a computational design and mechanism study

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Cite this: Phys. Chem. Chem. Phys., 2016, 18, 11539

Methane activation by metal-free Lewis acid centers only – a computational design and mechanism study† Gongli Ma and Zhen Hua Li* In the present computational study by using the density functional theory (DFT) method, we found that silylboranes, which have metal-free Lewis acid centers only, can break the C–H bond of the exceedingly unreactive methane. The study shows that, unlike the activation mechanism of small molecules by the frustrated Lewis pairs (FLPs), the Lewis acidic boron center plays a key role in breaking the C–H bond of methane. Detailed analyses indicate that in the transition state the C–H bond is substantially activated by the empty 2p orbital of boron (2pB) primarily due to the orbital interaction between the C–H s-bonding orbital and 2pB. On the other hand, the orbital interaction between the C–H s-anti-bonding orbital and the B–Si s-bonding orbital also contributes to the activation but plays a minor role. A statistical method was used to find the relationship between the reactivity of 57 silylboranes and their electronic properties. The results indicate that the boron center does have more prominent effect on the reactivity, especially the occupancy (nB2p) and energy (eB2p) of 2pB, where lowering nB2p and eB2p will increase the reactivity

Received 23rd January 2016, Accepted 23rd March 2016

of the silylboranes. Based on the activation mechanism and taking kinetic and thermodynamic possibilities, as well as the possible side reactions, into consideration, three silylboranes suitable for methane activation

DOI: 10.1039/c6cp00505e

under mild experimental conditions were designed. The analogous line of thought can be used as a hint for further experimental realizations, even under ambient conditions. This strategy can also be expected to

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be transplanted to more extensive C–H activation of hydrocarbons.

Introduction Hydrocarbons are ubiquitous in the organic world, yet a lot of them cannot be conveniently converted to synthetically valuable compounds.1,2 In particular, the selective functionalization of methane is an extremely tough challenge for synthetic chemists because methane possesses high C–H bond strength, negligible electron affinity, large ionization energy, and low polarizability.3 Exploiting them efficiently as more useful chemical raw materials or more available functional substances is one of the hottest research fields for chemistry researchers. To achieve the goal, the pivotal step is to cleave the unreactive C–H bonds. Numerous experimental and computational studies have reported that breaking C–H bonds can be achieved by using transition metal (TM) complexes as catalysts.4,5 However, the drawbacks in terms of economic and environmental factors become a strong spur to Collaborative Innovation Center of Chemistry for Energy Material, Shanghai Key Laboratory of Molecular Catalysis & Innovative Materials, Department of Chemistry, Fudan University, Shanghai 200433, China. E-mail: [email protected]; Fax: +86 21-65643977 † Electronic supplementary information (ESI) available: Details of the leastsquares fittings; derivatives of DG‡; and Cartesian coordinates of the reactants and transition structures. See DOI: 10.1039/c6cp00505e

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develop metal-free strategies. With respect to metal-free methane activation, some radical ionic oxides6 such as [P4O10] +,7 [SO2] +,8 [CO] +,9 and [SiO] +10 can activate methane through hydrogenatom transfer to generate methyl radicals. Meanwhile, efforts have also been directed to the development of closed-shell molecules in consideration of the extreme instability of free radicals or radical cations. Since the discovery of the frustrated Lewis pairs (FLPs) by Stephan and co-workers,11 a growing number of metal-free molecules/systems have been found capable of activating small molecules such as hydrogen,12 carbon dioxide,13 nitrous oxide,14 alkynes,15 sulfur dioxide16 and ammonia17 under ambient conditions. The C–H activation of heteroarenes by FLPs is considered to be ‘‘a leap ahead for activating C–H bonds’’.18,19 It is known by means of the computational and experimental studies that the unusual reactivity of FLPs is due to the intermolecular or intramolecular combination of unquenched Lewis acid and base centers.20 However, there is no experiment reported on methane activation by FLPs as far as we know. One explanation is that the CH3 moiety of methane in the middle of the Lewis acid and base hampers the efficient interaction of the vacant orbital of the Lewis acid with the C–H s-bonding orbital of methane, which reduces the Lewis acidity of FLPs in cleaving the C–H bond

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of methane.21 A few FLPs, which are energetically favorable to activate methane, could be computationally designed with an activation mechanism of the side-on attack of methane through a cyclic transition state (TS), and the driven force of the activation be attributed to the synergistic interaction between the acidity of the Lewis acid and the basicity of the Lewis base.22 Silylboranes, the B–Si compounds, have incredible diversities in synthetic chemistry because of the abundant substitutions on the boron atom and the silicon atom.23–26 Their synthetic methods have been reviewed in detail in ref. 23 and 24. The electronegativity difference and the distinct reactivity of the boryl and silyl groups are likely to make silylboranes easier to react with target molecules by chemoselective activation of the B–Si bond.27–30 B–Si bond activation not only has been applied to the functionalization of C–C multiple bonds31,32 but also is a reliable method for the functionalization of C–Het (Het stands for atoms other than C) double bonds such as CQO33 and CQN.34 Meanwhile, the functionalization of strained-ring compounds35 and cycloaddition reactions of multiple-bond systems36 by silylboranes are also promising research fields in organic syntheses. To the best of our knowledge, there has barely been any attempt to utilize silylboranes to activate the C–H bond of methane. Inspired by the previous experimental and computational studies about C–H activation by metal and metal-free catalysts,37–39 herein we report a systematic study on the mechanism and reactivity of silylboranes in activating the C–H bond of methane. Based on the energetic results of methane activation by a large amount of silylboranes with different substituents, a comprehensive data analysis40,41 has been performed to unveil the relationship between the reactivity of the silylboranes and the electronic properties of the boron and silicon centers. The analysis leads to a much deeper understanding of methane activation by metal-free Lewis acid. Side reactions and the solvent effect have also been taken into account for more effective guidance on the experimental feasibility.

Computational details The quantum chemical calculations in this work were all performed using the Gaussian 09 software package.42 All geometry optimizations of the reactants, products, transition states, and intermediates were carried out at the M06-2X/631+G(d,p) level. The M06-2X functional,43 developed based on the Kohn–Sham density functional theory (DFT) by Zhao and Truhlar, has proven to be very reliable for applications involving main-group thermochemistry and kinetics. For the molecules made up of main group elements, the M06-2X relative energies were found to be reliable in alignment with those at the CCSD(T)/aug-cc-pVTZ//MP2/aug-cc-pVTZ level.44 In the present study, all the DFT calculations were performed using a pruned (99 590) grid. Harmonic frequency calculations were carried out not only to provide zero-point energy (ZPE) and thermodynamic corrections but also to guarantee that all minima have no imaginary frequencies and all TSs have only one imaginary frequency.

