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Mechanistic Insights into Alkane Metathesis Catalyzed by SilicaSupported Tantalum Hydrides: A DFT Study Francisco Núñez-Zarur,*,†,§ Xavier Solans-Monfort,‡ and Albeiro Restrepo† †

Instituto de Química, Universidad de Antioquia, Calle 70 No. 52-21, 050010 Medellín, Colombia Departament de Química, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain

‡

S Supporting Information *

ABSTRACT: Alkane metathesis transforms small alkanes into their higher and lower homologues. The reaction is catalyzed by either supported d0 metal hydrides (M = Ta, W) or d0 alkyl alkylidene complexes (M = Ta, Mo, W, Re). For the silicasupported tantalum hydrides, several reaction mechanisms have been proposed. We performed DFT-D3 calculations to analyze the viability of the proposed pathways and compare them with alkane hydrogenolysis, which is a competitive process observed at the early stages of the reaction. The results show that the reaction mechanisms for alkane metathesis and for alkane hydrogenolysis present similar energetics, and this is consistent with the fact that the process taking place depends on the concentrations of the initial reactants. Overall, a modified version of the so-called one-site mechanism that involves alkyl alkylidene intermediates appears to be more likely and consistent with experiments. According to this proposal, tantalum hydrides are precursors of the alkyl alkylidene active species. During precursor activation, H2 is released and this allows alkane hydrogenolysis to occur. In contrast, the catalytic cycle implies only the reaction with alkane molecules in excess and does not form H2. Thus, the activity for alkane hydrogenolysis decreases. The catalytic cycle proposed here implies three stages: (i) β-H elimination from the alkyl ligand, liberating ethene, (ii) alkene cross-metathesis, allowing olefin substituent exchange, and (iii) formation of the final products and alkyl alkylidene regeneration by olefin insertion and three successive 1,2-CH insertions to the alkylidene followed by α abstraction. These results relate the reactivity of silica-supported hydrides with that of the alkyl alkylidene complexes, the other common catalyst for alkane metathesis.

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the reactivity at 150 °C of propane with well-defined, single-site Ta hydrides supported on silica, TaHx/SiO2, where x = 1, 3 (I in Scheme 1).1 The observed products were methane, ethane, and n-butane as well as low amounts of isobutene, pentanes, and hexanes. In addition to this, W hydrides (II in Scheme 1) supported on alumina or silica−alumina also catalyze alkane metathesis.9−11 Finally, d0 alkyl alkylidene complexes of tantalum,12−14 molybdenum,15,16 and rhenium17,18 (III−VII in Scheme 1) as well as some polyalkyl complexes of tantalum14 (VIII in Scheme 1) and tungsten carbynes9,19 and polyalkyls20−22 are also active in alkane metathesis. In all these systems the active metal sites are thought to be multifunctional, meaning that they catalyze both dehydrogenation/hydrogenation and olefin metathesis reactions. Silica-supported tantalum hydrides TaHx/SiO2 (x = 1, 3)23 are composed of a mixture of mono- and trihydride species of general formula (SiO)2Ta-H and (SiO)2Ta-H3, respectively.24 The two species have been characterized by elemental and mass balance analysis, IR, 1H and 13C solid-state NMR, and

INTRODUCTION The chemical transformation of alkanes remains one of the most challenging reactions in hydrocarbon chemistry, basically due to the high stability of their C−H and C−C bonds. Alkane metathesis (eq 1) has become in recent years one elegant method to manipulate low-value alkanes and transform them into higher and lower homologues under relatively mild conditions (150−200 °C).1−4 This can be used for the transformation of low-value fossil feedstocks such as natural gas and propane into high-value alkanes with applications as fuels, for instance.5 cat.

2CnH 2n + 2 HooI Cn − iH 2(n − i) + 2 + Cn + iH 2(n + i) + 2 i = 1, 2, ..., n − 1

(1)

The first evidence of the disproportionation of alkanes into lower and higher homologues appeared in the 1970s at Chevron Research Co. using dehydrogenation/hydrogenation and alkene metathesis heterogeneous catalysts in tandem.6 The tandem concept was also useful for designing homogeneous systems active in alkane metathesis.7,8 In 1997, the term “alkane metathesis” was introduced for the first time in a description of © 2017 American Chemical Society

Received: June 8, 2017 Published: August 15, 2017 10458

DOI: 10.1021/acs.inorgchem.7b01464 Inorg. Chem. 2017, 56, 10458−10473

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Inorganic Chemistry Scheme 1. Examples of Supported Single-Site Metal Complexes Used in Alkane Metathesis

Scheme 2. Proposed Pathways of Alkane Metathesis Using the Silica-Supported Ta Hydride via (a) the Two-Site Mechanism and (b) One-Site Mechanism Based on Alkyl Alkylidenes

EXASF spectroscopic techniques.23−25 The amounts of active sites in this mixture were discriminated by poisoning experiments with O2 and cyclopentane (only 50% of sites are active).25 Moreover, thorough kinetic experimental studies on dynamic conditions showed that H2 and olefins are primary products that are formed at the beginning of the reaction.26 This led to the proposal of two plausible reaction mechanisms (Scheme 2).2,3,27 The first is called as a two-site mechanism,26 and it involves two key intermediates, each with a particular functionality: the initial tantalum hydride (I) and a tantalum alkylidene (b). This mechanism consists of three stages (Scheme 2a): (i) initial alkane dehydrogenation and tantalum alkylidene formation (blue arrows), (ii) alkene cross-metathesis (red arrows), and (iii) hydrogenation of the newly formed alkenes and hydride regeneration (green arrows). The second proposal is called the one-site mechanism, and it is based on tantalum alkyl alkylidene species that are formed in situ and act as active

species (Scheme 2b).12−14,28 According to this proposal, the alkyl alkylidene species undergo β abstraction, which forms the required alkene molecule (pink arrows). Afterward, the olefin reacts with the alkylidene ligand through alkene metathesis (red arrows) and generates an olefin with an additional carbon and methylidene. Finally, propene insertion and two successive C− H σ-bond metathesis steps regenerate the tantalum alkyl alkylidene active species (orange arrows). Evidence in favor of this latter mechanistic proposal is the isolation of tantalum methyl methylidene silica-supported species (SiO2)2−xTa CH2(CH3)1+x that are active in metathesis14 and labeling experiments suggesting the formation of Ta ethylidene intermediates and products arising from the C−H activation.14,28,29 Overall, while the two-site mechanism has mainly been used to describe the reactivity of metal hydrides, the onesite pathway allows an easier explanation for the catalytic activity of alkyl alkylidene and polyalkyl metal complexes, such VI−VIII in Scheme 1. 10459


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cationic [TaH2]+ species supported on a zeolite framework.35 Overall, Schinzel et al.34 did not consider the full catalytic cycle of alkane metathesis with TaHx/SiO2 (x = 1, 3), while Mazar et al.35 did not consider the experimentally characterized active species. Moreover, the one-site mechanism has never been studied computationally and there is no information about (i) the stability of the tantalum hydride alkylidene, alkyl alkylidene, and Ta cyclobutane(s) species with respect to the initial reactants, (ii) the energy barriers that have to be overcome to form these species, and (iii) how these barriers compare between them and with those of the alkane hydrogenolysis. Notice that the contributions on alkane hydrogenolysis reactions31,32 only focus on this reaction and, thus, comparison with the alkane metathesis is not possible in these cases. In this contribution, we address the alkane metathesis process with density functional theory (DFT) calculations and consider ethane as the reacting paraffin and the experimentally proposed TaHx/SiO2 active site. We focus on both the two-site and onesite mechanisms, paying special attention to the three key stages of the reaction (alkylidene and olefin formation, ethene crossmetathesis process, and hydrogenation of the newly formed alkene and Ta alkylidene species). We also consider some alternative steps, especially for the one-site mechanism. Finally, with the aim of being as exhaustive as possible, we also compute the most favorable reaction path for ethane hydrogenolysis.

