A Computational Study of tert-Butylbenzenium Ions - The Journal of

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A Computational Study of tert-Butylbenzenium Ions Stein Kolboe* inGAP Center for Research Based Innovation, Department of Chemistry, University of Oslo, P.O. Box 1033, Blindern, N-0315 Oslo, Norway

bS Supporting Information ABSTRACT: A computational study of tert-butylbenzenium ions has been performed. Structures and energies of the various isomers and the transition states for their interconversions have been determined. The existence of a stable π-electron complex (called A1) between a tert-butyl cation and a benzene molecule has been confirmed. Other minimum points on the potential energy surface corresponding to π-complexes were found, but the barriers for transforming these complexes into the stable π-electron complex A1 are so low that the transformation into the stable structure can take place at all temperatures. The structures were evaluated at the DFT-B3LYP level of theory. The energies were evaluated with the Gaussian-3 (G3B3) and CBS (CBS-QB3) composite methodologies. A discussion of published experimental data in view of the computational results is given. It is pointed out that it should be possible to show the presence of the π-complex by IR spectroscopy. The computations show that the π-complex has a very strong IR band in an otherwise empty region.

’ INTRODUCTION Protonated alkylbenzenes (alkylbenzenium ions) have been the subject of much study in solution as well as in the gas phase. The chemistry of protonated species in solution became available for study with the advent of superacids in the early 1960s. An early but quite comprehensive work on the benzenium ion and monoalkylbenzenium ions was published by Olah et al. in 1972 as part of a long series of papers on stable carbocations.1 Chemical ionization mass spectrometry was introduced by Munson and Field, making gas-phase protonated species available for study. In an early paper, they applied the technique to a considerable number of aromatic hydrocarbons.2 In the following years, a very considerable number of papers studying the chemistry of protonated gas-phase hydrocarbons appeared. When carrying out studies on the alkylation/dealkylation of alkylbenzenium ions, often recurring issues are: Can stable π-electron complexes involving the benzene ring and the alkyl group form, and what is the mechanism of the reaction taking place when the alkyl group is split off?3-14 Comprehensive reviews of alkylarenium ion chemistry have been published by Kuck.15,16 Despite an increasing number of theoretical studies, there is still need to follow up the many experimental works by corresponding theoretical studies. We have recently carried out a theoretical study of the ethylbenzenium ion system.17,18 In this Article, the tertbutylbenzenium ion(s) and possible π-electron complexes, which may be formed when the C-C bond between a benzene ring carbon and the tert-butyl group is broken, is investigated. Such complexes may be of two types, C6H7þ/C4H8 or C6H6/C4H9þ. The mechanisms for the reactions involved and the inverse reactions, where the initially separated constituents meet and react, have been looked into. The study has been confined to the gas phase, where there is no influence from other species. r 2011 American Chemical Society

Computational studies of the tert-butylbenzenium ion and π-electron complexes have earlier been carried out by Berthomieu et al. who used semiempirical methods11 and by Heidrich.19 Heidrich based the computations on the MP2 level of theory with the basis set 6-31þG(d,p). In our previous study17,18 of the ethylbenzenium ion system, it was found that MP2 failed to find a stable ethene/benzenium complex, which was found when the B3LYP and CCSD methodologies were employed. Subsequent computations at the CCSD(T) level showed that B3LYP was right and that the failure of MP2 most likely was caused by an overcorrection.18 Computations based on density functional theory (DFT) in its B3LYP formulation and energy evaluations based on the high-level composite methods Gaussian-3 and CBS-Q may therefore be of interest. At the same time, the scope of the study may be widened to include reaction pathways other than those studied by Heidrich and looking for other possible complexes like an isobutene/benzenium complex. Catalytic reactions where variously substituted aromatic molecules are produced or reacted over acidic catalysts constitute an important part of chemical literature and practice.20 The understanding of these reactions is based on our present-day knowledge of aromatic carbocation chemistry. Further insight into this field of chemistry may be obtained by means of computational chemistry, and this deeper insight is of interest for an important part of chemistry.

’ COMPUTATIONAL DETAILS The computations that are presented have all been performed using the Gaussian 03 program package.21 Received: October 27, 2010 Revised: February 17, 2011 Published: March 23, 2011 3106

dx.doi.org/10.1021/jp110283t | J. Phys. Chem. A 2011, 115, 3106–3115

The Journal of Physical Chemistry A Geometries of the stationary states that were found and that are presented have been optimized at the B3LYP/6-311þþG (d,p) level of theory. Energies of all species have been calculated at the B3LYP/6-311þþG(d,p) level of theory with zero point energy (ZPE) corrections and at the much more accurate complete basis set level (CBS-QB3).22 With the exception of tert-butyl-2H-benzene, tert-butyl-3H-benzene, and the transition states for proton shifts on the benzenium ring, energies were also calculated at the Gaussian-3 (G3B3) level.23 To obtain convergence in structure optimizations, it is in many cases necessary to employ the Ultrafine integration grid. The geometric structures used in CBS-QB3 and G3B3 computations and the corresponding ZPE corrections are supposed to be based on B3LYP optimizations with the CBS basis set CBSB7 (=6-311G(d,p)), respectively 6-31G(d) for G3 computations. In their standard formulations, both composite methods search for an energy minimum during the structural optimization. When the intention is to determine a transition state energy, it is therefore necessary to carry out a transition state optimization (preferably using a tight convergence criterion) with the appropriate basis set and use the structure thus determined as input for the CBS and G3 computations so that the optimization stops at the transition state geometry because the input structure is a stationary state. To make comparisons with an earlier published computational study of the tert-butylbenzenium ion system at the MP2/631þG(d,p) level, some HF and MP2 computations with the 6-311þþG(d,p) and smaller basis sets have been carried out.