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Intrinsic reaction coordinate (IRC) calculations were carried out to confirm the proper reaction channel between the TS and its relevant minima.45,46 To obtain atomic charges and Wiberg bond orders to analyze bonding characteristics, the natural bond orbital (NBO)47,48 analysis at the M06-2X/6-31+G(d,p) level was carried out. It is known that the entropic contribution is ineluctably overestimated in the ideal gas phase model. Consequently, we took the solvation effect into account for the system of interest.49,50 The SMD solvation model was used to compute the solvation effect.51 In the following study, all the calculations were first performed using the ideal gas phase model and then were followed by calculations using the solvation model. By changing the substituents on the boryl and silyl groups, we have designed a hierarchy of silylboranes, and they are presented in Fig. 1. The first fourteen of them are treated as a representative set that will be discussed in more detail in the text. The geometries and Cartesian coordinates of all the silylboranes, and the TSs and minima involved in the activation of methane are available in the ESI.† In the present study, the free-energy barriers (DG‡) at 298.15 K and the standard state (1 atm in the gas phase or 1 mol L 1 in solution except for methane that is always in the gas phase) are used to characterize the reactivity of the silylboranes.

Results and discussion Mechanism of methane activation by silylboranes Learning from theoretical computations and matrix-isolation studies on the existence of a weakly bound complex between borane and dihydrogen (H3B


H2),52 the proposed activation mechanism of dihydrogen is the side-on interaction of dihydrogen with the Lewis acidic boron center first, then forming a central (closed) three-center bond connecting the two weakly bound hydrogen atoms with the boron atom.53,54 The TS of the activation is shown in Fig. 2(a). The orbital interaction of the H–H s-bonding orbital (sHH) with the unoccupied 2p orbital of B (2pB) plays an important role in the formation of the H3B


H2 complex. In the present study, a relatively low DG‡ of 11.9 kcal mol 1 was obtained, which is in line with previous experimental observations and computational results obtained using a more sophisticated method. By analogy with the reaction mechanism of dihydrogen and borane, we optimized the homologous TS for the activation of methane by borane (Fig. 2(b)) but obtained a much higher barrier (DG‡ = 28.5 kcal mol 1). Based on our cooperation experiences with experimentalists and simple estimations based on the classical transition-state theory (TST), the reaction could be realized under mild conditions. The preliminary calculations based on the above two model reactions show that Lewis acid alone can activate small molecules such as dihydrogen and methane. Further NBO analyses of the TSs show that the interaction between sHH of H2 or the s-bonding orbital of the C–H bond (sCH) of methane with 2pB plays a key role in the activation of H2 and methane.

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Fig. 1

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Structures of the designed silylboranes for methane activation.

Considering that in the activation of methane by borane, the breaking of the C–H and B–H bonds is compensated by the formation of the B–C and H–H bonds, we were wondering whether the activation of methane would become easier if the

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breaking B–H bond is replaced by a weaker bond and the Lewis acidity of the boron center is also tuned by substituting H of borane by other functional groups. In addition, although borane has remarkable activity in activating methane, it is difficult to

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Fig. 2

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Transition state structures of BH3 + H2 (a) and BH3 + CH4 (b).

handle and is easily subjected to dimerization, which makes the activation of methane actually much more difficult in experiments. Inspired by the successful application of silylboranes in synthetic chemistry, we designed a hierarchy of silylboranes to activate methane. We start with the simplest silylborane, H2BSiH3 (M7 in Fig. 1). The TS of the activation is shown in Fig. 3(a). The DG‡ of the reaction is 23.8 kcal mol 1, which is lower by 4.7 kcal mol 1 than that of methane activation by borane. This gives us confidence that the weaker B–Si bond in silylboranes does reduce the DG‡ for methane activation. In addition, the reaction is exothermic and the Gibbs free energy of the reaction is 5.9 kcal mol 1. Therefore, methane activation by silylboranes is thermodynamically and kinetically practicable. Similar to methane activation by borane, methane has a side-on interaction with M7 in the TS. The C–H bond of methane is stretched noticeably from 1.09 Å in the free methane to 1.40 Å in the TS. On the other hand, the B–Si bond is just elongated slightly by 0.05 Å to 2.07 Å. Both the C and H atoms of methane are close to the B atom of M7 with a B–C distance of 1.81 Å and a B–H distance of 1.25 Å. This is also similar to that of methane activation by borane. In both cases, the TSs are early TSs where the C–H bond is significantly activated and meanwhile short bonds between the boron center and C and H atoms are formed. On the other hand, the B–H bond in borane and the B–Si bond in M7 are just elongated slightly. The geometric data indicate that in the TS, the C–H bond is activated more than the B–Si bond. More details of the activation process can be obtained from NBO analysis of the electronic structure of the TS. The analysis indicates that sCH of methane has a significant overlap with

Fig. 3 (a) Transition state for methane activation by M7 and (b) the HOMO and the LUMO of M7. Bond lengths are given in Å.