These silica-supported TaHx/SiO2 (x = 1, 3) hydrides also catalyze the alkane hydrogenolysis of a variety of paraffins, including ethane.30−32 In this process, a mixture of H2 in excess and the selected hydrocarbon is converted into the smaller alkanes, the final product at full conversion being methane. Therefore, addition of H2 in the reaction mixture changes the reactivity of TaHx/SiO2 (x = 1, 3) species toward alkanes. This is summarized in Table 1, which shows the reaction conditions Table 1. Change in Reactivity of (SiO2)2Ta-Hx (x = 1, 3) with Ethane upon Addition of H2 to the Reaction Mixture reaction

ethanea

H2a

T (°C)

time (h)

TONb

ref

metathesis hydrogenolysis

800 43

710

150 160

50−80 40

1 30

a Reactant/Ta ratio. bNumber of alkane molecules transformed during the reaction.

for the two processes (alkane metathesis and alkane hydrogenolysis) as well as the number of alkane molecules transformed by the tantalum center after a fixed reaction time. Moreover, analysis of the species formed during ethane metathesis under flow reactor conditions shows that alkane hydrogenolysis is significant at the initial stages of the process.33 Therefore, determination of the factors controlling alkane metathesis selectivity with respect to alkane hydrogenolysis is important for further improvement of the catalytic process. Computational chemistry can be used for this purpose: identifying the most favorable pathways, the nature of the rate-determining transition states of the two processes, and the influence of reactant concentrations. There are a few computational studies focusing on the reactivity of alkanes with silica-supported tantalum hydrides. They all represent the silica surface with a cluster model when the full reaction profile is computed. In particular, alkane hydrogenolysis has been studied in detail and calculations provided insights to establish the currently accepted reaction mechanism.31,32 Regarding the alkane metathesis reaction, two computational studies exist. Schinzel et al.34 studied the degenerate alkene metathesis of ethene with a Ta methylidene hydride species, which models the second stage of the proposed mechanisms (reactions b → d in Scheme 2). They found that, in addition to the typical cycloaddition and cycloreversion steps, the Ta cyclobutane intermediate has to isomerize through a turnstile mechanism to allow the release of the olefin product. A second contribution studied the full two-site mechanism of the ethane metathesis using a hypothetical

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COMPUTATIONAL DETAILS

Models. The silica surface has been represented by three different models: the clusters 2T and 9T and the periodic model P. They are all depicted for the particular case of the tantalum trihydride in Figure 1. The 2T cluster consists of two vicinal tetrahedral Si sites (2T) that are bonded to the tantalum metallic fragment, and it includes the first SiO4 shell of the silica bulk. Here, it has been used for the determination of all reaction intermediates and transition states explored in this work. This model has been used with success previously,34,36−41 and in fact, it is equivalent to models used in other contributions dealing with the reactivity of tantalum hydrides with alkanes,32,34 for which some calibration has already been performed.32 Despite all this knowledge, we decided to determine the validity of the 2T cluster model with the larger 9T cluster as well as the periodic model P. 9T is formed by nine SiO4 units, and the periodic model (P) is constructed from the amorphous silica models developed by Ugliengo and Sodupe accounting for a silanol density of 4.5 OH/nm2.42 In this model, two vicinal silanols were replaced by Ta monohydride and Ta trihydride following a procedure reported previously.40,41 A comparison among the three models is provided at the end of this section. Methods. Molecular calculations (for 2T and 9T models) were performed with the B3PW91 hybrid functional43,44 and the Gaussian 09 suite of programs.45 The validity of the level of theory was analyzed

Figure 1. Computational models used to represent the TaH3/SiO2 catalyst: (left) 2T cluster; (middle) 9T cluster; (right) periodic model. Color code of the elements: Ta, brown; O, red; Si, dark yellow; H, white. 10460


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Scheme 3. Relative Gibbs Energies (ΔG423, in kcal mol−1) with Respect to Separated Reactants of All Intermediates and Transition States (Values over the Arrows) Involved in the (a) C−H Bond activation of Ethane and Ethane Dehydrogenation and (b) formation of Ta Alkylidene Hydrides 6 and 10a

a

For 1a and 9 the two spin states are reported: singlet (top, normal) and triplet (italic, bottom). DFT-optimized structures can be seen in Figure S7 in the Supporting Information.

by performing optimizations with the M0646,47 and PBE048,49 hybrid functionals and the MP2 level of theory and single-point energy calculations with the CCSD(T) method only on 2T models. The calculations on model 9T were performed representing main-group elements with the 6-31G(d,p)50,51 basis sets and Ta with the LanL2TZ(f)52,53 relativistic effective core potential (RECP) with the associated basis and including an f polarization function54 (BS1). Calculations on model 2T were performed using two different basis sets, the same BS1 used for 9T and a larger BS2 basis set where Ta is represented with the same LanL2TZ(f) RECP52−54 but the maingroup elements (H, C, O, Si) are described with the 6-311++G(d,p) basis set.50,51,55,56 That is, the smaller basis set (BS1) is used for comparing 2T and 9T models while the larger basis set (BS2) is used for the final energetics reported in the text. The MP2 and CCSD(T) calculations were performed with BS2. All structures were fully optimized without symmetry constraints, and the nature of all stationary points (minima and transition states) was verified by frequency calculations. The interconnected minima for each transition state were determined by visualizing the vibrational mode corresponding to the negative value. In some cases, intrinsic reaction coordinate (IRC) calculations were performed to unambiguously confirm the connection between reactants and products. Gasphase thermal corrections were evaluated at 1 atm and 423.15 K, the temperature at which the experiments were performed. Additionally, dispersion corrections (D3) were added a posteriori to the final energies obtained with B3PW91 and PBE0 functionals by using the method proposed by Grimme57 and including Becke−Johnson (BJ) damping.58 Periodic calculations were performed with the VASP4.8 code using the projector augmented wave (PAW) formalism.59−62 Energetics were computed with the PBE functional48 and a cutoff of 400 eV. The Brillouin zone was sampled with a Γ-centered (3 × 3 × 1) grid. These parameters are very similar to those used in previous works describing silica-supported systems.38,41 Additionally, for all transition states, the Hessian matrix was calculated using a finite-difference method as implemented in VASP. Visual inspection of the imaginary frequency confirmed the nature of all transition state structures. To allow proper comparison with the 2T cluster models, the same stationary points were calculated using the PBE correlation functional. Two different

