Alkane Metathesis by Tantalum Metal Hydride on Ferrierite: A

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Alkane Metathesis by Tantalum Metal Hydride on Ferrierite: A Computational Study M. N. Mazar,† Saleh Al-Hashimi,‡ A. Bhan,*,† and M. Cococcioni*,† †

Department of Chemical Engineering and Materials Science, University of Minnesota, 421 Washington Avenue SE, Minneapolis, Minnesota 55455, United States ‡ Department of Chemical Engineering, The Petroleum Institute, P.O. Box 2533, Abu Dhabi, United Arab Emirates

bS Supporting Information ABSTRACT:

The full catalytic cycle for the self-metathesis of ethane was studied by density functional theory (DFT). The active site was a Tadihydride grafted on a Brønsted acid site [(tAlO)2Ta(H2)] of the internal pore surface of the FER zeolite. The transition state geometries and activation energies were determined through the nudged elastic band (NEB) method for each elementary step, and the complete cycle was found to be thermodynamically consistent. Investigated elementary steps include ethane C
H σ-bond activation, ethylene desorption through R and β hydrogen elimination mechanisms, Ta-ethylcarbene formation, olefin metathesis, and hydrogenation of olefin metathesis products. For the activation of ethane, as compared to catalytic systems involving zeolitesupported Ga and Zn, a low barrier (∼64 kJ mol
1) was observed. In the olefin metathesis step, where Ta-ethylcarbene reacts with ethylene, it was found that the Ta-metallacyclobutane has a relatively high stability (∼143 kJ mol
1) as compared to similar metallacyclobutane species and that the forward decomposition of the Ta-metallacyclobutane is the most energetically demanding step.

I. INTRODUCTION The efficient and selective manipulation of stable, and therefore inert, sp3-hybridized bonding states has been an outstanding problem for nearly 50 years.1 The activation of gas-phase alkanes is of particular interest because of their low value and relative abundance, but poses marked difficulty because all carbon centers are sp3 hybridized. Homogeneous catalysts, such as the Ir host
guest assembly2 and Shilov-type Pt,3 have been shown to perform selective C
H activation. However, these techniques are not practical because of low reaction rates and the use of expensive catalysts that get consumed over time.3
6 With the first step being alkane activation, alkane metathesis (AM) offers a methodology for performing the direct nonoxidative molecular redistribution of alkanes into higher homologues (i.e., liquid fuels). AM has been shown to occur through a three-step process involving alkane dehydrogenation, olefin metathesis, and olefin hydrogenation7,8 (Figure 1). Electron deprived transition metals (TM) are often used to perform AM because they tend to insert between carbon and hydrogen r 2011 American Chemical Society

Figure 1. Alkane metathesis via dehydrogenation to form olefins and carbenes, which subsequently undergo olefin metathesis and hydrogenation.

atoms, preferring the least-substituted carbon atom. In this configuration, 2 electrons are shared among molecular orbitals belonging to 3 atomic centers (3c-2e). The tendency to form this chemical bonding state facilitates C
H bond activation and dissociative adsorption, often resulting in TM-alkyls.9 This is Received: January 24, 2011 Revised: April 6, 2011 Published: May 03, 2011 10087

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Figure 2. Left: Full periodic FER system viewed along the 10-membered pore axis (darkened atoms held fixed according to the EMB-34T approach). Right: ISO-5T cluster atoms (Ta = gray, Al = pink, Si = blue, oxygen = red).

essential to AM because the desorption of alkyls gives linear olefins and the dehydrogenation of alkyls gives TM-carbenes, both of which are needed to perform the olefin metathesis step. Systems known to perform AM include tandem and single site catalysts in homogeneous and heterogeneous settings.8,10,11 Burnett and Hughes reported a heterogeneous tandem catalyst system consisting of a dehydrogenation/hydrogenation catalyst (Pt on alumina) and an olefin metathesis catalyst (W-oxide on silica).10 Flowing butane (cofed with low levels of hydrogen) at ∼400 °C produced mostly propane and pentane. In 2006, Goldman et al.8 reported a homogeneous tandem AM catalyst system consisting of pincer-Ir (dehydrogenation/ hydrogenation) and Schrock-Mo (olefin metathesis) complexes. In the presence of n-hexane, this system showed good selectivity toward higher homologues, such as n-decane. However, the olefin metathesis catalyst was reported to decompose at 125 °C. In the past decade, Basset et al. have performed AM by single site, mononuclear TM-hydrides on amorphous supports.11,12 Systems with Ta-hydride supported on silica7,11
13 have been reported to catalyze the self-metathesis of propane with 60 turnover number (TON) and 6% conversion (120 h at 150 °C).14 The same reaction in systems with W-hydride on alumina14,15 showed nearly double the TON and greater production of higher homologues. This effect was attributed by the authors to a 7% reduced selectivity to methane. In these systems, coordination and location of the most active TM-hydride remains unclear. The coordination of Ta atoms with respect to each other has been studied. Nemana and Gates16 have reported the presence of tri-Ta clusters through extended X-ray absorption fine structure (EXAFS) studies, citing a Ta
Ta distance that is representative of tri-Ta clusters (2.93 Å). Soignier, Basset, et al.17 have also reported EXAFS data, for Ta-hydride on mesoporous MCM-41, citing a Ta
Ta distance that is “incompatible” with Ta clusters (∼2.7 Å) and establishing that “most of the Ta-hydrides are present as mononuclear species” that have a 2-fold coordination with surface oxygen atoms. In another study of silicasupported Ta-hydride, Saggio et al.18 confirm this result. They also report that one-half of the available Ta-hydride sites do not participate in AM. The stability of metallacycles has also been probed as a function of location. Handzlik et al. investigate various Mo-metallacyclobutane species on select crystallographic planes of alumina.19 Tens of different metallacycle geometries, surface coordinations, and site locations were investigated, and the Mo-

