1 Introduction

There is an increasing demand for the direct functionalization of light alkanes (C1–C4) to produce higher-value chemicals, such as olefins and alcohols. Methane (CH4) is one of the most important potential feedstocks due to its high concentration in natural gas, but it is the most challenging alkane for functionalization due to its strong C–H bonds [1,2,3]. Transition-metal-catalyzed methane borylation with bis(pinacolborane) (i.e., B2pin2) as the activating reagent (Fig. 1) is a promising method for methane activation under mild reaction conditions [3, 4]. However, conventional organometallic catalysts exhibit low chemoselectivity toward monoborylated methane (CH3Bpin) (reaction R1), which is the desired product for producing liquid fuel (i.e., CH3OH); instead, they yield diborylated methane (CH2Bpin2) (reaction R2) as the main product. The selectivity toward the diborylated species is due to the C–H bonds being more reactive in CH3Bpin than in CH4 [5].

Fig. 1
figure 1

(R1) Catalytic CH4 borylation to give CH3Bpin and the subsequent; (R2) CH3Bpin borylation over the same catalyst

Full size image

Metal–organic frameworks (MOFs) provide a promising platform for heterogenization and stabilization of homogeneous organometallic catalysts with high activity and selectivity [6,7,8,9,10,11,12,13,14,15,16,17]. Universitetet i Oslo-67 (UiO-67), is a MOF composed of Zr6 inorganic nodes (Zr6(μ3-O)4(μ3-OH)4) and 4,4′-biphenyl dicarboxylate (bpdc) linkers, and it is a particularly suitable catalyst support because of its high stability. Zhang et al. [5] have recently reported a catalyst, called UiO-67-Mix-Ir, that involves Ir(III) complexes supported on MOF UiO-67 through 1,10-phenanthroline-3,8-dicarboxylate (phendc) linker groups. The phendc linker is used in replacement of the bpdc linker for tethering the Ir(III) complex [5]. The newly synthesized complex was found to have excellent chemoselectivity (> 99%) to produce exclusively monoborylated methane, and the high selectivity was attributed to steric confinement effects of the microporous MOF UiO-67 [5]. The catalytic reaction on UiO-67 has both higher yield and higher selectivity for monoborylated methane than does the homogeneously catalyzed reaction [5, 18, 19], but the nature of the steric effect was not ascertained.

In the present study, we use density functional theory (DFT) calculations on model compounds to determine the selectivity of various UiO-67-supported Ir catalysts as potential active centers for the methane borylation reaction and to elucidate the confinement effect.

2 Computational methods

There are three kinds of calculations: (i) periodic calculations, (ii) octahedral model and triangular prism model (tpm) calculations, and (iii) calculations on the small complexes that do not involve any bpdc linkers. Calculations of types i and ii are electronic energies (including nuclear repulsion) in the gas phase. Calculations of type iii are gas-phase free energies with two exceptions in the borylation mechanism subsection: (1) In some cases we specify “electronic energy” or “electronic activation barrier” so that we can compare the energies with the CP2K results for larger cluster models. (2) In some cases we include solvation effects in the free energies by adding the free energy of solvation calculated by the SMD continuum model [20] with the gas-phase optimized geometries.

All periodic model calculations were performed using the Vienna Ab initio simulation package (VASP) [21,22,23,24]. We used the PBEsol density functional [25] with the PAW potential [26] and an energy cutoff of 500 eV for the periodic calculations. For pristine UiO-67, we calculated lattice parameters of a = b = c = 26.890 Å (Table 1), which is in good agreement with the experimentally measured value 26.881 Å [27], and hence, it validates the method.

Table 1 Lattice parameters (Å) for pristine UiO-67 and modified UiO-67 with coordinated Ir(Bpin)3 complex
Full size table

The triangular prism models and octahedral models have bpdc linkers and Zr6 nodes. They were calculated with the CP2K program [28]. For these calculations, formates were used as capping groups for the Zr6 nodes at places where the bpdc linkers were removed to make the cluster model as a truncated version of periodic crystal. The C atoms in the capping formate groups were fixed at their positions in the optimized periodic structure. The octahedral model geometries were optimized using the PBE [29] functional. The DZVP-MOLOPT basis set, a plane wave cutoff energy of 360 Ry, and pseudopotentials for core electrons (as formulated by Geodecker et al. [30]) were used for all atoms. The diffusion processes of the CH3Bpin and the CH2Bpin2 molecules in the triangular prism model were calculated using the CP2K program in the same way with the addition of the D3 damped dispersion terms of Grimme et al. [31].

