Effect of Ancillary Ligands on Oxidative Addition of CH4 to Ta(III

Nov 18, 2016 - Riffat Parveen and Thomas R. Cundari ... A DFT study of oxidative addition of methane to Ta(OC2H4)3A (where A ...... Debad , J. D.; Leg...
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Effect of Ancillary Ligands on Oxidative Addition of CH4 to Ta(III) Complexes Ta(OC2H4)3A (A = B, Al, CH, SiH, N, P): A Density Functional Theory Study Riffat Parveen and Thomas R. Cundari* Department of Chemistry and Center of Advanced Scientific Computing and Modeling, University of North Texas, 115 Union Circle, #305070, Denton, Texas 76203-5017, United States S Supporting Information *

ABSTRACT: A DFT study of oxidative addition of methane to Ta(OC2H4)3A (where A may act as ancillary ligand) was conducted to understand how A may affect the propensity of the complex to undergo oxidative addition. Among the A groups studied, they can be a Lewis acid (B or Al), a saturated, electronprecise moiety (CH or SiH), a σ-donor (N), or a σ-donor/π-acid (P). By varying A, we seek to understand how changing the electronic properties of A can affect the kinetics and thermodynamics of methane C−H activation by these complexes. For every reaction two transition states (H or CH3 trans to A) leading to two corresponding products were identified. For all A, the TS with H trans to A is favored kinetically; except for SiH and CH, the kinetically favored product is not thermodynamically favored. For the kinetic products, the ΔG⧧ values for A = B, Al are highest among the 2p and 3p elements, respectively. Upon moving from electron-deficient to electron-rich moieties (P and N) the computed C−H activation barrier for the kinetic product decreases significantly. Thus, changing A greatly influences the barrier for methane C−H oxidative addition by these complexes.

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ligand, or metal−ligand active site. There are five primary classes involving the formation of stable organometallic species: two of these (oxidative addition (OA) and σ-bond metathesis) occur quite commonly, another two (metalloradical activation and 1,2-C−H addition) are somewhat more rare for organometallics. The fifth class of activation reaction (electrophilic activation) involves transient generation of organometallic species as reaction intermediates.12 Oxidation addition entails 1,1-addition of C−H to a low-valent transition metal and results in an increase in the formal oxidation state and coordination number of the metal by two units.13 Computational studies of oxidative addition (the microscopic reverse of reductive elimination) have helped to explain the electronic structure details of this reaction.14 In previous computational works, concentration has been placed upon oxidative addition reactions by low-valent late transition metals, in particular 16-electron intermediate complexes of the type Cp*M(L) where M = Rh, Ir and L = PR3, CO are examples in which oxidative addition is the recognized C−H activation mechanism.13 Complexes possessing late transition metals with electrophilic character such as PtII and HgII have also garnered

INTRODUCTION A major focus in organometallic chemistry is to study hydrocarbon C−H bond activation by transition-metal complexes. An ultimate objective in this field is to convert hydrocarbon feedstocks into more intricate, functionalized, or utilizable organic compounds.1 Among saturated hydrocarbons, methane activation is of particular interest because the majority of natural gas consists of methane.2 Although methane is a current chemical feedstock, it is often used indirectly by conversion to syngas, which is then converted in a second step to a higher value compound. The development of efficient catalysts for direct alkane functionalization could open the door to increase the use of relatively inert alkanes as precursors for many industries.3 However, in addition to considerable C−H bond energies, the inert nature of the aliphatic C−H bond is an equally significant factor that renders C−H functionalization difficult.4 Methane functionalization processes involve breaking of the C−H bond as the first step; an understanding the mechanism of this step has been a “Holy Grail” in catalysis.5 Due to the fundamental economic significance of these processes, many theoretical6−9 and experimental10,11 studies have been carried out in search of highly active catalysts. Relating the activity to the intrinsic properties of the active site remains challenging. C−H activation reactions are conveniently classified according to their overall mode of activation via a metal, © XXXX American Chemical Society

Special Issue: Hydrocarbon Chemistry: Activation and Beyond Received: August 30, 2016

