A Reaction Mechanism of Methane Coupling on a Silica-Supported

Apr 30, 2014 - In a reaction system having high methane conversion, C2 products tend to be overoxidized to ...... York , A. P. E.; Xiao , T.; Green , ...
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A Reaction Mechanism of Methane Coupling on a Silica-Supported Single-Site Tantalum Catalyst Xufeng Lin,*,†,‡,§ Yanyan Xi,†,∥ Guodong Zhang,†,§ David Lee Phillips,*,⊥ and Wenyue Guo†,§ †

State Key Laboratory of Heavy Oil Processing, China University of Petroleum (East China), Qingdao 266580, P. R. China Key Laboratory of Catalysis of China National Petroleum Corporation, Qingdao 266580, P. R. China § College of Science, China University of Petroleum (East China), Qingdao 266580, P. R. China ∥ College of Chemical Engineering, China University of Petroleum (East China), Qingdao 266580, P. R. China ⊥ Department of Chemistry, The University of Hong Kong, Pokfulam Road, Hong Kong, P. R. China ‡

S Supporting Information *

ABSTRACT: Density functional theory calculations were utilized to study the reaction mechanisms of nonoxidative coupling of methane (NOCM) occurring on a silica-supported single-site tantalum (Ta) catalyst. Two catalytic cycles, namely, catalytic cycles A (CCA) and B (CCB), as well as other competing pathways, were investigated by exploring the potential energy surfaces for the reactions of interest. The supported methyltantalum [(SiO3)2Ta−CH3] and tantalum hydride [(SiO3)2Ta−H] catalyzed the reaction of NOCM through CCA and CCB, respectively. CCA and CCB comprise five and six elementary steps, respectively. The two ratedetermining states for both catalytic cycles were elucidated. The turnover number of methane conversion catalyzed by the supported methyltantalum was about 105 larger than that catalyzed by the supported tantalum hydride. This large difference indicates that the former species is predominantly responsible for the conversion of methane to ethane.

1. INTRODUCTION Conversion of methane, the main component of natural gas, to heavier hydrocarbons with a minimum number of steps has gained great interest in the petrochemical industry and fundamental chemical research.1,2 A well-established route, known as the syngas route, uses methane and converts it to syngas by reformation or partial oxidation,2−4 and this syngas is then converted to various heavier hydrocarbons through Fischer−Tropsch5,6 reactions combined with a water-gas shift reaction. However, the syngas route is energetically and atomically inefficient and hence is neither economical nor environmentally friendly. Among the alternatives to the syngas route are oxidative and nonoxidative coupling of methane (denoted as OCM and NOCM, respectively) to afford C2 (ethane and ethylene) products. These alternative routes are potentially improved ones for the selective conversion of methane, since in them most of the C−H bonds are kept intact during chemical transformations. However, the OCM7−13 and NOCM14−22 routes are still under research or at the pilot-plant stage of development despite substantial research efforts since their first report in 1982.7 From the late 1990s, the research activities focusing on the above-mentioned field decreased compared with the previous years (1980s to early 1990s). This decrease was brought about by the absence of a catalyst that can provide a single-pass C2 yield of over 30% from the methane © 2014 American Chemical Society

coupling reactions mentioned. This C2 yield is believed to be an economically viable threshold from investors’ point of view.13 An inherent shortcoming of the OCM route9,10 is that C2 products are usually easier to oxidize than methane in the presence of O2. In a reaction system having high methane conversion, C2 products tend to be overoxidized to undesirable carbon oxides, resulting in the rapid decrease of C2 product selectivity. In contrast to the OCM route, the NOCM route does not suffer from overoxidation. Furthermore, H2, which is a byproduct of NOCM, is more valuable than the H2O byproduct of the OCM route. These advantages make the NOCM route a potentially useful process for selective methane conversion. Compared with the number of reports on the search for suitable NOCM catalysts,14−21 the number of reports dealing with a mechanistic understanding of NOCM is substantially less.20,21 The mechanism of NOCM is still poorly understood, which can hinder the development of an effective catalyst. This study aims to provide deeper insights into how supported metal catalysts can catalyze the NOCM reaction. Density functional theory (DFT) calculations are used to explore the potential energy surfaces (PESs) of possible reaction pathways. Received: October 10, 2013 Published: April 30, 2014 2172

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answers for the above questions Q1−Q4 and a clearer picture of NOCM catalysis by a single-site Ta catalyst.