approaches have been adopted. On one site, molecular calculations with the Gaussian09 suite of programs using the larger BS2 basis set were used to evaluate the effect of the functional. On the other, periodic calculations with VASP4.8 using the same methodology described above and including the 2T cluster in a 20 × 20 × 20 Å cubic box allowed direct comparison with the periodic calculations. Methodology Validation. Results for the validation of the model and level of theory used here are reported in Table S1, Schemes S1− S3, and Figures S1−S6 in the Supporting Information. Comparisons between 2T and 9T clusters and the effect of functional choice were performed only on the first proposed steps of the two-site reaction mechanism: ethane dehydrogenation and formation of the Ta alkylidene hydride. Calculations show that, while the cluster size has essentially no effect (the only exception being TS(1a-1b), which is 4.1 kcal mol−1 lower with the larger model), a greater influence is observed regarding the level of theory. Overall, the results do not seem to depend on the functional or the cluster size; however, the use of large basis sets is desirable. Comparison between the cluster computed with Gaussian09 and periodic models using VASP4.8 can be found in Scheme S2 and Figures S3 and S4 in the Supporting Information for the ethene crossmetathesis with Ta ethylidene hydride (6). The geometries around the Ta center in all stationary points remain very similar for the two models, and the energies of the selected intermediates and transition states show the same general trends. It is worth noting that the values obtained with the 2T model using the methodology employed for the periodic calculations (Scheme S2) leads to values that are generally between those of the 2T molecular cluster and those of the periodic calculations, indicating again that the difference of a few kilocalories per mole arises not only from the representation of the surface but also from the level of theory. At this point it is worth highlighting that very good agreement between cluster and periodic calculations were achieved previously for the tantalum hydride species and other related systems.41,63,64 In fact, there is also some experimental evidence regarding the related alkene metathesis reaction which suggests that a comparison between supported and molecular analogues leads to the conclusion that silica has little electronic influence.65 Overall, 2T appears to be a reasonably accurate model allowing a large exploration of reaction pathways, the differences between 10461


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Scheme 4. Relative Gibbs Energies (ΔG423, in kcal mol−1) with Respect to Separated Reactants of All Intermediates and Transition States (Values over the Arrows) Involved in the Reaction of Ta Alkylidene 10 with Ethanea

a

DFT-optimized structures can be seen in Figure S8 in the Supporting Information.

methods and models arising from multiple factors. Note, however, that all considered models assume that tantalum is bonded to two oxygens bonded to vicinal silicon atoms. Other potential active sites may exist in which Ta is bonded to oxygens bonded to silicon atoms that are not vicinal. This may produce different strain and thus remarkable energy differences, as recently suggested by some of us in the Cr(III)/SiO2 polymerization catalyst66 or by Trunschke and co-workers for the classical heterogeneous catalyst for alkene metathesis reaction.67

computed geometries and IR stretching frequencies are in reasonable agreement with the experimental measurements (see Tables S2 and S3 in the Supporting Information for further details).23−25 Overall, 1b is more stable than 1a, which has a singlet ground state according to CCSD(T) calculations, by 30.3 kcal mol−1 and the barrier height connecting these two species is 22.2 kcal mol−1 above 1a. These data suggest that 1b is favored over 1a from both a thermodynamic and kinetic point of view and, thus, the reactivity of the TaHx/SiO2 catalyst toward alkanes takes place mainly on 1b. Stage I of the Alkane Metathesis: Ta Alkylidene and Ethene Formation. We have, first, explored the reaction pathways leading to the formation of ethene and Ta alkylidenes Ta(H)CHCH3 (6) and Ta(CH3)CH2 (10). Afterward, we have explored other pathways leading to the formation of alkyl alkylidene intermediates, Ta(CH3)CHCH3 (13) and Ta(CH2CH3)CHCH3 (14), potentially involved in the one-site mechanism, by reaction with additional ethane molecules. Scheme 3 summarizes the relative Gibbs energies with respect to 1b + ethane of all intermediates and transition states, and Figure S7 in the Supporting Information shows the optimized geometries around Ta. Ta alkylidene and ethene formation as well as the alkane hydrogenolysis from both 1a and 1b hydrides starts with the C−H activation of ethane (Scheme 3a). In the case of 1a, this occurs through the C−H oxidative addition to the Ta(III) center. This leads to the ethyl dihydride species 3a. The reaction is exergonic (−24.2 kcal mol−1) and proceeds in a single step. The 1a to 3a transition state is located 16.8 kcal mol−1 above 1a. The C−H activation process starting from 1b implies a σ-bond C−H metathesis that generates H2 and the same ethyl dihydride tantalum complex 3a. The global process is slightly endergonic (6.1 kcal mol−1). The dihydrogen intermediate 2 is found as a minimum in the potential energy surface. However, the dissociation of H2 from 2 is found to be barrierless and favorable in terms of Gibbs energy at 423 K. The σ-bond metathesis transition state is 33.3 kcal mol−1 above 1b + ethane, and it presents the characteristic wide (164°) C··· H···H angle of the four-centered transition state of d0 metals (Figure S7 in the Supporting Information).68,69 The barrier height associated with TS(1b-2) is similar to that reported by Basset and co-workers,31,32 the differences arising from the level of theory and the temperature considered. Overall, the

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RESULTS Two reaction mechanisms have been proposed for the alkane metathesis reaction catalyzed by silica-supported Ta hydrides. These mechanisms comprise a very complex network of interconnected elementary steps and side processes, each involving different surface species. Due to the complexity of the global reaction mechanism, we decided to divide the Results into five parts. We first briefly present the structure and energetics of the initial tantalum hydrides (SiO)2TaHx (x = 1, 3). The following three parts of the Results correspond to the three stages of the alkane metathesis through either the twosite or the one-site mechanism: (i) ethene and alkylidene formation, (ii) alkene metathesis, and (iii) hydrogenation of the new resulting olefins and alkylidenes. In each section we first focus on the two-site proposal, but we also address the mechanisms involving alkyl alkylidene species formed by reaction with several alkane molecules that are related to the one-site pathway. Finally, in the last part, we discuss the energetics of the alkane hydrogenolysis reaction through the mechanism proposed by Cavallo, Basset, and co-workers.31,32 This allows direct comparison of the two reaction mechanisms for the alkane metathesis and the alkane hydrogenolysis. All relative Gibbs energies presented along the text are at 150 °C (ΔG423) and refer to the 1b + nC2H6 reactant asymptote, where n denotes the number of ethane molecules. Structures and Stabilities of the Initial TaHx/SiO2 (x = 1, 3) Surface Species. According to EXAFS and IR spectroscopy, the initial surface Ta hydride is formed by a mixture of mono (1a)- and trihydride (1b) species.23,24 Since the differences in structures and reactivity between 1a and 1b have been considered before,31,32,40 we only address the most relevant points here (a detailed description of these systems can be found in Text S1 in the Supporting Information). Scheme 3a shows the associated energetics at 150 °C and Figure S7 in the Supporting Information the optimized geometries. The 10462


