Reactivity of a Silica-Supported Mo Alkylidene Catalyst toward

Apr 10, 2018 - The metathesis of alkanes is a process in which a given alkane is transformed into higher and lower homologues. Here, we carried out DF...
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Article Cite This: Organometallics XXXX, XXX, XXX−XXX

Reactivity of a Silica-Supported Mo Alkylidene Catalyst toward Alkanes: A DFT Study on the Metathesis of Propane Estefanía Díaz,† Albeiro Restrepo,† and Francisco Núñez-Zarur*,‡ †

Instituto de Química, Universidad de Antioquia, Calle 70 No. 52-21, 050010 Medellín, Colombia Facultad de Ciencias Básicas, Universidad de Medellín, Carrera 87 No. 30-65, 050026 Medellín, Colombia



S Supporting Information *

ABSTRACT: The metathesis of alkanes is a process in which a given alkane is transformed into higher and lower homologues. Here, we carried out DFT calculations in order to get insights into the most favorable reaction pathway for the metathesis of propane into mainly ethane and butane catalyzed by a silica-supported molybdenum alkylidene bearing an imido ligand at 150 °C. The overall catalytic process is divided into two stages, precursor activation and catalytic cycle, and both of them consist of the same types of reactions, (i) ligand exchange, (ii) proton transfer between two α-carbons, and (iii) ligand rearrangement, which in turn consists of several steps, such as β-H elimination, alkene cross-metathesis, and alkene insertion. Our results suggest that the formal ligand exchange reaction with propane proceeds through a dissociative mechanism with the formation of a high-energy molybdenum alkylidyne species. The calculated energetics at 150 °C indicates that the active species is a molybdenum propylidene species that is formed with an overall Gibbs activation barrier of 39.4 kcal mol−1. The catalytic cycle to the main products (ethane and butane) has an energy span of 43 kcal mol−1, whereas the cycle for the production of minor products (methane and pentane) has a much higher energy span, in agreement with experiments. These data suggest that the catalytic cycle is the rate-determining stage in the whole process and thus the precursor activation should be faster. The results obtained here help to rationalize the chemical reactivity of supported molybdenum alkylidene catalysts toward alkanes.



into liquid hydrocarbons. Afterward, in 1997, the term “alkane metathesis” was introduced for the first time by Basset and coworkers when they used the silica-supported single-site tantalum hydride [(SiO)2TaHx] (x = 1, 3) to catalytically transform propane into ethane and butane.1a Currently, alkane metathesis can proceed through supported single-site catalysts,1a−d through dual catalysts in the homogeneous phase as proposed by Goldman, Brookhart, and co-workers,6 and through dual systems in the heterogeneous phase as recently proposed by Basset and co-workers.7 Kinetic experiments on [(SiO)2TaHx] under dynamic conditions indicated that olefins and H2 are primary products, which are formed at the initial stages of the reaction.8 In addition, the reaction selectivity followed the same patterns observed in alkene metathesis. This collective evidence led to the idea that the key process for the C−C bond cleavage and formation of alkanes is an alkene metathesis step.8 On the basis of this knowledge, several supported alkene metathesis catalysts have also been used in alkane metathesis. These systems include catalysts based on different metals (tantalum,9 tungsten,7,10 molybdenum,11 and rhenium12), several ligands (hydrides, alkyl

INTRODUCTION Among the several methods for the transformation of alkanes, alkane metathesis1 has become one of the most promising approaches. In this reaction, as can be seen in eq 1, a given alkane is transformed into its lower and higher homologues at relatively low temperatures (150−200 °C).1a The main potential of this reaction is the production of added-value chemicals, such as fuels,2 from relatively cheap and abundant feedstock, such as natural gas and propane. 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 metathesis was developed by Banks and Bailey in 1964 at Phillips Petroleum Co. using alkenes, in a process known as “olef in disproportionation”.3 In this process, linear olefins were converted into homologues of shorter and longer carbon chains. A few years later, Chauvin proposed the currently accepted mechanism, which involves metal carbenes and metallacyclobutanes as key intermediates.4 In 1973, researchers at Chevron Research Co. studied the same process using alkanes.5 The disproportionation of alkanes was carried out over a dual-catalyst system combining a heterogeneous catalyst for dehydrogenation/hydrogenation and a catalyst for olefin metathesis. This system was used for the conversion of butane © XXXX American Chemical Society

Received: February 11, 2018

A

DOI: 10.1021/acs.organomet.8b00090 Organometallics XXXX, XXX, XXX−XXX

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Scheme 1. (a) Structure of Precursor 1 and Proposed Reaction Mechanisms of Alkane Metathesis by 1 following a (b) Ligand Exchange, (c) Proton Transfer between Two α-Carbons, and (d) Ligand Rearrangement

alkylidenes, alkylidynes, and polyalkyls) and a variety of supports (silica, alumina, and silica−alumina). The most studied catalyst from both experimental and computational points of view is the original tantalum hydride system [(SiO)2TaHx].13 This catalyst has been characterized by IR, 1H and 13C solid-state NMR, and EXAFS spectroscopic techniques.13,14 Two types of hydrides on the surface of silica have been identified: mono- and trihydride. The latter was identified as the actual active site on the basis of poisoning experiments with O2 and cyclopentane and accounts for about 50% of the total Ta sites.14 However, other tantalum systems have also been experimentally investigated, and the results suggested that the actual active species should be a Ta alkylidene species.9b,15 Moreover, it has been observed that tungsten alkylidynes can also catalyze the metathesis of alkanes.10c,16 Few computational studies have been dedicated only to [(AlsO)W(CtBu)(CH2tBu)2]17 and [(SiO)2TaHx] complexes18 using cluster and periodic models. These studies have focused on the identification of plausible reaction mechanisms and the nature of the active sites. The most recent contribution from our group on [(SiO)2TaHx] indicates that the Ta hydride is actually a precursor of the propagating tantalum alkyl alkylidene species, in agreement with previous experimental results, and that the productive catalytic cycle involves the participation of extra alkane molecules and not H2, which triggers the competitive alkane hydrogenolysis reaction.18c