The small complexes that do not involve any bpdc linkers were calculated using unrestricted DFT as implemented in the Gaussian 16 [32] program. These calculations used the M06-L functional [33], which shows high accuracy for transition metal chemistry [34, 35]. We used the def2-TZVP basis set [36, 37] for the Ir, B, N, O atoms and for C and H atoms that are directly bonded to the Ir atom. The def2-SVP basis set [36, 37] was used for other atoms. We verified that for all molecules, the singlet spin state is lower in energy than the triplet and quintet spin states, and the singlets converged to closed-shell configurations with no spin contamination. Transition structures were optimized using the eigenmode-following method by using the Gaussian keyword TS. We verified that all frequencies of stable species are real, and for each transition structure we verified that there is only one imaginary frequency. For each optimized geometry, we computed the Gibbs free energy (G) at 298.15 K. To obtain G, we used the FREQ [38] program to generate a vibrational frequency scaling factor of 0.976, and real frequencies below 100 cm−1 are raised to 100 cm−1 to simulate low-frequency anharmonic effects [39].

3 Results and discussion

3.1 Steric effect of the UiO-67 framework

We first consider the triangular prism model (tpm-UiO-67) in Fig. 2 for examining the UiO-67 framework confinement on CH3Bpin and CH2Bpin2 transport. This model was extracted from a geometry-optimized periodic structure of pristine UiO-67, and replication of this triangular prism model in space gives the UiO-67 periodic structure. Details of the geometry optimization are reported in the Computational Methods section. The triangular prism model includes 6 Zr6 nodes and 11 bpdc linkers. Formates were used as capping groups for the Zr6 nodes at places where the bpdc linkers were removed and the C atom in each formate is fixed at the position of the corresponding carbon in the optimized periodic structure.

Fig. 2
figure 2

Triangular prism model of UiO-67 (tpm-UiO-67) with six Zr6 nodes (labeled i to vi) showing the tetrahedral pore (position 1, surrounded by nodes i, ii, iii, and v) and the tetragonal pyramidal pore (position 3, surrounded by nodes iii, iv, v, and vi, which form a square, and node ii at the apex). The pores are connected by the triangular aperture (position 2, surrounded by nodes ii, iii, and v). C atoms are shown in gray, H in white, O in red, and Zr in cyan

Full size image

As shown in Fig. 2, the triangular prism model consists of two distinctive pore structures, namely the tetrahedral pore and the tetragonal pyramidal pore; the centers of the pores are marked, respectively, as positions 1 and 3 in Fig. 2. A triangular aperture marked as position 2 connects the two kinds of pores. For a molecule in the MOF to migrate to the surface of the MOF (so it can be released), it is necessary for it to pass between the two pores along a path like the path from 1 to 2 to 3.

Both CH3Bpin and CH2Bpin2 molecules can be fitted without steric strain into both the tetrahedral pore and the tetragonal pyramidal pore. We calculated the energy profile for diffusion of a CH3Bpin or a CH2Bpin2 from position 1 to 2 to 3. Activation barriers for the diffusion processes were estimated by the following steps: (i) Equilibrium structures were optimized with the CH3Bpin or the CH2Bpin2 molecule at positions 1, 2, and 3 (shown in Fig. 2) and with the C atoms of the capping formates fixed at their positions in the periodic structure; (ii) five intermediate geometries with the CH3Bpin or the CH2Bpin2 molecule between positions 1 and 2 and between positions 2 and 3 were constructed using linear interpolation of the C atom coordinate of the –CH3 or –CH2– group that binds with Bpin groups; (iii) partial geometry optimization was performed on each intermediate with C coordinates of the –CH3 or –CH2– group that binds with Bpin groups fixed with respect to the fixed C atoms of the capping formates; (iv) the highest energy of the intermediate structures was used as an approximation to the barrier height. The results for CH3Bpin are connected by red lines in Fig. 3, and they show a rate-determining barrier (highest-energy transition structure minus lowest-energy equilibrium structure) of 6.3 kcal/mol. The results for CH2Bpin2 are joined by black lines in Fig. 3, and they show a rate-determining barrier of 15.6 kcal/mol. Detailed results are provided in the Electronic Supplementary Material (ESM).