Recently, single-site tantalum (Ta) and tungsten catalysts supported on silica or alumina have been used for nonoxidative conversion of methane to ethane at temperatures lower than 475 °C.20,21 These catalysts convert methane at a certain thermodynamic limit, and the product selectivity to ethane is exceedingly high. Because single-site heterogeneous catalysis is an important new research area in heterogeneous catalysis, this study focuses on the reaction mechanism for NOCM catalyzed by silica-supported single-site Ta. In ref 20, the authors proposed a reaction mechanism that involves alkyl-, methylidene-, and carbyne-Ta species. The presence of Ta−C, TaC, and TaC bonds have been observed using solid-state NMR spectroscopic measurements.20,22 This reaction mechanism has been redrawn by us as indicated in Scheme 1. Although the

2. COMPUTATIONAL METHODS DFT calculations were performed using the hybrid B3LYP exchange− correlation functional to explore the PES of silica-supported Tacatalyzed nonoxidative coupling of methane. The B3LYP functional is appropriate for application in organotantalum compounds.25 The 6311G(d,p) basis sets were used for all C, H, O, and Si atoms, and the SDD basis set was used for Ta. These basis sets are denoted as BS1 in this paper. The PESs for the reactions of interest were explored by optimizing the geometries of the energy minima for the reactants, intermediates, and products and the first-order saddle points for transition states using the Gaussian 09 program suite (revision B01).26 All species at the minima of their PESs (i.e., reactants, products and intermediates) are denoted as bold digits (i.e., 1, 2, ..., n). Each elementary reaction step studied is denoted as m → n or m → TS-m-n → n, where m and n are the notations for the species at the local minima of the PES and TS-m-n denotes the corresponding transition state. TS-m-n is identical to TS-n-m on a PES. Vibrational analyses were performed to confirm the energy minima and first-order saddle points and obtain the zeropoint energy (ZPE)-corrected energies and free energies (at 723.15 K and 49.3 atm or 50 bar, typical reaction conditions in ref 20) of the optimized geometries. Intrinsic reaction coordinate computations were performed to confirm the transition states connecting the appropriate reactants and products.27,28

Scheme 1. Reaction Mechanism for the Supported SingleSite Ta-Catalyzed Nonoxidative Coupling of Methane Proposed in Reference 20

3. RESULTS AND DISCUSSION The NOCM production of ethane can be expressed by 2CH4 = C2H6 + H 2

(i)

In ref 20, (SiO3)2Ta−H (1) and (SiO3)2Ta(H)3 (2) were used as part of the starting materials to generate the working catalyst. It has been established22,29 that 1 is in equilibrium with 2 and with (SiO3)2Ta−CH3 (3) in the presence of CH4. Because the working catalytic cycle is believed to be Ta(III)−Ta(V)29 and both 1 and 3 are tricoordinated species, catalytic cycles utilizing 1 and 3 as catalysts were structurally and energetically examined in this work (see the note in ref 30). To model the silica support, a fragment of Si3O10H6 with two O atoms bound to the Ta center was used. Figure 1 presents the optimized geometries of the reactant, the products, and the two possible catalysts 1 and 3 for NOCM. In the model catalyst for 1, Si(1) and Si(2) are the two atoms bonded with Ta through O. A third Si atom, Si(3), fixes the positions of Si(1) and Si(2) during the geometry optimization. Six hydroxyl groups were used to saturate the boundary dangling bonds of the Si atoms. Notably, a slightly different model of the silica support was used in other computational studies, such as that of Eisenstein and co-workers.31 In Eisenstein’s silica support model, the Ta atom is bound to two O atoms connected to two Si centers through a Si−O−Si motif. By contrast, our model uses Ta coordinated to two O atoms on two Si centers that are not directly connected by a Si−O−Si motif. Our model is consistent with the experimentally identified single-site surface Ta structure, where Si(1) and Si(2) may not necessarily connect to each other through the same O atom.29 3.1. Catalytic Cycle with a Surface Methyltantalum Species as the Catalyst. The present study aimed to use DFT to elucidate the feasibility of alternative reaction pathways for NOCM. The proposed mechanisms follow the reactions of (SiO3)2Ta−CH3 3 and (SiO3)2Ta−H 1 on closed-shell PESs. For convenience, the sum of Gibbs free energies of the