The silica-supported alkyl alkylidenes of tantalum, rhenium, and molybdenum have also shown activity in alkane metathesis.11b The first two showed moderate to low activity, whereas for a series of molybdenum alkylidenes only those with a neopentyl ligand were active in alkane metathesis. Within a series of catalysts with different substituents at the imido and alkylidene ligand, the [(SiO)Mo(NAr)(CHtBu)(CH2tBu)] catalyst (1, Scheme 1a) showed a catalytic activity similar to that of the original [(SiO)2TaHx] in the metathesis of propane at 150 °C.11 Catalyst 1 has been characterized by IR and solid-state NMR spectroscopy and also by mass balance,19 thus confirming the structure shown in Scheme 1a. The 1H and 13 C NMR spectra on the alkylidene ligand of 1 indicated that the dominant species on the surface is the syn isomer, where the alkylidene proton points toward the surface (or siloxy ligand in molecularly defined analogues19). The other isomer, anti, where the alkylidene proton points to the imido ligand, is barely observed in the solid state.20 Furthermore, in contrast to [(SiO)2TaHx], 1 does not catalyze the competitive alkane hydrogenolysis reaction,21 in which the alkane is successively cleaved by H2 to produce methane at a final stage. Therefore, this reaction changes the selectivity of the alkane metathesis toward the desired products. In fact, the selectivity toward alkane metathesis products with 1 approaches 98%, in contrast to 90% for the tantalum hydride.11b Moreover, propane metathesis experiments with different metal loadings led to the conclusion that the system is based on a single site, ruling B

DOI: 10.1021/acs.organomet.8b00090 Organometallics XXXX, XXX, XXX−XXX

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metathesis, and alkene insertion (Scheme 1d). The general mechanism of propane metathesis by 1 can be divided into two main stages: precatalyst activation and a catalytic cycle. During the activation, the first reaction is a ligand exchange of 1 with propane that leads to C (Scheme 1b, R1 = R2 = tBu). From C, proton transfer between two α-carbons (Scheme 1c, R1 = tBu) or ligand rearrangement may occur (Scheme 1d, R1 = tBu). The latter pathway can take place through two different approaches (1,3- and 1,2-approaches) leading to the formation of 1,3- and 1,2-disubstituted Mo cyclobutanes Fa and Fb, to finally produce the two new alkylidenes Ha and Hb. From these latter species, the actual active catalysts can be formed, which by reaction with other propane molecules and after the same steps (ligand exchange, proton transfer between α-carbons, and ligand rearrangement) release the main products, ethane and butane (R1 = R2 = Et). The mechanism previously described is based on the observation of several intermediates in the gas phase and is consistent with the distribution of products observed during the experiments. However, several issues remain unsolved. For instance, the ligand exchange between 1 and propane (Scheme 1b, R1 = R2 = tBu) has been proposed to occur via three different pathways:1c,d,11b (i) a dissociative pathway in which neopentane is first released from 1, forming a molybdenum alkylidyne intermediate A, and then propane 1,2-CH addition to form C, (ii) an interchange (concerted) pathway through a σ-bond metathesis step, and (iii) an associative mechanism starting by propane 1,2-CH addition to form B and then release of neopentane. To the best of our knowledge, there is no

out the presence of other molybdenum species on the surface of silica.11b Table 1 shows some experimental data for a comparison between 1 and [(SiO)2TaHx]. Table 1. Catalytic Activity (TON and TOF) of 1 and [( SiO)2TaHx] in the Metathesis of Propane (730 hPa, ∼500 equiv) at 150 °C, Selectivity in Alkane Metathesis (AM) in Comparison to Other Competitive Processes, and Product Selectivity11b product selectivity (%)c precatalyst 1 (SiO)2TaHx

TONa TOFb 55 65

1.1 0.5

AM (%)

C1

C2

C4d

C5 d

98 90

0.1 18.0

56.1 40.0

35.3 24.4

5.2 5.1

a

TON is calculated as moles of propane transformed per mole of metal. bTOF is calculated as TON/h taken after a reaction time of 24 h. cThe selectivities are defined as the amount of the given product over the total amount of products. dLinear and branched alkanes are detected, but only the former are shown.

On the basis of the observation of primary cross-metathesis products (secondary alkanes) and the knowledge that the key C−C bond cleavage and formation is an alkene metathesis step, a mechanism based on three types of reactions was proposed (Scheme 1b−d),1d,11 (i) ligand exchange with propane (Scheme 1b), (ii) proton transfer between the two α-carbons of a molybdenum alkylidene (Scheme 1c), and (iii) ligand rearrangement, which consists of β-H elimination, alkene cross-

Figure 1. Computational representation of precatalyst 1 (syn configuration) with the silica surface simulated as a cluster with one (11T) and four tetrahedral Si sites in open (14TO) and cage forms (14TC). Only the first coordination sphere around Mo and the cluster models are highlighted with ball and stick models (top). Plain structure representations of the three models are also shown (bottom). Color code of the elements: Mo is shown in purple, Si in yellow, N in blue, O in red, C in gray, and H in white. C

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Scheme 2. Relative Gibbs Energies at 150 °C (ΔG150, in kcal mol−1) of the Intermediates and Transition States (Numbers Next to the Arrows) Involved in the Ligand Exchange of 11T with Propane following the Formation of (a) n-Propyl and (b) Isopropyl Intermediates via Three Possible Mechanisms: Dissociative (11T → 2E → 4E(i)), Interchange (11T → 4E(i)), and Associative (11T → 3E(i) → 4E(i))a

a

The spectator imido ligand and the cluster surface are not shown for simplicity. The origin of the energies is the system 11T + propane. without symmetry constraints, and the nature of all stationary points (minima and transition states) was verified by frequency calculations. In some cases, intrinsic reaction coordinate (IRC) calculations were performed to unambiguously confirm the connection between reactants and products. Gas-phase thermal corrections were evaluated at 1 atm and 150 °C, the temperature at which the experiments were performed. Energetic refinement was performed by using the same representation for Mo and Si described before and the 6-311++G(d,p) basis set for the rest of the atoms (this combination is called BS2).26,27 These energies were added to the entropic corrections with BS1 at 150 °C, and therefore final energies reported along the paper are Gibbs energies at 150 °C (ΔG150) relative to the initial catalyst 11T + n propane, where n is the number of propane molecules involved in a given process. Finally, the M06 functional was used to validate the results and trends obtained with the B3PW91 functional and also to evaluate the effect of dispersion on the calculations with the small model 11T but also with the larger model 14TO. All these results are shown in Text S1 of the Supporting Information. In summary, results obtained here indicate that inclusion of dispersion forces do not modify the trends and provide results similar to the data obtained with the B3PW91 functional.

