Superacid-Promoted Ionization of Alkanes Without Carbonium Ion

Article pubs.acs.org/JPCA

Superacid-Promoted Ionization of Alkanes Without Carbonium Ion Formation: A Density Functional Theory Study Peter Dinér* Department of ChemistryBMC, Uppsala University, Box 576, S-751 23 Uppsala, Sweden S Supporting Information *

ABSTRACT: The carbonium ion has been suggested to be the intermediate in superacid-promoted reactions (SbF5−HF) such as hydrogen−deuterium exchange and in the electrophilic C−H cleavage into hydrogen and the carbenium ion. In this study, the superacid-promoted C−H cleavage into hydrogen and the carbenium ion was studied using density functional theory (B3LYP and M062X) and ab initio methods (MP2 and CCSD). The calculations suggest that the superacid-promoted C−H cleavage proceeds via a concerted transition state leading to hydrogen (H2) and the carbenium ion without the formation of the elusive carbonium ion. The reactivity for the superacidpromoted C−H cleavage decreases upon going from isobutane (tertiary) > propane (secondary) > isobutane (primary) > propane (primary) > ethane ≫ methane.

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INTRODUCTION In the late 1960s, Olah and Hogeveen reported of hydrogen− deuterium exchange and ionizations of alkanes in superacidic solutions, such as HSO3F/SbF5 and HF/SbF5.1−8 Olah suggested a mechanism involving the protonation of the C− H bond and the formation of a pentacoordinated carbonium ion intermediate with a three-center two-electron bond (3c-2e). The protonated carbonium ion was then suggested to either react back to an alkane in a hydrogen exchange process or decompose into a carbenium ion and hydrogen (H2)

Another proposed mechanism for the ionization of isobutane suggests that the ionization of alkanes proceeds via a hydride abstraction from the alkane by the Lewis acid (SbF5).7,33,34 The formed antimony hydride reacts with antimony pentaflouride and forms SbF6−, SbF3, and a superacidic specie, HF-SbF5. The suggestion of the formation of the antimony hydride is controversial and evidence for this mechanism is still missing. Since the first investigations of the ionization of alkanes in superacidic media, several studies have been performed in order to elucidate the mechanism.35−39 Several studies have shown that hydrogen and carbenium ions are not always formed in a 1:1 ratio, which is in contradiction with the first mechanism (eq 2 of Figure 1). Sommer and co-workers have shown that the ratio of hydrogen and carbonium ions in the superacid HF/ SbF5 is related to the concentration of SbF5.35,36 In lower concentrations of SbF5, hydrogen and carbenium ions are formed in a 1:1 ratio, and in solutions with higher

The parent carbonium ion, the methonium ion, has been investigated extensively experimentally9−19 and computationally using quantum chemical calculations,20−27 but the direct detection of the structurally fluxional methonium ion in superacidic solutions has not been reported. The hydrogen− deuterium exchange between alkanes and superacids has been extensively studied, and Olah showed that alkanes react with superacids according the so-called σ-basicity and the reactivity order decreases from tert-C-H > C−C > sec-C-H > prim-C−H > CH4.28 The carbonium ion was suggested to be an intermediate both in the hydrogen exchange and in the ionization of alkanes. However, several computational studies of the hydrogen exchange between alkanes and model superacid systems have shown that the carbonium ion is not formed as an intermediate but is only involved as part of the transition state for the hydrogen−deuterium exchange reaction.29−32 These quantum chemical calculations suggest that the pentacoordinated carbonium ion is not the key intermediate in the ionization of alkanes, and therefore, other mechanisms must be involved in the formation of hydrogen and carbenium ions. © 2012 American Chemical Society

Figure 1. Simultaneously occurring reactions of alkanes in superacidic media. Received: June 27, 2012 Revised: September 18, 2012 Published: September 21, 2012 9979

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of the hydrogen exchange in alkanes. The methonium ion and the transition state for hydrogen exchange between methane and the SbF5−HF superacid cluster have been calculated at the B3LYP/6-311+G(d,p) level of theory in order to compare these structures to the structures of the transition states for the protolytic C−H cleavage at the same level of theory (Table 1).