Scheme 1. Reaction Intermediates and Gas-Phase Molecules Involved in the Self Metathesis of Ethane

metallacycles were observed to be 36
137 kJ mol
1 more stable than reactants, illustrating the wide variety of stabilities possible for these types of catalysts.19 Many outstanding issues for single-site AM catalysts remain, in particular, the catalytic role of the support as well as the nuclearity and coordination of the TM with the support. The present investigation aims to elucidate some of these questions by using a mononuclear Ta catalyst, with formal þ1 charge, on a welldefined crystalline support. Zeolites, a class of crystalline aluminosilicates, were chosen as the support. The microporous nature of these materials introduces confinement effects through noncovalent interactions, stabilizing adsorbed species.20 Furthermore, the high internal surface area provides a large set of welldefined, potential active sites. The siliceous ferrierite (FER) framework was chosen, and a Brønsted acid site was introduced through Al substitution at the intersection of the linear 8- and 10membered pores. Grafting of the mononuclear Ta-dihydride complex was accomplished through bonding of the Ta atom with two bridging oxygen atoms of the aluminum atom [tSi
O
Alt], creating two oxygen atoms with 3-fold coordination (Figure 2). On the basis of previous findings, a catalytic cycle for the self-metathesis of ethane was developed (Scheme 1).7,11
15 The formation of carbenes and olefins, and their subsequent coordination in the olefin metathesis step, were assumed. 10088

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The Journal of Physical Chemistry C The present work uses DFT to explore the entire AM catalytic cycle, determining activation energies and transition state geometries. A key aspect of this investigation is the location of the catalytic center on a single isolated Brønsted acid site. The Ta atom was found to have a 2-fold coordination with the oxygen atoms of the FER support. We demonstrate, for each elementary step, how the present system compares to previous DFT studies of TM-hydrides on various supports, including silica/alumina and ZSM-5. The remainder of this Article is organized as follows. Section II explains the computational methods used to conduct the calculations. Section III presents the results, discussing each elementary step in separate subsections.

II. COMPUTATIONAL METHODS Calculations were performed on cluster models of the active site and on the periodic zeolite unit cell. All calculations in this work were conducted using density functional theory21,22 (DFT) in the plane-wave pseudopotential (PW/PP) implementation of the Quantum-ESPRESSO package.23 The exchange-correlation energy functional was constructed using the Perdew
Burke
Ernzerhof (PBE) Generalized Gradient Approximation (GGA).24 Ultrasoft pseudopotentials25 were employed to model the interaction of valence electrons with the atomic cores (nuclei and core electrons). The electronic Kohn
Sham states were expanded in plane waves up to a kinetic energy cutoff of 45 Ry (612 eV) while the charge density required a cutoff of 450 Ry (6120 eV). Optimization of atomic positions was achieved using the Broyden
Fletcher
Goldfarb
Shanno26 (BFGS) method. The nudged elastic band27
30 (NEB) method, with climbing images, was used to find the minimum energy pathway (MEP) for each elementary step. In this constrained optimization, a number of reaction intermediates (images) span the space between the reactant and product configurations. These images are held from falling into their local energy minima by fictitious springs. The path from image to image is the “band”, which converges to the MEP. Each intermediate image experiences the forces of the fictitious springs as well as the component of the true force that is perpendicular to the band. In the climbing image method,28 the highest energy image is selected to “climb”. This climbing image (CI) continues to experience the forces perpendicular to the band, but the spring forces are replaced with the inverse of the component of the true force parallel to the band. Therefore, the CI seeks out saddle points in the energy surface. The initial atomic positions of the periodic FER unit cell were obtained from X-ray diffraction data in Accelrys’ Materials Studio.31 The single cell dimension along [001] is 7.541 Å. As verified by our calculations, this is too small to host the Brønsted acid site, the Ta center, gas-phase molecules, and the lattice distortions introduced by these species. Therefore, a supercell was created by stacking two siliceous unit cells along the [001] direction (72 tetragonal sites, or 72T). Both atomic positions and supercell parameters were optimized without any constraints. Using the final configuration of the siliceous supercell, an Al substitution was performed and a H counterion placed upon an O atom adjacent to the defect. The Al atom was placed at the intersection of the linear 8- and 10-membered pores to give the active site access to the largest open volume. The atomic positions of this second supercell (Si/Al ratio of 71:1) were then optimized with the unit cell parameters fixed at the size and shape