Fig. 3
figure 3

Energy profiles for CH3Bpin and CH2Bpin2 transport in UiO-67. Positions 1, 2, and 3 represent equilibrium geometries in the tetrahedral pore, the triangular window, and the tetragonal pyramidal pore of the tpm-UiO-67 model, respectively. Electronic energy for each intermediate was calculated using the CP2K program [28] with the PBE + D3 functional [29, 31]

Full size image

In the 2 → 3 transition structure for CH2Bpin2, we see bending and twisting of the bpdc linker groups, whereas only minor deformation of the linkers is observed for the CH3Bpin case. We conclude from this that the comparatively higher barrier of the CH2Bpin2 transport is mainly due to noncovalent steric interactions between the CH2Bpin2 molecule and the bpdc linkers. Figure S1 in the ESM shows the optimized 2 → 3 transition structure with the bent bpdc linker groups.

The higher barrier for moving CH3Bpin and CH2Bpin2 through the UiO-67 framework implies that CH2Bpin2 will have a much smaller diffusion rate than CH3Bpin within UiO-67. This trend should not change (however the barrier difference might vary) when the aperture size of the framework decreases due to the existence of modified linkers and tethered catalysts. Therefore, assuming that both CH3Bpin and CH2Bpin2 were generated through the borylation reaction over the Ir catalyst anchored to the modified UiO-67, it will be comparatively easier for CH3Bpin to diffuse out of the framework, and the Ir catalyst supported on UiO-67 will experimentally appear to have high selectivity toward CH3Bpin. This hypothesis is further tested using the triangular prism model of the modified UiO-67 with a coordinated Ir(Bpin)3 complex (tpm-UiO-67-Ir).

A schematic representation of the tpm-UiO-67-Ir model is given in Fig. 4. Using the same procedure as for the construction of the tpm-UiO-67 model, the tpm-UiO-67-Ir model was extracted from a geometry-optimized periodic structure of modified UiO-67 with a coordinated Ir(Bpin)3 complex. Details of the geometry optimization for modified UiO-67 with coordinated Ir(Bpin)3 complex (UiO-67-Ir(Bpin)3) are reported in the Computational Methods section. In comparison with the tpm-UiO-67 model, the tpm-UiO-67-Ir has one Ir center between Zr6 nodes iii and v with three attached Bpin groups. The bpdc linker between Zr6 nodes iii and v in the tpm-UiO-67 model is replaced with a phendc linker to provide the anchoring point for the Ir atom.

Fig. 4
figure 4

Triangular prism model of modified UiO-67 with coordinated Ir(Bpin)3 complex (tpm-UiO-67-Ir). For the clarity of the figure, we use red circle (labeled Ir) to represent 1 Ir atom bound with 3 Bpin groups. We use red and blue sticks to represent, respectively, the phendc and the bpdc linkers. Six Zr6 nodes (blue circles labeled i to vi) showing the tetrahedral pore (position 4), the tetragonal pyramidal pore (position 6), and the triangular aperture (position 5). Optimized coordinates for tpm-UiO-67-Ir are provided in the ESM

Full size image

The diffusion of CH3Bpin and CH2Bpin2 passing through the tpm-UiO-67-Ir model individually from position 4 to 5 to 6 is simulated in the same manner as our previous calculations with the tpm-UiO-67 model. The corresponding energy profiles for the diffusion processes are provided in Fig. 5 with the results for CH3Bpin and CH2Bpin2 connected, respectively, by red and black lines. The estimated rate-determining barrier for CH3Bpin transport in tpm-UiO-67-Ir is 10.5 kcal/mol and is 4.2 kcal/mol higher than its transport in tpm-UiO-67. Moreover, as anticipated, the steric confinement effect in the tpm-UiO-67-Ir compared to that of the tpm-UiO-67 is increased to a greater extent for the CH2Bpin2 diffusion process than for the CH3Bpin one. In particular, we find an increase of 9.1 kcal/mol in the rate-determining barrier (from 15.6 to 24.7 kcal/mol) for the diffusion of CH2Bpin2 when tpm-UiO-67 is replaced by the more sterically crowded tpm-UiO-67-Ir. This confirms that the modified UiO-67 framework with coordinated Ir(Bpin)3 complex provides higher steric confinement effect than the pristine UiO-67 in the CH3Bpin and CH2Bpin2 diffusion processes. Comparing CH3Bpin with CH2Bpin2, the diffusion of the latter in the framework is more strongly affected by the confinement effect than the diffusion of the former.