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2pB of M7 with sCH being the donor while 2pB is the acceptor. As a result of the interaction, the occupancy of sCH is just 1.43, much lower than the expected value of 2.0 for a single bond. On the other hand, the occupancy of 2pB is 0.58, which deviates significantly from the ideal value of 0.0 for an unoccupied orbital. The analysis of the second order perturbation theory regarding the interaction between the two orbitals indicates that the interaction has an E(2) value as high as 610.8 kcal mol 1. In fact, the interaction is so strong that a three-center-two-electron bond (3C bond) can be viewed as formed among C, H, and B. The NBO analysis with this 3C bond gives an occupancy of 1.99 for this bond and the TS is described better by this Lewis structure. In addition, the C–H s-anti-bonding orbital (sCH*) of methane also has a strong interaction with the B–Si s-bonding orbital (sBSi) with an E(2) value of 117.8 kcal mol 1. This decreases the occupancy of sBSi to just 1.68 while increasing the occupancy of sCH* to 0.33. As a result of the donor–acceptor interactions between the two pairs of orbitals, the NBO charge of the B atom decreases from 0.07e in M7 to 0.63e by 0.70e in the TS, and the net electron transfer, which is 0.24e, is from methane to M7. From the analysis we can see that the C–H bond of methane is significantly activated due to the synergetic interactions between sCH and 2pB, and between sCH* and sBSi. In addition, the former interaction is much stronger than the latter one, as can be seen from the E(2) values and the net electron transfer. As a result, the C–H bond is activated more than the B–Si bond. These electronic structure analysis results are in accordance with the geometric data for the TS as discussed above. According to previous computational studies, methane activation by intramolecular B/N-based FLPs involves two critical orbitals.55 The HOMO and the LUMO of the acid and the base are dominated by 2pB and the lone pair orbital of N (LPN), respectively. The activation of the C–H bond of methane stems from the synergistic interactions of two donor–acceptor pairs where sCH donates electrons to 2pB and LPN donates electrons to sCH*. However, in silylboranes there is no lone pair orbital as that of N in FLP. As shown in Fig. 3(b), the HOMO of M7 is dominated by sBSi while the LUMO is dominated by 2pB. Therefore, to effectively activate the C–H bond of methane by silylboranes one can either lower the energy of 2pB (eB2p) or raise the energy of sBSi (eBSi) or both. This can be realized by changing the substituents on the B and Si centers. One might expect that lowering eB2p would increase the electrophilicity and thus the acidity of the boron center according to Lewis acid– base theory. This is similar to the use of FLPs to activate small molecules where the acidity of the boron center is tuned by the substituent groups on B. To gain further mechanistic insight into this activation process, we carried out bond-order analyses for every structure along the IRC reaction pathway. In Fig. 4, the Wiberg bond orders of the bonds involved in the activation are plotted with respect to the reaction coordinate. As illustrated in the figure, the evolution of bond orders for the breaking C–H and B–Si bonds shows a similar trend and the two curves are parallel and non-overlapping. The bond orders of both bonds decrease

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Fig. 5

Fig. 4 Variation of the Wiberg bond orders of the B–Si, B–C, B–H, Si–H, and C–H bonds along the IRC. The vertical straight line represents the position of the TS.

along the reaction coordinate, but the bond order of B–Si (WBSi) is always higher than that of C–H (WCH). In the TS, WBSi is still higher than 0.7, while WCH is already lower than 0.3. This indicates that the cleavage of C–H is always ahead of B–Si. The evolution of the bond orders of the forming B–C and Si–H bonds also has a parallel trend. They both increase along the reaction coordinate but the bond order of B–C (WBC) is always higher than that of Si–H (WSiH). In the TS, WBC already reached about 0.7 while WSiH is just about 0.1. The results indicate that the formation of B–C is much earlier than Si–H. We have to call attention to the evolution of the B–H bond order (WBH). WBH firstly increases to its summit slightly after the TS and then decreases. In the TS, WBH reaches up to 0.5 while at the summit it is about 0.6. These results clearly show that the C–H bond is firstly activated and broken by the boron center with the formation of partially formed B–H and B–C bonds or a B–H–C 3C bond and then the breaking of the B–Si bond and the formation of the Si–H bond. This further confirms the finding that the boron center plays a key role in the activation of the C–H bond while the leaving Si group plays a minor role since sBSi has much weaker interaction with sCH* and the B–Si bond is only broken after the complete breaking of the C–H bond. This is different from the mechanism of the FLPs where both the acid and base centers are involved in the activation process deeply and synchronously in most cases. Substituent effects Although activating methane by the simplest silylborane is thermodynamically and kinetically feasible, there is a gap between computational design and experimental realization. It is not just to find a silylborane with the highest reactivity toward methane. Many factors should be considered, such as the side reactions, solvent effect, ease of synthesis of the silylboranes, and so on. For example, a serious drawback of M6 and M7 is that they are easy to dimerize (as shown in Fig. 5). The formation of the M7 dimer is due to its strong tendency to form the B–H–B 3C bonds. To separate them an additional 25.7 kcal mol 1 is needed. The formation of the M6 dimer, on the other hand, is due to the formation of the dative bond

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Optimized structures of the dimers of M7 (a) and M6 (b).

between the Lewis acidic B center and the Lewis basic N center of the cyan group. Other silylboranes might suffer different problems. For example, although M30 and M35 have extraordinary reactivity toward methane, they are not stable since M30 would form an O–B bond while F on the CF3 group in M35 may migrate to B with a very low energy barrier and thus M35 would transform into a more stable structure. Therefore, in this section we will design a hierarchy of silylboranes for the following purposes: (1) to elucidate the factors that affect the reactivity of the silylboranes toward methane and (2) to find some silylborane candidates with fairly high reactivity toward methane, but that might be easy to synthesize and with as few side reactions as possible. Firstly, we focus on the substituent effect on the reactivity and the activation mechanism of the silylboranes toward methane. In Table 1, the energy barrier at 0 K (DE‡), the free-energy barrier at 298.15 K (DG‡), the energy change of the reaction at 0 K (DE), and the free-energy change of the reaction at 298.15 K (DG) are tabulated. Almost all DEs and DGs are negative, indicating that the reactions are thermodynamically feasible. Here we will first examine the substituent effect of M1 to M14 in detail, seeking inspirations for the analysis on all the silylboranes later. M1 to M7 were obtained by fixing the silyl group as SiH3 while varying the substituents on B. On the other hand, M8 to M14 were obtained by fixing the boryl group as B(C6F5)2 while varying the substituents on Si. In each class, the silylboranes are sorted according to the calculated DG‡ values in a descending order. The results indicate that the substituent effect on DE and DG is not prominent except for M8. It is possible that the higher exothermicity of the reaction of M8 with methane is related to the tert-butyl effect because of steric effects.56 On the other hand, DE‡ and DG‡ have a much wider span than DE and DG, implying a much more prominent effect of substituents on the reactivity of the silylboranes. Obviously, the substituent effect on B is more prominent than on Si, where from M1 to M7, DG‡ changes from 67.2 kcal mol 1 to 23.8 kcal mol 1, while from M8 to M14, DG‡ changes just from 40.7 kcal mol 1 to 30.2 kcal mol 1. This is in agreement with the above analysis on the activation of methane by M7 that the boron center plays a major role. It can also be seen that the substituent effect on both B and Si is not so intuitive and straightforward. For example, it is expected that replacing H on B by more electronegative groups might lower eB2p and thus raise the Lewis acidity of the boron center. However, the results show that replacing H by other groups increases DG‡, no matter what their electronegativities are. Replacing H on Si with more electronegative groups might lower eBSi and thus increase DG‡. However, the results are