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obtained from the relaxation of the completely siliceous supercell. A comparison of the internal coordinates (bond lengths/ angles) between these two optimized structures was made, as a function of distance from the Al, to determine the range of the structural reorganization induced by the Al substitutional defect. Bond lengths and angles were found to be nearly identical in the third Si shell from the Brønsted acid, encompassing 34T sites including the Al atom. Therefore, in subsequent full-periodic optimizations, these 34T sites, their bridging oxygens, and the catalytic site were allowed to move without constraint while keeping all other atoms fixed in their purely siliceous positions. This 34T embedded cluster (EMB-34T) approach was used to optimize the reactant and product states of the elementary steps. Isolated 5T clusters (ISO-5T) were then “carved” from the EMB-34T configurations and employed in the NEB calculations. This smaller system was chosen for computational efficiency, and results obtained from these calculations are to be considered as initial estimates of the computed quantities. The results of calculations performed with the ISO-5T clusters were validated through subsequent, periodic system calculations, in which the active site was frozen in its ISO-5T configuration. Limitations of the cluster-based approach have been discussed in the literature.32 Figure 2 illustrates, for the case of the Ta-dihydride reaction intermediate, the carving and termination of a 5T cluster from the EMB-34T results. The oxygen atoms at the edge of each cluster were replaced with hydrogen atoms along the same bond vector and at a distance of 1.472 Å, resulting in terminating SiH3 groups. This method was chosen to avoid the overly strong electrostatic potential that results from Si
O
H termination.33 SiH4 was optimized at the same level of theory to obtain the equilibrium Si
H bond length (1.472 Å). The terminating SiH3 groups were then held fixed during subsequent calculations, and their positions were obtained from a linear interpolation of the reactant and product configurations. Each elementary step was initially studied using 10 images. These NEB calculations were performed without restricted magnetization and without climbing images until the forces across all images converged to 0.05 eV/Å. A second round of NEB calculations was then performed with the climbing images enabled until the forces converged to 0.01 eV/Å. Results from this first round of NEB calculations indicated that, with the exception of the olefin metathesis step, a triplet spin state [a total magnetization (Mtot) of 2.0 μB cell
1] was always maintained. The triplet state is often preferred because of electron spin pairing in Ta d-states. Unlike the other elementary steps, the reaction intermediates of the olefin metathesis step were found to span both singlet (Mtot = 0.0 μB cell
1) and triplet (Mtot = 2.0 μB cell
1) states. Therefore, two restricted magnetization NEB calculations were performed for the olefin metathesis step. For all other steps, the second round of NEB calculations was performed with Mtot magnetization restricted to 2.0 μB cell
1. The strength of the artificial springs was set using a variable elastic constant scheme,28 which increases image resolution around the climbing image; a range of 0.0010
0.0001 Ry/a20 was used. In specific cases, to obtain a better mechanistic understanding of the MEP, additional NEB calculations were carried out between intermediate states of interest. To capture the effects of zeolite confinement, several of the ISO-5T configurations from the NEB results were reintroduced 10089

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Figure 3. Summary of energy profiles for the entire alkane metathesis catalytic cycle. The rectangles connected by dotted lines represent the ISO-5T cluster results. The dots indicate the energies from reintroducing the ISO-5T clusters back into the periodic system. Energies are in kJ mol
1.

into the periodic system. EMB-34T clusters were again employed; in this case, both the active site and the atoms outside the EMB-34T region were held fixed while the intermediate region was relaxed. In this way, the geometry of the catalytic site was preserved, and the energies obtained provided an estimate of the magnitude of confinement effects in Ferrierite. Because they were not obtained through an NEB calculation, these configurations represent a first approximation to the true MEP of the considered reactions in the periodic system. To assess the charge of every species involved in the reaction, L€owdin atomic charges were evaluated from the projection of Kohn
Sham states onto orthogonalized atomic orbitals.34 While the sum rule of the obtained occupation numbers is nearly satisfied, some deviations can be expected from the imperfect overlap between the Kohn
Sham and the atomic orbital basis sets.35,36