Fig. 5
figure 5

Energy profiles for CH3Bpin and CH2Bpin2 transport in tpm-UiO-67-Ir. Positions 4, 5, and 6 represent equilibrium geometries in the tetrahedral pore, the triangular window, and the tetragonal pyramidal pore of the tpm-UiO-67-Ir model, respectively. Electronic energy for each intermediate was calculated using the CP2K program [28] with the PBE + D3 functional [29, 31]

Full size image

Note, the Ir loading in the tpm-UiO-67-Ir model is considerably lower than that of the experimental system reported by Zhang et al. [5]. According to the reported experimental procedures, about 33% of the bpdc linkers were replaced with phendc linkers in the modified UiO-67 [5]. Therefore, for each tpm-UiO-67 fragment, there would be around 3-to-4 Ir active centers experimentally instead of 1 as in the tpm-UiO-67-Ir model. We believe that a further increase of the Ir loading from 1 per tpm-UiO-67 model to 2 or 3 would result in an even higher diffusion barrier than 24.7 kcal/mol for CH2Bpin2 which would further lower its diffusion rate inside the framework. And as discussed earlier, the diffusion of the smaller CH3Bpin molecule inside the MOF suffers less energy penalty from the increasing steric congestion, so the CH3Bpin molecule would still be able to pass through the framework with higher Ir loadings. Due to the large amount of possible Ir binding-position combinations and the lack of experimental information on local catalyst structures, simulations of CH3Bpin and CH2Bpin2 diffusions in models with 2 or more Ir centers are not performed in the current study.

We also note that the trapped CH2Bpin2 molecule in the modified MOF UiO-67 will not cause permanent congestion of the framework because the CH2Bpin2 molecule can be dissociated into CH2Bpin and Bpin by a nearby tethered Ir center to give Ir(CH2Bpin)(Bpin) and consequently free up the diffusion path of the framework. Details regarding the CH2Bpin2 dissociation reaction will be discussed in the “Further analyses of the chemoselectivity of the Ir-decorated UiO-67 catalyst” subsection. In addition, we will discuss the possible situation in which the reaction pathway of reaction R2 is blocked due to the steric confinement of the modified UiO-67 framework, which is another possible cause for the experimentally observed chemoselectivity of the UiO-67-supported Ir catalyst. However, our calculations do not show any evidence for such steric confinement effect of the framework at the Ir center.

3.2 Methane borylation catalyzed by Ir-decorated UiO-67

3.2.1 Relative stability of Ir(III) species

Experimentally, the Ir catalyst supported on UiO-67 was synthesized by first adding modified UiO-67 to a [Ir(COD)(μ-Cl)]2 (COD = 1,5-cyclooctadiene) solution that was then reacted with B2pin2 molecules [5]. Based on this experimental procedure, we propose four possible Ir(III) complexes as potential active species for catalyzing the methane borylation reaction: (a) (phen)Ir(Bpin)3, (b) eq-(phen)Ir(Bpin)2Cl, (c) axi-(phen)Ir(Bpin)2Cl, and (d) (phen)Ir(Bpin) +2 ; the structures are given in Fig. 6. In calculations on these complexes, the 1,10-phenanthroline (phen) ligand is used in replacement of the MOF support for simplicity and, as will be discussed below, has only a minor effect on the reactivity of the catalyst.

Fig. 6
figure 6

Ir(III) complexes: a (phen)Ir(Bpin)3, b eq-(phen)Ir(Bpin)2Cl, c axi-(phen)Ir(Bpin)2Cl, d (phen)Ir(Bpin) +2 cation

Full size image

The stability of these complexes is evaluated relative to complex a as follows:

$$\Delta E\left( {\mathbf{a}} \right) = 0,$$
(1)
$$\Delta E\left( {\mathbf{b}} \right) = E\left( {\mathbf{b}} \right) + E\left( {{\text{B}}_{2} {\text{pin}}_{2} } \right) - E\left( {\mathbf{a}} \right) - E\left( {\text{ClBpin}} \right),$$
(2)
$$\Delta E\left( {\mathbf{c}} \right) = E\left( {\mathbf{c}} \right) + E\left( {{\text{B}}_{2} {\text{pin}}_{2} } \right) - E\left( {\mathbf{a}} \right) - E\left( {\text{ClBpin}} \right),$$
(3)
$$\Delta E\left( {\mathbf{d}} \right) = E\left( {\mathbf{d}} \right) + \Delta E\left( {\mathbf{b}} \right) - E\left( {\mathbf{b}} \right) + E\left( {{\text{Cl}}^{ - } } \right),$$
(4)

where \(\Delta E\left( i \right) \left( {i = {\mathbf{a}}, {\mathbf{b}}, {\mathbf{c}}, {\mathbf{d}}} \right)\) is the relative energy, and \(E\left( j \right) \left( {j = {\mathbf{a}}, {\mathbf{b}}, {\mathbf{c}}, {\mathbf{d}}, {\text{B}}_{2} {\text{pin}}_{2} , {\text{ClBpin}}, {\text{Cl}}^{ - } } \right)\) denotes the DFT energy of the corresponding molecule or ion. Table 2 shows the relative stability of the complexes. We see that complex a has the lowest energy.