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Table 1 Energetic data (all in kcal mol 1) for the reaction: reaction energy at 0 K (DE), reaction free energy at 298.15 K (DG), energy barrier at 0 K (DE‡), free-energy barrier at 298.15 K (DG‡); results of NBO analysis for the silylboranes: NBO charges (in a.u.) of B (qB) and Si (qSi) atoms; Wiberg bond order of the B–Si bond (WBSi); energy of the bonding orbital of the B–Si bond (eBSi, in kcal mol 1); occupancy (nB2p) and energy (eB2p, in kcal mol 1) of the empty 2p orbital of B

TS

Product ‡

‡

Silylborane

DE

DG

M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 M12 M13 M14 M15 M16 M17 M18 M19 M20 M21 M22 M23 M24 M25 M26 M27 M28 M29 M30 M31 M32 M33 M34 M35 M36 M37 M38 M39 M40 M41 M42 M43 M44 M45 M46 M47 M48 M49 M50 M51 M52 M53 M54 M55 M56 M57

58.5 46.1 33.1 25.2 22.5 14.4 14.4 28.2 26.2 22.8 21.1 20.3 19.1 18.4 27.4 19.1 25.7 20.2 26.4 20.0 18.4 23.8 21.6 18.8 17.8 26.9 21.7 19.5 23.2 0.4 56.4 20.3 28.6 55.5 4.8 64.0 62.7 62.0 56.4 27.8 25.9 29.7 27.3 26.4 11.2 12.1 9.1 14.8 18.4 18.1 12.7 26.6 26.6 56.0 12.2 44.6 21.4

67.2 55.6 43.3 36.6 32.3 24.5 23.8 40.7 38.1 35.1 33.3 32.4 30.2 30.2 38.9 30.6 35.6 31.0 38.3 32.0 29.1 34.3 32.4 29.9 27.9 37.0 32.4 29.6 32.7 12.3 66.5 30.3 39.1 65.3 15.7 74.0 72.8 71.9 66.3 37.6 36.5 40.0 38.0 37.4 21.8 21.6 18.6 25.1 28.7 28.4 23.2 36.2 37.9 67.0 21.3 54.3 32.6

DE 2.1 4.8 4.5 4.9 1.4 9.9 7.5 2.3 3.0 4.8 4.4 5.1 3.7 2.9 3.6 2.5 6.0 18.4 2.6 2.8 6.3 5.8 1.5 6.4 5.6 3.6 3.2 2.9 5.8 5.6 0.6 2.4 5.5 5.5 1.9 7.6 4.3 7.1 2.6 5.4 2.5 4.9 6.1 2.9 5.8 5.3 4.0 2.6 8.6 3.2 2.3 2.8 1.5 4.5 5.5 7.6 2.0

Property of silylborane DG 4.2 7.1 8.0 5.1 5.3 10.2 7.4 4.9 3.0 4.9 8.5 7.7 7.9 3.2 3.5 2.7 4.9 22.5 8.6 5.5 5.9 9.1 0.2 9.5 5.7 8.3 6.4 7.5 5.5 6.1 5.1 3.8 8.5 9.9 7.9 10.1 6.2 7.6 2.9 5.6 6.4 4.9 6.9 3.3 6.9 8.9 7.7 9.5 9.2 5.7 4.9 5.5 0.2 8.0 8.5 10.1 6.0

not as expected. For example, replacing H on Si in M5 by an ethyl (Et) or methoxy (OMe) group has the same effect where the DG‡s for M13 and M14 are the same. The above analysis indicates that a single factor such as the electronegativity of the substituent cannot be used as the

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qB 0.78 1.00 0.06 0.49 0.44 0.26 0.07 0.37 0.47 0.44 0.44 0.44 0.44 0.32 0.45 0.43 0.45 0.49 0.46 0.45 0.42 0.39 0.44 0.43 0.34 0.46 0.45 0.42 0.43 0.15 0.76 0.48 0.41 0.82 0.37 0.51 0.54 0.52 0.58 0.45 0.53 0.02 0.04 0.60 0.22 0.05 0.17 0.41 0.42 0.44 0.21 0.33 0.44 0.67 0.05 0.97 0.41

qSi

WBSi

0.55 0.45 0.60 0.56 0.60 0.61 0.50 1.72 1.50 1.47 1.53 1.53 1.53 2.22 1.51 1.47 1.24 0.51 1.50 1.52 1.45 1.21 1.53 0.91 1.94 0.57 0.88 1.32 1.42 0.60 1.41 0.56 0.57 0.50 0.56 0.58 0.57 0.56 0.55 0.63 0.56 0.62 1.46 0.55 1.46 2.16 1.43 1.45 1.45 1.47 1.54 2.22 1.19 2.13 1.41 1.30 1.52

0.96 0.97 0.95 0.98 0.95 0.92 1.01 0.87 0.90 0.89 0.89 0.89 0.89 0.83 0.90 0.89 0.91 1.00 0.90 0.89 0.89 0.86 0.89 0.92 0.83 0.97 0.93 0.91 0.92 0.93 0.92 0.97 0.97 0.96 0.96 0.97 0.97 0.96 0.96 0.96 0.98 0.95 0.90 0.98 0.86 0.93 1.05 0.91 0.91 0.91 0.86 0.89 0.89 0.88 0.96 0.93 0.90

eBSi 308.7 324.0 342.6 301.5 325.3 340.1 317.0 325.8 324.5 312.6 327.1 318.4 310.8 327.5 344.2 310.9 358.6 337.8 326.7 311.6 309.1 352.0 333.1 319.5 317.1 305.0 320.2 331.3 290.5 371.0 295.3 306.3 322.1 305.5 349.8 304.6 306.1 293.8 296.0 327.3 306.4 348.2 332.5 308.7 319.0 327.8 283.0 282.2 292.7 298.2 319.6 314.6 336.1 297.4 306.2 306.9 334.7