III. RESULTS AND DISCUSSION The reaction intermediates, which were optimized with the EMB-34T method, are shown in Scheme 1. They are Ta-hydride (1), Ta-ethyl (2), Ta-ethylcarbene (3), Ta-metallacyclobutane (5), and Ta-methylcarbene (6). Configuration 4 indicates the coordination of the double bonds of ethylene and Ta-ethylcarbene (3). Every unique atomic configuration is given a two character label. The first character is a number that corresponds to a particular elementary step. The second character is a letter, which corresponds to the reaction coordinate. The proposed reaction mechanism (Scheme 1) proceeds through the activation and dissociative adsorption of ethane by Ta (1 f 2). Subsequently, the Ta-ethyl can desorb, forming ethylene and regenerating Ta-hydride (2 f 1), or undergo dehydrogenation, forming Ta-ethylcarbene (2 f 3). The two double bond containing species (ethylene and Ta-ethylcarbene) are necessary for the olefin metathesis step, which involves the formation of a Ta-metallacyclobutane (4 f 5). The forward products of olefin metathesis are propylene and Ta-methylcarbene (5 f 6). Rehydrogenation of these species completes the catalytic cycle, regenerating the Ta-hydride and producing the primary ethane self-metathesis products: methane and propane (6 f 1). From Figure 2, we note that three of the four (Al
O
Si) bridging oxygen atoms are accessible from the 10-membered

pore. To verify the coordination of Ta to the FER support, a test system was relaxed with the Ta atom (of Ta-dihydride) equidistant (2.3 Å) to all 3 bridging oxygen atoms. The result was the formation of two Ta
O σ-bonds with lengths of ∼2.15 Å . The third Ta
O distance was ∼3.97 Å . This is the same configuration that is shown in Figure 2, which has a total coordination of four [(tSi
O
Alt)2Ta(H)2]. The 2-fold coordination of the Ta atom with framework oxygen is in agreement with EXAFS studies,17,18 which report Ta
O σ-bond lengths of ∼1.9 Å . Slightly longer Ta
O bond lengths are observed in the present case because, unlike the 2-fold coordinated oxygen atoms of the above studies, the oxygen atoms are 3-fold coordinated. Therefore, one would expect elongated Ta
O bond lengths for the present system. In addition, the GGA functional is known to overestimate bond lengths of this kind. L€owdin atomic charges for the Ta-dihydride (1a) were also determined and found to be þ0.30 for Ta, þ1.38 for Al, and
0.71 for each bridging oxygen [Al
O
Ta]. The electrondonating nature of the Ta atom is in agreement with many reports of TM-complexes.9,37
43 As stated by Basset et al. and confirmed here, supported Ta
H2 is electron-deficient and shows a unique ability for C
H σ bond activation.37 The Ta atom carried a positive charge in all investigated configurations with an average of þ0.26. Other observed atomic charges include an average þ0.16 charge for H atoms bound to C atoms, an average
0.07 charge for H atoms bound to the Ta atom, an average
0.31 charge for C atoms, and an average þ1.36 charge for the Al atom. Details regarding atomic charges of all atomic configurations are given in the Supporting Information. In the following sections, the progression along the MEP of atomic configurations (in 3D and schematic representations) and the total energy is shown. The schematics contain atomic labels that are used to reference various bond lengths. The evolution of bond lengths over the reaction coordinate is given for each elementary step in the Supporting Information. A summary of the energy profiles for each elementary step, and the overall cycle, is shown in Figure 3. A detailed discussion on each of the chemical steps involved in the catalytic cycle is developed below. Step 1: Ethane Activation. Ethane approaches the Tadihydride catalytic site, until in 1a (the first configuration shown in Figure 4), the distance between one of its hydrogen atoms and 10090

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Figure 4. The activation of ethane by Ta produces Ta-ethyl and H2 (Ta = gray, Al = pink, Si = blue, oxygen = red, carbon = yellow).