initial form of the single-site Ta species is silica-supported tantalum hydride, (SiO3)2Ta−H (1), which is in equilibrium with tantalum trihydride, (SiO3)2Ta(H)3 (2),22 silicasupported methyltantalum, (SiO3)2Ta−CH3 (3), was proposed to be the actual catalyst, as indicated in Scheme 1. This proposed mechanism was mainly based on the NMR spectroscopic data for the surface species and the results of similar reactions involving a Ti reagent23 and those involving Cp*2Ta(CH2)CH3.24 However, further research works to support the validity of this mechanism as well as to update it to a more detailed form have not been reported to date. In this paper, the following interesting questions regarding the above reaction mechanism remain open for investigation: (Q1) Are the catalytic cycles in Scheme 1 plausible in terms of their PESs, and what are the species involved in the working catalytic cycle? (Q2) Are the reaction steps presented in Scheme 1 elementary reactions, and if not, how do the elementary reactions occur? (Q3) Given that the initial form of the single-site Ta species is 1, can it effectively work as a catalyst? (Q4) If 1 is not an effective catalyst, then how can it be transformed into an actual working catalyst? Answering these questions is clearly important to gain a deeper understanding of the metal-catalyzed NOCM reaction mechanism. Moreover, answering these questions becomes more important when one considers that this reaction mechanism is rather speculative because of the different reaction conditions under which the NMR spectroscopic measurements and catalytic tests were carried out. This paper reports a DFT computational study of two catalytic cycles of NOCM taking place on a single-site Ta catalyst supported on silica. This study provides tentative 2173

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the results when only singlet PESs are considered. A more detailed explanation is in Content No. (2) (including Figure S1) in the Supporting Information. In the main text, only the results based on the singlet PESs are presented. Scheme 2a shows the catalytic cycle (solid lines) for 3catalyzed NOCM. This catalytic cycle is slightly similar to the left portion of the cycle shown in Scheme 1, whereas all of the reaction steps presented in Scheme 2a are elementary reactions. This catalytic cycle is denoted hereafter as catalytic cycle A (CCA). Figures 1 and 2 present all of the optimized geometries involved in CCA. Species 3 is a tricoordinated Ta(III) species, and the addition of methane to the Ta center affords a pentacoordinated Ta(V) species, namely, (SiO3)2Ta(H)(CH3)2 (4). The geometries of 3, TS-3-4, and 4 displayed in Figures 1 and 2 show that the approach of a CH4 molecule to the Ta center is accompanied by the breaking of one C−H bond and the formation of a Ta− H bond. This process is similar to the case of the C−H bond activation of methane on an isolated Mo atom.32 Species 4 can change to the methyl(methylidene)tantalum species ( SiO3)2Ta(CH3)CH2 (5) through the elimination of a hydrogen molecule. In this reaction step, a hydrogen atom detaches from a methyl group and approaches the H atom that is bound to Ta to form a hydrogen molecule, which can be seen by comparison of the geometries of 4, TS-4-5, and 5 (see Figure 2). The transformation of 5 into an ethyltantalum species, ( SiO3)2Ta−CH2CH3 (6), can take place through the elementary step of intramolecular carbene insertion. The approach of one C atom to the other in species 5 is accompanied by cleavage of the Ta−Cmethyl bond and an increase in the Ta−Cmethylene bond length. The variation of the Ta−Cmethylene bond length as well as its bond order indicates a process in which a double bond

Figure 1. Optimized geometries of the reactant, the products, and the two suggested model catalysts (1 and 3) for nonoxidative coupling of methane. Key distances are indicated in Å.

separated closed-shell singlet state of 3 and CH4 was used as the reference to define the energy profiles. The study considered two new catalytic cycles and their competing pathways, as described in Scheme 2. We note that the calculations predict 1 to have a triplet ground state (similar to the case in ref 31). However, in the Supporting Information we show that the barriers on the triplet PESs are relatively high in energy compared with those on the singlet PESs. Thus, the consideration of the triplet state for 1 will not affect the conclusions in this paper, which are based on

Scheme 2. Two Catalytic Cycles for Silica-Supported Single-Site Tantalum-Catalyzed NOCM Investigated in This Work (Solid Lines): (a) CCA; (b) CCBa

a

Reaction pathways indicated with the dotted lines are unfavorable pathways competing with these two catalytic cycles. [Ta] is used to represent the silica-supported Ta part for clarity. 2174

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Figure 2. Optimized geometries of the species involved in CCA. Key distances are indicated in Å. In this and the following figures, a line between two atomic symbols indicates only their connection and not their bond order. See the geometry of 3 in Figure 1 for comparison.