conclusive information about the applying mechanism for this step. The proper knowledge about this specific step is critical, since the formal ligand exchange reaction takes place several times during the catalysis. Additionally, there is no detailed information at the molecular level about the overall catalytic cycle and the stabilities of the reaction intermediates along the proposed reaction pathway. Finally, other possible routes for the formation of the products have not been explored. In this work, we use the tools of computational chemistry based on density functional theory (DFT) in order to evaluate the reaction mechanism for the metathesis of propane by 1 into mainly ethane and butane. The three proposed reaction pathways for the alkyl ligand exchange with propane, an alternative mechanism to obtain the main products, and the catalytic cycle to minor products are considered. The results obtained here will help to rationalize the activity of well-defined molybdenum alkyl alkylidene catalysts toward alkanes.



MODELS AND METHODS



Model Catalyst. The silica-supported, molybdenum alkyl alkylidene complex 1 was represented with all ligands around the metal center without any simplification, whereas the silica support was simulated by a cluster approach, in which silica is represented by a single tetrahedral Si site −OSi(OH)3 (model 11T). Similar cluster models have been successfully used before to assess the reactivity of supported d0 metal alkylidenes in alkene22 and alkane metathesis.18a,c Nonetheless, in order to validate the suitability of this model, larger cluster models were designed, with four tetrahedral Si sites in open (model 14TO) and cage forms (model 14TC). These three models can be seen in Figure 1, where only the syn isomers are shown, together with plain structures for better visualization. The comparison of the three models is described in detail in Text S1 of the Supporting Information. Briefly, the results suggest that the geometries and energetics are not dependent on the cluster model and therefore model 11T is suitable to assess the reaction pathways investigated here. Methods. Calculations were carried out with the Gaussian 09 suite of programs23 and the B3PW91 hybrid functional.24 All geometries were obtained using the Stuttgart effective core potential augmented with d and f polarization functions25 for Si and Mo, respectively, and the split valence 6-31G(d,p) basis set for the rest of the atoms (this combination is called BS1).26 All structures were fully optimized

RESULTS

The results of this investigation will be presented in two separate sections. The first section will deal with precursor activation by successive reactions of 11T with propane, and the second part will be dedicated to the catalytic cycle for the formation of main (ethane and butane) and minor products (methane and pentane). In addition, a brief comment on an alternative cycle to the main products will be introduced. The nomenclature along the text will be organized as follows: each intermediate in Scheme 1b−d will be identified with consecutive integers (1, 2, 3, ...) and each process with a capital letter (E = ligand exchange, A = proton transfer between two α-carbons, and R = ligand rearrangement). In the case of ligand rearrangement, where two possible approaches of propene to the Mo−alkylidene fragment are possible, the two pathways will be identified with a lower case letter (a = 1,3approach and b = 1,2-approach). The transition states will be named by adding “TS” before the minima they connect. When D

DOI: 10.1021/acs.organomet.8b00090 Organometallics XXXX, XXX, XXX−XXX

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Scheme 3. Relative Gibbs Energies at 150 °C (ΔG150, in kcal mol−1) of the Intermediates and Transition States (Numbers Next to the Arrows) Involved in the (a) Proton Transfer between the Two α-Carbons and Ligand Exchange from 4E, (b) Ligand Rearrangement from 4E following the 1,3-Approach, and (c) Ligand Rearrangement from 4Ei following the 1,2-Approach and Relative Energies of the (d) TBP and (e) SP Mo Cyclobutanesa

a

The spectator imido ligand and the cluster surface are not shown for simplicity. The origin of the energies is the system 11T + propane.

isopropyl intermediates are discussed, a lower case letter i (in italics) will be added to the name. Precursor Activation. The catalyst 11T may exist as two isomers, namely syn and anti (vide supra). We studied in detail the energetics of these two species and the interconversion process between them. The results, which can be found in Text S2 and Figure S1 of the Supporting Information, suggest that the syn isomer is lower in energy than the anti isomer. Therefore, the syn isomer will be considered as the active precursor. The activation of 11T leads to molybdenum species where all tert-butyl substituents have been replaced by alkyl groups derived from propane. The first reaction between 11T and propane is a ligand exchange in which the neopentyl ligand is replaced by a propyl group. The energetics of this reaction in terms of Gibbs energies at 150 °C is shown in Scheme 2, where activation of propane by its terminal (Scheme 2a) and central C−H bonds (Scheme 2b) is considered. The formation of isopropyl species is important, since they are involved in the subsequent ligand rearrangement pathway following the 1,2 approach (vide infra). Figures S4 and S7 of the Supporting Information show the optimized structures of the minima and transition states leading to the n-propyl and isopropyl derivatives 4E and 4Ei, respectively. It is worth noting that the reaction of propane with any of the Mo alkylidene or alkylidyne species investigated here takes place without prior formation of a σ-alkane adduct: that is, the reaction takes place in a single step. The exchange of the

neopentyl ligand by propane produces the supported complexes 4E and 4Ei with slightly favorable Gibbs reaction energies (−1.2 and −2.3 kcal mol−1, respectively). We explored the formation of these species through the pathways described in Scheme 1b (dissociative, interchange, associative). The dissociative mechanism involves an α-H abstraction from the alkylidene ligand at 11T. This step releases neopentane (2,2dimethylpropane), leading to the high-energy species 2E, a Mo alkylidyne intermediate that is 24.5 kcal mol−1 above the initial system. In 2E, the Mo center shows a slightly distorted trigonal geometry with a Mo−Cyne distance of 1.762 Å (yne = alkylidyne). Interestingly, the imido ligand is bent in such a way that it is closer to the surface cluster model, and the Mo− N−CAr angle is about 148° (Ar = aryl substituent of the imido ligand). The energy barrier for the release of neopentane is 33.9 kcal mol−1, and the transition state TS(11T-2E) shows a fourmembered ring where the proton being transferred is somewhere between the carbon atoms of the alkylidene and alkyl fragments, with Cene···H and Calkyl···H distances of 1.610 and 1.454 Å, respectively. Following the formation of 4E, the transition state for propane addition TS(2E-4E) shares features very similar to those of TS(11T-2E) and has an energy of 31.3 kcal mol−1 above the initial system; therefore, the energy barrier for this reaction is 6.8 kcal mol−1. The resulting surface species 4E presents geometrical parameters similar to those of 11T (Figure S4). The interchange mechanism is characterized by a transition state connecting 11T to 4E in a single step (TS(11TE

DOI: 10.1021/acs.organomet.8b00090 Organometallics XXXX, XXX, XXX−XXX

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Scheme 4. Relative Gibbs Energies at 150 °C (ΔG150, in kcal mol−1) of the Intermediates and Transition States (Numbers Next to the Arrows) Involved in the Ligand Exchange from (a) 4Ra and (b) 4Rb with Propanea

a

The spectator imido ligand and the cluster surface are not shown for simplicity. The origin of the energies is the system 11T + propane.