nB2p 0.34 0.24 0.58 0.09 0.19 0.17 0.02 0.20 0.18 0.16 0.18 0.18 0.16 0.18 0.19 0.17 0.22 0.21 0.18 0.17 0.17 0.20 0.19 0.18 0.18 0.20 0.18 0.19 0.18 0.21 0.40 0.13 0.14 0.34 0.08 0.42 0.44 0.48 0.45 0.36 0.12 0.75 0.74 0.11 0.16 0.01 0.42 0.16 0.16 0.15 0.16 0.13 0.14 0.34 0.03 0.23 0.20

eB2p 18.7 4.3 80.3 17.7 11.7 22.8 2.5 2.6 3.1 1.1 16.0 10.0 2.3 5.1 30.8 4.5 34.9 14.8 11.3 4.2 4.0 26.4 21.1 9.2 3.5 16.1 6.2 12.8 22.9 74.8 112.5 16.4 5.1 17.3 32.7 23.9 20.5 112.9 18.6 36.3 24.0 124.7 118.2 28.6 11.6 27.9 4.6 10.6 11.3 12.0 9.7 1.3 0.3 22.9 0.9 14.5 14.7

guideline to choose substituent groups. Substituents seem to have a profound influence on the reactivity of the silylboranes. Taking M2 and M3 as examples, M2 was obtained by replacing H on B in M7 by F, while in M3, the H is replaced by Cl. Both F and Cl are electron withdrawing groups. NBO charge analysis

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results indicate that the charge on B (qB) of M2 becomes more positive compared with M7 (0.56 vs. 0.02, see Table 1). However, qB of M3 remains almost the same as that of M7. On the other hand, eB2p does lower greatly for M3 but is increased for M2. Inspecting the orbital interactions in M2 and M3 indicates that although F and Cl draw electrons from B through the F–B or Cl–B s-bonding orbital, they also donate electrons back to B from their lone pairs to 2pB through the formation of p-orbitals. The lone pair of Cl has higher energy than that of F and thus has better overlap with 2pB. In addition, F has higher electronegativity than Cl. As a result, Cl donates back more electrons to B, which increases the occupancy of 2pB (nB2p) from near zero in M7 to 0.58 in M3. In comparison, nB2p of M2 is just 0.24. These detailed analyses indicate that the Lewis acidity of the boron center is not simply determined by the electronegativity of its substituents. There are complicated interactions between the substituents and the boron center. Since a Lewis acid center is the acceptor of a pair of electrons, it is reasonable to deduce that not only eB2p and qB, but also nB2p may affect the Lewis acidity of the boron center. In addition, the substituents on Si may also affect the electronic structure of the boron center through the B–Si bond. For example, for M8–M14, not only WBSi and the charge on Si (qSi), but also qB, nB2p, and eB2p are affected by the substituents on Si. Therefore, the factors that affect the reactivity of the silylboranes are multiple and there may be a reciprocal effect among these factors also. In Fig. 6, DG‡s of the reactions between all silylboranes with methane are plotted vs. various electronic properties of the silylboranes to characterize the boron and silicon centers. These properties are tabulated in Table 1 and they are qB, qSi, WBSi, eBSi, nB2p, and eB2p. No remarkable regularity can be intuitively observed from these plots. More importantly, these properties are not completely independent. The analysis of the Pearson’s correlation coefficients (r) among the 6 properties show that qSi has a fairly strong negative correlation with WBSi with an r of 0.76, i.e. the B–Si bond can be weakened by increasing the positive charge on Si. On the other hand, qB has a weak positive correlation with eBSi with an r of 0.39 and eB2p has fairly strong positive correlations with qB and eBSi, with r being

Fig. 6

Scatter plots of the DG‡ vs. single property for all silylboranes.

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0.64 and 0.71, respectively. Clearly, statistical methods should be applied to find the relationship between DG‡ and these electronic properties. Relationship between free-energy barrier and electronic properties of silylboranes Polynomial models have been proved to be simple but appropriate for fitting and forecasting free-energy barriers of chemical reactions.57 We employed the least-squares fitting method to fit the first 50 DG‡s (training set) in Table 1 with respect to the six properties to obtain a good model for these data. The last seven DG‡s were used as testing sets to test the predictive ability of the model. The seven silylboranes were actually designed after we had successfully fitted the 50 data points. We started from the simplest model that DG‡ is the first order polynomial function of the six properties (variables) and then gradually added second order and third order terms. The best second order model (Mod1) we obtained by using the rootmean-square error (RMSE) as the criterion has an R2 of 0.97, a mean unsigned error (MUE) of 2.0 kcal mol 1, and a maximum error of 6.7 kcal mol 1. The third order model, which was named Mod2, has an R2 of 0.98, an MUE of 1.6 kcal mol 1, and a maximum error of 6.0 kcal mol 1. The detailed fitting procedure can be found in the ESI,† and the resulting two models are: DG‡ (Mod1) = a0 + a1WBSi + a2(nB2p)2 + a3(eB2p)2 + a4qBqSi + a5qBeB2p + a6qSinB2p + a7qSieB2p + a8WBSinB2p + a9eBSinB2p + a10nB2peB2p DG‡ (Mod2) = b0 + b1WBSi + b2(nB2p)3 + b3WBSi(eB2p)2 + b4qBqSieBSi + b5qBeB2p + b6(eBSi)2nB2p + b7qSieBSieB2p + b8(WBSi)2nB2p + b9qSieBSinB2p + b10nB2peB2p The fitted parameters are 118.6, 143.2, 272.6, 0.005547, 37.43, 0.8733, 47.90, 0.2586, 506.4, 1.524, and 0.8889 for a0 to a10, respectively, and 97.71, 119.4, 333.7, 0.007002, 0.1022, 0.9200, 0.002767, 0.0007769, 236.5, 0.1529, and 1.092 for b0 to b10, respectively. Excluding the constant, three terms of the two models are the same and they are WBSi, qBeB2p, and nB2peB2p. The remaining 7 terms in Mod2 are just the corresponding terms in Mod1 multiplied by a variable, for example, (nB2p)3 is (nB2p)2 in Mod1 multiplied by nB2p, WBSi(eB2p)2 is (eB2p)2 in Mod1 multiplied by WBSi, etc. Since Mod2 is much better than Mod1, we will focus our discussion on Mod2. First of all, all six properties we selected appear in the final model. This validates our choice of the properties to characterize the reactivity of the silylboranes. Secondly, the influence of these properties on DG‡ is not independent but is reciprocal. Except the second and third terms, i.e. WBSi and (nB2p)3, all other terms are cross-terms. To find out how prominent the influence of each property on DG‡ is, we did two analyses. For the first one we chose three silylboranes with low, middle, and high DG‡s, and varied each of the six properties by s where s is the