Table 2 Relative electronic energies (kcal/mol) for complexes a, b, c and d
Full size table

3.2.2 Electronic effect of the UiO-67 framework

The relative stability of complexes a, b, and c was further tested using three larger models to be called the octahedral models: oct-a, oct-b, and oct-c.

The oct-a model is shown in Fig. 7; it was extracted from a DFT-optimized periodic structure, UiO-67-Ir(Bpin)3, and formate groups were added to cap the Zr6 nodes at places where the bpdc linkers were removed. (Details of the periodic calculations are in the Computational Methods section.) Models oct-b and oct-c are prepared by replacing one of the Bpin groups in oct-a with a Cl group to, respectively, reproduce the Ir-centered bonding motifs as in complexes b and c.

Fig. 7
figure 7

Ir(Bpin)3 complex (oct-a) supported on UiO-67 viewed along the c and a directions (C atoms in gray, H in white, O in red, B in pink, N in blue, and Ir in teal, with the Ir(Bpin)3 complex and part of the phendc linker shown as balls and sticks)

Full size image

Geometry optimizations were performed for the octahedral models with C atoms of capping formates fixed at the corresponding C positions of the carboxylate groups of the replaced bpdc linkers. The relative energies of the three octahedral models are calculated based on Eqs. 1–3 with E(a), E(b), and E(c) replaced by E(oct-a), E(oct-b), and E(oct-c), respectively; results are in Table 3. Comparing Table 3 with Table 2, we see the same trend of energies for the three Ir(III) complexes, and this suggests a negligible effect of the framework on the Ir(III) complexes.

Table 3 Relative energies (kcal/mol) for octahedral models
Full size table

To further verify the negligible effect of the framework, Charge Model 5 (CM5) charge analyses [40] were performed for complexes a, e, and f with structures shown in Fig. 8, where Zr6 denotes a node. The latter two complexes were made by appending various functional groups to the third and eighth C positions of the 1,10-phenanthroline ligand. The CM5 charges of the Ir atoms in complexes a, e, and f are, respectively, 0.591, 0.597, and 0.609. The small charge differences observed between the three complexes suggest that the UiO-67 framework would have no significant electronic effect on the Ir catalytic active center. We therefore used complexes a and b without the UiO-67 framework to study the mechanism of methane borylation.

Fig. 8
figure 8

The (phen)Ir(Bpin)3 complex (a) and two modifications in which two H atoms are replaced by (e) COOH or (f) (COO)Zr6

Full size image

3.2.3 Methane activation over Ir(III) species

Because complexes a and b have similar relative energies (Tables 2 and 3), we assume they are both accessible under the experimental [5] 150 °C reaction conditions, and we consider both of them in studying the catalytic mechanisms. Two activation mechanisms were considered: (1) oxidative addition of methane to give Ir-hydride and Ir-methyl bonds, and (2) σ-bond metathesis to give an Ir-hydride intermediate with CH3Bpin or a methyl intermediate with HBpin. All attempts at optimizing a transition state geometry of the σ-bond metathesis reaction gave the transition state that connects to the reactant and product of the oxidative addition reaction instead. Therefore, we consider the oxidative addition in the rest of the article.

For complex a, the oxidative addition reaction (Fig. 9) gives a free energy of activation of 29 kcal/mol for methane activation. The product of oxidative addition is a seven-coordinated (phen)Ir(H)(methyl)(Bpin)3 complex (g in Fig. 10) with an axial methyl group and an equatorial hydride group.

Fig. 9
figure 9

Methane activation by oxidative addition over (phen)Ir(Bpin)3

Full size image
Fig. 10
figure 10

The possible products of oxidative addition: (g) seven-coordinated (phen)Ir(H)(methyl)(Bpin)3 complex; (iso-g) its isomer. Dotted lines indicate partial bonds; numbers in red are for identifying Bpin groups

Full size image

For complex b, the oxidative addition of methane requires a minimum free energy of activation of 40 kcal/mol, indicating low catalytic activity for the borylation reaction. We conclude that complex a is the dominant active species of the Ir catalyst supported on UiO-67.