A

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Organometallics much attention in alkane functionalization.15 Along with late transition metals, early-transition-metal complexes were also studied for their C−H activation ability. For example, in 1996 Vidal et al. reported the synthesis of a surface-bound tantalum(III) monohydride species, (SiO)2TaIIIH, that can activate the C−H bond of cycloalkanes (C5−C8) to form tantalum(III) monoalkyls at room temperature, which can convert under oxygen to the corresponding (SiO)2TaV( O)(O-alkyl).16 A computational investigation of [2 + 2] and oxidative addition of methane to d2 W(OH)2(NH) was conducted by Cundari to evaluate the role of d orbital occupation in C−H functionalization; the [2 + 2] activation pathway for the d2 tungsten complex was also compared with that for d0 Ti(OH)2(NH). It was concluded that as compared to [2 + 2], the OA reaction has a much larger thermodynamic driving force for the above reaction.17 Although it is difficult to determine by experimental methods, it is important to understand the electronic state of activating species along the reaction coordinate to fully understand the reasons a particular reaction mechanism is preferred. Previous research on a d2 system (group 5) showed that olefin substitution in M(silox)3(olefin), where M = Nb, Ta, olefin = C2H4, C2H3Me, C2H3Et, cis-2-C4H8, iso-C4H8, C2H3Ph, c-C5H8, c-C6H10, norbornene, and silox = OSitBu3, was governed by the density of states (DOS) at the metal.18 Greater nd/(n + 1)s mixing for Ta (n = 5) in comparison to Nb (n = 4) was proposed to result in a low DOS for the Ta complexes.19−22 The high DOS in Nb systems yielded an energetically accessible transition state for olefin association/ dissociation, but for Ta complexes, the transition states were much more dependent on the nature of the olefin substrates. Another study by Marshak et al. was conducted on the “triggering” of cyclometalation (intramolecular C−H activation) by (silox)2W = NtBu where silox = tBu3SiO.23 With a filled dz2 orbital on the d2-WIV center, the oxidative addition of a C−H bond is Woodward−Hoffmann forbidden. For cyclometalation to occur, there must be an electrophilic site at metal center, and thus a promotional energy is required to “remove” electron density from the dz2 orbital. With the addition of a suitable base, these electronic changes can be encouraged and compensated for by the formation of a W−adduct bond and as a result a distorted-tetrahedral geometry (approximating a trigonal monopyramid) that permits displacement of the adduct by the C−H bond of the silox ligand.23 Furthermore, for the cyclometalation of d2-MIII(silox)3, where M = Nb, Ta, the electrons from dz2 should be “removed” to minimize σCH/ dz2 repulsion early in the reaction coordinate and thus permit C−H activation to occur. In addition to the electronic state of the activating complex, C−H bond activation is also effected by the position of ligands attached to the central transition metal-atom. In the research reported by Prince and Cundari for the C−H bond activation of methane by PtII−N-heterocyclic carbene complexes, a neutral bis-methoxy adduct, trans-[Pt II (OCH 3 ) 2 (NHC) (CH4)], is more favored for C−H activation by ∼10 kcal/ mol in free energy over the isomer in which the OCH3 ligands are cis. In the trans isomer the more strongly trans influencing NHC is trans to weakly bound methane resulting in facile C−H activation.24 Another study conducted by O’Reilly et al. focused on the effect of the supporting ligand donor strength on the oxidative addition and reductive functionalization of RhIII complexes using tBu3terpy and (NO2)3terpy ligands. It was found in this research that, when the 4,4′,4″-tert-butyl groups

were replaced with NO2 in [(NO2)3terpy]RhICl, the donating ability of the ligand was significantly decreased, and hence this significantly diminished the RhI complex’s ability to undergo oxidative addition.25 In this paper the effect of ancillary ligands on oxidative addition of CH4 to TaIII complexes is reported. The effect of changing the identity and electronic properties of the ancillary ligand in the reactant complex on the activation energy barrier of methane activation has been investigated using density functional theory methods.

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COMPUTATIONAL METHODS

All calculations were performed using the Gaussian 0926 software package. DFT calculations were carried out using the BP8627,28 functional in conjunction with the CEP-31G29−31 pseudopotential/ valence basis set for Ta and the 6-31+G(d)32,33 all-electron basis set for other elements. Geometry optimizations were performed in the gas phase; however, single-point calculations at all stationary points were done in acetone using the SMD34 continuum solvent model with the larger 6-311++G(d,p) basis set. An empirical dispersion correction (GDB3J) was applied for some test calculations but were not found to have any substantial effect on the kinetics and thermodynamics of the reactions (see the Supporting Information); hence, for this reason, in this study calculations do not include dispersion correction. The free energies (reported in kcal/mol) were calculated at 298.15 K and 1 atm. Ground states possessed no imaginary frequency, whereas transition states contained one imaginary frequency. As Ta belongs to the 5d transition metal series, the most plausible spin state to be analyzed is low spin. Note also that no weakly bound methane adducts of the TaIII reactants were found either through geometry optimization or via intrinsic reaction coordinate (IRC) calculations.

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RESULTS AND DISCUSSION Reactant Complexes. Reactants for the present research are methane and Ta(OC2H4)3A, where A may act as an ancillary ligand. The d2-TaIII reactant complex has a cyclic structure with a trigonal arrangement of three oxygen atoms around Ta (Scheme 1). The calculated average for the sum of Scheme 1

the three O−Ta−O angles for the six reactants is 342.4° (360.0° for trigonal planar), suggesting a perturbation of the reactant complexes toward a distorted-pyramidal geometry. The tantalum in the Ta(OC2H4)3A reactant possesses a formal oxidation state of 3+ and is thus d2, as indicated by a predominantly dz2 HOMO (see below). We have focused on the singlet state for the present calculations, as triplets were computed to be significantly higher (∼1 eV) in energy for related complexes.35,36 Among the A species in this study, they can be a Lewis acid (B or Al), a saturated, electron-precise moiety (CH or SiH), a σ-donor (N), or a σ-donor/π-acid (P). By varying A in the reactant complex, we seek to understand how changing the electronic properties (from electron-deficient to electron-rich) and the identity of the ancillary ligand can affect the kinetics and thermodynamics of methane C−H activation via oxidative addition. B

