved C-H distance is elongated to 1.55 Å, and both the atomic H and ethylidene C share the Rh atom at the distances
of 1.66 and 1.95 Å, respectively. Then the atomic H moves toward the neighboring hollow site and the involved C end toward the bridge site forming the FS. The calculated energy barrier and reaction energy of this step are +0.92 and -0.18 eV. Further dehydrogenation of ethylidene to ethylidyne has been discussed above. Hydrogenation of Ethyl to Ethane. Further hydrogenation of ethyl affords ethane, which is only weakly physisorbed on the surface. In TS3-2b (see Figure 3), the atomic H is close to the CH2 group of ethyl at a off-top site forming a H-Rh bond of 1.58 Å; the C-Rh distance is 2.24 Å, 0.16 Å longer than it in IS, whereas the C-H distance decreases to 1.49 Å. The present calculation yields an activation barrier of 0.42 eV and a reaction energy of -0.24 eV for the ethyl hydrogenation. 4. Discussion As mentioned above, direct isomerizations of the C2Hx imtermediates on Rh(111) are always not surface mediated and are thus hindered by very high barriers; hence, the direct isomerization steps involving ethylene and vinyl as shown in Figure 1 can be excluded. In the following, we mainly discuss the mechanisms via initial hydrogenation and dehydrogenation, and the corresponding PESs are shown in Figures 4 and 5, respectively. Recent experimental studies reveled that ethylene is adsorbed in the π-adsorbed fashion on hydrogen-precovered Rh(111),58
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TABLE 2: Calculated Energy Barriers Ea (eV), Reaction Energies ∆H (eV), Pre-exponential Factors A0 (s-1), and Rate Constants k (s-1) for the Elementary Steps Involved in the Conversion of Ethylene to Ethylidyne on Rh(111)a 190 K reaction
Ea
∆H
300 K
A0
k
A0
k
2.78 × 1018
3.94 × 104
3.37 × 1016
5.71 × 107
6.69 × 1012
1.69 × 10-3
9.04 × 1012
1.20 × 103
-0.97 (-1.00)
CH2CH2 + * f CH2CH2* CH2CH2 f CH2CH +H
0.52 (0.68)
0.02 (0.14)
CH2CH2*(di-σ) f CH3CH*
2.15 (2.30)
0.14 (0.15)
CH2CH2*(π) f CH3CH*
2.27 (2.44)
0.11 (0.17)
CH2CH +H f CH3CH
0.59 (0.59)
0.14 (0.00)
CH2CH* f CH3C*
1.62 (1.78)
-0.60 (-0.62)
CH3CH* f CH3C*+H*
0.11 (0.27)
-0.66 (-0.53)
1.52 × 1017
1.71 × 1014
8.16 × 1015
1.11 × 1014
CH2CH* f CH2C*+H*
0.21 (0.32)
-0.26 (-0.19)
2.71 × 1015
7.39 × 109
3.54 × 1014
1.06 × 1011
CH2C*+H* f CH2CH*
0.49 (0.50)
0.28 (0.19)
1.36 × 1013
1.84
1.39 × 1013
9.84 × 104
CH2C*+H f CH3C*
0.66 (0.67)
-0.30 (-0.44)
4.88 × 10
7.03 × 10
12
5.03 × 101
CH2CH2*(di-σ)+H* f CH3CH2* ·
0.63 (0.71)
-0.02 (0.11)
3.13 × 1015
6.11 × 10-2
8.17 × 1014
2.14 × 104
CH2CH2*(π)+H* f CH3CH2* ·
0.57 (0.63)
-0.02 (-0.14)
2.78 × 1013
1.90 × 10-2
1.51 × 1013
3.76 × 103
CH3CH2 +H f CH3CH3
0.42 (0.44)
-0.24 (-0.37)
*
*
*
*
*
*
*
*
*
*
CH3CH2 f CH3CH +H · *
*
*
*
*
*b
CH2CH2 (di-σ)+H f CH3CH2 *
*
CH2CH2 (π)+H f CH3CH2
*·b
a
12
1.23 × 10
-5
0.92 (1.11)
-0.18 (0.00)
0.53 (0.59)
-0.16 (-0.27)
8.43 × 1013
6.49 × 10-1
5.33 × 1013
6.14 × 104
0.49 (0.54)
-0.12 (-0.22)
5.77 × 10
6.45 × 10
3.31 × 10
2.07 × 106
14
1
14
Values in parentheses are energies before zero-point-energy corrections. b Reactions at the higher coverage of 1/3 ML.