concentrations of SbF5, the formation of hydrogen decreases considerably relative to the carbenium ion formation. NMR spectroscopic investigations have shown that the concentration of un-ionized SbF5 increases in HF/SbF5 solutions at a high concentration of SbF5.40 The t-butyl ion is also formed from isobutane in SbF5/SOClF solutions. In particular, Sommer and co-workers have studied the ionization of isobutane in SbF5/ SOClF, showing that hydrogen, the t-butyl cation, and SbF3 are formed in a 1:2:1 ratio.41 Further studies of the ionization reaction in SbF5/SOClF in the presence of an excess of acetone showed the formation of acidic protons (protonated acetone) and SbF3 but no formation of hydrogen. This indicates that there is a second mechanism for the ionization of isobutane, not involving the electrophilic C−H cleavage of isobutane.41 All simultaneously occurring reactions are presented in Figure 1. The pathways that involve hydrogen exchange (eq 1 of Figure 1), protolytic C−C-bond cleavage (eq 3 of Figure 1), and hydride transfer between alkanes and carbenium ions have previously been studied computationally.29,30,32,42−44 In this work, a combined density functional theory (DFT, B3LYP and M062X) and ab initio (MP2, CCSD) study of the transition states for the protolytic C−H cleavage with subsequent formation of hydrogen and a carbenium ion is presented (eq 2 of Figure 1). The pathway is discussed in the light of the previously computationally investigated pathways for hydrogen−deuterium exchange. The presented results suggest that the protolytic ionization of isobutane proceeds without the formation of a pentacoordinated carbonium ion.

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Table 1. Geometric Parameters of the Protolytic Cleavage of the C−H Bond of Methane at the B3LYP/6-311+G(d,p), M062X/6-311+G(d,p), MP2(full)/6-311+G(d,p), and CCSD/6-311+G(d,p) Levels of Theory distance (Å)

B3LYP/6311+G(d,p)

M062X/6311+G(d,p)

MP2(full)/6311+G(d,p)

CCSD/6311+G(d,p)

r(Sb−F1) r(F1−H1) r(H1−H2) r(C1−H1) r(C1−H2) r(F2−H3)

1.998 1.875 0.763 2.073 2.165 2.037

1.952 1.963 0.754 2.184 2.262 1.959

1.959 1.967 0.751 2.165 2.251 1.920

1.943 2.003 0.754 2.198 2.274 1.918

The lowest energy conformer of methane is the so-called Cs conformer with one of the methyl hydrogens eclipsed to the H2 hydrogens. At the B3LYP/6-311+G(d,p) level of theory the C−H bond lengths are 1.18 Å, and the H−H distance is 0.998 Å, which clearly show the three-center two-electron bond of the methonium ion (Figure 2). Previous calculations of the

COMPUTATIONAL DETAILS

Reactants and transition states were optimized in the Gaussian09 program45 at the B3LYP/6-311+G(d,p), M062X/ 6-311+G(d,p), MP2(full)/6-311+G(d,p), and CCSD/6311+G(d,p) levels of theory46−57 and using an effective core potential (LANL2DZ) basis set for Sb atoms.58 Optimizations were performed with a tight convergence criteria and a fine grid (grid = 96032) for the DFT calculations. All geometries were characterized as minima or saddle points on the potentialenergy surface (PES) by using the sign of the eigenvalues of the force-constant matrix obtained from a frequency calculation. Transition states with one imaginary frequency were confirmed to describe the correct movement on the PES by a mode analysis. IRC (intrinsic reaction coordinate) calculations59,60 were performed for all transition states at the DFT level of theory to connect the transition state (TS) with its corresponding reactant and product.

Figure 2. Optimized structure and the most important geometric parameters of the transition states for the transition state for hydrogen exchange and the methonium ion at the B3LYP/6-311+G(d,p) level of theory (distances in Å).

methonium ion suggests that DFT methods, especially B3LYP, have difficulty in reproducing the geometries of the three-center two-electron bond from high level ab initio calculations.20 The transition state for hydrogen exchange between the SbF5−HF superacid and methane resembles the structure of the methonium ion, although the C−H and H−H bond distances (1.23 and 1.057 Å, respectively) are slightly elongated and with the additional difference that the CH3hydrogens are in a staggered conformation in relation to the H2 hydrogens. It should be pointed out that the imaginary frequency of the transition state represents a concerted motion in which one of the protons is transferred from the superacid specie to the methane while one proton is transferred back from methane to the superacid specie. Initially, all transition states were optimized at the B3LYP/6311+G(d,p) level of theory. The optimized structure for the transition state of the electrophilic ionization of methane (TSMe) can be categorized as a late transition state in which the F−H bond in the superacid cluster (1.876 Å) and the C−H bond (2.165 Å) are relatively broken and that the H−H bond