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the electron-deficient A (group 13) and proceeding toward the electron donor A (group 15). Oxidative Addition Products for A = Al. In the case of A = Al, oxidative addition of methane leading to formation of the product with CH3 trans to Al (1a) is slightly exergonic (ΔG = −0.7 kcal/mol, relative to separated reactants) (Scheme 2),

Analysis of the optimized structures showed that all Ta− reactant complexes possess similar geometries; the major differences are the varied distances between Ta and A ranging from 2.43 (A = B) to 3.61 Å (A = P) (Table 1). Optimized Table 1. Comparison of Ta−A Distances (Å) in Reactants with the Sum of Ta−A Covalent Radii (Å)37 and van der Waals Radii (Å)38 A

Ta- - -A distance (in reactants)

sum of Ta−A covalent radii

sum of Ta−A van der Waals radii

Al SiH P B CH N

2.73 3.09 3.61 2.43 3.10 2.93

2.56 2.49 2.44 2.20 2.15 2.13

3.8439 4.10 3.80 3.9239 3.70 3.55

Scheme 2. Calculated Free Energy (kcal/mol) Pathway for Oxidative Addition of CH4 to Ta(OC2H4)3Al

Ta- - -A distances in these reactants, in comparison with estimates from the sum of the Ta−A covalent radii (Å) and the sum of the Ta- - -A van der Waals radii (Å), suggest that it may be possible for A to have electronic interactions with Ta, thus imparting a trigonal-monopyramidal geometry to Ta(OC2H4)3A. According to the structural data in Table 1, the Ta- - -B distance in Ta(OC2H4)3B (2.43 Å) is closer to the Ta− B covalent radii sum (2.20 Å) than the Ta−B van der Waals radii sum (3.92 Å). The same observation applies to Ta(OC2H4)3Al, where the optimized Ta- - -Al distance of 2.73 Å in the reactant is closer to the sum of the Ta−Al covalent radii (2.56 Å) than the sum of van der Waals radii (3.84 Å). The values for T- - -B and Ta- - -Al distances in the reactants suggest the potential for strong interaction between Lewis acidic ancillary ligands (B and Al) and the d2 TaIII center. When occupied molecular orbitals were plotted for reactant complexes with A = B and Al (vide infra), it is evident that there is interaction between Ta (dz2) and B (2p) and Ta (dz2) and Al (3p) orbitals. In the case of Ta(OC2H4)3B, the interaction appears to be strong, thus resulting in a short Ta- - B distance in the reactant complex (2.43 Å). For electron donor ancillary ligands, A = P, N, the optimized Ta- - -A distances are far more than the sum of the Ta−A covalent radii (Table 1), suggesting that interaction between Ta and N, P is more of a van der Waals type interaction in the ground state reactant. Saturated electron-precise moieties (i.e., A = CH, SiH) showed intermediate behavior. Oxidative Addition. The oxidative addition of methane to Ta(OC2H4)3A may result in the formation of two coordination isomers for the five-coordinate d 0 -Ta V products Ta{(OC2H4)3A}(CH3)(H): one with CH3 approximately trans to A (methyl occupies an approximately axial coordination site), and the other isomer with H trans to A (methyl occupies an approximately equatorial coordination site). The geometry of these complexes is closer to a trigonal bipyramid (TBP5) than a square pyramid (SQP5), with two oxygen atoms occupying equatorial positions and the third atom in an axial position. Results for the oxidative addition reactions of TaIII complexes are discussed below starting with the ancillary ligands (A) that belong to the third period (group 13−15) and then for the second period ancillary ligands in the same manner. In order to better understand how the electronic properties of A affect the kinetics and thermodynamics of methane C−H oxidative addition, the order followed for discussion for each periods is from left to right, starting from

whereas for the isomer in which H is trans to Al (1b) the reaction is endergonic (ΔG = 4.2 kcal/mol). Therefore, the ΔG value for this reaction showed that the product with CH3 trans to Al is thermodynamically more stable than that with H trans to Al by ∼5 kcal/mol, perhaps reflecting the modest difference in trans influence for methyl versus hydride. The most noticeable changes in bond distances occur between Ta and Al; this distance lengthens by 0.48 Å (for 1a) and by 0.45 Å (for 1b) in comparison to the distance in Ta(OC2H4)3Al (2.73 Å). The Ta−H distances are almost the same in both product isomers, while the Ta−C distance in 1b is slightly greater (by 0.03 Å) than in 1b (Figure 1).

Figure 1. Optimized geometries for products of the oxidative addition of CH4 to Ta(OC2H4)3Al. Distances are given in Å.