4E)) with an energy barrier of 69.8 kcal mol−1. It also presents a four-membered ring with similar Calkyl···H and Cpropane···H distances (1.432 and 1.448 Å, respectively) and a very wide Calkyl···H···Cpropane angle of 170°, characteristic of a σ-bond metathesis step on d0 metals.28 Finally, the associative pathway starts with the coordination of propane to the Mo center through a 1,2-CH addition, forming the intermediate 3E. The Mo center at 3E shows a distorted-trigonal-bipyramidal (TBP) geometry with the imido and the silica surface being the axial ligands and the three alkyl ligands belonging to the equatorial plane. 3E is a high-energy species (ΔG150 = 35.4 kcal mol−1), and its formation passes through a transition state that is about 72 kcal mol−1 above the initial reactants. TS(11T-3E) already shows a distorted-TBP structure with Cene···H and Cpropane···H lengths of 1.495 and 1.547 Å, respectively. From 3E, α-H abstraction releases neopentane with an energy barrier of 35.4 kcal mol−1 through a transition state with geometry similar to that of TS(11T-3E). Regarding production of 4Ei, the three ligand exchange pathways show very similar geometrical features (see Figure S7), while most of the intermediates and transition states are within 1−5 kcal mol−1 higher in energy than those for production of 4E. Overall, calculations indicate that the initial activation of propane can take place at any of the available C−H bonds, leading to n- and isopropyl derivatives. From a strictly energetic point of view, the thermodynamics of the process would favor the production of the isopropyl intermediate (4Ei is lower in energy than 4E) but the kinetics of the process would favor the production of the n-propyl intermediate, as it presents a smaller energy barrier. Nevertheless, the energy differences calculated for the generation of these species are not large enough to rule out any of them. Therefore, 4E and 4Ei should be formed in roughly the same quantities from 11T and propane. Regarding the three possible routes to the propyl derivatives, while the associative and interchange mechanisms show intermediates with energies higher than 35 kcal mol−1 and transition states that are higher than 70 kcal mol−1, the formation of the Mo alkylidyne species 2E appears as the most feasible pathway, even though this is also a high-energy species (ΔG150 = +24.5 kcal mol−1). However, the associated energy barriers for addition of propane to 2E are 6.8 and 10.4 kcal mol−1 for production of 4E and 4Ei, respectively, which indicates that formation of these species should easily take place at 150 °C. Since the dissociative mechanism was calculated to be the most favorable and since the energies are lower by ca. 30 kcal mol−1 than those of the associative and interchange mechanisms, all

ligand exchange steps in the further reactions will be considered only through a dissociative pathway. From 4E and 4Ei several processes may occur (Scheme 3). On one hand, from 4E the proton transfer between the two αcarbons of the alkyl and alkylidene ligands and ligand exchange with propane produce the new propylidene species 6E and 6Ei (Scheme 3a), while ligand rearrangement leads to species 4Ra (Scheme 3b). On the other hand, ligand rearrangement from 4Ei leads to species 4Rb (Scheme 3c). Unlike the proposal from the literature,11 intrinsic reaction coordinate (IRC) calculations carried out here starting at metallacycles 2Ra and 2Rb indicated that the ligand rearrangement via the 1,2approach is only possible from an isopropyl intermediate, whereas the 1,3-approach starts from an n-propyl species. This appears obvious when the reactions starting from 2Rb are considered, for instance, in forward and backward directions. In both cases, isoalkyl derivatives should be formed, which is corroborated by our IRC calculations. At this point it is worth mentioning that, although 4Ei may also undergo the transfer of the H atoms of the two α-carbons of the alkyl and alkylidene ligands, the resulting Mo alkylidene fragment (MoC(CH3)2) will have no hydrogen on the alkylidene carbon and therefore it will not be possible to exchange with an incoming propane, thus leading to a dead-end pathway. Finally, ligand exchange of 4Ra and 4Rb with propane leads to the new alkylidene species 8E, 8Ei, 10E, and 10Ei (Scheme 4). All optimized geometries of this part of the mechanism are depicted in Figures S8−S12 of the Supporting Information. The proton transfer between the two α-carbons at 4E produces 1A (Scheme 3a) in a reaction that is essentially degenerate and is associated with a transition state that is 38.2 kcal mol−1 above the separated reactants. The transition state TS(4E-1A) shows a four-membered ring with Cpropyl···H and Cene···H distances of 1.733 and 1.720 Å, respectively. 1A preserves a distorted-tetrahedral geometry around Mo with Mo−Cene and Mo−Calkyl bond distances of 1.868 and 2.133 Å, respectively. Neopentane is released from 1A, producing 5E in a highly endergonic reaction by 24.7 kcal mol−1. 5E shows structural features very similar to those of 2E (Figure S8). The transition state TS(1A-5E) has an energy of 32.6 kcal mol−1 above the initial reactants. Finally, propane addition to 5E produces the n-propyl and isopropyl intermediates 6E and 6Ei with final energies of −4.3 and −5.6 kcal mol−1 and energy barriers of 5.2 and 9.8 kcal mol−1, respectively. Remarkably, the geometrical features and energetics for the ligand exchange F