a hydrogen atom from the catalytic site is ∼2.7 Å . In 1b, the proximity of ethane distorts the Ta-dihydride site, resulting in a 20 kJ mol
1 barrier. An R-H abstraction produces 1c, where the Ta atom has a 6-fold coordination. This state corresponds to the energy minimum for this step (Figure 5). The subsequent desorption of the dihydrogen generates the transition state (1d). Here, the distance between the near H atom of the dihydrogen molecule and the Ta atom is ∼2.36 Å . Together with the energy minimum of 1c, our results predict a remarkably low activation energy (∼64 kJ mol
1) for the dissociative adsorption of ethane on Ta-hydride. In two studies involving extra-framework Ga-hydrides grafted onto a Brønsted acid site of ZSM-5,44,45 energies for the activation of ethane were reported to be 159 and 120 kJ mol
1, significantly higher than the present result. Ga-dihydride [Ga
H2]1þ (coordination with one Al atom) was studied in the former and Ga-monohydride [Ga
H]2þ (coordination with two Al atoms) in the latter; both cases have Ga coordinated with two oxygen atoms. Therefore, the catalytic complex with greater positive charge (Ga-monohydride) was observed to have a lower ethane activation energy. In another DFT study, ethane activation by extra-framework Zn on Brønsted acid sites of ZSM-5 was studied in several configurations of the surface;46 two of these configurations are considered. The first consists of an isolated Brønsted acid site, where the Zn is 2-fold coordinated with surface oxygen atoms (geometrically similar to 1). The second involves two such sites with the Zn atoms separated only by a bridging oxygen atom. The energies for the activation of ethane were reported to be 117 and 77 kJ mol
1, respectively. Again, as formal charge increases ([Zn]þ1 f [Zn]þ2), the energy barrier for the activation of ethane was found to decrease. In a related metathesis study, Joubert et al. report that the activation of ethane15 (methane47) requires only ∼25 kJ mol
1 (∼22 kJ mol
1) by tricoordinated Al from an alumina surface. In both cases, the strong Lewis acidity of tricoordinated Al is thought to contribute to the activation. Results from three separate systems indicate that the barrier for C
H activation decreases with increasing formal charge of the catalytic complex. As the Ta complex of the present system is positively charged, our results are consistent with the trend in the literature and show that hydridic forms of high-valent cations are remarkably efficient for alkane activation. Steps 2 and 3: Ethylene Desorption via r-H and β-H Elimination. Both R and β hydrogen elimination mechanisms were investigated for ethylene desorption from Ta-ethyl (2), which regenerates Ta
H2 (1) (Scheme 1). In the case of R-H elimination (Figures 6 and 7), calculations indicate that the converged MEP proceeds through three energy

Figure 5. The MEP of the activation of ethane for [Ta
H2] epitaxed on FER. Energies are in kJ mol
1.

barriers. These correspond to hydrogen elimination (2a f 2c), internal hydrogen transfer from β-C to R-C (2c f 2e), and ethylene desorption (2e f 2g); the energy barriers were found to be 98.4, 120.6, and 75.3 kJ mol
1, respectively. R-H elimination from the ethyl group to the Ta atom forms Ta-dihydrogenethylcarbene (2c), which is oversaturated. A subsequent internal hydrogen transfer results in the creation of a Ta-dihydrogenethylidene species [Ta
H2
CH2CH2] (2e). It is during this transfer from the β-C to the R-C that the highest energy configuration (TS) occurs. The geometry of the TS structure (2d) is such that the transferring hydrogen atom is nearly equidistant (∼1.30 Å) to both carbon atoms. In 2e, the R-C is oversaturated, while the β-C is undersaturated, enabling the desorption of ethylene. During the desorption, the energy barrier reaches a maximum in 2f. In this configuration, the shortest distance between the Ta center and the desorbing ethylene occurs between the Ta atom and an R-H (2.10 Å). This is within the range of dispersion interactions. In the case of β-H elimination (Figures 7 and 8), the formation of ethylene proceeds via the elongation of the Ta
(R-C) bond. The R-C becomes negatively charged, while the Ta gains positive charge, introducing polarization. The electrophilic Ta then attacks the (βC)
H bond, abstracting a β-H and forming ethylene. The converged MEP was found to have two energy barriers. These correspond to hydrogen elimination (3a f 3c) and ethylene desorption (3c f 3f) and have energy barriers of 95.5 and 118.7 kJ mol
1, respectively. In β-H elimination, a hydrogen atom is transferred directly to the Ta. Here, the ligand bends, reducing the distance for the β-H to move, until, in 3b, the β-H is transferred. Structure 3c, a Ta-cyclopropane, is an intermediate state, which results from the hydrogen transfer. The decomposition of this species forms the same Ta-ethylidene species (3d) as found in R-H elimination (2e). In both the R-H and the β-H elimination mechanisms, the desorption of ethylene from Ta-ethylidene proceeds along the same path. For the β-H elimination mechanism, the TS (3e) occurs during the desorption of ethylene (3c f 3f). 10091

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Figure 6. The desorption of ethylene from Ta-ethyl via R-H elimination.

Figure 7. The MEP’s of the desorption of ethylene. Left: Via R-H elimination. Right: Via β-H elimination. Energies are in kJ mol
1.

Figure 8. The desorption of ethylene from Ta-ethyl via β-H elimination.