Figure 4. Energy profile for the initial hydrogenation mechanism involved in the ethylene conversion to ethylidyne over Rh(111). All energies (eV) are relative to the total energy of the gas-phase CH2CH2, the clean slab, and two adsorbed H atoms with ZPE corrections. 1, [CH2CH2 + H]* + H*; 2, CH3CH2* + H*; 3, CH3CH* + 2H*; 4, [CH3CH2 + H]*; 5, CH3CH3*. [A + B]* denotes the coadsorbed A and B, and A* + B* represents the respective adsorptions of A and B on two separated slabs.
and our results indicate that the hydrogenation barriers are comparable for the π- and di-σ ethylene (0.57 and 0.63 eV) at the low coverage of 1/4 ML, and the rate constant k of the di-σ ethylene hydrogenation is a little higher than that for the π-ethylene hydrogenation at the experimental reaction temperatures (see Table 2). Considering that under the real reaction conditions, the coverage of the coadsorbed ethylene and hydrogen is high, thus the hydrogenation barriers of the π- and di-σ ethylene are also calculated at the higher coverage of 1/3 ML. As shown in Table 2, at the higher coverage, although the hydrogenation barrier of π-ethylene is only 0.04 eV lower than
that of the di-σ ethylene, the rate constant k of the π-ethylene hydrogenation are almost 100 times higher than that of the di-σ ethylene hydrogenation at 190K, and even about 340 times higher at 300 K, in agreement with the experimental results that the hydrogenation of ethylene are mainly occurred through the π-ethylene mode.58 As shown in Figure 4, hydrogenation of π-ethylene to ethyl involves a reasonable energy barrier of 0.57 eV; however, ethyl dehydrogenation to ethylidene involves a rather high energy barrier (0.92 eV), which is 0.36 eV higher than the barrier for its hydrogenation to ethane. Moreover, the reverse reaction of ethylene
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Figure 5. Energy profile for the initial dehydrogenation mechanism involved in the ethylene to ethylidyne conversion over Rh(111). All energies (eV) are relative to the energy of the gas-phase ethylene plus the clean slab with ZPE corrections. 1, CH2CH2*; 2, [CH2CH + H]*; 3, CH2CH* + H*; 4, CH3CH*; 5, [CH3C + H]*; 6, CH3C* + H*; 7 [CH2C + H]* + H*. Other notations are the same as in Figure 4.