Oxidative Addition Transition States for A = Al. Ta(OC2H4)3Al activated the C−H bond through a threecentered, triangular Ta- - -H- - -C transition state (TS) as expected for oxidative addition. Two isomeric transition states were found, reminiscent of the two isomeric products just discussed, one with CH3 trans to Al (2a) and the other with H trans to Al (2b) (Figure 2). The energy Hessian showed only C

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Figure 3. Optimized geometries for products of the oxidative addition of CH4 to Ta(OC2H4)3SiH. Distances are given in Å.

Figure 2. Optimized geometries of oxidative addition transition states for Ta(OC2H4)3Al(CH3)(H). Distances are given in Å.

Scheme 3. Calculated Free Energy (kcal/mol) Pathway for Oxidative Addition of CH4 to Ta(OC2H4)3SiH

one imaginary vibrational frequency for each: 926i cm−1 (2a) and 932i cm−1 (2b). These imaginary frequencies correspond primarily to C−H bond breaking (formation for the microscopic reverse). From reactant to TSs the distance between Ta and Al increases from 2.73 to 2.93 ± 0.03 Å for 2a and 2b. This distance increases further in the products (3.21 Å in 1a and 3.18 Å in 1b). Another important structural feature is the notable decrease in the distance between Al and one of the axial oxygens from the TS to the products: 2.29 Å in TS 2b to 1.99 Å in the corresponding product 1b and 2.65 Å in TS 2a to 1.97 Å in the product 1a. It is interesting to note that the Al−O distance in the products (1.97 Å in 1a and 1.99 Å in 1b) is nearly identical with the sum of the Al and O covalent radii37 (1.91 Å). In the OA products, TaV is d0 and is thus a Lewis acid, unlike the d2 configuration of the reactant; therefore, AlIII (which is, of course, a Lewis acid) prefers a stronger interaction with oxygen, as indicated by a short Al−O distance and long Ta- - -Al distances along the reaction coordinates (from reactant to product). Methane activation by Ta(OC 2 H 4 ) 3 Al to form Ta{(OC2H4)3Al}(CH3)(H) may proceed by two isomeric transition states. The isomer with H trans to Al (2b) was calculated to be ∼15 kcal/mol more stable than the TS with CH3 trans to Al (2a); the former is 37.8 kcal/mol uphill in free energy relative to both reactants at 298.15 K and 1 atm (Scheme 2). Following the intrinsic reaction coordinate from the oxidative addition transition state that leads to the formation of corresponding product, it is confirmed that the TS with CH3 trans to Al connects with the product in which CH3 is trans to Al. Hence, although product 1b is kinetically preferred, 1a is thermodynamically preferred. Oxidative Addition Products for A = SiH. As for A = Al, there were two products identified for OA of methane to Ta(OC2H4)3SiH: CH3 trans to SiH (3a) and H trans to SiH (3b) (Figure 3). Unlike A = Al, however, oxidative addition of methane is exergonic for formation of either product with a ΔG value of −5.9 kcal/mol for 3b and −5.6 kcal/mol for 3a, as shown in Scheme 3. Also, unlike A = Al, for the siliconcontaining reagent, the product Ta{(OC2H4)3SiH}(CH3)(H) with H trans to SiH (3b) is thermodynamically more stable than the product with CH3 trans to SiH (3a) by 0.3 kcal/mol, although the free energy difference is much less than that of Al, where ΔΔG ≈ 5 kcal/mol. Analysis of the optimized structural parameters showed that the Ta- - -Si distance increased from 3.09 Å in the organometallic reactant to >3.5 Å in the products (3.51 Å for 3a, 3.56 Å for 3b). This change in Ta- - -Si distance

(∼0.44 Å) is only slightly less than the change in distance observed for Ta- - -Al from reactant to products (∼0.46 Å). Oxidative Addition Transition States for A = SiH. The calculated free energy barrier for OA of methane to form the complex Ta{(OC2H4)3SiH}(CH3)(H) with H trans to SiH, 4b, was calculated to be 28.5 kcal/mol (relative to Ta(OC2H4)3SiH plus methane) (Scheme 3), while the corresponding free energy barrier for the complex with CH3 trans to SiH (4a) is 45.9 kcal/mol. The imaginary frequencies for the TSs are 874i and 953i cm−1 for 4a and 4b, respectively (Figure 4). The results indicated ΔΔG⧧ = 17.4 kcal/mol in favor of the complex

Figure 4. Optimized geometries of oxidative addition transition states for Ta(OC2H4)3SiH(CH3)(H). Distances are given in Å. D