energy of activation among the five steps (46.4 kcal/mol), indicating at first glance that it is the rate-determining step for CCA. According to the energetic span model developed by Shaik et al.,34−36 the energetic span of a catalytic cycle (δE) determines whether or not it is favorable. The energetic span, as defined in ref 34, is the free energy difference between the highest transition state and the lowest intermediate in a catalytic cycle. A smaller δE results in a larger turnover frequency, leading to a favorable catalytic cycle. On the basis of the energetic span model, the overall turnover frequency of CCA is determined by the free energy of (3 + CH4) (the lowest point in Figure 3) and that of the transition state TS-6-7 (the highest point). Thus, the energetic span of CCA, δECCA, is 66.0 kcal/mol on the basis of Figure 3. In other words, no rate-determining step for CCA exists; rather, there are only two rate-determining states,36 which are the species (3 + CH4) and TS-6-7.

changes into a single bond. The transformation of 6 into a pentacoordinated Ta(V) species, (SiO3)2Ta(CH3)(H)− CH2CH3 (7), is very similar to the reaction step in which 3 evolves into 4 (see Scheme 2a or Figures 1 and 2). The only difference is that the methyl group in 3 is replaced by an ethyl group in 6. Elimination of an ethane molecule from 7 recycles 3, the catalyst of CCA. This step is also similar to 4 → 3, the opposite of 3 → 4, as shown from the comparison of the geometrical changes that occur in 7 → TS-7-3 → 3 and 4 → TS-4-3 → 3. CCA comprises of five elementary reaction steps. The free energy profile (about the energetic reference, see the note in ref 33) for CCA is shown in Figure 3 (the corresponding internal energy and enthalpy profiles for each free energy profile are shown in Figures S2−S5 in the Supporting Information). Figure 3 shows that the first two steps (3 → 4 → 5) can take place in a facile way on the basis of the encountered free energies of activation. The step 5 → 6 has the largest free 2175

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(CCB). Figure 4 presents the optimized geometries of all of the species involved in CCB. The addition of a methane molecule to 1 to afford a pentacoordinated methyltantalum dihydride, (SiO3)2Ta(H)2−CH3 (8), occurs in a concerted manner, as shown from the geometries of 1, TS-1-8, and 8 (Figure 4). This transformation is similar to the case of the 3 → TS-3-4 → 4 step. The elementary reaction step for the transformation of 8 into 3 through the elimination of a hydrogen molecule formed from the two H atoms bound to Ta was not found despite several attempts to find it. Instead, another hydrogen elimination pathway was found, namely, 8 → 9, where 9 denotes (SiO3)2Ta(H)CH2. The geometries of 8, TS-8-9, and 9 show that the H atom migrates from the methyl group in 8 to the nearby H atom to form a hydrogen molecule. One H atom in this formed hydrogen molecule comes from H−Ta in 8, whereas the other comes from the methyl group in 8. The tantalum methylidene species 9 is then formed. In the 9 → TS9-3 → 3 step, the H atom bound to Ta is transferred from Ta to C to form a methyl group to afford 3. The 3 → 4 step in CCB is the same as that in CCA. Two methyl groups are bound to Ta; thus, a reductive elimination of these two methyl groups to directly afford ethane may be expected to occur. This speculated “reductive elimination” step looks similar to the case in alkyl−alkyl cross-coupling reactions.37 However, this step was not found in this work. Instead, the cleavage of one C−H bond in a methyl group is

Figure 3. Relative free energy (723.15 K, 49.3 atm) profile for CCA.

3.2. Catalytic Cycle with a Surface Tantalum Hydride Species as the Catalyst. Because the working catalytic cycle is assumed to be a Ta(III)−Ta(V) cycle29 and 1 is analogous to 3, the feasibility of 1 to act as a catalyst for NOCM was interesting to study. Thus, the possible catalytic cycle operating with 1 as the catalyst was also investigated. This catalytic cycle, depicted in Scheme 2b, is denoted hereafter as catalytic cycle B

Figure 4. Optimized geometries of the species involved in CCB. Key distances are indicated in Å. The geometries of 1, 3, TS-3-4, and 4 are shown in Figures 1 and 2 2176