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Table 2 The change in DG‡ (DDG‡ = DG‡(s) DG‡( s), in kcal mol 1) by changing each one of the six properties by s and the mean absolute value (MA) of DDG‡

M35 M44 M36 MA

qB

qSi

21.4 4.8 19.7 15.3

7.0 18.2 9.1 11.5

WBSi 5.8 6.9 7.0 6.6

eBSi 7.9 7.4 27.1 14.1

nB2p

eB2p

20.0 21.9 67.8 36.6

11.6 57.7 37.6 35.6

standard deviation of the corresponding property. The silylboranes we selected are M35, M44, and M36, with DG‡s of 15.7 kcal mol 1, 37.4 kcal mol 1, and 74.0 kcal mol 1, respectively. The changes in DG‡ (DDG‡ = DG‡(s) DG‡( s)) predicted using Mod2 are presented in Table 2. The entry MA (mean absolute value of DDG‡ for each property) of Table 2 indicates that DG‡ is affected more by the properties of B. Inspecting the MA values in Table 2 reveals that among the three properties of B, the influence of nB2p and eB2p is most prominent. On the other hand, among the three properties of Si, the influence of eBSi is most prominent. This is in accordance with our NBO analysis of the TS of the activation of methane by H2BSiH3 (M7). In addition, the influence of qB, qSi and WBSi on DG‡ is not consistent. For example, an increase in qB increases DG‡ for M35 but lowers DG‡ for M44. On the other hand, the influence of eBSi, nB2p, and eB2p on DG‡ is consistent where an increase in eBSi, or a decrease in nB2p, or a decrease in eB2p lowers the DG‡ values for all three silylboranes. The second analysis we performed is calculation of the derivatives of DG‡ with respect to the properties of the silylboranes. The tabulated results can be found in the ESI.† Here we present a graphical view of these results in Fig. 7. Similar conclusions can be deduced from the results where all qDG‡/qeBSi values are negative, while most qDG‡/qnB2p and qDG‡/qeB2p values are positive. Positive derivatives imply that the increase of the corresponding property will increase DG‡, and vice versa for negative derivatives. The results, therefore, indicate that in order to lower DG‡, i.e. to increase the reactivity of the silylboranes, we may change the substituents on B and Si to increase eBSi, or to lower nB2p, or to lower eB2p. The increase in

Fig. 7 Scatter plots of the derivatives of DG‡ vs. single properties.

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Fig. 8 Comparison of the DG‡ values predicted using Mod2 and the calculated DG‡ values in the training set (a) and the testing set (b).

qB by using electron-withdrawing substituents on B, counterintuitively, does not help in most cases: most qDG‡/qqB are positive, which implies that an increase in qB would increase DG‡. To lower eB2p, we should avoid the use of substituents in which the atoms directly bonding to B have lone pairs such as halogens, nitrogen, phosphorus, oxygen, and sulphur. These substituents will donate electrons to 2pB. Substituents with p-bonds that can delocalize electrons to 2pB should better be avoided. In practice, however, aromatic substituents are often used and this can be compensated by adding electronwithdrawing groups to the aromatic rings, e.g. C6F5. To lower eB2p, electron-withdrawing groups such as C6F5 on B can be used. However, we should keep in mind that they may increase nB2p as well. Lastly, our model not only fits the data in the training set well (see Fig. 8(a)), but also has fairly good ability for prediction (see Fig. 8(b)). Consideration of experimental feasibility For theoretical predictions to be realized by experiments, not only the reactivity of the silylboranes should be considered, but also other factors such as side reactions should be considered. Due to the limitation of computational studies that are in some sense idealized, we cannot consider all possibilities. Nevertheless, we will try our best to design several candidates with promising reactivity toward methane that might be realized in not so harsh experimental conditions. The first consideration is the reactivity of the silylboranes. According to the classical TST, DG‡ is directly related to the reaction rate of a reaction, thus we would expect that the lower the DG‡ is, the higher the reactivity of the silylborane is. Based on our cooperation experiences with experimentalists and preliminary calculations with TST, we tentatively set a somewhat arbitrary threshold of 33.0 kcal mol 1 for DG‡. Moreover, there are just a few data points between 33 kcal mol 1 and 35 kcal mol 1 for DG‡ and the threshold of 33 kcal mol 1 coincidentally divides all 57 data points into two sets of similar size. Applying the threshold, 28 out of 57 candidates are left. The second consideration is the dimerization of the silylboranes. This rules out those compounds with BH bonds and with QO, –O–, –NH2, and –CN substituent groups with strong Lewis basicity. These compounds can easily form a dimer by