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Organometallics with H trans to SiH. Hence, the kinetic preference for one product (for the Ta complex with SiH as ancillary ligand) is slightly more than that for the Ta complexes with Al (ΔΔG⧧ = 15.0 kcal/mol). Another interesting point of comparison is that moving from left to right in a period (i.e., replacing Al with SiH) decreases the calculated energy barriers for OA of methane to Ta complexes, as ΔΔG⧧ (Al-SiH) is 9.3 kcal/mol (for the kinetically preferred products). According to the calculations, OA of methane to Ta(OC2H4)3SiH is favored kinetically as well as thermodynamically versus Ta(OC2H4)3Al (ΔΔG(Al−SiH) = 5.2 kcal/mol, for most stable products). Structural analysis of the TSs showed that the Ta- - -Si distance increases significantly on moving from reactants (3.09 Å) to TSs (3.41 Å in 4a and 3.44 Å in 4b). In the case of SiH as the ancillary ligand, Ta- - -Si distances in TSs (3.41 Å in 4a to 3.51 Å in 3a and 3.44 Å in 4b to 3.56 Å in 3b) are closer to products in comparison to reactants. Oxidative Addition Products for A = P. The oxidative addition of methane to Ta(OC2H4)3P is exergonic: ΔG = −8.0 kcal/mol for formation of the product with H trans to P (5b). Like A = Al, but unlike A = SiH, the formation of the product with CH3 trans to P, 5a, is thermodynamically more feasible than the product with H trans to P, 5b (ΔΔG = 7.1 kcal/mol) (Scheme 4). The thermodynamic preference for one product

Figure 5. Optimized geometries for products of the oxidative addition of CH4 to Ta(OC2H4)3P. Distances are given in Å.

Scheme 4. Calculated Free Energy (kcal/mol) Pathway for Oxidative Addition of CH4 to Ta(OC2H4)3P Figure 6. Optimized geometries of oxidative addition transition states for Ta(OC2H4)3P(CH3)(H). Distances are given in Å.

to C−H bond making/breaking. The free energy barrier for oxidative addition of methane to Ta(OC2H4)3P results in the formation of a TS with H trans to P and was calculated to be 18.4 kcal/mol (versus separated reactants), while ΔG⧧ for the TS with CH3 trans to P is 35.3 kcal/mol (Scheme 4); thus, the former is kinetically favored by 16.9 kcal/mol. In comparison with other ancillary ligands, the free energy values indicate that when A is phosphorus the activation energy barrier goes down significantly in comparison to that of Al and SiH by 19.4 and 10.1 kcal/mol, respectively (for the TS leading to the formation of the most stable kinetic products). As for A = SiH, when A = P, the kinetic and thermodynamic products of methane oxidative addition are different. Oxidative Addition Products for A = B. For Ta(OC2H4)3B, methane oxidative addition is calculated to be endothermic by 18.6 kcal/mol for 7b (when H is trans to B) and by 13.7 kcal/ mol for 7a (when CH3 is trans to B) (Scheme 5). In comparison to the 3p member of group 13 (i.e., Al), OA of methane to Ta(OC2H4)3B is more endothermic than that of OA of methane to Ta(OC2H4)3Al by 14.4 kcal/mol for the thermodynamically most stable product (CH3 trans to A). Like previous cases where P and Al acted as ancillary ligands, the product with CH3 trans to B is more stable by 4.9 kcal/mol in comparison to that with H trans to B. This value of ΔΔG (A = B) is similar to the value obtained for OA of methane to Ta(OC2H4)3Al (ΔΔG = 4.9 kcal/mol). Analysis of the products revealed that the distance between Ta and B increased from 2.43 Å in reactant to ∼3.01 Å in the products, although B becomes closer to an O atom occupying an axial site. Comparison of the optimized structures showed that the increase in Ta- - -A distance from reactant to products for Ta

over the other is greater in comparison to that of Ta complexes with Al and SiH as ancillary ligands, where the ΔΔG values were 4.9 and 0.3 kcal/mol, respectively. The OA of Ta complex for A = P is more exergonic by 14.4 and 9.2 kcal/mol in comparison to Al and SiH, respectively (for the most stable products). Optimized Ta- - -P distances in the products (in comparison to reactant) showed that the distance between P and Ta increases from 3.61 Å (in reactants) to ∼3.82 Å in products (3.79 Å in 5a and 3.84 Å in 5b) (Figure 5). For Ta complexes with P as ancillary ligand the change in Ta- - -P distance from reactant to product is ∼0.2 Å, which is less in comparison to the change in Ta−Al and Ta−SiH bond distances (∼0.47 and ∼0.45 Å, respectively). Oxidative Addition Transition States for A = P. Transition states corresponding to both isomeric Ta{(OC2H4)3P}(CH3)(H) products, one with CH3 trans to P (6a) and another with H trans to P (6b), were located (Figure 6). The lone imaginary frequencies of 501i cm−1 (6a) and 780i cm−1 (6b) correspond E

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reactant to 2.88 Å in the TS with H trans to B (8b) and it reaches up to 3.00 Å for the corresponding Ta{(OC2H4)3B}(CH3)(H) products (Figure 8). For these same TSs the B and

Scheme 5. Calculated Free Energies (kcal/mol) for Oxidative Addition of CH4 to Ta(OC2H4)3B

Figure 8. Optimized geometries of oxidative addition transition states for Ta(OC2H4)3B(CH3)(H); distances are given in Å.