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Scheme 5. Relative Gibbs Energies (ΔG423, in kcal mol−1) with Respect to Separated Reactants of All Intermediates and Transition States (Values over the Arrows) Involved in the Reaction of Ta Alkyl 3a with Ethanea

a


5) transition state is 26.8 kcal mol−1 above the reactants. The overall process, 3a to 6, is endergonic by only 4.7 kcal mol−1, indicating that the Ta alkylidene hydride intermediate, which is only 10.8 kcal mol−1 above the separate reactants, can be formed during the reaction. The Ta alkylidene hydride 6 can also be formed through β-H abstraction to one hydride ligand in 3a. This forms 7 in a first stage, which is 17.3 kcal mol−1 above the initial species. Nevertheless, barrierless liberation of H2 readily leads to 8. The 3a to 8 overall process is marginally exergonic (−0.8 kcal mol−1). The associated transition state TS(3a-7) implies overcoming an energy barrier of 11.3 kcal mol−1. These data suggest that β-H abstraction would be easier than the α-H abstraction process that leads directly to alkylidene 6 in both thermodynamic and kinetic terms. However, the subsequent migratory insertion of the ethene ligand into the Ta−H bond that gives the alkyl intermediate 9 is unfavorable (ΔG423 K = +23.5 kcal mol−1), and it implies overcoming an energy barrier of 26.8 kcal mol−1, which is higher than that of the α-H abstraction. This is probably because it implies tantalum reduction to Ta(III), which usually leads to less stable species. Therefore, the subsequent alkylidene 6 or 10 formations by either α-elimination (9 to 6 step) or C−C bond cleavage (9 to 10 step) are highly unlikely (Scheme 3b). Direct transformation of 8 into 10 shows a transition state that is significantly higher than those of other explored pathways. Overall, the results show that the Ta alkylidene hydride 6 formation is feasible and would mainly occur through α-H abstraction from 3a to a hydride ligand, because this process does not require a change in the formal oxidation state of the metal center. The alkylidene formation is slightly endergonic, and the transition state highest in Gibbs energy corresponds to the initial ethane C−H activation of the 1b to 3a step. Since ethane is in excess in the reaction mixture, one can envisage that the most stable intermediates 3a, 6, 8, and even 9 could react with other alkane molecules, leading to the formation of polyalkyl or alkyl alkylidene intermediates that could be involved in the one-site reaction mechanism as

transition state associated with the 1b to 3a interconversion is significantly lower than that of the reaction starting from the monohydride 1a. Several processes from 3a may take place (Scheme 3b). For instance, according to the two-site mechanism, α-H abstraction and β-H elimination from the ethyl ligand produces the Ta alkylidene 6 and ethene, respectively. Dehydrogenation either by a direct path (3a → 9) or through the reductive coupling of one hydride and the ethyl ligand (3a → 7 → 8 → 9) connects with the hydrogenolysis pathways. Finally, 3a may react with additional ethane molecules, forming polyalkyl or alkyl alkylidene complexes, as suggested in the one-site mechanism (Schemes 4 and 5). We start with the formation of 6 and ethene (Scheme 3). The other processes will be discussed below. The β-H elimination to Ta from 3a proceeds by previous formation of Ta alkyl species 3b that is 1.2 kcal mol−1 below 3a. In 3b, the alkyl fragment accommodates to get closer to the Ta metal and forms the β-agostic interaction Ta···Cβ−Hβ that stabilizes 3b with respect to 3a. The β-H elimination to Ta from 3b is significantly endergonic (ΔG423 K = 23.0 kcal mol−1), and the associated transition state TS(3b-4) is 35.8 kcal mol−1 above the reactant asymptote. This transition state connects 3b with intermediate 4, from which the release of ethene is barrierless and slightly exergonic (−5.7 kcal mol−1) and regenerates the initial species 1b. Ethane dehydrogenation is strongly endergonic, the computed value being +22.2 kcal mol−1, and requires overcoming a relatively high transition state. Overall, the energy barriers and thermodynamics obtained here suggest that alkene molecules in the presence of Ta−Hx and H2 would be easily hydrogenated. The α-H abstraction from 3a transfers an H from the alkyl to one hydride ligand and forms species 5 in an endergonic step (ΔG423 K = 17.8 kcal mol−1). Intermediate 5 presents a coordinated H2 that readily decoordinates in a very exergonic process. The resulting Ta alkylidene 6 presents a strong αagostic interaction, as evidenced by the small Ta−C−Hα (91°) angle (Figure S7 in the Supporting Information). The TS(3a10463


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Scheme 6. Relative Gibbs Energies (ΔG423, in kcal mol−1) with Respect to Separated Reactants of All Intermediates and Transition States (Values over the Arrows) Involved in the Reaction of Ta Alkylidenes 6 (R = −H, Top) and 13 (R = −Me, Bottom) with Ethenea

a

The structure given in the red square represents a very high energy intermediate. DFT-optimized structures can be seen in Figures S10 and S11 in the Supporting Information.

β-H elimination from the ethyl ligand in 14 leads to the tantalum ethylidene hydride 6 and ethene, through a process that involves an energy barrier of 29.6 kcal mol−1. Overall, both 13 and 14 tantalum alkyl alkylidenes appear to be accessible if the 9 to 10 interconversion occurs, despite the high Gibbs energy barrier. This could open an alternative pathway for the one-site mechanism which cannot be ruled out. It is also interesting to note that all of these processes occur in parallel with the formation of methane, the most abundant product in the metathesis of ethane with Ta hydrides and the result of ethane hydrogenolysis. The alkyl complex 3a can also react with additional ethane molecules (Scheme 5 and Figure S9 in the Supporting Information). The σ-bond metathesis between ethane and one of the hydrides gives access to the Ta dialkyl hydride 16, through a slightly endergonic process of +4.5 kcal mol−1. The Gibbs energy barrier is 33.2 kcal mol−1. Formation of 16 can also take place by σ-bond metathesis from 8 or by 1,2-CH bond addition to 6. The associated energy barriers are similar to those of the 3a to 16 process, the lowest value being obtained for the 8 to 16 conversion. Three different processes have been considered starting from the hydride bis-alkyl complex 16. The first corresponds to the intramolecular α-H abstraction from an ethyl ligand producing the ethylidene ethyl dihydrogen intermediate 17. This process is analogous to the 3a to 5 step. It is worth noting that species 17 releases H2 in a barrierless process, forming the alkyl alkylidene 14. The TS(1617) transition state is 31.5 kcal mol−1 above the separate reactants and shares geometrical features similar to those of TS(3a-5). Overall, the 3a → 8 → 16 → 14 process is thermodynamically disfavored with respect to the 9 → 10 → 13 → 14 pathway. This arises from the fact that the formation of 14 from 3a is not associated with the exergonic alkane hydrogenolysis process. However, this process is kinetically favored, and its highest transition state is 10.8 kcal mol−1 lower in energy than that of the process starting from 9. In analogy with the reactivity of 3a, the second process from 16 that we have considered is the ethyl β-H abstraction to the hydride, forming 19 through the unstable H2 adduct 18. The overall process is degenerate and, as in the case of 3a, occurs on overcoming an energy barrier that is significantly lower than that of the α-H abstraction process. Consequently, the