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either forming B–H–B 3C bonds or dative bonds between Lewis acids and bases. This further rules out 10 from the 28 candidates. The third consideration is the self-destruction21 of the silylboranes. The C–H bond of methane is one of the most difficult C–H bonds to activate. The candidates thus should better not contain easily accessed and activated C–H bonds. This rules out those silylboranes with methyl, methylene, methylidyne or unsubstituted phenyl groups. This rules out 11 from the remaining 18 candidates and only seven are left. The seven candidates are M5, M12, M18, M23, M28, M35, and M57. M5, M18, and M35 all contain at least one SiH3 group and its Si–H bond can be easily activated by the silylboranes. Using SiH4 as the model for the SiH3 group, our results show that the activation of SiH4 by M5 to form (C6F5)2BH + Si2H6 has a DG‡ of just 17.6 kcal mol 1, much lower than that required for activating methane by M5, which is 32.3 kcal mol 1. The remaining four candidates are then M12, M23, M28, and M57, and all of them have the same boryl group that is (C6F5)2B. M12 and M23 contain a silyl group with three fluorine substituted phenyl groups (see Fig. 1). The use of fluorine to replace H on the phenyl group is to protect the neighboring C–H bonds of the fluorine atoms. Due to electrostatic repulsion the phenyl C–H bonds in M12 and M23 are well protected. Using fluorobenzene to mimic the phenyl groups in M12 and M23, we found that the DG‡ for the activation of the ortho C–H bonds in fluorobenzene by M12 is 39.6 kcal mol 1, which is higher than the 32.4 kcal mol 1 required for methane activation. On the other hand, the silyl group of M28 is Si(CH2F)3 while that of M57 is Si(CH2Cl)3. The presence of F and Cl protects the C–H bonds on the silyl groups from being activated by M28 or M57. Using MeSi(CH2F)3 and MeSi(CH2Cl)3 to mimic M28 and M57, respectively, we found that the DG‡s for activating the C–H bonds of the CH2F and CH2Cl groups by M28 and M57 increase by 6.9 kcal mol 1 and 14.5 kcal mol 1, respectively. Last, we consider the solvent. Obviously, solvents such as benzene and cyclohexane that contain methyl, methylene, or unsubstituted phenyl groups cannot be used since they might be activated by the silylboranes. In previous experiments cyclohexane was used as a solvent for TM-mediated methane activation.58 However, we found that cyclohexane cannot be used as a solvent since the DG‡ for the activation of the cyclohexane C–H bond by M12 is higher than that of methane by just 1.2 kcal mol 1. In addition, the chosen solvent should be better to lower DG‡. We found that for the four candidates their TSs all have larger dipole moments than the corresponding silylboranes. Therefore, solvents with high dielectric constants can be used. Finally, we chose 1,2-dichloroethane as the solvent. The DG‡ for the activation of the C–H bond of 1,2-dichloroethane by M12 is 44.2 kcal mol 1, much higher than that for methane activation. In 1,2-dichloroethane solution, the DG‡ values for methane activation by M12, M23, M28, and M57 are 32.8 kcal mol 1, 34.7 kcal mol 1, 28.9 kcal mol 1, and 30.4 kcal mol 1, respectively. The DG‡ for M23 in solution is higher than the 33 kcal mol 1 threshold and we decided to remove it from our final list. Although the three DG‡s are still a

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little bit high, it should be noted that the DG‡s can be further lowered by increasing the pressure of methane. Due to unexpected side reactions and the uncertainties in the calculated DG‡s, for example, due to the DFT functional, the basis set, and the harmonic-oscillator-rigid-rotor approximation employed to calculate thermal contributions to DG‡, one can never be certain that the predicted reactions can be realized by experiments for sure. However, the analogous line of thought can be used as a hint for further experimental realizations.

Conclusions In this work, we systematically explored the possibility of using silylboranes with only Lewis acid centers to activate the C–H bonds of methane. The NBO analysis results show that the C–H bond is activated through the synergetic interaction between two pairs of orbitals, the C–H s-bonding orbital with the empty 2p orbital of B and the C–H s-anti-bonding orbital with the B–Si s-bonding orbital, and the former interaction plays a more important role. Bond order analysis along IRC also confirms the major role the Lewis acidic B center plays where the C–H bond is almost completely broken by B in the transition state with the formation of short B–C and B–H bonds. We have systematically studied the influence of substituents on B and Si using a statistical method. The results show that no single property of the silylboranes can be used to characterize their reactivity toward methane. These electronic properties are not completely independent. Their influence on the reactivity of the silylboranes is reciprocal. Using a statistical method, we determined an accurate mathematical model for the relationship between the free-energy barriers of the activation process and the six electronic properties we selected to characterize the properties of the silylboranes. The results show that the substituent effect on the boron center is more prominent than on Si. Among the six properties, lowering the occupancy or energy of the empty 2p orbital of B, or increasing the energy of the B–Si s-bonding orbital would increase the reactivity of the silylboranes. After considering many factors, such as the reactivity of the silylboranes toward methane, the dimerization and selfdestruction of the silylboranes, the possible reactions between the solvent and the silylboranes, and the solvent effect on the activation process, we finally screened three candidates that might be realized in experiments under mild conditions. The three candidates are M12, M28, and M57 (see Fig. 1), and the free-energy barriers at 298.15 K for their activation of methane in 1,2-dichloroethane solution are 32.8 kcal mol 1, 28.9 kcal mol 1, and 30.4 kcal mol 1, respectively.

Acknowledgements Financial support from National Natural Science Foundation of China (No. 21273042 and 21573044) is gratefully acknowledged. We thank the super computer center of Fudan University for computer time.

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Notes and references 1 J. A. Labinger and J. E. Bercaw, Nature, 2002, 417, 507–514. 2 R. G. Bergman, Nature, 2007, 446, 391–393. 3 X. Guo, G. Fang, G. Li, H. Ma, H. Fan, L. Yu, C. Ma, X. Wu, D. Deng, M. Wei, D. Tan, R. Si, S. Zhang, J. Li, L. Sun, Z. Tang, X. Pan and X. Bao, Science, 2014, 344, 616–619. 4 A. E. Shilov and G. B. Shul’pin, Chem. Rev., 1997, 97, 2879–2932. 5 M. Lersch and M. Tilset, Chem. Rev., 2005, 105, 2471–2526. 6 A. A. Fokin and P. R. Schreiner, Chem. Rev., 2002, 102, 1551–1593. 7 N. Dietl, M. Engeser and H. Schwarz, Angew. Chem., Int. Ed., 2009, 48, 4861–4863. 8 G. de Petris, A. Troiani, M. Rosi, G. Angelini and O. Ursini, Chem. – Eur. J., 2009, 15, 4248–4252. 9 N. Dietl, A. Troiani, M. Schlangen, O. Ursini, G. Angelini, Y. Apeloig, G. de Petris and H. Schwarz, Chem. – Eur. J., 2013, 19, 6662–6669. ´mez Martı´n and J. M. C. Plane, Phys. Chem. Chem. 10 J. C. Go Phys., 2011, 13, 3764–3774. 11 G. C. Welch, R. R. San Juan, J. D. Masuda and D. W. Stephan, Science, 2006, 314, 1124–1126. 12 G. C. Welch and D. W. Stephan, J. Am. Chem. Soc., 2007, 129, 1880–1881. ¨mming, E. Otten, G. Kehr, R. Fro ¨hlich, S. Grimme, 13 C. M. Mo D. W. Stephan and G. Erker, Angew. Chem., Int. Ed., 2009, 48, 6643–6646. 14 E. Otten, R. C. Neu and D. W. Stephan, J. Am. Chem. Soc., 2009, 131, 9918–9919. 15 M. A. Dureen and D. W. Stephan, J. Am. Chem. Soc., 2009, 131, 8396–8397. 16 M. Sajid, A. Klose, B. Birkmann, L. Liang, B. Schirmer, ¨hlich, C. G. T. Wiegand, H. Eckert, A. J. Lough, R. Fro Daniliuc, S. Grimme, D. W. Stephan, G. Kehr and G. Erker, Chem. Sci., 2013, 4, 213–219. 17 P. A. Chase and D. W. Stephan, Angew. Chem., Int. Ed., 2008, 47, 7433–7437. 18 S. K. Bose and T. B. Marder, Science, 2015, 349, 472–473. ´. Rochette and F. G. ´gare ´, M. A. Courtemanche, E 19 M. A. Le Fontaine, Science, 2015, 349, 510–513. 20 A. L. Kenward and W. E. Piers, Angew. Chem., Int. Ed., 2008, 47, 38–41. 21 G. Lu, L. Zhao, H. Li and F. Huang, Eur. J. Inorg. Chem., 2010, 2254–2260. 22 H. Li, L. Zhao, G. Lu, Y. Mo and Z. X. Wang, Phys. Chem. Chem. Phys., 2010, 12, 5268–5275. 23 M. Oestreich, E. Hartmann and M. Mewald, Chem. Rev., 2012, 113, 402–441. 24 M. Suginome and Y. Ito, Chem. Rev., 2000, 100, 3221–3256. 25 T. Kajiwara, N. Takeda, T. Sasamori and N. Tokitoh, Chem. Commun., 2004, 2218–2219. 26 T. Ohmura, T. Torigoe and M. Suginome, Organometallics, 2013, 32, 6170–6173. 27 I. Beletskaya and C. Moberg, Chem. Rev., 1999, 99, 3435–3461.