axial O distance was 2.70 Å and in the product it decreases to 1.78 Å. For the TS with CH3 trans to B, 8a, the Ta- - -B increases to 2.73 Å (this value is 0.15 Å less than that for 8b) and the value is 3.02 Å in the product 7b. In addition, the B and axial O distance decreases from 2.74 Å in TS 8a to 1.72 Å in the product 7a. These values indicate that the increase in Ta- - -B distance (from TS to product) is not as significant as the decrease in the B- - -axial O distance (from TS to product). As with A = Al, these changes in Ta- - -B and B- - -O distances from reactant to products are consistent with the OA of methane to a TaIII (d2 system) resulting in formation of products in which TaV is d0. Since trivalent B is an electron deficient, Lewis acid, it can interact more closely with an oxygen atom on the supporting ligand than the TaV (d0) of the product. Oxidative Addition Products for A = CH. The oxidative addition of methane to Ta(OC2H4)3CH is exothermic with a free energy of −18.4 kcal/mol for the product with H trans to CH (9b) and −17.6 kcal/mol for the product with CH3 trans to CH (9a) (Figure 9). Unlike Ta complexes with A = P, Al, B,

complexes with B as ancillary ligand is more (Δr = 0.57 Å) than that of Al (Δr = 0.47 Å) (Figure 7).

Figure 7. Optimized geometries for products of the oxidative addition of CH4 to Ta(OC2H4)3B. Distances are given in Å.

Oxidative Addition Transition States for A = B. Transition states that lead to the two isomers of Ta{(OC2H4)3B}(CH3)(H), one with CH3 trans to B (8a) and other one with H trans to B (8b), were located. The imaginary frequencies for both transition states are 922i cm−1 (8b) and 891i cm−1 (8a). The free energy barrier for the oxidative addition reaction is 43.2 kcal/mol for 8b (in comparison to separate reactants). This TS is more stabilized by 12.5 kcal/mol in comparison to TS 8a (Scheme 5). The ΔΔG⧧ value for A = B is 5.4 kcal/mol greater in comparison to that of A = Al. The energy barrier for the most stable TS for OA of methane (with B as ancillary ligand) is higher than that of all the other Ta complexes discussed thus far. As observed for A = P, Al, in this case, the more stable TS (with H trans to B) leads to the formation of the thermodynamically less stable product. The present results suggest that OA of methane to Ta(OC2H4)3B is kinetically as well as thermodynamically less favored in comparison to OA of methane to Ta(OC2H4)3Al (ΔΔG⧧(B−Al) = 5.4 kcal/mol, ΔΔG(B−Al) = 14.4 kcal/mol). It may also be inferred from these free energies that thermodynamic differences are more significant than kinetic differences for boron versus aluminum. The optimized structural parameters of TSs 8a and 8b showed that the Ta- - -B distance increased from 2.43 Å in the

Figure 9. Optimized geometries for products of the oxidative addition of CH4 to Ta(OC2H4)3CH. Distances are given in Å.

for A = CH the most stable product is that with H trans to CH. Although this product is more stable than the other by 0.8 kcal/ mol (Scheme 6), the small ΔΔG value suggests that the thermodynamic preference for one product over the other is not significant. When calculated ΔG values for methane oxidative addition for A = SiH, CH were compared, the results F

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comparison to that for A = B, ΔΔG⧧(B−CH) = 22.1 kcal/mol (for the most stable TS) (Scheme 6). The energy barrier difference is more significant when moving from B to CH than when moving from SiH to CH. As expected for CH (on the basis of the result obtained for SiH), the kinetics and thermodynamics both prefer the product with H trans to CH, although kinetic preferences are larger than thermodynamic preferences. Oxidative Addition Products for A = N. For the Ta complex with N as an ancillary ligand (Ta(OC2H4)3N), the oxidative addition process is calculated to be exothermic by −31.2 kcal/ mol (when H is trans to N, 11b), and by −36.6 kcal/mol (when CH3 is trans to N, 11a) (Scheme 7). Like some previous

Scheme 6. Computed Free Energy (kcal/mol) Pathway for Oxidative Addition of CH4 to Ta(OC2H4)3CH

Scheme 7. Calculated Free Energy (kcal/mol) Pathway for Oxidative Addition of CH4 to Ta(OC2H4)3N

indicated that OA is more exothermic for the latter by 12.5 kcal/mol (for most stable products). The calculated ΔΔG value for A = CH (0.8 kcal/mol) is greater than the ΔΔG value for A = SiH (0.3 kcal/mol), although a very small magnitude difference (ΔΔG = 0.5 kcal/mol) is computed. In addition to SiH, results for the Ta complex with A = CH were also compared with Ta complexes having B as the ancillary ligand. Thermodynamic data indicate that OA (A = CH) is more exothermic than for A = B as ΔΔG(B-CH) = 32.1 kcal/mol (for most stable products); this value indicates that the thermodynamic feasibility of methane oxidative addition increases more significantly when moving from left to right in a period than from top to bottom in a group for the choice of ancillary ligand (A). Oxidative Addition Transition States for A = CH. The free energy barrier for OA of methane to Ta(OC2H4)3CH is 21.1 kcal/mol (versus separate reactants) for the TS with H trans to CH (10b) and 33.6 kcal/mol for the TS with CH3 trans to CH (10a) (Figure 10). Similar to all the cases already discussed, the