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RESULTS AND DISCUSSION Quantum chemical calculations suggest that the pentacoordinated carbonium ion is not an intermediate in the ionization of alkanes but rather a part of the transition state for the concerted hydrogen exchange between alkanes and superacids.29,30,32 This suggests that there are other mechanistic pathways involved in the electrophilic C−H cleavage, which leads to the ionization of alkanes into hydrogen and carbenium ions. Here we wish to present a DFT study of the transition states involved in the superacid-promoted (SbF5/HF) protolytic ionization of methane, ethane, propane, and isobutane. In the calculations, the SbF5−HF superacid specie has been used to model the superacid solution. This model has successfully been used in the quantum chemical calculations 9980

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Figure 3. Optimized structure and the most important geometric parameters of the transition states for the transition state for protolytic C−H bond cleavage at the B3LYP/6-311+G(d,p) (normal) and M062X/6-311+G(d,p) (italics) levels of theory (distances in Å).

level of theory. The activation parameters obtained at the B3LYP level of theory are slightly higher than the activation parameters obtained at the M062X level of theory (Table 2),

in the forming H2 is almost completely formed (0.763 Å compared to 0.74 Å in free H2) (Figure 3). Although the geometry of the transition state “looks” similar to the 2-electron-3-center methonium ion, a comparison shows that the ionization transition state has considerably longer C− H distances and H−H bond distances and a higher degree of planarity of the CH3+-moiety (−164.5°) compared to both the pure methonium ion and the transition state for the hydrogen exchange in methane. The transition state was analyzed by following the IRC (24 points) and the transition state leads to methane and the SbF5−HF superacid on the reactant side and to H2 and a CH3+·SbF6− − complex on the product side. The late character of the transition state (long C−H distances) suggests that dispersion forces influence the geometry and the thermodynamics of the transition state. Recently, Truhlar and co-workers have developed a highly parametrized meta-GGAs (meta-Generalized Gradient Approximations) in order to quantitatively account for dispersion effects and to produce more reliable barriers of proton transfers.52,61 Therefore, we also performed the optimizations of the transition state for the C−H cleavage of methane at the M062X/6-311+G(d,p) level of theory using a tight convergence criteria for the optimization (opt = tight) and a fine grid (grid = 96032). At the M062X/6311+G(d,p) level of theory, the C−H bonds are considerably elongated (2.184 and 2.262 Å compared to 2.073 and 2.165 Å at the B3LYP/6-311+G(d,p) level of theory, respectively) together with longer F1···H1 distances (1.963 Å compared to 1.875 Å at the B3LYP/6-311+G(d,p) level of theory), which places the H2 moiety further away from the forming CH3+ ion. To benchmark these two DFT-functionals (B3LYP and M062X), the transition state for the C−H cleavage of methane was also located at the MP2(full)/6-311+G(d,p) and CCSD/6311+G(d,p) levels of theory. The geometric parameters at the M062X/6-311+G(d,p) level of theory are in better agreement with both the optimized geometries at the MP2(full)/311+G(d,p) and the CCSD/6-311+G(d,p) level of theory, which suggest that the M062X functional produces more reliable geometries of the transition states of the superacidpromoted C−H-cleavage compared to B3LYP functional (Table 1). Therefore, the M062X/6-311+G(d,p) level of theory will be used as the standard method in the optimization of the transition states for ethane, propane, and isobutane, and the results at the B3LYP level of theory will only be included as a comparison to the M062X results. The activation energy and enthalpy for the reaction, starting from methane and the SbF5−HF superacid specie, are 68.8 and 64.9 kcal mol−1, respectively, at the M062X/6-311+G(d,p)