With barriers of 98.4 and 95.5 kJ mol
1, respectively (Figure 7), both R (2a f 2c) and β (3a f 3c) hydrogen eliminations are equally likely to occur. However, in the case of βH elimination, a Ta-cyclopropane (3c) is formed, which requires only 46 kJ mol
1 to form Ta-ethylidene (3d). Comparatively, for the R-H elimination, 121 kJ mol
1 is required to promote 2c to the Ta-ethylidene (2e). Also, the overall energy barrier for the βH elimination mechanism (173 kJ mol
1) is ∼34 kJ mol
1 less demanding than the R-H elimination mechanism (Figure 7). The determination that β-H elimination is preferred is in agreement with the literature.44,46,48,49 Similar β-H elimination

mechanisms have been studied44,45,50 in systems with Ga-hydrides grafted on the Brønsted acid sites of ZSM-5. The reported activation energies were between 254 and 265 kJ mol
1, while the reaction enthalpies varied from 44 to 134 kJ mol
1. β-H elimination was also favored in the Zn/ZSM-5 system,46 having an activation energy of 147 kJ mol
1. The heat of reaction for the dehydrogenation of ethane in the gas phase51 is 136 kJ mol
1, and values between 129 and 139 kJ mol
1 have been reported in ZSM-5.44
46,50 Our calculations indicate that (through the C
H activation of ethane and desorption of ethylene via β-H elimination) ethane dehydrogenation has 10092

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Figure 9. The MEP’s of the formation of Ta-ethylcarbene. Energies are in kJ mol
1.

Figure 11. The MEP of olefin metathesis. Energies are in kJ mol
1.

Figure 10. Ta-ethyl dehydrogenation to form Ta-ethylcarbene.

a heat of reaction of 154 kJ mol
1 in the FER environment. Possible sources of this 20 kJ mol
1 discrepancy include interactions between the gas-phase species and the active site and finite temperature effects (e.g., the temperature dependence of the heat of reaction), which are not explicitly accounted for in our study. Step 4: Ta-ethylcarbene Formation. Another possible outcome of the decomposition of the Ta-ethyl is its dehydrogenation to form Ta-ethylcarbene. This occurs by R-H elimination and subsequent desorption of molecular hydrogen from the Ta atom. The formation of Ta-ethylcarbene from Ta-ethyl (Figures 9 and 10) was found to have an activation energy of 133 kJ mol
1. However, no reverse energy barrier was found, suggesting that, with the exception of the entropic barrier, Taethylcarbene will spontaneously re-form Ta-ethyl in the presence of hydrogen. In an intermediate state (4b), two hydrogen atoms are coordinated on the Ta atom at a distance of 1.92 Å and a separation of 0.86 Å just prior to the formation and desorption of the dihydrogen molecule. Step 5: Olefin Metathesis. Having generated the requisite carbene and olefin, the metathesis step proceeds by the coordination of both species via double bonds (Figures 11 and 12). In 5a, the shortest interatomic distance between the ethylene and Ta-ethylcarbene is 5 Å . Ethylene approaches the Ta-ethylcarbene intermediate to form the ethylene complex (5b) shown in Figure 12. In this configuration, the C atoms of the ethylene are nearly equidistant to the Ta atom (∼2.8 Å). The atoms of the ethylene are no longer in the same plane; relative to the C atoms, the plane containing the H atoms has shifted away from the Ta. This continues until the C atoms adopt a sp3 hybridized

Figure 12. The olefin metathesis step. Ethylene and Ta-ethyl carbene produce propylene and Ta-methyl carbene.

configuration in 5c, resulting in the Ta-metallacyclobutane. The formation of σ-bonds at the expense of π-bonds lowers the energy of the system by 143 kJ mol
1 (Figure 11). The forward ring-opening of the Ta-metallacyclobutane to form propylene and Ta-methylcarbene (5c f 5e) was found to have an activation energy of 183 kJ mol
1, 40 kJ mol
1 higher than the reformation of ethylene (5c f 5a). No intermediate transition state was localized in the olefin metathesis step. Propylene moves away from the Ta atom until, in 5e, the shortest interatomic distance is 2.29 Å between a sp2 hybridized H atom from the propylene and a H atom from the Ta-methylcarbene. The angle that the latter H atom forms with the Ta
C bond is 166.1°; the corresponding angle of the singlet state of a [TadCH2]1þ molecule in the gas phase is reported to be 169.4°.52 During olefin metathesis, the energy surfaces corresponding to the singlet (Mtot = 0.0 μB cell
1) and triplet (Mtot = 2.0 μB cell
1) states were found to cross. In particular, the only image found to have a lower energy in the singlet state was the Ta-metallacyclobutane (5c). This species was optimized on its own with its magnetic state unrestricted and found to have no magnetization in its lowest energy configuration. The geometry of 5c is such that the Ta, Ca, Cc, and Cd atoms all lie in the same plane. A metallacycle geometry similar to the present one was investigated by Schinzel et al.13 They reported a Ta-metallacyclobutane 10093