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9 and 10 → 1 require free energies of activation of 29.2 and 24.4 kcal/mol, respectively. Similar to the case observed in CCA, no rate-determining step in CCB was found; only two rate-determining states were present. The points in CCB with the lowest and highest free energies are (9 + H2) and TS-4-10, respectively. These two rate-determining states determine that CCB has an energetic span of 74.1 kcal/mol, which is higher than the value determined for CCA. 3.3. Reaction Pathways Competing with Those of Catalytic Cycle A. The reaction pathways that compete with CCA and CCB were also investigated in order to better understand the broader landscape of the PESs for NOCM catalyzed by 3 and 1. These competing pathways are indicated by the dotted lines in Scheme 2. In the CCA route, the transformation of 5 into 7 with the 5 → 11 → 7 pathway can occur competitively with the 5 → 6 → 7 pathway, as indicated in Scheme 2a, where 11 is a trimethyltantalum species, (SiO3)2Ta(CH3)3. For the transformation of 5 into species 6, the 5 → 12 → 13 → 6 pathway can take place competitively with the concerted 5 → 6 pathway, where 12 and 13 denote (SiO3)2TaCH and (SiO3)2Ta(H)CH−CH3, respectively. Figure 6 presents the optimized geometries of the species involved in these two pathways other than the 5 → 6 → 7 pathway. In the 5 → 11 → 7 pathway, an addition of methane to 5 to afford a trimethyltantalum species 11 can occur. The geometry changes in the 5 → TS-5-11 → 11 step show that a hydrogen atom shifts from the molecular methane to the methylidene group, accompanied by the formation of a C−Ta bond. The 11 → TS-11-7 → 7 step is substantially similar to the case of the 4

accompanied by the detachment of the other methyl group from Ta, shifting to the first methyl group. This concerted process can be clearly seen from the geometry changes in the step 4 → TS-4-10 → 10, where 10 denotes (SiO3)2Ta(H)2− CH2CH3. Similar to the addition of methane to 1, ethane elimination can occur in 10. The elimination of ethane from 10 recycles 1, the catalyst of CCB. CCB comprises six elementary reaction steps. The free energy profile displayed in Figure 5 shows that most of the

Figure 5. Relative free energy (723.15 K, 49.3 atm) profile for CCB.

elementary reaction steps in CCB occur rather quickly, except for 4 → 10, on the basis of the free energies of activation and the reaction temperature (723 K). For example, the steps 8 →

Figure 6. Optimized geometries of the species involved in the competing pathways with those of CCA. For the optimized geometries of species 5, 6, and 7, see Figure 2 2177

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aside from the stepwise 9 → 3 → 4 pathway involved CCB. The transition-state structure of the 9 → 4 pathway is shown in the left panel of Figure 8. The transformation of 9 into 4 is very

→ TS-4-10 → 10 step, which is also an intramolecular methylene shift step. From the catalytic cycle proposed in ref 20 as shown in the right portion of Scheme 1, the authors also proposed a catalytic cycle involving a carbyne−Ta complex. Therefore, the reaction pathway with the participation of a carbyne−Ta complex was also explored. The silica-supported carbyne−Ta species 12 (see Figure 6) may be generated from 5 through a methane elimination step. This insertion of the carbyne−Ta complex into a methane molecule affords a carbene−Ta complex, indicated as the 12 → TS-12-13 → 13 step in Figure 6. Species 13, which is analogous to 9, can change into 6 in a similar manner as 9 transforms into 3. For competing pathways that share the same reactant, the relative rate constant can be estimated from the Boltzmann distribution of the highest transition states in the free energy profile38 by utilizing the following equation: ⎛ G⧧ − G ⧧ ⎞ ki j i ⎟ = exp⎜⎜ ⎟ kj ⎝ RT ⎠

Figure 8. Optimized geometries of the transition states TS-9-4 and TS-9-10.

(ii)

where ki is the rate constant of a certain reaction pathway and G⧧i is the free energy of the highest transition state in the corresponding pathway relative to an arbitrary reference. Therefore, the relative rate constant of the 5 → 11 → 7 pathway over the 5 → 6 → 7 pathway can be calculated through the free energy difference between TS-11-7 and TS-67 (Figure 7). This relative rate constant is 3.3 × 10−4. Therefore, the contribution of the 5 → 11 → 7 pathway to the overall catalytic cycle A is trivial.

similar to that of 5 into 11. Both processes involve methane addition to a methylidene−Ta species. The relative contribution of the 9 → 4 pathway over the 9 → 3 → 4 pathway can also be calculated using eq ii and the free energy profiles of these two pathways depicted in Figure 9. The relative rate