3.2.4 Borylation mechanism and isomerization of the Ir(V) complex

Figure 11 shows the energetically most favorable catalytic cycle for methane borylation to produce monoborylated methane (CH3Bpin). The corresponding free energy profile is given in Fig. 12 (in black). This catalytic cycle involves five reaction steps, and it agrees with the reaction mechanism proposed by other research groups [18, 19] for the homogeneous catalyst in having the following steps: (1) C–H bond activation through oxidative addition to produce seven-coordinated g; (2) isomerization of g to iso-g; (3) formation of the main product (CH3Bpin); (4) activation of the B2pin2 molecule; and (5) catalyst regeneration accompanied by the formation of the HBpin byproduct. According to our calculations, the C–H bond activation (oxidative addition) step has the highest free energy of activation (29.0 kcal/mol) of any step and is in good agreement with the free energies of activation reported by Smith et al. [18] (31.4 kcal/mol) and Ahn et al. [19] (35.4 kcal/mol) for the homogeneous mechanism.

Fig. 11
figure 11

Energetically most favorable catalytic cycle for CH4 borylation over the (phen)Ir(Bpin)3 complex

Full size image
Fig. 12
figure 12

Gibbs free energy profiles for catalytic CH4 (black) and CH3Bpin (red) borylation reactions over complex a. Corresponding free energy (kcal/mol) is shown beside each intermediate and was calculated using the M06-L functional [33] as implemented in the Gaussian 16 program [32]. The methyl groups in g and iso-g become –CH2Bpin groups in complex g′ and iso-g′

Full size image

We then computed the overall free energy of activation for methane borylation, where overall free energy of activation is defined as the free energy span in the energetic span model as reviewed by Kozuch and Shaik [41]. This requires determining the turnover-determining intermediate (TDI) and the turnover-determining transition state (TDTS). The TDI is the intermediate which if chosen as the starting point of the catalytic cycle, will give the highest free energy span along one complete forward cycle which returns to the TDI; and the transition state producing this free energy span is defined as the TDTS. For the catalytic cycle in Fig. 11 and the black profile of Fig. 12, the TDI is determined as intermediate a, the TDTS is the transition state that connects intermediate g and iso-g, and the overall free energy of activation (the highest free energy span) for generating CH3Bpin is 34.6 kcal/mol.

The overall free energies of activation were computed with the same procedure for other explored catalytic cycles. Details regarding the other explored reaction cycles are provided in the ESM. Our results show that other explored catalytic cycles exhibit higher than 34.6 kcal/mol overall free energies of activation. We conclude that the turnover-determining transition state is that corresponding to isomerization after the C–H bond activation in Figs. 11 and 12, and this state cannot be avoided.

The analogous reaction steps are now considered for the borylation of the CH3Bpin molecule to produce CH2Bpin2. The associated energy profile is provided as the red profile in Fig. 12. The prime symbol for intermediates g′ and iso-g′ denotes that the methyl group in the corresponding intermediates g and iso-g is replaced with a −CH2Bpin group. Based on the energetic span model, the overall free energy of activation is 32.2 kcal/mol with intermediate a again being the TDI and the transition state that connects intermediate g′ and iso-g′ being the TDTS. The slightly lower overall barrier indicates that the diborylated methane is an energetically more favorable product than CH3Bpin. Therefore, we conclude that the experimentally observed chemoselectivity toward the CH3Bpin is not due to the electronic effect of either the UiO-67 framework or the Ir reactive center, and is most likely due to the UiO-67 framework confinement on CH3Bpin and CH2Bpin2 transport that we discussed earlier in the subsection on steric effects.

The implicit inclusion of solvent effect with n-dodecane as the solvent slightly increases the overall activation energy but does not change the reaction mechanism. The overall free energy of activation becomes 35.7 and 35.4 kcal/mol for producing CH3Bpin and CH2Bpin2, respectively.