hydrogenation (ethyl dehydrogenation to ethylene) is expected to be also a competitive pathway to the ethyl dehydrogenation to ethylidene for its low barrier (0.59 eV). Therefore, we can conclude that surface ethyl would preferentially hydrogenate to ethane or dehydrogenate back to ethylene once formed, while dehydrogenation of ethyl to ethylidene should be difficult. This point is consistent with the experimental results that ethyl dehydrogenates to coadsorbed ethylene and hydrogen, and hydrogenation of ethylene leads to the desorption of ethane.27,58 For the initial dehydrogenation mechanism, as indicated above, ethylene first dehydrogenate to adsorbed vinyl with an energy barrier of 0.52 eV; the formed vinyl species would either hydrogenate back to ethylene or convert to ethylidyne through channels II and/or III, isomerization of vinyl to ethylidyne (channel I) can be abandoned for the rather high barrier (1.62 eV). As shown in Figure 5, channel II has a higher initial hydrogenation barrier but a lower dehydrogenation barrier; in contrast, channel III has a higher dehydrogenation barrier but a lower hydrogenation barrier. In order to determine which one is preferable, rate constants k for all steps involved in channels II and III at 190 and 300 K are calculated (see Table 2). In the above-indicated mechanisms, the elementary steps on the surface are as follows: kII1
CH2CH* + H* 98 CH3CH* + * kII2
CH3CH* + * 98 CH3C* + H* kIII1
CH2CH* + * 798 CH2C* + H*
(II1)
(II2)
(III1)
k-III1 kIII2
CH2C* + H* 98 CH3C* + H*
(III2)
Here “*” represents a surface site. Reactions II1 and II2 are the elementary steps of channel II, and reactions III1 and III2
are for channel III. As shown in Table 2, at both temperatures of 190 and 300 K, step II1 is obviously the rate limiting step of channel II for it has a much lower rate constant (kII1) compared to that of step II2 (kII2); thus, the total reaction rate of channel II, r(II), can be expressed as:
r(II) ) kII1θCH2CHθH For channel III, the rate constants for forward and reverse reactions of step III1 (kIII1 and k-III1) are obviously both larger than that of step III2 (kIII2), leading to a swift equilibrium of step III1, so r(III) can be represented as
r(III) ) KIII1kIII2θCH2CHθ* Here, KIII1 is the relevant equilibrium constant obtained usingKIII1 ) kIII1/k-III1, and θX represents the surface coverage of adsorbate X. Thus at the temperature for vinyl conversion (190 K)29
r(III)/r(II) )
KIII1kIII2 θ* θ* ) 2.87 × 107 kII1 θH θH
and at the initial temperature of ethylidyne decomposition (300 K)30
r(III)/r(II) )
KIII1kIII2 θ* θ* ) 4.52 × 104 kII1 θH θH
Because θ* are much higher than θH at the beginning of the reaction, thus r(III) are much larger than r(II); as the reaction goes on, dehydrogenation leads to the increase of surface H coverage (θH) and the decrease of free sites; thus, r(III) declines and r(II) rises. However, considering under the hydrogenation condition θH/θ* was estimated to be between about 1 and 10,59
Ethylene Conversion to Ethylidyne and the adsorbed H would desorb with the increase of temperature, thus, even though r(III) declines, it is still larger than r(II) by at least 107 and 104 times at 190 and 300 K, respectively. So it is clear that the conversion of ethylene to ethylidyne on Rh(111) is mainly via the intermediate of vinylidene (channel III) with the vinylidene hydrogenation as the rate limiting step. This aspect is in good agreement with the experimental result that conversion of vinyl to ethylidyne is the rate limiting step;29 hydrogenation of vinylidene consumes the surface H atoms and releases free sites, which