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The Journal of Physical Chemistry C with trigonal bipyramidal (TBP) geometry on an amorphous silica surface. These materials have framework hydroxyl groups. The catalytic center used was a Ta atom with 2-fold coordination to surface oxygen atoms, a methylcarbene group, and a hydride group. In the present work, a Ta atom with 2-fold coordination to surface oxygen atoms, an ethylcarbene group, and no hydride group was used. While the metallacycles are similar, Schinzel et al. report that their Ta-metallacyclobutane on silica is 107 kJ mol
1 more stable than reactants (Ta-methylcarbene and ethylene),13 36 kJ mol
1 lower than for the present case (143 kJ mol
1). The stability of metallacycles with respect to reactants has been reported in several studies,13,19 including homogeneous catalytic systems.41,53 Handzlik et al. have explored the stability of metallacycles with mononuclear Mo centers on alumina.19,54 Energies from 36 to 137 kJ mol
1 below that of the reactants were reported for a diverse set of metallacycles, including square pyramidal (SP) and TBP geometries with several different coordinations and locations on the (100) and (110) planes. Poater et al. studied homogeneous olefin metathesis using a variety of transition metals (Mo, W, and Re) and ligand combinations.41,53 Using the same ligands (tNCH3, dCHCH3,
CH2CH3, and
OSiH3), the energy pathways for olefin metathesis were studied as a function of the TM. The metallacycles were determined to be 71, 76, and 102 kJ mol
1 more stable than the reactants for Re, Mo, and W, respectively. Recently, Handzlik has reported on the olefin metathesis of mononuclear Mo-methylcarbene with ethylene in H-ZSM-5.39 In this study, the reaction pathway was investigated for two configurations of the catalytic site: one with a single Al substitutional impurity nearby (Al
O
Mo) and the other with two Al substitutional impurities nearby. The metallacycle stabilities were 62 kJ mol
1 in the former and 25 kJ mol
1 in the latter. Therefore, it was demonstrated that the Mo-metallacyclobutane with greater formal positive charge was less stable. Another study by Li et al., which investigated the olefin metathesis of Moethylcarbene with ethylene as a function of framework acidity, determined that the energy barriers decrease with increasing acidity.55 The acidity of the framework was varied by adjusting the Si
H bond lengths used to terminate the cluster model.56 The transition state energies are greatly affected, while the energies of reaction intermediates do not change much. Therefore, in the present case, the activation barrier for olefin metathesis will likely be reduced by coordinating the catalytic complex with multiple Al atoms. In each of these studies, the metal center of the metallacycle had a coordination of 5. Most reported metallacycles have a spectator hydride ligand, which does not participate in the chemistry. The geometry of the present Ta-metallacyclobutane is unique because the metal is only 4-fold coordinated and lacks this hydride ligand. Such a difference in geometry may account for the relatively high stability of the present metallacycle. Rehydrogenation. The MEP for hydrogenation of the olefin metathesis products was not calculated because it would likely occur through the following elementary steps. The hydrogenation of propylene will proceed in a manner similar to the reverse of the dehydrogenation of ethane. Propylene will likely form a Ta-propylidene species (similar to 3f f 3d), undergo a H transfer from the Ta to Cβ (similar to 3d f 3a), and (in the presence of molecular hydrogen) desorb as propane (similar to 1e f 1a). The maximum energy barrier for the reverse pathways indicated above is ∼61 kJ mol
1, which is attributed to the desorption of ethane (1c f 1a). The hydrogenation of