11548 | Phys. Chem. Chem. Phys., 2016, 18, 11539--11549

PCCP

28 T. Ohmura, T. Torigoe and M. Suginome, J. Am. Chem. Soc., 2012, 134, 17416–17419. 29 E. Hartmann, D. J. Vyas and M. Oestreich, Chem. Commun., 2011, 47, 7917–7932. 30 Y. Tani, T. Fujihara, J. Terao and Y. Tsuji, J. Am. Chem. Soc., 2014, 136, 17706–17709. 31 A. Matsumoto and Y. Ito, J. Org. Chem., 2000, 65, 5707–5711. 32 T. Ohmura, K. Oshima, H. Taniguchi and M. Suginome, J. Am. Chem. Soc., 2010, 132, 12194–12196. 33 C. Kleeberg, E. Feldmann, E. Hartmann, D. J. Vyas and M. Oestreich, Chem. – Eur. J., 2011, 17, 13538–13543. ¨hlich and M. Oestreich, Org. Lett., 2011, 13, 34 D. J. Vyas, R. Fro 2094–2097. 35 M. Suginome, T. Matsuda and Y. Ito, J. Am. Chem. Soc., 2000, 122, 11015–11016. 36 T. Ohmura, K. Masuda and M. Suginome, J. Am. Chem. Soc., 2008, 130, 1526–1527. 37 C. Jia, T. Kitamura and Y. Fujiwara, Acc. Chem. Res., 2001, 34, 633–639. 38 P. B. Arockiam, C. Bruneau and P. H. Dixneuf, Chem. Rev., 2012, 112, 5879–5918. 39 D. W. Stephan, J. Am. Chem. Soc., 2015, 137, 10018–10032. 40 K. C. Harper and M. S. Sigman, Proc. Natl. Acad. Sci. U. S. A., 2011, 108, 2179–2183. 41 K. C. Harper, E. N. Bess and M. S. Sigman, Nat. Chem., 2012, 4, 366–374. 42 M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G. A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H. P. Hratchian, A. F. Izmaylov, J. Bloino, G. Zheng, J. L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, J. A. Montgomery, Jr., J. E. Peralta, F. Ogliaro, M. Bearpark, J. J. Heyd, E. Brothers, K. N. Kudin, V. N. Staroverov, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J. M. Millam, M. Klene, J. E. Knox, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, R. L. Martin, K. Morokuma, V. G. Zakrzewski, G. A. Voth, P. Salvador, ¨ . Farkas, J. J. Dannenberg, S. Dapprich, A. D. Daniels, O J. B. Foresman, J. V. Ortiz, J. Cioslowski and D. J. Fox, Gaussian 09, Revision B.01, Gaussian Inc., Wallingford CT, 2009. 43 Y. Zhao and D. G. Truhlar, Theor. Chem. Acc., 2007, 120, 215–241. 44 Z. X. Wang, G. Lu, H. X. Li and L. L. Zhao, Chin. Sci. Bull., 2010, 55, 239–245. 45 K. Fukui, Acc. Chem. Res., 1981, 14, 363–368. 46 C. Gonzalez and H. B. Schlegel, J. Phys. Chem., 1990, 94, 5523–5527. 47 J. P. Foster and F. Weinhold, J. Am. Chem. Soc., 1980, 102, 7211–7218. 48 A. E. Reed, R. B. Weinstock and F. Weinhold, J. Chem. Phys., 1985, 83, 735–746.

This journal is © the Owner Societies 2016

PCCP

49 M. Strajbl, Y. Y. Sham, J. Villa and Z. T. Chu, J. Phys. Chem. B, 2000, 104, 4578–4584. 50 Z.-X. Yu and K. N. Houk, J. Am. Chem. Soc., 2003, 125, 13825–13830. 51 A. V. Marenich and C. J. Cramer, J. Phys. Chem. B, 2009, 113, 6378–6396. 52 J. D. Watts and R. J. Bartlett, J. Am. Chem. Soc., 1995, 177, 825–826. 53 J. F. Stanton, W. N. Lipscomb and R. J. Bartlett, J. Am. Chem. Soc., 1989, 111, 5173–5180.

This journal is © the Owner Societies 2016

Paper

54 P. R. Schreiner and H. F. Schaefer III, J. Chem. Phys., 1994, 101, 7625–7632. ´pai, J. Am. Chem. Soc., 2009, 55 T. A. Rokob, A. Hamza and I. Pa 131, 10701–10710. 56 M. E. Jung and G. Piizzi, Chem. Rev., 2005, 105, 1735–1766. 57 K. C. Harper and M. S. Sigman, Science, 2011, 333, 1875–1878. 58 C. C. Cummins, S. M. Baxter and P. T. Wolczanski, J. Am. Chem. Soc., 1988, 110, 8731–8733.

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