facilitates additional dehydrogenation of ethylene and allows the overall reaction to complete.29 We know that at low coverages the product species, particularly adatom H, are able to diffuse away from the reactant readily, whereas at high coverages, the inhibited or even blocked diffusions of surface H lower the availability of surface free sites for dehydrogenation, and the desorption of H facilitated by the increased lateral interactions lowers the coverage of adsorbed H atoms for hydrogenation. These two factors lower the reaction rate because of the ensemble requirement for the reaction.29,30 A quantitative determination of the reaction rate may be obtained by a complete kinetic modeling. The ethylene-to-ethylidyne conversion over both Pt(111) and Pd(111) have been theoretically investigated,57,60-63 and we can compare the present results of Rh(111) with these two systems. On Pt(111), DFT cluster calculations indicated that the conversion of vinyl to vinylidene is impossible because of the high energy uphill, whereas the pathways through isomerization of ethylene and vinyl are the most favorable from thermodynamics.60,61 On Pd(111), DFT slab calculations suggested both the mechanisms via ethylidene and vinylidene intermediates with the initial dehydrogenation of ethylene as the rate limiting step;57,62 kinetics experiments suggested the correctness of the pathway via the ethylidene intermediate.63 As discussed above, the conversion on Rh(111) mainly involves the route via the vinylidene intermediate with the hydrogenation of vinylidene as the rate-limiting step. 5. Conclusions Using the DFT method, we have carried out a periodic slabmodel study to examine the binding of C2Hx (x ) 2-6) species and the complete conversion mechanism of ethylene to ethylidyne on Rh(111). The adsorption modes and energies for ethylene, ethyl, vinyl, vinylidene, ethylidyne, ethylidene, and ethane have all been examined at the surface coverage of 0.25 ML. Ethylene could form two adsorption configurations designated as di-σ and π adsorptions with the binding energy of 0.97 and 0.95 eV, respectively. Ethyl, vinyl, vinylidene, ethylidyne, and ethylidene, with the binding energies of 1.73, 2.95, 4.32, 5.67, and 1.49 eV, respectively, prefer to adsorb in a saturated sp3 configuration of both C atoms with the lost H atoms replaced by the metals. The saturated molecules of ethane adsorbs weakly over Rh(111) with the adsorption energy of 0.31 eV. DFT calculations and kinetic analyses suggest that at low coverage the ethylene conversion to ethylidyne is through a three-step pathway, i.e., ethylene f vinyl f vinylidene f ethylidyne, with the vinylidene hydrogenation being the ratelimiting step. The pathway of ethylene f vinyl f ethylidene f ethylidyne is impractical with a conversion rate at least 104 times lower. Conversion of ethylene to ethylidyne through initial hydrogenation seems unlikely for the high barrier of ethyl dehydrogenation to ethylidene as well as the low barriers for ethyl conversions to ethane and/or ethylene. The formation of ethylidyne through the direct isomerization path are unlikely to take place because all the isomerization processes are not surface mediated and thus hindered by very high energy barriers.