The isomerization of complex g to give iso-g was further examined through the DDEC6 [42] bond order analysis. This analysis shows that the relatively high barrier associated with the isomerization step between complex g and iso-g is caused by the breaking and forming of partial bonds between the hydride and the Bpin groups near the Ir atom. The computed bond orders and bond lengths of selected bonds of g and iso-g are summarized in Table 4. According to the DDEC6 bond order analysis, averaging the results over g and iso-g, the sum of bond orders (SBO) is 5.1 for the Ir atom, 3.5 for B and N atoms, 1.1 for the hydride, and 3.9 for the C atom in methyl. For complex g, the bond order between the hydride and the B atom in the first Bpin group (Fig. 10) is 0.21, which is reduced to 0.02 in iso-g. On the other hand, the bond order between the hydride and the B atom in the second Bpin group increases from 0.03 in g to 0.23 in iso-g. We also found B–B bond breaking and C–B bond forming. The bond order between the B atoms of the first and third Bpin decreases from 0.23 in g to 0.06 in iso-g, and the bond order between the C in methyl and the B in the second Bpin increases from 0.04 in g to 0.12 in iso-g. Optimized geometries and DDEC outputs for complexes g and iso-g are provided in the ESM.

Table 4 Computed bond lengths (L, Å) and DDEC6 bond orders (BO) of selected atom pairs in complexes (g) and (iso-g)
Full size table

3.2.5 Further analyses of the chemoselectivity of the Ir-decorated UiO-67 catalyst

As noted in the earlier steric effect subsection, the CH2Bpin2 molecule can be dissociated into CH2Bpin and Bpin groups by the tethered Ir reaction center to free up the diffusion path of the framework. This process corresponds to the step to go from complex h to iso-g′ as shown in the red profile of Fig. 12 with a free energy of activation of 17.3 kcal/mol. The corresponding electronic activation barrier (see Computational Methods) for this step (h → iso-g′) is 16.5 kcal/mol and is smaller than that for CH2Bpin2 diffusion in model tpm-UiO-67-Ir which is 24.7 kcal/mol, as presented in the earlier paragraph. Furthermore, as shown in Fig. 5, the CH2Bpin2 molecule energetically prefers to reside at position 5 of Fig. 4, which corresponds to the closest distance between the Ir center and the CH2Bpin2 molecule, while it moves along the diffusion pathway and therefore increases the possibility for the CH2Bpin2 molecule to react with the Ir center.

The competition between diffusion and possible reverse reaction of CH2Bpin2 may be further analyzed as follows: To reverse the diborylation reaction by following the red profile of Fig. 12 from right to left, an overall free energy of activation of 39.4 kcal/mol is required with intermediate a on the right-hand side of Fig. 12 as TDI and the transition state that connects intermediate g′ and iso-g′ as TDTS. In comparison, generating CH3Bpin through CH4 borylation by following the black profile of Fig. 12 from left to right, requires an overall free energy of activation of 34.6 kcal/mol with intermediate a on the left-hand side of Fig. 12 as TDI and the transition state that connects intermediate g and iso-g as TDTS.

The result of the previous paragraph may be compared to that for the octahedral complexes. In particular, when we applied the octahedral model oct-a instead of complex a as the catalyst for the reverse diborylation reaction and followed the right-to-left reaction mechanism in the red profile of Fig. 12, we found an overall activation barrier of 38.9 kcal/mol with oct-a as TDI and the corresponding transition state that connects intermediate oct-g′ and oct-iso-g′ as TDTS. In comparison, using complex oct-a for CH4 borylation and following the reaction mechanism as going from left to right in the black profile of Fig. 12, require an overall activation barrier of 42.8 kcal/mol with oct-a as TDI and the transition state that connects intermediate oct-g and oct-iso-g as TDTS.

Octahedral models with more Ir sites are not evaluated in this study because (1) even though having more than one Ir site in an octahedral cage could potentially impose more steric congestion at the active site, it would also require a higher activation barrier for the C–H bond activation of CH3Bpin to happen, and the oct-a complex with one Ir site will become the more energetically favorable reaction site, and (2) even though the experimentally reported UiO-67-Mix-Ir catalyst has higher concentration of Ir sites on average [5], uneven distribution of the Ir atoms within the framework should allow at least some low-Ir-concentration areas where only one Ir atom per one octahedral cage is possible. Therefore, the C–H bond activation of CH3Bpin through oxidative addition to give Ir–hydride and Ir–CH2Bpin was examined using the octahedral complex oct-a, which contains one Ir active site in one octahedral cage of the framework, and in the next paragraph we will use this model to consider the possibility of having the reaction pathway of reaction R2 (diborylation reaction) blocked due to the steric confinement of the modified UiO-67 framework, which is another possible cause for the experimentally observed chemoselectivity of the UiO-67-supported Ir catalyst. However, our calculations do not show any evidence for such steric confinement effect of the framework at the Ir center.