Table 2. Activation Energies and Enthalpies for the Protolytic Cleavage of the C−H Bond of Methane, Ethane, Propane, and Isobutane Calculated at the B3LYP/6311+G(d,p), M062X/6-311+G(d,p), MP2(full)/6311+G(d,p), and CCSD/6-311+G(d,p) Levels of Theorya

state

B3LYP/6311+G(d,p) ΔE/ΔH (kcal mol‑1)

M062X/6311+G(d,p) ΔE/ΔH (kcal mol‑1)

MP2(full)/6311+G(d,p) ΔE/ΔH (kcal mol‑1)

CCSD/6311+G(d,p) ΔE (kcal mol‑1)

TSMe TSEt TSPr‑prim TSPr‑sec TSi‑Bu‑prim TSi‑Bu‑tert TSi‑Bu‑tert2

70.2/66.4 44.7/39.4 41.5/37.8 30.7/26.5 38.8/35.1 24.6/20.7 20.7/18.1

68.8/64.9 42.4/37.1 38.4/34.6 28.5/24.2 35.8/32.1 23.1/19.0 17.9/15.1

77.6/73.7

74.0

a

The activation energies and enthalpies for the protolytic cleavage are calculated from the isolated species (alkane and superacid cluster).

and this trend is seen for all the transition states of the C−H cleavage (ethane, propane, isobutane). The high activation parameters for the C−H cleavage in methane are probably due to the poor stabilization of the parent methyl cation. In ethane, an additional methyl group stabilizes the forming carbenium ion, and the activation energy and enthalpy for the ionization decrease to 42.4 and 37.1 kcal mol−1, respectively. However, this activation energy is still considerably higher than for the theoretical and experimental activation energy for the hydrogen exchange (16 and 18 kcal mol−1, respectively).8,29−31 The transition state for the ionization of ethane resembles the transition state for the ionization of methane but with more symmetric and longer C−H distances and with a longer F···H distance. In propane, the ionization can take place both on the hydrogen atoms at the primary and secondary carbons (Figure 4). The transition state for the ionization at the primary carbon (TSPr‑prim) resembles the transition state for the ionization of ethane, except for the fact that the C−H bonds (1.956 Å and 1.930 Å) and the F...H distance (2.016 Å) are considerably shorter than in the ethane transition state. The activation energy and enthalpy (38.4 kcal mol−1 and 34.6 kcal mol−1) are slightly lower than for the activation parameter for ethane. The extra stability of the transition state can be explained by the C− 9981

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Figure 4. Optimized structure and the most important geometric parameters of the transition states for the ionization of propane at the B3LYP/6311+G(d,p) (normal) and M062X/6-311+G(d,p) (italics) levels of theory (distances in Å).

Figure 5. Optimized structure and the most important geometric parameters of the transition states for the ionization of isobutane at the B3LYP/6311+G(d,p) (normal) and M062X/6-311+G(d,p) (italics) levels of theory (distances in Å).

The activation energy and enthalpy are 23.1 and 19.0 kcal mol−1, respectively, which are lower than for the protolytic cleavage in the secondary carbon atom in propane. The experimentally most investigated protolytic ionization in the superacidic media is the C−H cleavage of isobutane. Hogeveen determined the activation parameters for the protolytic cleavage of isobutane (18.3 kcal mol−1) in HF/ SbF5 and for the formation of isobutane from hydrogen and the hexafluoro-antimonate stabilized t-butylcation (12.7 kcal mol−1).3,4 The calculated activation enthalpy for the protolytic cleavage of the tertiary C−H bond in isobutane (19.0 kcal mol−1) is in good agreement with the experimentally obtained activation enthalpy for isobutane. NMR spectroscopic investigations have shown that larger superacidic species, e.g., Sb2F11−·H+, are formed in HF/SbF5 solutions at increasing concentration of SbF5 as seen in Figure 6.40 A previous DFT study by Mota and Esteves and co-workers of the nature of the electrophilic species suggest that Sb2F11−·H+ is one of the major components of a HF/SbF5 solution (1/1).65 At the M062X/6-311+G(d,p) level of theory,