Figure 9. Relative free energy (723.15 K, 49.3 atm) profiles for three competing pathways for CCB. Dotted lines: 9 → 3 → 4 → 10 pathway as indicated in CCB. Dashed-dotted lines: 9 → 4 → 10 pathway. Dashed lines: 9 → 10 pathway. Figure 7. Relative free energy (723.15 K, 49.3 atm) profiles for the three competing pathways for CCA. Dotted lines: 5 → 6 → 7 pathway as indicated in CCA. Dashed-dotted lines: 5 → 12 → 13 → 6 → 7 pathway. Dashed lines: 5 → 11 → 7 pathway.

constant of the former pathway over the latter one is determined by the free energy difference between TS-9-4 and TS-3-4. This relative rate constant is 6.3 × 10−5. For the transformation of 9 into 10, a concerted 9 → 10 pathway occurs competitively, as indicated in Scheme 2b, aside from the stepwise 9 → 3 → 4 → 10 pathway involved in CCB. The right panel of Figure 8 shows the structure of transition state TS-9-10, which is similar to that of TS-9-4, with the only differences being in the H3C···Ta and H3C···CH2 distances. In the case of TS-9-10, the methyl group is relatively close to CH2 and far from Ta compared with that in TS-9-4. As a consequence, the C−C bond is formed instead of the C−Ta bond in the product following TS-9-10. The relative

In a same manner, the relative rate constant of the 5 → 12 → 13 → 6 pathway over the 5 → 6 pathway can be calculated with the free energy difference between TS-12-13 and TS-5-6. This relative rate constant is 4.9 × 10−9. Thus, the contribution of the 5 → 12 → 13 → 6 pathway to the overall catalytic cycle A is minimal. 3.4. Reaction Pathways Competing with Those of Catalytic Cycle B. For the transformation of 9 into 4, a concerted 9 → 4 pathway (see Scheme 2b) was also found 2178

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contribution of the 9 → 10 pathway over the 9 → 3 → 4 → 10 pathway can also be calculated using eq ii and the data shown in Figure 9. The relative rate constant of the former over the latter pathway, which is determined by the free energy difference between TS-9-10 and TS-4-10, is 8.4 × 10−6. To briefly summarize the preceding results, both the 9 → 10 and 9 → 4 → 10 pathways appear to make trivial contributions to CCB. In addition, the higher relative free energy of TS-9-4 compared with TS-3-4 shows that the 3 → 9 → 4 pathway (see Scheme 2a) is less favorable than the 3 → 4 pathway in the CCA route. Species 5 and 9 are both metal carbenoid compounds. The direct insertion of the C atom from the carbene fragment into a saturated C−H bond through a metal carbenoid has been wellestablished for some metal complexes, such as dirhodium tetracarboxylate.39 When a similar reaction can occur on 5 or 9, this reaction step directly produces ethane and recycles 3 or 1. However, such a reaction step was not found in this work, which may be attributed to the existence of a hydrogen atom bound to Ta in 5 and 9 that may lead to insufficient electrophilicity of the CH2 moiety also bound to Ta. 3.5. Comparison between the Two Catalytic Cycles Using Different Catalysts and a Hint for Catalyst Design. Inspection of the energy profiles depicted in Figure 5 shows that 3 can be formed from 1 by the following reaction: 1 + CH4 ⇄ 3 + H 2

° KNOCM =

(vii)

(viii)

By substitution of eqs vii and viii into eq vi, the following equation can be obtained: ⎛ ΔGtrans ⎞ ° − 0.5ΔG NOCM ° [1] = exp⎜ ⎟ ⎝ ⎠ [3] RT

(ix)

Finally, the relative contribution of catalyst 3 over catalyst 1 to NOCM can be calculated by the following equation: no. of methane molecules converted by 1 no. of methane molecules converted by 3 ⎛ δE ° ° ⎞ − δECCB − 0.5ΔG NOCM + ΔGtrans = exp⎜ CCA ⎟ ⎝ ⎠ RT (x) 40