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exhibits geometrical parameters similar to those of TS(1Ra2Ra), although with slightly larger Mo···Calkene and Cene···Calkene distances as a consequence of the bulkier substituent group at the CH2CHtBu coordinated alkene in comparison to propene (2.308 and 2.228 Å, respectively). The last step for the ligand rearrangement from 4E is the insertion of CH2CHtBu into the Mo−H bond. The energy barrier for this step is ca. 19 kcal mol−1, and the associated transition state shows a geometry similar to that of β-H elimination (its microreverse step). The resulting species 4Ra is 6.4 kcal mol−1 below the initial reactants, indicating that the overall ligand rearrangement from 4E is exergonic at 150 °C. Finally, from 4Ei, the same ligand rearrangement pathway as from 4E occurs (Scheme 3c). However, coordination of propene in 1Rb is such that the methyl group is closer to the alkylidene ligand. As a result, the geometrical features of all stationary points within this pathway are similar to those from 4E, the only difference being the position of the propane methyl group. As a consequence, although most of the individual energy barriers are similar for both 4E → 4Ra and 4Ei → 4Rb processes, the most significant differences in terms of Gibbs energies are the lower stabilities (i.e., more positive energies) of the involved intermediates (up to 15 kcal mol−1) and higher total energy barriers (up to 7.4 kcal mol−1) of the pathway starting from 4Ei. We note at this point that the insertion steps (from the olefin complexes) are higher in energy than the olefin metathesis. This is mainly due to the fact that in the former the hydride and the olefin are trans to each other and therefore significant geometry reorganization is needed in order to insert the olefin. In contrast, for metathesis, the olefin and alkylidene ligand are cis, which facilitates the cycloaddition reaction. This results in a higher energy for insertion than for metathesis. The last step of the activation stage is a ligand exchange from 4Ra and 4Rb, which leads to the new potentially catalytic species 8E, 8Ei, 10E, and 10Ei. The energetics of these pathways at 150 °C is shown in Scheme 4, and the optimized structures are depicted in Figures S11 and S12 in the Supporting Information. The release of secondary alkanes 2,2-dimethylbutane and 2,2-dimethylpentane from 4Ra and 4Rb results in Mo alkylidynes 7E and 9E, respectively, and the associated energy barriers are 38.3 (TS(4Ra-7E)) and 37.0 kcal mol−1 (TS(4Rb-9E)). Propane 1,2-addition leads to n-propyl and isopropyl derivatives. As discussed before, addition via the central C−H bond is slightly favorable, with energy barriers of 6.6 and 10.2 kcal mol−1 for production of 8E and 10E, respectively, while production of 8Ei and 10Ei needs to overcome energy barriers of 10.4 and 13.8 kcal mol−1, respectively. Species 8E and 8Ei are 3.3 and 4.5 kcal mol−1 below the initial reactants, respectively, whereas 10E and 10Ei are only 0.3 and 1.1 kcal mol−1 below 11T + propane, respectively. In summary, the activation of precatalyst 11T leads to different Mo alkylidene species: 6E, 6Ei, 8E, 8Ei, 10E and 10Ei. The first two species are formed via proton transfer between the two α-carbons plus ligand exchange from 4E (Scheme 3a), while the rest are formed via a ligand rearrangement reaction plus ligand exchange with propane from 4E and 4Ei (Schemes 3b,c and 4a,b). From an energetic point of view, calculations carried out at 150 °C indicate that the rate-determining step for the production of 6E and 6Ei is the transfer of a proton between α-carbons at 4E to produce 1A, which corresponds to a total barrier of 39.4 kcal mol−1 (with respect to 4E), while production of 8E and 8Ei is determined by two competitive

from 1A are very similar to those from 11T to 4E and 4Ei (Figures S4 and S7 of the Supporting Information). The second process from 4E is a ligand rearrangement to produce species 4Ra (Scheme 3b). The elementary steps are (i) β-H elimination to form the alkene hydride complex Mo(H)(CHtBu)(CH2CHCH3) (1Ra), (ii) alkene cross-metathesis at 1Ra to form the new alkylidene Mo(H)(CHCH3)(CH2CHtBu) (3Ra), and (iii) insertion of the freshly formed alkene into the Mo−H bond to produce 4Ra. The β-H elimination transition state TS(4E-1Ra) has an energy of 38.9 kcal mol−1 with respect to the initial reactants, and its geometry already shows the Mo···Hhydride interaction (Mo···Hhydride distance of 1.747 Å). Here, the propene ligand is almost formed, with a Csp2···Csp2 distance of 1.381 Å, in comparison with the distance of 1.333 Å in free propene and consistent with a switch in carbon hybridization from sp3 to sp2. The Mo··· Cpropene and Hhydride···Cpropene distances are 2.415 and 1.894 Å, respectively. The resulting alkene complex, 1Ra, is 19.6 kcal mol−1 above 11T + propane and shows a highly distorted TBP structure where the imido and the surface are roughly trans to each other, with a NAr−Mo−O angle of about 138°. In this intermediate, propene is weakly coordinated to Mo (Mo− propene distances of 2.721/2.818 Å) and is trans to the strong σ donor, the hydride. The Mo−H and Mo−Cene bond distances are 1.680 and 1.879 Å, respectively. Cycloaddition between propene and the MoCene fragment in 1Ra leads to the 1,3substituted cyclobutane 2Ra. The energy barrier for cycloaddition from 1Ra is 11.7 kcal mol−1, and the transition state TS(1Ra-2Ra) shows the typical distorted-TBP structure found for cycloaddition with d0 transition-metal alkylidenes.18c,22d,29 The Mo···Cpropene and Cene···Cpropene distances are 2.283 and 2.225 Å, respectively, indicating an early interaction between propene and the Mo center. 2Ra is a 1,3-disubstituted metallacycle that also preserves the TBP structure around Mo with the Mo−Cα1−Cβ−Cα2 fragment being essentially planar, Mo−Cα distances of 2.058/2.078 Å, and a typical Mo···Cβ distance of Mo metallacycles (2.375 Å).29c This metallacycle is 22.1 kcal mol−1 above the initial reactants. Schrock type metallacyclobutanes have been experimentally detected in homogeneous30 and heterogeneous catalysis31 and studied in detail with computational chemistry.22a,b,29,32 From all of these studies there is a common agreement that there exist two types of metallacycles with different geometries: the TBP structure (already discussed here) and the square-based-pyramidal structure (SP). While the TBP intermediate has been found as a reactive species within the productive alkene metathesis, the SP isomer has been associated with a deactivation pathway with energies lower than those of the TBP structure.22a,b,32 Therefore, we also computed the SP isomers of 2Ra and 2Rb. These structures have relative energies of 12.1 and 16.2 kcal mol−1, respectively (Scheme 3d,e), and therefore they are 10 and 12 kcal mol−1 lower in energy than the corresponding TBP structures. The high energy of these metallacycles with respect to the initial reactants indicates that these intermediates are not amenable to be experimentally detected. This is mainly due to the fact that in alkane metathesis the alkane must be dehydrogenated before the alkene metathesis step, which is always a highly endergonic step.18b,c Thus, after alkane dehydrogenation, the potential energy surface of the reaction is well above the initial species. Cycloreversion from 2Ra leads to 3Ra in a slightly exergonic reaction. The associated transition state TS(2Ra-3Ra) has an energy of 32.1 kcal mol−1 above the initial reactants and G