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Ta-methylcarbene is likely to proceed with little or no barrier, as is the case for Ta-ethylcarbene (4c f 4a). Finally, the desorption of methane (in the presence of hydrogen) should occur with a barrier similar to that of ethane. The actual activation energies should not be very different from the reverse barriers for the elementary steps already investigated, and even with dramatic increases over these estimates, the likelihood that they will exceed 183 kJ mol
1 is remote. Therefore, the decomposition of the metallacycle remains the most energetically demanding step. The energy change due to hydrogenation of the olefin metathesis products was assessed. The species involved were the olefin metathesis products of 5e (i.e., Ta-methylcarbene and propylene) together with three dihydrogen molecules and the hydrogenation products (i.e., Ta-dihydride, methane, and propane). The gas-phase molecules (i.e., propylene, diatomic hydrogen, methane, and propane) were geometrically optimized in isolation and used to construct the reactant and product states of the hydrogenation process; a minimum interspecies distance of 10 Å was enforced for both states. The energies of these two states were then calculated and compared, completing the catalytic cycle. The results, (5e f 6) in Figure 3, indicate that the heat of reaction for the self-metathesis of ethane is 16.6 kJ mol
1 in the FER environment. This is in agreement with the thermodynamic gas-phase heat of reaction (20 kJ mol
1).51 Reaction Energies from the Periodic Zeolite. Shown in Figure 3 are the relative energies calculated after reintroducing selected ISO-5T cluster configurations back into the periodic FER framework. This was achieved by geometry optimizations that were performed while keeping the positions of atoms around the active site fixed to their configurations obtained from ISO-5T calculations. Atoms outside the EMB-34T cluster were also kept fixed during optimizations. Therefore, only the positions of the atoms in the intermediate region were optimized. The data points shown have been zeroed to each step’s reactant state (i.e., 1a, 2a, 3a, 4a, and 5a). Results indicate that many of the energy minima and maxima are “softened” in the periodic system. The energy barrier for the internal hydrogen transfer of the R-H elimination mechanism (2c f 2e), which was observed to decrease by 17%, was especially affected. It should be noted that these energies are from independent relaxations (unlike the linked relaxations of the NEB method). Therefore, these data points represent an initial estimate of the actual reaction pathway in the periodic FER system (whose barriers are likely lower). Consideration of these new data points along with the other ISO5T energies indicates that the decomposition of the Ta-metallacyclobutane, while having a reduced energy barrier, remains the most energetically demanding step (∼145.3 kJ mol
1).

IV. DISCUSSION AND CONCLUSIONS In this Article, we examined the entire catalytic cycle for ethane self-metathesis by Ta-dihydride on a Brønsted acid site; from alkane activation, olefin, and TM-carbene formation to olefin metathesis and rehydrogenation. Geometry optimizations of the full periodic FER system were conducted to find the lowest energy atomic configurations of reactants and products at each elementary step. The Ta atom was found to have 2-fold coordination with surface oxygen atoms. Results from the ISO5T clusters, which provided a first estimate to the MEP, were refined by single point total energy calculations in the periodic 10094

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The Journal of Physical Chemistry C zeolite crystal and were found to be in good qualitative agreement with those in the literature. As compared to Ga-hydrides, the Ta-hydride complex on a single Brønsted acid site was found to activate ethane, and probably higher homologues, with relative ease (64 kJ mol
1). At 183 kJ mol
1, the step with the largest activation energy (Figure 3) is the decomposition of the Ta-metallacyclobutane (5c f 5e) into Ta-methylcarbene and propylene. A reduction of this barrier (145 kJ mol
1) was observed when the ISO-5T results were substituted back into the zeolite crystal (full periodic system). Recent studies39,55 indicate reduced metallacycle stability with increased coordination of the TM to Al, suggesting that, in the right environment, the present catalyst may be capable of performing AM at moderate temperatures. This could be accomplished by using a zeolite framework with a lower Si/Al ratio, which increases the likelihood that a grafted metal center coordinates to multiple Al atoms. As much of this investigation was performed on 5T clusters, these results likely provide an upper bound to the performance of single-site Ta-hydride catalytic centers on Brønsted acid sites of aluminosilicate materials. A more accurate refinement of these results would be achieved through NEB calculations in the periodic zeolite crystal, and by including van der Waals interactions. The complete evaluation of the viability of alkane metathesis on zeolite supported transition metal hydrides requires more studies assessing the role of the support (coordination of the active site) and of the framework acidity (Al content). If comparison is to be made with experiments, a means of synthesizing these catalysts reproducibly is needed.

’ ASSOCIATED CONTENT

bS

Supporting Information. Atomic positions and data regarding select bonds. The atomic positions included are 1a
1e, 2a
2g, 3a
3f, 4a
4c, and 5a
5e (Tables 6 and 31) as well as the atomic positions for the intermediate region relaxations. Interatomic distance tables (Tables 1 and 5) and figures (Figures 13 and 17) illustrating the progression of select interatomic distances over each elementary step. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected] (A.B.); [email protected] (M.C.).

’ ACKNOWLEDGMENT This work was supported by the Abu Dhabi
Minnesota Institute for Research Excellence (ADMIRE), a partnership between the Petroleum Institute of Abu Dhabi and the Department of Chemical Engineering and Materials Science of the University of Minnesota. We are also grateful to the University of Minnesota Supercomputing Institute for providing computational resources and technical support. ’ REFERENCES (1) Crabtree, R. Chem. Rev. 1985, 85, 245–269. (2) Leung, D.; Bergman, R.; Raymond, K. J. Am. Chem. Soc. 2006, 128, 9781–9797. (3) Chen, G.; Labinger, J. A.; Bercaw, J. E. Abstr. Pap., Am. Chem. Soc. 2008, 235, 1–2.

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