C hyperconjugation interaction, which has previously been reported in the literature62−64 and is manifested in a short C1− C3 distance (2.160 Å) and a bent C1−C2−C3 angle (90.3°). The optimized transition state of the ionization at the secondary carbon (TSPr‑sec) resembles the previously calculated transition states for ethane and at the primary position of propane but with the difference that the H2-moiety is shifted toward the secondary carbon in propane (C−H, 1.920 Å and 1.844 Å). The activation energy and enthalpy for the ionization are 30.7 and 26.5 kcal mol−1, respectively. This activation energy and enthalpy are significantly lower than for the activation parameters of ethane. This suggests that the direct protolytic ionization could be a probable pathway in the ionization of alkanes with secondary carbons. The transition state for the ionization at the primary carbon atom of isobutane (TSi‑Bu‑prim) resembles the transition state for the ionization for propane, i.e., with a pronounced C−C hyperconjugation interaction, which leads to a shortened C−C distance (2.157 Å). The activation energy and enthalpy (38.8 and 35.1 kcal mol−1) are slightly lower than for propane, which is probably due to the increased stability from the additional methyl group in the forming carbenium ion. The protolytic C− H bond cleavage of the tertiary position of isobutane (TSi‑Bu‑tert) is seen in Figure 5. The transition state for formation of the H2 moiety is earlier than the previously calculated transition states and is manifested in a shorter F···H distance (1.887 Å) and less symmetric C−H distances (1.951 and 1.806 Å, respectively).

Figure 6. Relative enthalpy of the superacidic species at the B3LYP/6311+G(d,p) (italics) levels of theory. 9982

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the formation of Sb2F11−·H+ species is strongly favored (Figure 6). Therefore, we also optimized the geometry of the transition state of of the C−H cleavage of isobutane and the larger superacidic cluster Sb2F11−·H+ (TSi‑Bu‑tert2) (Figure 7).

of the alkanes can be arranged according to (highest to lowest): iso-butane (tert) > propane (sec) > isobutane (prim) > propane (prim) > ethane ≫ methane. The activation enthalpies for the protolytic cleavage of the C−H bond of isobutane and the formation of isobutane from hydrogen and the hexafluoroantimonate stabilized t-butylcation are in agreement with the experimentally determined activation parameters.

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ASSOCIATED CONTENT

S Supporting Information *

Absolute energies, enthalpies, and free energies for all calculated species and Cartesian coordinates for all the optimized transition states are provided in the Supporting Information. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS P. D. thanks Vetenskapsrådet (Grant No. 621-2009-4018) for financial support and the National Supercomputing Center in Linköping (NSC) for computational resources.

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Figure 7. Optimized structures of the superacid species and transition states for the C−H cleavage of isobutane at the M062X/6-311+G(d,p) (italics) level of theory (distances in Å).

REFERENCES

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The transition state resembles the transition state for the C− H cleavage in the tertiary position of isobutane (TSi‑Bu‑tert) using the smaller SbF5−HF cluster as a model, and the activation energy and enthalpy decrease to 17.9 and 15.1 kcal mol−1, respectively, which is also in quite good agreement with the experimentally obtained activation enthalpy. These results show that the calculated enthalpy of activation for the C−H cleavage in the tertiary position of isobutane (TSi‑Bu‑tert and TSi‑Bu‑tert2) are in good agreement with the experimentally obtained activation enthalpy for this reaction and that the transition states do not include the formation of a pentacoordinated carbonium ion as a discrete intermediate or as part of the transitions state state structure. However, in the present study, the electrostatic stabilization effects of the solvent are not taken into account, which could have a stabilizing effect of the carbonium ion.

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CONCLUSION A new mechanistic pathway for the protolytic cleavage of C−H bonds using a SbF5−HF superacid cluster has been investigated at the B3LYP/6-311+G(d,p) and the M062X/6-311+G(d,p) levels of theory. Benchmark calculations suggest that the M062X/6-311+G(d,p) geometries are more in agreement with the geometries obtained at the MP2(full)/6-311+G(d,p) and CCSD/6-311+G(d,p) levels of theory than the geometries obtained at the B3LYP/6-311+G(d,p) level of theory. The calculated transition states for the protolytic cleavage are different from the previously calculated transition states for hydrogen exchange and do not include the formation of a pentacoordinated carbonium ion as a discrete intermediate or as part of the transition state structure. The calculated reactivity 9983

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dx.doi.org/10.1021/jp306319s | J. Phys. Chem. A 2012, 116, 9979−9984