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Organometallics barriers of 43.7 and 45.3 kcal mol−1, corresponding to the energy difference between the β-H elimination (TS(4E-1Ra)) transition state and the alkene insertion (TS(3Ra-4Ra)) transition state with respect to 4Ra, the lowest energy intermediate. Finally, production of 10E and 10Ei needs to overcome a total barrier of 48.7 kcal mol−1, which is given by the energy difference between the transition state for the release of 2,2-dimethylpentane TS(4Rb-9E) and 4Ei. These results indicate that, while 6E and 6Ei may be produced in similar amounts, 8E, 8Ei, 10E, and 10Ei are expected to be less abundant species. Remarkably, the reaction barriers calculated here are in qualitative agreement with the experimental data regarding the formation of the secondary alkanes detected in the gas phase: 2,2-dimethylpropane, 2,2-dimethylbutane, and 2,2-dimethylpentane.11b According to our calculations at 150 °C, the first product can be produced via two highly efficient ligand exchange reactions (the first ligand exchange at 11T (Scheme 2) and the ligand exchange at 1A (Scheme 3a)), both of them presenting the lowest energy barriers within their corresponding processes, whereas the last two products are only produced during the third ligand exchange step from 4Ra and 4Rb (Scheme 4) via energy unfavorable pathways. In particular, the very low observed abundance of 2,2dimethylbutane and 2,2-dimethylpentane (0.34 and 0.10 equiv per mole of Mo11b) is consistent with the very high energy barrier required to release them into the gas phase (ΔG⧧150 = 45−49 kcal mol−1). Catalytic Cycles. Several catalytic species are formed during the activation of precursor 11T, 6E, 6Ei, 8E, 8Ei, 10E, and 10Ei, which include intermediates with n-propyl and isopropyl as alkyl ligands and propylidene, ethylidene, and methylidene as alkylidene ligands. From all of these species, however, only a few lead to the main products, ethane and butane. In particular, our results suggest that species 6E and 8E are involved in the most efficient productive catalytic cycle of the metathesis of propane (Scheme 5 and Figure S13). In contrast, 6Ei and 10E are part of a productive catalytic cycle leading to methane and pentane, the minority products observed during the metathesis of propane (Scheme S4 and Figure S14). Moreover, an alternative catalytic cycle for the production of ethane and butane which does not involve the proton transfer between the two α-carbons can be envisaged from species 8Ei and 10E (Scheme S5 and Figure S15). The catalytic cycles from 6E and 6Ei involve the same elementary steps as described before in a specific sequence: ligand rearrangement (1,3-approach from 6E and 1,2-approach from 6Ei), ligand exchange, proton transfer between the two α-carbons, and, again, a ligand exchange with propane. On the other hand, the catalytic cycle from 8Ei consists only of two ligand rearrangement steps and two ligand exchange steps with propane. Briefly, the catalytic cycle from 6Ei for the production of methane and pentane shows a slightly exergonic Gibbs reaction energy at 150 °C (ΔG150 = −1.0 kcal mol−1) and an energy span of about 51 kcal mol−1 (see Scheme S4). As will be shown later, this span is ca. 8 kcal mol−1 higher than that of the productive cycle from 6E (vide infra), which is in agreement with the low abundance of methane and pentane observed during experiments.11 Along the same line, the alternative catalytic cycle from 8Ei to ethane and butane has an energy span of almost 49 kcal mol−1 (Scheme S5). This span is 5.6 kcal mol−1 higher in energy than that from 6E. Therefore, in this section we will focus on the most efficient catalytic cycle for the production of ethane and butane.

Scheme 5. Relative Gibbs Energies at 150 °C (ΔG150, in kcal mol−1) of the Intermediates and Transition States (Numbers Next to the Arrows) Involved in the Catalytic Cycle of the Metathesis of Propane to Ethane and Butane from 6Ea

a The value in italics for 6E is the energy after the catalytic cycle. The spectator imido ligand and the cluster surface are not shown for simplicity. The origin of the energies is the system 11T + propane.

The Gibbs energies at 150 °C for the metathesis of propane starting by 6E are shown in Scheme 5, and the corresponding B3PW91 optimized structures are shown in Figure S13 of the Supporting Information. Globally, the Gibbs reaction energy at 150 °C for the process 2 C3H8 → C2H6 + C4H10 is +1.6 kcal mol−1, suggesting a slightly endergonic reaction energy and consistent with the thermoneutral nature of the reaction.1b The initial ligand rearrangement from 6E takes place via the same elementary steps as described above from 4E to 4Ra (Scheme 3b), and the general geometrical features for this step are similar to those from 4E with only minor differences due to the less bulky substituent at the alkylidene ligand (Et vs tBu). The β-H elimination in 6E leads to intermediate 5Ra in an endergonic reaction by 19.0 kcal mol−1. The energy barrier for this step is 39.5 kcal mol−1, a barrier that is very similar to that of the 4E → 1Ra process during the precursor activation (Scheme 3b). The calculated energy barrier for cycloaddition from 5Ra to 6Ra is 11.4 kcal mol−1, also almost identical with that of the cycloaddition from 1Ra to 2Ra (Scheme 3b). The resulting Mo cyclobutane 6Ra has an energy of 16.8 kcal mol−1 above 11T + propane, and therefore its formation is slightly endergonic by ca. 2 kcal mol−1. From 6Ra cycloreversion takes place to the alkene complex 7Ra, which has an energy of 14.6 kcal mol−1 above the initial species. The transition state for cycloreversion has an energy of almost 25 kcal mol−1. Finally, migratory insertion of the coordinated butenyl ligand into the Mo−H bond in 7Ra produces 8Ra, a new Mo ethylidene species with a n-butyl ligand instead of a propyl. This insertion needs to overcome an energy barrier of about 20 kcal mol−1 and is highly exergonic (ΔG150 = −22.2 kcal mol−1). Therefore, the overall process 6E → 8Ra is exergonic by 3.3 kcal mol−1. H