cases (A = P, Al, B), the product with CH3 trans to N is more stable, in this case by 5.4 kcal/mol in comparison to other cases with H trans to N. In comparison to the heavier member of group 15, i.e., P, the OA of methane to Ta(OC2H4)3N is calculated to be more exergonic than that of Ta(OC2H4)3P by 21.5 kcal/mol (for the most stable product). It is worth mentioning that the oxidative addition products for A = N are the thermodynamically most stable among all candidates for ancillary ligands investigated. Structural analysis of the products revealed that the distance between Ta and N decreased from 2.93 Å (in reactant) to ∼2.5 Å in products (2.49 Å in 11a and 2.51 Å in 11b) (Figure 11). This is the only case where A is closer to Ta in products versus reactants; for P, Al, SiH, CH, and B the distance between A and Ta increases. Oxidative Addition Transition States for A = N. In the case of A = N, it was only possible to locate one true transition state,

Figure 10. Optimized geometries of oxidative addition transition states for Ta(OC2H4)3CH(CH3)(H). Distances are given in Å.

TS with H trans to CH is more stable by 12.5 kcal/mol in comparison to TS with CH3 trans to CH. This value of ΔΔG⧧ is equal to that obtained for A = B. Although upon moving from Al to B the free energy barrier (ΔΔG⧧(B−Al) = 5.4 kcal/ mol) increases, from SiH to CH it decreases by 7.4 kcal/mol (for the most stable TS). The energy barrier is also lower in

Figure 11. Optimized geometries for products of the oxidative addition of CH4 to Ta(OC2H4)3N. Distances are given in Å. G

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concluded that for all ancillary ligands the transition state with H trans to A is kinetically favored over the other with CH3 trans to A. (3) For the Ta{(OC2H4)3A}(H)(CH3) products, except for A = SiH, CH the kinetically favored product is not thermodynamically favored. The thermodynamic preference for the product with CH3 trans to H over the other with H trans to A is 4.9 and 7.1 kcal/mol for Al and P and for A = B, N these values are 4.9 and 5.4 kcal/mol, respectively. For A = SiH, CH, the products with H trans to A are thermodynamically preferred by 0.3 and 0.8 kcal/mol, respectively, a much smaller difference in comparison to other ancillary ligands. (4) A comparison of calculated activation barriers for the kinetically favored TSs of 3p elements revealed that OA is most favorable for A = P (ΔG⧧ = 18.4 kcal/mol) and least favorable for A = Al (ΔG⧧ = 37.8 kcal/mol). For the 2p element ancillary ligands, the order of activation energy barrier is B > CH > N. Overall A = N yielded the smallest oxidative addition barrier, 14.9 kcal/mol, among all Ta(OC2H4)3A studied. (5) For both heavy and light main-group elements, the oxidative addition reaction becomes more feasible upon moving from left to right within a period (from B to N and from Al to P). (6) In moving down a group from CH to SiH and from N to P the activation energy barrier increases (from 21.1 to 28.5 kcal/mol and 14.9 to 18.4 kcal/mol, respectively) but from B to Al, it decreases from 43.2 to 37.8 kcal/mol. (7) For A = N the distance between Ta and N decreases along the reaction pathway. This is the only case where A is closer to Ta in products versus reactants; for P, Al, SiH, CH, and B the distance between A and Ta increases. Oxidative addition of CH4 to Ta(OC2H4)3A is kinetically as well as thermodynamically most feasible with N acting as ancillary ligand. The second most promising candidate on the basis of the kinetic data is A = P. On the other hand, for B and Al acting as ancillary ligands the energy barrier was quite high, 43.2 and 37.8 kcal/mol, respectively, for the lower energy transition states. On the basis of these results, it can be inferred that having an electron-deficient moiety as the ancillary ligand will raise the activation energy barrier for oxidative addition of CH4 to Ta reactant complex and an electron-donating group lower the energy barrier. The ground states (reactant complex) are (dz2)2 and can be considered to be σ2 with respect to the reaction coordinates of oxidative addition. Similarly, the pair of electrons in the C−H bond of methane that is to be activated also possesses a σ2 electron configuration. As a result, the oxidative addition of C−H to Ta complex is formally Woodward−Hoffmann forbidden. Thus, the OA reaction must overcome this constraint by acquiring a correct orbital configuration at the activating complex. This can be achieved by promoting electrons from dσ2 to the empty (in the ground electronic state) dπ orbitals, thus generating an empty dσacceptor orbital that can attract the electron pair from the C−H σ bond. The filled dπ-type orbital has the appropriate symmetry to interact with the C−H σ* to initiate scission during the addition via a back-bonding process.21 When the frontier Kohn−Sham molecular orbitals were plotted for the reactant complexes (Figure 13), it was seen that for Ta(OC2H4)3B there is a strong interaction of Ta and B orbitals in the HOMO, thus making the electron pair in the Ta dz2 less available and resulting in higher activation energy for this reaction; we hypothesize that more energy is required to promote electron density from dσ to dπ type orbitals in

with H trans to N (12b), with the free energy barrier of 14.9 kcal/mol (as compared to separate reactants) (Scheme 7). For the constrained transition state (with frozen Ta−H, C−H, and Ta−C bonds of 1.86, 1.29, and 2.48 Å, respectively) (Figure 12), optimization was needed to isolate the isomer 12a with a