proposed experimentally. In this way, we explored the addition of a second ethane molecule to the previously mentioned intermediates. The results are summarized in Schemes 4 and 5, which show the relative Gibbs energies of all intermediates and transition states, and in Figures S8 and S9 in the Supporting Information, which illustrate the coordination around tantalum of all involved species. Starting with the reactivity of 9 (Scheme 4), the cleavage of the C−C bond of the alkyl ligand leads to the Ta methyl alkylidene 10 in a reaction that is very exergonic (ΔG = −27.6 kcal mol−1) but that presents an energy barrier of 19.4 kcal mol−1. This implies overcoming a transition state located 48.2 kcal mol−1 above the separate reactants. Since TS(9-10) is very high in Gibbs energy, mainly due to 9, one could envisage a direct pathway connecting 8 and 10 (Scheme 3b). This process implies a hydride transfer to the formally [CH2CH2]2− ligand. However, the associated transition state TS(8-10) is even higher (57.9 kcal mol−1, Scheme 3b) than the pathway through the Ta(III) species 9. This is consistent with previous results on N2 splitting by the same tantalum hydride complexes, and it can be rationalized by the strong repulsion occurring when a negatively charged hydride is transferred to a formally doubly negative ligand.40 Further reaction of 10 with ethane leads to the Ta methyl ethylidene intermediate 13. This can take place through two different pathways: (i) σ-bond metathesis + intramolecular αH-transfer (10 → 11 → 13) as proposed by Basset and coworkers14 or (ii) 1,2-CH bond addition to the alkylidene and subsequent α-H abstraction from the newly form ethyl ligand (10 → 12a → 12b → 13). The latter is more favorable and it implies overcoming transition states that lie 29.5 and 27.0 kcal mol−1 above the separate reactants. Interestingly, isomerization of 12a should occur before the α-H abstraction to allow the abstracted hydrogen to be trans to an oxygen of the surface. The Ta methyl alkylidene 13 is 1.5 kcal mol−1 lower than the initial reactants. Finally, reaction of a third ethane molecule with 13 leads to the Ta ethyl alkylidene 14 in an essentially degenerate process. Again, two processes can be envisaged: by a direct path through σ-bond metathesis or in two steps consisting of 1,2-CH bond addition to 15 and α-H abstraction. The second possibility is preferred. That is, the C−H σ-bond metathesis does not appear to be the most favorable pathway for the formal exchange of alkyl alkylidene substituents. Finally, 10464


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the opening of a vacant site.71−73 Then, the [2 + 2] cycloaddition between the coordinated ethene and Ta alkylidene leads to the Ta cyclobutane 22H in an almost isoergonic step. Formation of 22H passes through the transition state TS(21H-22H) that is only 2.2 kcal mol−1 higher in energy than 21H but 40.6 kcal mol−1 above initial reactants. The direct [2 + 2] cycloreversion from metallacyclobutane 22H is not possible, since it would involve a very high energy intermediate (see the red square in Scheme 6), in which the olefin decoordinates trans to one weakly donating alkoxy ligand.34 Therefore, isomerization of the Ta cyclobutane must occur in order to allow the release of propene trans to the hydride ligand. Accordingly, 22H easily rearranges via a series of turnstile steps to the Ta metallacycle 25H, which is only 2.2 kcal mol−1 higher in energy than 22H. This species presents the methyl substituent of the Ta cyclobutane fragment trans to the hydride ligand and shares structural similarities with 22H. The intermediate Ta cyclobutanes 23H and 24H are similar to those reported previously34 and are more stable than 22H by 16 kcal mol−1. All of these metallacycles (22H−25H) present a trigonalbipyramidal structure around the metal center. However, while 22H and 25H have an alkyl and a hydride in apical positions, complexes 23H and 24H have one siloxy group in an apical position. This latter conformation reduces the trans influence between the ligands in apical positions, and it is responsible for the 16 kcal mol−1 stabilization. This stabilization of the trigonalbipyramidal metallacycle when the trans influence of the apical ligands is reduced was already outlined recently for related Moand W-based species.74 The [2 + 2] cycloreversion from 25H generates the Ta methylidene hydride 26 and propene without formation of the hypothetical propene complex intermediate (all our attempts evolved to either 25H or propene release). This fact could be attributed to the cluster model employed, since the calculations carried out with the periodic model allowed us to locate a Ta alkylidene propene intermediate whose energy is very close to that of 21H (see Scheme S2 and Figure S4 in the Supporting Information). The energy barrier for cycloreversion from 25H is 8.4 kcal mol−1, but TS(25H-26) lies 47.6 kcal mol−1 above the separate reactants, becoming a transition state that is one of the highest in energy of the alkane metathesis mechanism. The fact that cycloreversion is the step that is highest in energy of the alkene metathesis process is in agreement with other works on alkene metathesis with Grubbs and Schrock metal alkylidenes.71−73,75−80 Finally, although all elementary steps involving 13 as the initial reactant have energy differences similar to those involving 6, the Gibbs energy surface associated with 13 is about 9−13 kcal mol−1 lower than that of 6. This is mainly due to the different origin of energies, 13 + methane and ethene being 12.2 kcal mol−1 lower in energy than 6 + ethene and ethane. This indicates that the production of propene by ethene metathesis is favorable for both Ta alkyl alkylidenes and Ta hydride alkylidenes and the species acting as catalyst would strongly depend on their abundance in the reaction mixture. It is worth noting that, while 13 is more stable, its formation needs to overcome an overall barrier of 48 kcal mol−1 (9 to 10, Schemes 3 and 4), which is significantly higher than that for the formation of 6. Overall, the results indicate that the reaction of 6 and 13 with ethene involves intermediates that are close to or lower in energy than the ethene + alkylidene asymptote and requires overcoming transition states with relatively low Gibbs energy barriers. However, the large endergonicity associated with the

formation of 19 is only slightly endergonic with respect to reactants, 10.6 kcal mol−1, and the transition state involved that is highest in Gibbs energy is located at 37.4 kcal mol−1 of the reacting asymptote (TS(8-16)). This suggests that in excess ethane significant amounts of 19 could be formed and thus its potential role in the alkane metathesis stage should be considered. Finally, the β-H elimination from 16 forms ethene and 3c, through a transition state that is significantly higher than those of the α- and β-abstraction processes. This suggests that ethene formation through this process is unlikely. Overall, the formation of both the hydride alkylidene (6) and alkyl alkylidene (14) tantalum complexes appears to be plausible under the reaction conditions (excess alkane). Both processes are slightly endergonic (+10.8 and +15.9 kcal mol−1 for 6 and 14, respectively) and imply overcoming energy barriers that should be accessible at 150 °C. In fact, the energy spans with respect to separate reactants are 33.3 and 37.4 kcal mol−1 for 6 and 14, respectively. Stage II of the Alkane Metathesis: Ethene CrossMetathesis by 6 and 13. Formation of 6 (Scheme 3) and of 13 and 14 (Schemes 4 and 5) opens access for several processes to occur. On one hand, they can react with H2 and then go back to the regeneration of alkanes and 1b. They can also react with additional ethane molecules as was discussed before (Schemes 4 and 5). Finally, they can react with ethene, leading to the proposed productive cross-metathesis process. Here, we discuss the cross-metathesis process of 6 and 13. The relative Gibbs energies at 150 °C are shown in Scheme 6, and all involved stationary points can be found in Figures S10 and S11 in the Supporting Information. It is worth noting that Ta ethyl ethylidene (14) species can also undergo this reaction70 with ethene. However, since we do not expect significant differences between 13 and 14, we have not considered it. At this point it is worth mentioning that we also explored if 19 could form propane and methane in a catalytic reaction. The α abstraction from the ethyl ligand of 19 requires overcoming an energy barrier of more than 40 kcal mol−1 (TS(19-42) is almost 52 kcal mol−1 above the initial reactants). This suggests that this process is slightly less likely than those implying the usual alkene metathesis process. See Scheme S4 and Figure S12 in the Supporting Information for further details. The formation of the Ta alkylidene hydride 6 is endergonic. In contrast, 13 is formed in a slightly exergonic process that involves the generation of CH 4 . However, since the dehydrogenation of ethane is always unfavorable (ΔG423 = +22.2 kcal mol−1), the relative stability of the alkylidene + ethene, which results from the summation of both processes, is always endergonic regardless of the nature of the alkylidene. In fact, the system 6 + C2H4 lies 33.0 kcal mol−1 above reactants while 13 + C2H4 is located 20.7 kcal mol−1 above 1b + 3 ethane molecules. This has as a consequence that all intermediates of the alkene metathesis process lie largely above the initial species, although all individual steps have relatively small reaction energies and low energy barriers. Regarding the reactivity with 6, the previous work by Schinzel et al.34 already studied its cross-metathesis process and our data do not differ significantly from their results. Therefore, here we only outline the most relevant points. Ethene coordination occurs in a barrierless way in a very determined manner, cis to the alkylidene fragment and trans to the hydride ligand, and this leads to the olefin complex 21H (Scheme 6). This is related to the fact that alkene coordination always occurs trans to the most strongly donating ligand, which favors 10465