as derived from eqs v and ix. The data needed for eq x can be obtained from Figures 3 and 5, which show that δECCA, δECCB, ΔG°NOCM and ΔG°trans are 66.0, 74.1, 18.8, and 1.1 kcal/mol, respectively. Thus, the left side of eq x is 1.1 × 10−5, which indicates that the conversion of methane catalyzed by 1 is negligible compared with the conversion catalyzed by 3. Comparison of the free energy profiles of CCA and CCB displayed in Figures 3 and 5 shows that the free energy of the highest transition state in CCA, TS-6-7, is actually slightly higher than that of TS-4-10 in CCB. However, the free energy of 9 in CCB (−10.2 kcal/mol) is extremely low compared with that of 5 (2.1 kcal/mol) in CCA. Species 9 has the lowest free energy in CCB, but 5 does not have the lowest free energy in CCA. Thus, CCA appears to be more effective than CCB not because the highest point of the free energy profile for CCA is lower than that for CCB but rather because the lowest point of the free energy profile for CCA is higher than that for CCB. Our results reinforce an important idea in catalysis, namely, that the activity of a catalyst can be improved by increasing the energy of the lowest-energy intermediate and not only by lowering the energy of the highest-energy transition state.36 The preceding calculated results show that the catalysis of 3 proposed in ref 20 is plausible. However, the catalytic cycle proposed in ref 20 (Scheme 1) is less favorable than CCA proposed in this work (Scheme 2a). CCA provides new insights into the reaction mechanism at the elementary-reaction level. Step (1) indicated in Scheme 1 can occur in one elementary step (3 → 9). However, this step is not involved in the real working catalytic cycle (CCA) but rather appears in a catalytic cycle making a trivial contribution (CCB). The pentacoordinated species 4 is more plausibly involved in the working catalytic cycle than 9. As a consequence, the product of step (1) is also not involved; hence, step (2) is also not involved in the working catalytic cycle. When 4 is formed, it can be converted to 5, which is the reactant of step (3) indicated in Scheme 1. Step (3), which is the 5 → 6 reaction in this work, is plausible. Step (4) seems plausible, but it comprises two elementary steps, namely, the 6 → 7 and 7 → 3 reactions in this work. Step (5) was not found in this work despite significant efforts to locate this pathway. Although step (6) can occur in an

(iii)

(iv)

TOFB no. of methane molecules converted by 1 [1] = × no. of methane molecules converted by 3 TOFA [3] (v)

where [1] and [3] are the surface concentrations of 1 and 3, respectively. The reaction barrier required for the conversion of 1 to 3 is 38.6 kcal/mol (see Figure 5), which is significantly lower than that of the overall NOCM reaction. Therefore, these two species can be considered to be in a reasonably fast equilibrium under the reaction conditions typically employed for NOCM. Thus, the relative concentration of 3 over 1 for the transformation reaction shown in eq iii is governed by ⎛ ΔGtrans ° ⎞ [3][H 2] = exp⎜ − ⎟ ⎝ [1][CH4] RT ⎠

[CH4]

⎛ ΔG NOCM ⎞ ° = exp⎜ − ⎟ ⎝ RT ⎠

[C2H6] = [H 2]

The relative contribution of CCA using catalyst 3 over CCB using catalyst 1 can be determined by

° = K trans

2

and

through the 1 → 8 → 9 → 3 reaction pathway. The energetic span model34−36 was utilized to determine which of the catalytic cycles is more plausible for NOCM. In sections 3.1 and 3.2, the energetic spans of CCA and CCB (δECCA and δECCB) were determined to be 66.0 and 74.1 kcal/ mol, respectively. Because the overall reactions for CCA and CCB are the same, the relative turnover frequency (TOF) of each catalytic species for these two catalytic cycles can be determined by ⎛ δE − δECCB ⎞ TOFB ⎟ = exp⎜ CCA ⎝ ⎠ TOFA RT

[C2H6][H 2]

(vi)

where Ktrans ° and ΔGtrans ° are the standard equilibrium constant and the standard molar free energy, respectively, of the reaction shown in eq iii. From the experimental results reported in ref 20, the authors found that the NOCM reaction reaches thermodynamic equilibrium. Thus, the following equations are valid: 2179

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ZR2012BQ020), the Research Grants Committee of Hong Kong (Grant HKU-7048/11P), and the Collaborative Research Fund (HKU1/CRF/08) is gratefully acknowledged. This research was conducted using the HKU Computer Centre research computing facilities, which are supported in part by the Hong Kong UGC Special Equipment Grant (SEG HKU/ 09).

elementary reaction, the catalytic cycle involving step (6) is not energetically feasible (see section 3.3). From eq ix, the [1]/[3] concentration ratio was 0.0031, suggesting that the “catalytic material” added into the reaction system may not be the real active catalyst that makes the largest contribution to the conversion of the reactant to the product. The “active catalyst” may be formed in situ in the reaction system when the involvement of the reactants is considered. In this special case, the starting material 1 is converted to 3 in the presence of methane, and 3 is the real active catalyst instead of the starting material 1. A supported single-site metal catalyst is regarded as a bridge for connecting the fields of heterogeneous and homogeneous organometallic catalysis.41 Similar studies are useful in gaining more insights into the reaction mechanisms of alumina- or silica-supported single-site tungsten-catalyzed21 alkane coupling or metathesis reactions29 as well as into those of methyl migration processes in organotantalum42 or organotungsten complexes.43