Figure 12. Optimized geometries of oxidative addition transition states for Ta(OC2H4)3Al(CH3)(H). Distances are given in Å.

free energy barrier of 35.2 kcal/mol. Several combinations of constrained Ta−C, Ta−H, or C−H distances were tried to obtain the transition state 12a; however, the only combination that worked was in which all three atoms involved in bond breaking or formation processes were constrained. The constrained distances were chosen from the data obtained for other transition states of Ta−A complexes. The imaginary frequencies for both transition states were 279i cm−1 (for TS with H trans to N) and 720i cm−1 (for “transition state” 12a). The ΔG⧧ value for the most stable TS of with A = N is kinetically more favored than that of P and CH by 3.5 and 6.2 kcal/mol, respectively. The OA reaction in the case of Ta(OC2H4)3N has the smallest free energy barrier among all Ta complexes studied.

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SUMMARY AND CONCLUSION The activation of methane by d2-Ta(OC2H4)3A (where A may act as ancillary ligand) has been studied using DFT methods. A can be a Lewis acid (B or Al), a saturated, electron-precise moiety (CH or SiH), a σ-donor (N), or a σ-donor/π-acid (P). Methane activation by oxidative addition yields two isomeric five-coordinate d0 Ta{(OC2H4)3A}(H)(CH3) complexes as products. The activation pathways were modeled for different A. By varying A in the Ta(OC2H4)3A reactant, we sought to investigate if changing the electronic properties of A from electron-deficient to electron-rich systems could affect the kinetics and thermodynamics of methane C−H activation via oxidative addition. Tables 2 and 3 in the Supporting Information summarize the calculated thermodynamic and kinetic data for oxidative addition of CH4 to Ta(OC2H4)3A for different ancillary ligands used. Several important points emerged from this study, which are summarized below. (1) For each oxidative addition reaction, two transition states (one with H trans to A and other one with CH3 trans to A) yielding two isomeric products were identified. (2) Comparison of ΔG⧧ for both isomeric transition states showed that ΔΔG⧧ values for A = Al, SiH, P are 15.0, 17.4, and 16.9 kcal/mol, respectively, indicating stabilization of the TS with H trans to A, while for 2p elements (A = B, CH, N), the calculated ΔΔG⧧ values are 12.5, 12.5, and 20.3 kcal/mol, respectively, again in favor of TS with H trans to A. Thus, it is H

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Figure 14. Plot of ΔG⧧ versus energy of Kohn−Sham HOMOs of Ta(OC2H4)3A reactant complexes.

are in agreement with our hypothesis, as the Ta−B reactant complex has the lowest energy HOMO among all reactant complexes and it has the highest activation energy barrier, while the Ta−N reactant complex has the highest energy HOMO, which results in the lowest energy barrier for OA of methane to the Ta−reactant complex.

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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.organomet.6b00690. Cartesian coordinates of all calculated species (XYZ) Calculated thermodynamic and kinetic data (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail for T.R.C.: [email protected].

Figure 13. Kohn−Sham pictures of the HOMOs of Ta(OC2H4)3A reactant complexes, revealing their dz2 character (isovalue = 0.045).

Notes

The authors declare no competing financial interest.

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Ta(OC2H4)3B in comparison to other ancillary ligand types. In the case of Ta(OC2H4)3N, there is a lone pair of electrons on the nitrogen ancillary ligand and Ta and N orbitals overlap less (and unlike B, the Ta- - -N interaction is antibonding), thus making the dz2 lone pair of Ta more available for oxidative addition reactions. Energies of the Kohn−Sham HOMOs and LUMOs of all Ta−reactant complexes were compared with the corresponding ΔG⧧ values of the kinetic products (H trans to A). The results showed that higher energy HOMOs result in a lower activation energy barrier (Figure 14). This is reasonable, as it implies that a more electron rich tantalum center should be more prone to undergo oxidative addition. Also, in general, lower ΔG⧧ values correlate with smaller differences between HOMO and LUMO energies. It is reasonable to expect that higher energy HOMOs and lower energy LUMOs will decrease the energy required for promotion of dσ → dπ electrons, which in this present research can be accomplished by changing the ancillary ligand (A) in Ta−reactant complexes; energies of LUMOs vary from −2.02 to −1.80 eV, which is not a significant variation in comparison to HOMO energies (ranging from −4.03 to 2.54 eV). Thus, it is concluded that the oxidative addition energy barrier is mostly effected by a change in the HOMO energy. The calculated data

ACKNOWLEDGMENTS This study was supported by the National Science Foundation (NSF) under grant number CHE-1464943. REFERENCES

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