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Inorganic Chemistry

Scheme 7. Relative Gibbs Energies (ΔG423, in kcal mol−1) with Respect to Separated Reactants of All Intermediates and Transition States (Values over the Arrows) Involved in the Formation of Propane Involving (a) 1b and (b, c) 26a

a


Scheme 8. Relative Gibbs Energies (ΔG423, in kcal mol−1) with Respect to Separated Reactants of All Intermediates and Transition States (Values over the Arrows) Involved in the Formation of Methane from 26 by Direct Hydrogenation with H2a

a For 33 the two spin states are reported: singlet (top, normal) and triplet (italic, bottom). DFT-optimized structures can be seen in Figure S14 in the Supporting Information.

1a, 1b, or the Ta alkylidenes 6 and 26. We have only explored the pathways of propene with 1b and 26, since 1a corresponds to a high-energy species and we do not expect large differences between 6 and 26. The corresponding relative Gibbs energies of all extrema (intermediates and transition states) are shown in Scheme 7 and the optimized structures are given in Figure S13 in the Supporting Information. On the other hand, the Ta methylidene hydrogenation forming methane can be achieved by two processes: (i) reaction with H2 and (ii) reaction with nonreacted alkane molecules. The energetics for these

formation of ethene leads to an overall energy profile in which all species are largely above the initial reactants. In this case, since the production of 13 is slightly exergonic, the Gibbs energies with respect to separate reactants associated with the reaction with the Ta alkyl alkylidene are lower. Stage III of the Alkane Metathesis: Hydrogenation of Propene and Ta Methylidene. The last part of the two-site mechanism is the formation of the products (propane and methane) by hydrogenation of propene and Ta methylidene species 26 with H2. Propene hydrogenation can take place with 10466


Article

Inorganic Chemistry Scheme 9. Proposed Catalytic Cycle for the Production of Propane and Methane from Ta Alkyl Alkylidene 14a

Relative Gibbs energies (ΔG423) with respect to separate reactants are given in kcal mol−1. DFT-optimized structures can be seen in Figure S16 in the Supporting Information.

a

(ΔG423 K = −14.3 and −14.1 kcal mol−1, respectively). The processes require overcoming transition states that are less than 13.2 kcal mol−1 higher in Gibbs energy than 26 + C3H6. Then, addition of H2 forms the dihydrogen complexes 31a/31b in an endergonic processes of about 13 kcal mol−1 that further proceeds through σ-bond metathesis, releasing propane and regenerating 26. Overall, the energetics associated with propene hydrogenation with both 1b and 26 are similar: they are exergonic by −20 kcal mol−1 and involve transition states that are always less than 15 kcal mol−1 above 26 (or 1b) + C3H6 (45.4 kcal mol−1 above initial reactants). Overall, the energetics reported here indicate that propene hydrogenation in the presence of 26 or 1b and H2 is feasible under the reaction conditions and is favorable. The preference for one or another Ta species for hydrogenation of propene will depend on the relative abundance of these species after the productive olefin metathesis stage. In the case of 26, there is no preference for one of the particular propene insertion modes. Regarding the Ta methylidene hydrogenation to form methane, this can be achieved by reaction with H2 or nonreacted alkane molecules. The reaction with H2 (Scheme 8 and Figure S14 in the Supporting Information) corresponds to the reverse steps of the alkylidene. The reaction mechanism involving ethane implies overcoming energy barriers that are higher than those involving H2 (Scheme S5 and Figure S15 in the Supporting Information). Therefore, the pathway for formation of methane with the most favorable energetics proceeds first by H2 coordination to 26 in an endergonic reaction of 12 kcal mol−1 to form 32. From 32 the H2 insertion across the TaC double bond forms 34 in a highly exergonic reaction (ΔG423 K = −19.5 kcal mol−1). The transition state is only 3.6 kcal mol−1 above 32, which implies overcoming a barrier of 15.6 kcal mol−1 with respect to 26. Finally, the coupling between the methyl group and one hydrogen atom of an additional H2 molecule via a σ-bond metathesis step in 35 leads to the liberation of methane and the regeneration of the catalyst 1b. The energy barrier for this step is about 17 kcal mol−1 (51.2 kcal mol−1 above the initial species). Overall, the

processes are shown in Scheme 8 and Scheme S5 in the Supporting Information, respectively, and the optimized structures for the reaction with ethane are given in Figures S14 and S15 in the Supporting Information. Finally, we also explored the one-site mechanism that involves the reaction of propene with 26 and two ethane molecules. This leads to the formation of propane and methane, regenerating ethene and the tantalum ethylidene hydride 6. That is, this process forms a catalytic cycle in which the active species are alkyl alkylidene complexes that do not require the participation of tantalum hydrides. The energetics of this latter process is shown in Scheme 9. The reaction of propene and 1b involves equivalent steps of the ethane dehydrogenation occurring in a reverse manner. In terms of energies, 1b + C3H6 is 30.7 kcal mol−1 above the reactant asymptote. This arises from the fact that the production of propene also implies the formation of 26. Therefore, the energy cost to produce 26 + propene has to be included in the energy of 1b + propene. It is worth noting that the large exergonicity of the propene hydrogenation causes all transition states of this process to be only about 15 kcal mol−1 above 1b + propene, which is indicative of a feasible process. In fact, the transition state that is highest in energy corresponds to the σ-bond metathesis between H2 and the propyl ligands, TS(29-1b), which is located 27.6 kcal mol−1 above the intermediate that is lowest in energy (28) of the propene hydrogenation with 1b. Scheme 7b shows the energetics for the formation of propane by reaction with 26. All values are reported with respect to the initial reactants 1b + 2 ethane molecules. As in the previous case, 26 + C3H6 is almost 31 kcal mol−1 above the initial reactants. It is worth noting that alkene insertion into the Ta−H bond can occur through two possible pathways depending on the relative orientation of propene with respect to the Ta−H bond (Scheme 7c). We have considered the two possibilities (Scheme 7b), and they are discussed together. Propene insertion takes place in a one-step reaction to form Ta alkyl alkylidene species 30a and 30b in a very exergonic process 10467