Considering that reaction R2 utilizes CH3Bpin as a reactant to produce CH2Bpin2, and that CH3Bpin was generated at the Ir active center and can diffuse within and out the framework under the experimental conditions [5], we believe that the CH3Bpin molecule can easily reach and react with the Ir active center for the diborylation reaction (R2). The C–H bond activation of the methyl group in CH3Bpin using oct-a was calculated, and the corresponding reaction energy and activation barrier are, respectively, 3.4 and 11.5 kcal/mol. The same C–H bond activation step over the homogeneous Ir catalyst (complex a) gives an electronic reaction energy of 3.9 kcal/mol and an electronic activation barrier of 16.1 kcal/mol. Therefore, we conclude that the steric confinement of UiO-67 does not inhibit the C–H bond activation reaction.

As mentioned earlier, we also considered using oct-a as the catalyst for both CH4 borylation and diborylation reactions. For the CH4 borylation reaction we obtained an overall activation barrier of 42.8 kcal/mol. For the diborylation reaction (following the reaction mechanism as going from left to right in red profile of Fig. 12), we obtained an overall activation barrier of 33.5 kcal/mol with oct-a as TDI and the corresponding transition state that connects intermediate oct-g′ and oct-iso-g′ as TDTS. The barrier difference between CH4 borylation and diborylation reactions using oct-a as the catalyst further suggests that the UiO-67-supported Ir catalyst tends to give CH2Bpin2 as the energetically more favored product and that the chemoselectivity of the catalyst toward CH3Bpin comes from the effect of steric confinement of the framework on the product diffusion process.

4 Summary and concluding remarks

Confinement effects are often invoked as a feature that can increase selectivity in catalysis by nanoporous materials [43], but understanding the origin of the confinement effect in detail is rare. In this study, we employed density functional calculations on model Ir(III) catalysts in an effort to probe the overall mechanism of methane borylation and to interpret recent experimental evidence for high chemoselectivity of the metal–organic framework-supported iridium catalyst toward monoborylated methane instead of the undesired over-borylated product, diborylated methane.

Our calculations indicate that the energetic barrier for the formation of diborylated methane is actually lower than that for monoborylated methane. The Ir(III) with three binding pinacolborane ligands is identified as the most energetically favorable active species for methane borylation within the UiO-67-supported Ir catalytic system. Our mechanistic study performed using the (phen)Ir(Bpin)3 complex, after validating that the electronic effect of the framework is negligible, yielded an overall free energy of activation for methane borylation over (phen)Ir(Bpin)3 of 34.6 kcal/mol, which is 2.4 kcal/mol higher than that of the CH3Bpin borylation to give CH2Bpin2 and which makes the CH2Bpin2 the energetically more favorable product. Our calculation also shows that in contrast to common assumptions [18, 19], the isomerization of seven-coordinated Ir(V) complex, instead of the methane activation through oxidative addition, is the turnover-limiting step in the catalytic methane borylation. The relatively large barrier associated with the isomerization reaction comes from the breaking and forming of partial bonds between the hydride and Bpin ligands around the Ir center.

Our results thus imply that the high selectivity of UiO-67-supported Ir borylation catalyst toward CH3Bpin solely comes from the inhibited transportation of the CH2Bpin2 molecule; that is, the steric confinement effect of MOF UiO-67 is a beyond-the-active-site effect arising solely from the UiO-67 framework inhibiting the migration of borylated methane molecules within the MOF. Barriers of 10.5 and 24.7 kcal/mol were estimated for, respectively, moving CH3Bpin and CH2Bpin2 between pores inside modified UiO-67 with coordinated Ir(Bpin)3 complex. Having computed a low barrier for diffusion for the monoborylated product and a high barrier for diffusion of the diborylated product, we conclude that monoborylated methane, once formed, can easily interact with the catalyst to readily form diborylated methane. However, the much larger diborylated product diffuses very slowly through the MOF. This product is suggested to remain near the catalyst where it can decompose into the monoborylated product. Thus, the chemoselectivity of the catalysis comes from the effect of steric confinement of the framework on the product diffusion rate.

We also considered the possibilities in which the UiO-67 framework obstructs the borylation reaction over the Ir active site. However, our results do not support this assumption with the model systems we used. Our conclusions are not in full agreement with experiment because the experiment showed no production CH2Bpin2 rather than just a reduced yield. More detailed analysis, both computationally and experimentally, on the local structure of the UiO-67-Mix-Ir catalyst could shed more light on the nature of the steric confinement effect of the UiO-67 MOF. It would be particularly interesting to study the effect of varying the loading.