J. Phys. Chem. C, Vol. 114, No. 18, 2010 8447 Acknowledgment. This work was supported by the Program for Changjiang Scholars and Innovative Research Team in University (IRT0759) of MOE, PRC, NSFC (20476061 and 10979077), State Key Basic Research Program of China (2006CB202505), CNPC Science & Technology Innovation Foundation (2009D-5006-04-07), and Independent Innovation Program of China University of Petroleum (09CX05002A). References and Notes (1) Stacchiola, D.; Calaza, F.; Burkholder, L.; Schwabacher, A. W.; Neurock, M.; Tysoe, W. T. Angew. Chem., Int. Ed. 2005, 44, 4572. (2) Segura, Y.; Lo´pez, N.; Ramı´rez, J. P. J. Catal. 2007, 247, 383. (3) Stacchiola, D.; Azad, S.; Burkholder, L.; Tysoe, W. T. J. Phys. Chem. B 2001, 105, 11233. (4) Zaera, F.; Bernstein, N. J. Am. Chem. Soc. 1994, 116, 4881. ¨ fner, H.; Zaera, F. J. Am. Chem. Soc. 2002, 124, 10982. (5) O (6) Kaltchev, M.; Thompson, A. W.; Tysoe, W. T. Surf. Sci. 1997, 391, 145. (7) Stacchiola, D.; Burkholder, L.; Tysoe, W. T. Surf. Sci. 2002, 511, 215. (8) Sheppard, N.; De La Cruz, C. AdV. Catal. 1998, 42, 181. (9) Frank, M.; Baumer, M. Phys. Chem. Chem. Phys. 2000, 2, 3723. (10) Shaikhutdinov, S; Heemeier, M.; Lear, T.; Lennon, D.; Oldman, R. J.; Jackson, S. D.; Freund, H. J. J. Catal. 2001, 200, 330. (11) Filhol, J. S.; Simon, D.; Sautet, P. J. Phys. Chem. B 2003, 107, 1604. (12) Ge, Q.; Neurock, M. Chem. Phys. Lett. 2002, 358, 377. (13) Mei, D.; Sheth, P.; Neurock, M.; Smith, C. M. J. Catal. 2006, 242, 1. (14) Sock, M.; Eichler, A.; Surnev, S.; Andersen, J. N.; Kltzer, B; Hayek, K.; Ramsey, M. G.; Netzer, F. P. Surf. Sci. 2003, 545, 122. (15) Papageorgopoulos, D. C.; Ge, Q.; Nimmo, S.; King, D. A. J. Phys. Chem. B 1997, 101, 1999. (16) Nieskens, D. L. S.; Bavel, A. P.; Ferre, D. C.; Niemantsverdriet, J. W. J. Phys. Chem. B 2004, 108, 14541. (17) Marinova, T. S.; Kostov, K. L. Surf. Sci. 1987, 181, 573. (18) Barteau, M. A.; Broughton, J. Q.; Menzel, D. Appl. Surf. Sci. 1984, 19, 92. (19) Zaera, F.; Chrysostomou, D. Surf. Sci. 2000, 457, 71. (20) Haryanto, A.; Fernando, S.; Murali, N.; Adhikari, S. Energy Fuels 2005, 19, 2098. (21) Gates, J. A.; Kesmodel, L. L. Surf. Sci. 1983, 124, 68. (22) Bent, B. E.; Mate, C. M.; Kao, C. T; Slavin, A. J; Somorjai, G. A. J. Phys. Chem. 1988, 92, 4720. (23) Calhorda, M. J.; Lopes, P. E. M.; Friend, C. M. J. Mol. Catal. A: Chem. 1995, 97, 157. (24) Koestner, R. J.; Van Hove, M. A.; Somorjai, G. A. Surf. Sci. 1982, 121, 321. (25) Wander, A.; Van Hove, M. A.; Somorjai, G. A. Phys. ReV. Lett. 1991, 67, 626. (26) Somorjai, G. A.; Van Hove, M. A.; Bent, B. E. J. Phys. Chem. 1988, 92, 973. (27) Zaera, F. J. Phys. Chem. 1990, 94, 8350. (28) Zaera, F. J. Am. Chem. Soc. 1989, 111, 4240. (29) Borg, H. J.; Hardeveld, R. M.; Niemanteverdriet, J. W. J. Chem. Soc. Faraday Trans. 1995, 91, 3679. (30) Parageorgoulos, D. C.; Ge, Q.; King, D. A. Surf. Sci. 1998, 397, 13. (31) Delley, B. J. Chem. Phys. 1990, 92, 508. (32) Delley, B. J. Chem. Phys. 1996, 100, 6107. (33) Delley, B. J. Chem. Phys. 2000, 113, 7756. (34) Perdew, J. P.; Wang, Y. Phys. ReV. B. 1992, 45, 13244. (35) Perdew, J. P.; Wang, Y. Phys. ReV. B. 1986, 33, 8800. (36) Delley, B. Phys. ReV. B 2002, 66, 155125. (37) Monkhorst, H. J.; Pack, J. D. Phys. ReV. B 1976, 13, 5188. (38) Halgren, T. A.; Lipscomb, W. N. Chem. Phys. Lett. 1977, 49, 225. (39) Wynne-Jones, W. F. K.; Eying, H. J. Chem. Phys. 1935, 3, 492. (40) Hill, T. L. An introduction to Statistical Thermodynamics; Dover: New York, 1986. (41) Netzer, F. P.; Ramsey, M. G. Crit. ReV. Solid State Mater. Sci. 1992, 17, 397. (42) Starke, U.; Barbieri, A.; Materer, N.; Van Hove, M. A.; Somorjai, G. A. Surf. Sci. 1993, 286, 1. (43) Somorjai, G. A.; Van Hove, M. A.; Bent, B. E. J. Phys. Chem. 1988, 92, 973. (44) Dubois, L. H.; Castner, D. G.; Somorjai, G. A. J. Chem. Phys. 1980, 72, 5234. (45) Levis, R.; Winograd, N. J. Am. Chem. Soc. 1987, 109, 6873. (46) Gates, J. A.; Kesmodel, L. L. Surf. Sci. 1983, 124, 68.
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