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Inorganic Chemistry whole process is strongly exergonic (−13.6 kcal mol−1) and the energy span between the lowest intermediate (34) and the highest transition state (TS(25-1b)) is 28 kcal mol−1, an energy difference that should be easily surpassed at 150 °C. Finally, we explored the one-site mechanism in which propane and methane are formed directly from 26 and which implies the reaction of 30a with ethane molecules in excess (Scheme 9). This process does not regenerate the initial tantalum trihydride 1b but the tantalum ethylidene hydride 6. Successive alkene metathesis involving 6 and ethene defines a catalytic cycle that does not involve either 1b or 1a. According to this mechanistic proposal, tantalum hydrides are precursors of tantalum alkyl alkylidene complexes such as 14, which act as the active species, as they can generate ethene by β-H abstraction and perform the alkene metathesis process (see the one-site mechanism in Scheme 2b). The relative Gibbs energies associated with this process are reported in Scheme 9, and the geometries associated with all intermediates and transition states are given in Figure S16 in the Supporting Information. As in the case of the hydrogenation of propene, the pathway starts with olefin insertion into the Ta−H bond in 26. Again two possibilities can be envisaged, depending on the relative orientation between the alkene and the metal fragment. However, since they have been found previously to present very similar energetics, we have only explored one as a representative example. After that, two successive 1,2-CH additions to 30a and 15 + α-abstraction from alkyl ligands allow the exchange of the substituents of the alkylidene and alkyl groups from the initial propyl and methylidene to the final ethyl and ethylidene ligands. The energetics associated with the 1,2-CH addition and α-abstraction processes are similar to those reported before; all steps are essentially degenerate and present energy barriers for each individual step that are lower than 30 kcal mol−1 and lower than those for the direct σ-bond metathesis steps proposed experimentally. This leads to transition states that are between 40.9 and 45.4 kcal mol−1 above the initial reactants. These values are lower than some of those of the transition states involved in the alkene metathesis process and are competitive with those of transition states of the hydrogenation of propane with H2 (45.4 kcal mol−1). From 14, β-H elimination regenerates 6, overcoming a transition state that is located 42.6 kcal mol−1 above the separate reactants. The overall process, without consideration of the 1b activation process, implies an energy span between the intermediate that is lowest in Gibbs energy and higher transition state of 33.1 kcal mol−1, which again suggests a reasonably feasible process at 150 °C. Overall, three feasible pathways exist for the formation of methane and propane. On one hand, those proposed in the two-site mechanism follow the same elementary steps already described for the first stage but in the reverse way. Alternatively, formation of propane and methane from 26 and ethane as suggested in the one-site pathway presents competitive energy barriers. This process regenerates ethene and Ta alkylidene 6 and thus allows the definition of a catalytic cycle without the participation of tantalum hydrides. It is worth noting that the most favorable pathway does not imply C−H σ-bond metathesis steps but the participation of the alkylidene ligand through a two-step process formed by 1,2-CH addition and αabstraction processes. Since the energetics of the two propane hydrogenation processes are very similar, the process taking place would strongly depend on the concentrations of the

reacting species and, in particular, the concentrations of ethane and H2. Hydrogenolysis of Ethane by TaHx/SiO2 (x = 1, 3). We have also computed the ethane hydrogenolysis, as it is a competitive process of alkane metathesis mainly occurring at the early stages of the reaction and becomes the main process when H2 is added in excess in the reaction mixture. The presence of H2 changes the reactivity of the silica-supported tantalum hydrides with alkanes from alkane metathesis to alkane hydrogenolysis. Since alkane hydrogenolysis has already been extensively studied computationally, we limited our efforts to the most favorable pathway as proposed previously.31,32 Scheme 10 shows a simplified catalytic cycle for this reaction Scheme 10. Relative Gibbs Energies (ΔG423, in kcal mol−1) with Respect to Separated Reactants of the Most Important Intermediates and Transition States (Values over the Arrows) Involved in Hydrogenolysis of Ethane by 1ba

a

A full catalytic cycle can be found in Scheme S6 in the Supporting Information, and the DFT-optimized structures not shown already can be seen in Figure S17 in the Supporting Information.

with the corresponding relative Gibbs energies at 150 °C for the stationary points. Scheme S6 in the Supporting Information shows the complete cycle, and Figure S17 in the Supporting Information shows the DFT-optimized structures of those intermediates and transition states not already shown in this paper. The ethane hydrogenolysis pathway shares with ethane metathesis some of the elementary steps already discussed in previous sections: that is, initial C−H bond activation in ethane to form 3a and then β-H elimination to a hydride ligand to 7, ethene insertion to species 9, and C−C bond cleavage to 10. From this species a series of successive hydrogenations with relatively low energy barriers (16−23 kcal mol−1) finally release two molecules of methane and regenerate the initial catalyst 1b. From an energetic point of view, the highest energy step of the whole hydrogenolysis reaction pathway is the C−C bond cleavage at 9, with an energy barrier of 48.2 kcal mol−1 above the initial reactants. Overall, the hydrogenolysis reaction C2H6 10468


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Scheme 11. Summary of the Reaction Pathways Explored in This Work, Indicating the Relative Gibbs Energies with Respect to Separated Reactants of the Most Important Intermediates and Total Barriersa

a

Reaction pathways correspond to (a) the two-site mechanism, (b) the one-site mechanism to the formation of Ta alkyl alkylidene 14, and (c) the one-site mechanism with 14 as the active species, proposed here as the most favorable pathway (in blue). Red arrows denote unfavorable reaction pathways. Values are Gibbs energies (in kcal mol−1) at 150 °C.

+ H2 → 2CH4 has a global Gibbs reaction energy of −16.7 kcal mol−1 at 150 °C, much more favorable than the thermodynamics of the metathesis pathway (−3.0 kcal mol−1 at 150 °C). This indicates that methane should be the thermodynamically preferable product in the reactivity of TaHx/SiO2 (x = 1, 3) with ethane but requires the presence of H2 either added to the reaction mixture or formed in situ to take place.

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This vast exploration made us consider several elementary steps such as C−H and H−H σ-bond metathesis, α- and βabstraction reactions, β-elimination, olefin insertion, 1,2-CH bond addition, and the cycloaddition and cycloreversion steps of the alkene metathesis reaction. Most of these processes have already been described for d0 early-metal alkyl and alkylidene complexes. The results show that, for the species considered here, the ligands around the metal center have little influence and thus each type of reaction has its characteristic energetics. The most favorable processes correspond to olefin insertion (ΔG⧧ = 11.9−14.5 kcal mol−1) and β-abstraction (ΔG⧧ = 11.3−11.7 kcal mol−1 when involving hydrides) and αabstraction (ΔG⧧ ≈ 20 kcal mol−1). On the other hand, the C−H σ-bond metathesis steps are among the most energetically demanding processes, the energy barriers being above 30.0 kcal mol−1. All other processes present intermediate values that range mainly between 27.6 and 30.0 kcal mol−1. None of these values suggest that these individual steps could not occur at 150 °C, and in fact, products resulting from the C−H σ-bond metathesis have been characterized experimentally.23,24,81 Therefore, the applicable mechanism seems to strongly depend on the relative stabilities of the intermediates as well as their concentration in the reaction mixture. In this way, formation of Ta(III) is strongly thermodynamically disfavored, as already observed in the reactivity of tantalum hydrides with other substrates,32,38,40,41 and ethane dehydrogenation is largely endergonic, which suggests very little concentration of olefin specially if H2 is present in the reaction media. On comparison of the three reaction mechanisms, they all present very similar energetics. The transition states that are highest in energy are in the three cases between 47.6 and 51.8