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Scheme 6. Summary of the Reaction Pathways of the Metathesis of Propane by 11T at 150 °C, Indicating the Energies of the Intermediates with Respect to 11T + Propane, the Total Energy Barriers (ΔG⧧150) during the Precursor Activation, and the Energy Spans (δG150) of the Evaluated Catalytic Cycles (All Energies in kcal mol−1)a

a The most efficient process to the main products is highlighted in blue, the alternative cycle is shown in orange, and the catalytic cycle to minor products is given in red. The spectator imido ligand and the cluster surface are not shown for simplicity.

barrier for this step is 41.1 kcal mol−1, and 2A is located 6.5 kcal mol−1 below the initial species, indicating an exergonic reaction by about 1 kcal mol−1. From 2A, a new ligand exchange with propane liberates ethane and produces the Mo alkylidyne 5E, which by reaction with another propane molecule regenerates the active species 6E. The transition state TS(2A-5E) has an energy of 30.3 kcal mol−1, and thus the energy barrier needed to release ethane is 36.8 kcal mol−1. Again, the intermediate 5E

From the latter, a ligand exchange with propane allows the liberation of butane with an energy barrier of 36.1 kcal mol−1. The resulting species, 7E and 8E, are common intermediates to the last part of the precursor activation stage (Scheme 4a), and therefore the individual energy barrier for propane addition and the reaction energy are the same as those discussed previously. From 8E the intramolecular α-H abstraction produces 2A, a Mo propylidene intermediate with an ethyl ligand. The energy I

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During the catalytic process, however, all reactions are based on the same type of elementary steps: ligand exchange with propane, proton transfer between the two α-carbons, β-H elimination, alkene insertion, and the typical alkene crossmetathesis steps of cycloaddition and cycloreversion. Ligand exchange (ΔG⧧150 = 33−42 kcal mol−1), the proton transfer between the two α-carbons (ΔG⧧150 = 39−43 kcal mol−1), and β-H elimination (ΔG⧧150 = 40−44 kcal mol−1) are the most energetically demanding processes, while alkene cross-metathesis (ΔG⧧150 = 8−15 kcal mol−1) and insertion (ΔG⧧150 = 19−24 kcal mol−1) present lower barriers. However, our calculations show that the energy barriers of the activation stage are not higher than 40 kcal mol−1 for the most feasible pathway to generate the catalytically active species (6E and 6Ei) and that the overall activation process is exergonic. The most favorable pathway for the precursor activation implies the formation of an alkylidyne complex to finally produce 4E and 4Ei and then proton transfer between the two α-carbons and ligand exchange with propane. However, other side reactions also take place from 4E and 4Ei, which ultimately allow the liberation of secondary alkanes such as 2,2-dimethylbutane and 2,2-dimethylpentane. The high energy barriers calculated for these steps are in agreement with the low abundance of these products in the gas phase.11b The catalytic cycles for the production of main and minor products from 6Ei and 10E/8Ei were computed to have very high energy spans (δG = 49−51 kcal mol−1). This is in agreement with the low abundance of methane and pentane observed during the experiments.11b The alternative catalytic cycle involving 8Ei and 10E as active species is highly disfavored due to two reasons: the aforementioned high energy span needed to reach products during the catalytic cycle and the high energy barrier necessary to produce the active species (ΔG⧧150 = 45−49 kcal mol−1), thus indicating a very low concentration of those species on the silica surface. The most favorable catalytic cycle to the main products (ethane and butane) starts with 6E as the active species and is only slightly endergonic at 150 °C, in contrast to the metathesis of ethane by (SiO)2TaHx, where the reaction is favorable by almost 3 kcal mol−1 at the same temperature.18c Nevertheless, the computed Gibbs energy change is in agreement with the thermoneutral nature of the alkane metathesis.1b The energy span of this catalytic cycle is about 43 kcal mol−1, indicating that this should be the rate-controlling stage and that the precursor activation would be slightly faster. One important result of this investigation is the discovery that the ligand exchange of a Mo alkyl alkylidene with propane proceeds via a dissociative mechanism with the concomitant formation of a Mo alkylidyne species. While the formation of a Mo polyalkyl intermediate by addition of propane on 11T or the σ-bond metathesis processes give very high energy barriers (ΔG⧧150 = 70−75 kcal mol−1), the dissociative mechanism provides the lowest energy barriers for the exchange of ligands (ΔG⧧150 = 34−35 kcal mol−1) even if the formation of the Mo alkylidyne is highly endergonic (ΔG150 = 22−29 kcal mol−1). These results suggest that Mo alkylidynes are also active alkane metathesis catalysts. In fact, several examples exist in the literature in favor of a dissociative mechanism for ligand exchange in both homogeneous and heterogeneous catalysis. In the field of homogeneous catalysis, the data obtained here are consistent with the results for molecular Ti alkylidenes, which activate C−H bonds of aromatics by a dissociative mechanism with the formation of Ti alkylidyne complexes. 37 In