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4. CONCLUSION The DFT computational results presented in this work provide new insights into the reaction mechanism of NOCM occurring on a single-site Ta catalyst. The main conclusions of this work can be summarized as follows: (1) For questions Q1 and Q2 in the Introduction, the reaction mechanism proposed in ref 20 should be revised to include CCA found in this work, where (SiO3)2Ta− CH3 (3) catalyzes NOCM. The two rate-determining states for the CCA route are (3 + CH4) and TS-6-7. (2) For Q3, (SiO3)2Ta−H (1) catalyzes NOCM through CCB. The two rate-determining states for the CCB route are (9 + H2) and TS-4-10. (3) The turnover number of the methane conversion catalyzed by 3 is around 105-fold larger than that by 1. This finding indicates that 3 (rather than 1) is actually responsible for most of the conversion of methane to ethane. (4) For Q4, the initial catalytic material added into the reaction system, 1, can undergo a three-step reaction (1 → 8 → 9 → 3) to form the real working catalyst, 3.

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AUTHOR INFORMATION

REFERENCES

S Supporting Information *

Full citation of ref 26, Figures S1−S5, and a text file (in .xyz format) containing Cartesian coordinates, zero-point-corrected energies, enthalpies, free energies (at 723.15 K, 49.3 atm), and imaginary frequencies for all of the optimized structures at the B3LYP/BS1 level of theory. This material is available free of charge via the Internet at http://pubs.acs.org. Corresponding Authors

*Email: [email protected]. *Email: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Supports from the National Natural Science Foundation of China (21003159, 21306230, 21303267, 21303266), Shandong Province Natural Science Foundation (ZR2011EMZ002, 2180

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Organometallics

Article

the whole NOCM process is also unlikely to proceed via a Ta(III)− Ta(V) scheme using (SiO3)2Ta(H)3 as a catalyst. Therefore, this paper does not deal with cases using (SiO3)2Ta(H)3 or other Ta(V) compounds as active catalysts. (31) Solans-Monfort, X.; Chow, C.; Gouré, E.; Kaya, Y.; Basset, J.-M.; Taoufik, M.; Quadrelli, E. A.; Eisenstein, O. Inorg. Chem. 2012, 51, 7237−7249. (32) Guo, Z.; Ke, Z. F.; Phillips, D. L.; Zhao, C. Y. Organometallics 2008, 27, 181−188. (33) In this study, (3 + CH4) was used as the energetic reference in the free energy profiles presented. Notably, the way of reference selection does not affect the data such as the reaction energy barrier and relative reaction rate. (34) Kozuch, S.; Amatore, C.; Jutand, A.; Shaik, S. Organometallics 2005, 24, 2319−2330. (35) Kozuch, S.; Shaik, S. J. Am. Chem. Soc. 2006, 128, 3355−3365. (36) Kozuch, S.; Shaik, S. Acc. Chem. Res. 2011, 44, 101−110. (37) Lin, X.; Sun, J.; Xi, Y.; Lin, D. Organometallics 2011, 30, 3284− 3292. (38) Balcells, D.; Maseras, F. New J. Chem. 2007, 31, 334−343. (39) Nakamura, E.; Yoshikai, N.; Yamanaka, M. J. Am. Chem. Soc. 2002, 124, 7181−7192. (40) Considering the reaction conditions (723 K, 50 bar) for NOCM reported in ref 20, the gases approximately follow ideal gas behavior at high temperatures, not high pressures. Therefore, the concentration was used instead of fugacity in the expressions employed to describe the equilibrium constants. The free energy change at 723 K and 50 bar is equal to that at 723 K and 1 bar when the species is treated as an ideal gas. (41) Thomas, J. M.; Raja, R.; Lewis, D. W. Angew. Chem., Int. Ed. 2005, 44, 6456−6482. (42) Agapie, T.; Day, M. W.; Bercaw, J. E. Organometallics 2008, 27, 6123−6142. (43) Shortland, A. J.; Wilkinson, G. J. Chem. Soc., Dalton Trans. 1973, 872−876.

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