DISCUSSION

The viability of the two-site and one-site reaction mechanisms for ethane metathesis with TaHx/SiO2 (x = 1,3) as well as some variations implying alternative elementary steps has been analyzed and compared with the energetics of ethane hydrogenolysis. We have analyzed first the two-site mechanism consisting of three stages: ethane dehydrogenation and Ta alkylidene formation, alkene cross-metathesis, and finally hydrogenation of the resulting propene and methylidene species with H2. We also explored the possibility that additional ethane molecules participate in the catalytic process. This led to two additional pathways in which the tantalum hydrides act as precursors of alkyl alkylidene or related species that act as active catalysts. It is worth noting that in these processes, once the active species are formed, H2 is neither formed nor consumed. The first pathway is a variation of the one-site mechanism involving 1,2-CH addition and α-abstraction processes instead of C−H σ-bond metathesis steps as proposed experimentally. The second pathway is similar to the one-site mechanism, but it does not involve the classical alkene metathesis pathway. The most probable reaction pathways are depicted in Scheme 11, where the most favorable mechanism is highlighted with blue arrows. 10469


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Inorganic Chemistry kcal mol−1 above the initial reactants (Scheme 11). These values are comparable with those of the alkane hydrogenolysis (ΔG⧧ = 48.2 kcal mol−1) and are in accordance with the experimental evidence that shows a change in the reactivity of tantalum hydrides depending on the presence/absence of H2.33 At this point it is worth mentioning that these barriers seem to be high for a heterogeneous process at 150 °C. However, it is well-known that grafting of metal sites on amorphous silica leads to a distribution of sites with different local structures,82 some of them not being fully represented with the present model. In fact, it has recently been proposed that the reactivity of these sites strongly depends on the ring strain and coordination around the metal site, the energy differences between different sites being remarkable.66,67,83 The results reported here can explain the observation of alkane hydrogenolysis at the early stages of the alkane metathesis reactions. The presence of H2 even released during the mandatory formation of alkylidene hydride complex 6, ethene, or alkyl−alkylidene species 14 allows the alkane hydrogenolysis to occur. It is worth noting that, if tantalum hydrides are regenerated in each catalytic cycle, H2 would be generated in each catalytic cycle and thus no decrease in the amount of paraffin undergoing alkane hydrogenolysis should be observed. In contrast, if the one-site mechanism applies, alkane hydrogenolysis should decrease. Experiments suggest the latter, which is in favor of the one-site pathway. Moreover, when the real catalytic cycle does not involve 1b and the active species are alkyl alkylidene intermediates, the Gibbs energy span between the lowest intermediate and the highest transition state of the catalytic cycle decreases about 10 kcal mol−1 with respect to the process starting from 1b. That is, the energy span in the catalytic cycle is 31.7 kcal mol−1 and, thus, the process becomes more accessible, especially considering that the reaction takes place at 150 °C and that there is a large excess of alkane (800 equiv) that could favor the reaction of more than one ethane molecule per tantalum center. Within the two processes involving alkyl−alkylidene species, that showing lower energy barriers corresponds to the process associated with the one-site mechanism in which the C−H σ-bond metathesis processes are substituted by successive 1,2-CH addition and α-abstraction steps (Scheme 11). This mechanistic proposal is in agreement with the detection of tantalum alkylidene complexes as well as products coming from alkane C−H activation by means of NMR spectroscopy using isotopically marked reagents.14,28,29 Overall, the present calculations suggest that the alkane metathesis catalytic cycle does not involve the regeneration of tantalum hydrides and that more likely the reaction proceeds through alkyl alkylidene intermediates. In view of this proposal, silica-supported tantalum hydrides are catalysts for the alkane hydrogenolysis and the precursors of alkyl alkylidene complexes that act as active species of the alkane metathesis. Moreover, during the formation of the alkyl alkylidene species H2 is released, which favors the alkane hydrogenolysis in the first stages of the reaction. Finally, the one-site mechanism allows relation of the catalytic activities of Ta, W, and other supported metal hydrides with those of the d0 Ta, Mo, W, and Re alkyl alkylidene alkane metathesis catalysts.

reliability was assessed by comparison with larger clusters and periodic calculations. Special attention was paid to the two-site and one-site mechanisms proposed from experimental evidence. These reaction mechanisms involve alkene metathesis linked to an alkene/alkane hydrogenation/dehydrogenation process that occurs through well-described elementary steps of d0 transitionmetal complexes such as σ-bond metathesis, α- and βabstraction, and elimination reactions, olefin insertion, and 1,2-CH bond additions. Most of these elementary steps present energy barriers that are only slightly affected by the ligands on the tantalum center and are consistent with processes taking place at 150 °C. Therefore, the applicable mechanism seems to be strongly related to the presence of the reactants and reaction intermediates. In this view, the alkane dehydrogenation appears as a challenging process and Ta(III) species are strongly disfavored. A comparison of the energetics for the different mechanisms for alkane metathesis as well as those associated with alkane hydrogenolysis shows that the energetics of all processes are similar, the transition state of each pathway that is highest in Gibbs energy lying between 47.6 and 51.8 kcal mol−1 above the initial reactants. These values are consistent with the observation of different reactivities as a function of the presence (alkane hydrogenolysis) or absence of H2 (alkane metathesis). Moreover, values obtained for the one-site mechanism are slightly lower than those of the two-site mechanism, and this allows the rationalization of the origin of the alkane hydrogenolysis process observed at the early stages of the reaction. According to the one-site pathway, tantalum hydrides act as precursors of alkyl alkylidene tantalum complexes that act as active species. During this activation process, H2 is formed and this allows hydrogenolysis to occur. In contrast, in the catalytic cycle there is no liberation of H2 and, thus, the activity for the alkane hydrogenolysis decreases. Moreover, the one-site reaction mechanism relates the catalytic activity of the supported hydrides with that of the alkyl alkylidene supported complexes, as both precursors share the same active species. Overall, the ethene formation through β-H elimination, the propane release by ethane 1,2-CH bond addition to the alkylidene, and the less favorable C−H σ-bond metathesis appear as important processes controlling the catalytic activity. Therefore, understanding how the nature of the metal center and the ligand influences their energetics seems to be crucial for the development of the reaction.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.7b01464. Detailed description of the computed structure and spectroscopic responses of (SiO2)Ta-Hx initial species, results associated with the methodology validation, results for the full catalytic cycle starting with 19, for the formation of methane from 26 and ethane, and for the full catalytic cycle for ethane hydrogenolysis by 1b, all optimized geometries of stationary points reported in the text, and Cartesian coordinates and absolute energies of all stationary points presented in the paper (PDF)

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CONCLUSIONS The energetics of several reaction pathways for the alkane metathesis reaction catalyzed by silica-supported tantalum hydrides have been explored using DFT (B3PW91) calculations. Silica was modeled with a cluster model whose 10470


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Inorganic Chemistry

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AUTHOR INFORMATION

Corresponding Author

*Francisco Núñez-Zarur: E-mail: [email protected]; Tel: +57-4-3405312. ORCID

Francisco Núñez-Zarur: 0000-0002-9244-9328 Present Address

§ F.N.-Z.: Facultad de Ciencias Básicas, Universidad de ́ Carrera 87 No. 30-65, 050026 Medellin, ́ Colombia. Medellin,

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS F.N.-Z. and A.R. wish to thank the Universidad de Antioquia for financial support (grant 20502301-007). F.N.-Z. thanks COLCIENCIAS for the “Es Tiempo de Volver” fellowship through the Special Cooperation Agreement FP44842-5052014 with the Universidad de Antioquia. X.S.-M. acknowledges financial support from the Spanish Government (CTQ201459544-P) and the Generalitat de Catalunya (2014SGR-482). He is grateful for a Profesor Agregat Serra-Húnter position.

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