and its associated transition state for the addition of propane were already described during the activation stage (Scheme 3a). The overall efficiency of a catalytic cycle could be evaluated as the energy difference between the most stable intermediate and the highest energy transition state, regardless of the relative position of these structures (i.e., transition state after intermediate or intermediate after transition state), as proposed by the energetic span model developed by Kozuch and coworkers.33 Such a model has been successfully applied in the field of heterogeneous catalysis to simulate volcano plots for different transition-metal surfaces,33a to analyze the catalytic cycle of the Haber−Bosch process for the synthesis of ammonia as a function of reactant concentrations,34 and more recently to find the most favorable reaction pathway for catalytic oligomerization of ethylene using Ni-containing zeolites.35 The energy span of a catalytic cycle can be evaluated simply by δG = ΔGTS − ΔGI, where ΔGTS and ΔGI are respectively the Gibbs energies of the highest energy transition state and the lowest energy intermediate, when the transition state comes af ter the intermediate.36 In the present case, the calculated energy span for the production of ethane and butane from 6E is 43.3 kcal mol−1, given by the energy difference between 8Ra and TS(8E-2A). The latter transition state competes with the transition state for β-H elimination TS(6E-5Ra), giving a calculated span of 42.8 kcal mol−1, thus suggesting that those two transition states could be relevant to define the overall kinetics of the catalytic cycle. The computed span for the catalytic cycle is about 4 kcal mol−1 higher in energy than that for the most favorable pathway of the precursor activation (ΔG⧧150 = 39.4 kcal mol−1, Scheme 3a), indicating that the catalytic cycle is the rate-determining stage of the overall process. At this point it is worth mentioning that the energy span of 43 kcal mol−1 seems to be high for a process carried out at 150 °C. However, energy barriers of more than 40 kcal mol−1 have been computed for supported Ta hydrides in the context of alkane metathesis18c and hydrogenolysis.21b,c Nevertheless, it would be meaningful to analyze the dependence of the calculated span on the methodology used here. For this, we computed the energy span of the catalytic cycle in Scheme 5 at three different levels of theory (B3PW91, PBE0, and M06) and basis set (BS1 and BS2, see Models and Methods) in terms of electronic energies, as shown in Table S1 of the Supporting Information, considering the species 8Ra and TS(8E-2A) as the rate-determining states. The results indicate that all methods give roughly the same span (within 2 kcal mol−1), although enlarging the basis set tends to give slightly lower energy spans.



DISCUSSION The two stages of the metathesis of propane by [( SiO)Mo(NAr)(CHtBu)(CH2tBu)] have been analyzed using computational chemistry based on density functional theory via a cluster approach with the model catalyst 11T. These stages are the precursor activation by reaction with up to three propane molecules and the catalytic cycle, in which two molecules of propane are transformed into ethane and butane. An alternative catalytic cycle to the main products and a process leading to minor products (methane and pentane) were also considered. Scheme 6 shows the most important reaction pathways considered in this study, with the most feasible catalytic cycle highlighted in blue. J

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heterogeneous catalysis, the formation of a silica-supported Ta methylidyne has been detected by solid-state NMR from Ta methyl species following ligand dissociation steps similar to those proposed here for 11T.13b Moreover, supported alkylidyne complexes have also been observed in alkane metathesis with tungsten hydrides and polyalkyls.10b−d,16,17,38 Further investigations are in progress in order to fully understand whether different d0 metal alkylidynes are always involved in the alkane metathesis reaction.



Article

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.organomet.8b00090. Results associated with the validation of the computational models and methods, results on the structure of the initial catalyst, results concerning the catalytic cycle of the metathesis of propane leading to the minor products methane and pentane, results of the alternative catalytic cycle leading to the main products, ethane and butane, and all optimized geometries of stationary points reported along the paper (PDF) Cartesian coordinates and absolute energies of all stationary points presented in the paper (XYZ)

CONCLUSIONS

The metathesis of propane at 150 °C catalyzed by the d0 Mo alkyl alkylidene 1 was computationally explored by means of DFT calculations following a cluster approach, in which the amorphous silica surface is simulated by a cluster of one Si site. The mechanism of metathesis of propane consists of two main stages: precursor activation and catalytic cycle. However, both stages are based on the same type of reactions, (i) ligand exchange, (ii) proton transfer between two α-carbons, and (iii) ligand rearrangement, which in turn consists of several steps, such as β-H elimination, alkene cross-metathesis, and alkene insertion. The activation process starts by a ligand exchange that allows the release of neopentane and leads to a propyl intermediate. More importantly, this step has been proposed to occur via several mechanisms: dissociative, interchange (concerted), and associative. The calculations carried out here suggest that the dissociative pathway would be preferred, as it presents lower Gibbs energy barriers. The whole activation process leads to a Mo propylidene species, with an overall barrier is about 39 kcal mol−1. Other side processes that lead to different species and release secondary alkanes (2,2-dimethylbutane and 2,2-dimethylpentane) may also occur, but the calculated energies suggest that these pathways lead to species in very low abundance on the surface of silica. This is consistent with the experiments that show that 2,2-dimethylbutane and 2,2-dimethylpentane are present in small quantities. Two catalytic cycles leading to main (ethane and butane) and minor (methane and pentane) products and an alternative catalytic cycle to the main products are considered. The first two cycles consist of the same steps: ligand rearrangement, ligand exchange, proton transfer between the two α-carbons, and another ligand exchange, the only difference between them being the orientation of propene when the β-H elimination takes place. For these two cycles, that leading to the main products of the metathesis of propane has an energy span of 43 kcal mol−1, while that leading to the minor products has an energy span of 51 kcal mol−1. The alternative cycle to the main products consists only of ligand rearrangement and ligand exchange reactions and shows an energy span of 49 kcal mol−1, indicating that this process could be discarded. These data are consistent with the fact that ethane and butane are found as the main products of the metathesis of propane and that methane and pentane are only barely observed (see Table 1). When one looks at the energetics of the activation and productive catalytic cycle stages, it can be observed that the precatalyst activation is faster than the catalytic cycle, thus suggesting that the latter controls the overall kinetics of the process. Overall, the results presented in this work are very insightful and are expected to help to rationalize the chemical behavior and reactivity of supported Mo alkylidenes toward alkanes.



AUTHOR INFORMATION

Corresponding Author

*F.N.-Z.: e-mail, [email protected]; tel, +57-4-3405312. ORCID

Francisco Núñez-Zarur: 0000-0002-9244-9328 Notes

The authors declare no competing financial interest.



ACKNOWLEDGMENTS The authors wish to thank the Universidad de Antioquia for financial support (grant 20502301-007). F.N.-Z. thanks the COLCIENCIAS for the “Es Tiempo de Volver” fellowship and the Universidad de Medelliń for financial support to the project ref 892. Partial funding for this work was provided by COLCIENCIAS via project 111571249844 (contract 3782016).



REFERENCES

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Organometallics

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DOI: 10.1021/acs.organomet.8b00090 Organometallics XXXX, XXX, XXX−XXX