’ RESULTS The presentation of the species that have been studied is divided in two parts. The first (smaller) part comprises the different isomers that result when the tert-butylbenzene molecule is protonated. The proton addition may lead to para-, meta-, ortho-, or ipso-protonation. In addition to the stable species, the transition states for proton walk from one position to another are studied. The other part concentrates on the species that may form when the bond connecting the tert-butyl group to the benzene ring is broken. When in the following there is need to distinguish between the atoms in the species that are discussed, the atoms will be numbered as shown in Figure 1, which is a very schematic description of tert-butylbenzene. The numbering also applies in cases where the C1C7 bond is broken. tert-Butylbenzenium Ions. An impression of the main structural characteristics of tert-butylbenzene and the tert-butylbenzenium ion isomers as given by geometry optimizations is obtained from Figures 2-4. The parent molecule tert-butylbenzene is shown in Figure 2. This molecule has Cs symmetry with the benzene ring in the symmetry plane. C7 and C8 are also in the symmetry plane. Full structure details of all discussed species are given in the Supporting Information. It is found that the structures that result when the proton attaches to any of the carbon atoms except C1 largely retain the structural characteristics seen in Figure 2 (with replacement of a C-H group on benzene by CH2 at the appropriate position). In accordance with the numbering used in Figure 1, they are termed tert-butyl-2H-benzene (in the following called bu-2h-b), tertbutyl-3H-benzene (hereafter bu-3h-b), and tert-butyl-4H-benzene (hereafter bu-4h-b). The tert-butylbenzenium ion where the protonation has taken place on C4 with formation of bu-4h-b is

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Figure 1. The atomic numbering that is used.

Figure 2. The geometry-optimized structure of tert-butylbenzene.

Figure 3. The geometry-optimized structure of tert-butyl-4H-benzene (bu-4h-b), the most stable tert-butylbenzenium ion.

shown in Figure 3. Apart from the positions of the CH2 groups, visually indistinguishable figures result when bu-3h-b and bu-2h-b are depicted. Further computations have shown that the energy needed for rotating the tert-butyl group about the C1C7 bond is very low. The rotational barriers for tert-butylbenzene, bu-4h-b, bu-3h-b, and b-2h-b are, in the same order, 2.6, 1.8, 4.5, and 1.2 kJ/mol. The rotation barrier of ethane, which to a large extent behaves as if the methyl groups are freely rotating, is known to be about 12.5 kJ/mol. On this background, it is clear that the above species all may be taken to have freely rotating tert-butyl groups at all but the lowest temperatures. Consequently, even though the structures shown in Figures 2 and 3 represent minima on the potential energy surface, they do not represent particularly preferred structures or rotamers. While the other protonation sites led to tert-butylbenzenium ions where the tert-butyl group is freely rotating, this is no more the case for tert-butyl-1H-benzene (bu-1h-b). The rotational barrier in this case is 23.6 kJ/mol, implying that at room temperature the bu-1h-b species is well represented by the structure displayed in Figure 4. Also, this ion has Cs symmetry, but the symmetry plane is perpendicular to the benzene ring plane. The tert-butyl group is, relative to the situation in Figures 2 and 3, rotated 30° about the C1C7 bond, and the C1C7 and C7C8 axes are in the symmetry plane. At the same time, the angle C4C1C7 is changed from 180° to about 130° to make room for the protonating hydrogen. The C1C7 bond is unusually long, 3107

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Table 1. Energies for tert-Butylbenzenium Ions and Transition State Energies for Proton Shifts between the Benzene Ring Carbons B3LYP/6-311þþG(d.p) species

CBS-QB3

-1

E(CBS)/Eh ΔE/kJ mol-1

ΔE/kJ mol

E/Eh

bu-1h-b -389.691853

30.6

-388.988667

bu-2h-b -389.701764

4.6

-388.997405

4.7

bu-3h-b -389.696470

18.5

-388.992679

17.1

bu-4h-b -389.703513

0.0

-388.999185

0.0

27.6

a

Transition States for Hydrogen Ring Walk

Figure 4. The geometry-optimized structure of tert-butyl-1H-benzene (bu-1h-b), the least stable tert-butylbenzenium ion. Note the long C1C7 bond.

1.684 Å, as compared to the usual 1.51-1.54 Å found for the other protonated species and the unprotonated tert-butylbenzene. This ion species was also studied by Heidrich at the MP2/631þG(d,p) level.19 The structure predicted by the two methodologies is generally similar; in both cases, there is Cs symmetry, and, as is to be expected, the corresponding C-C bonds in the benzene ring and in the tert-butyl group never differ by more than 0.02 Å, and usually much less. However, the length of the C1C7 bond connecting the benzene ring and the tert-butyl group is very different. In both cases, this bond is very long, but the 1.684 Å found in the present work is dwarfed by the bond length given by the MP2 computations, 1.769 Å. To look a bit closer at this discrepancy, the MP2 computation has been repeated with the larger basis set 6-311þþG(d,p). The bond length then increased still further to 1.807 Å. The 6-311þþG(d,p) is still not a very large basis set, so it seemed worthwhile to see the effect of going further to the basis set cc-pVTZ, which may represent a practical upper limit for a molecule this size. The bond length then increased again, to 1.849 Å, an enormous length for a C-C bond. Simultaneously with the lengthening of the C1C7 bond, there is a shortening of the C4C8 distance. The plane of the tertbutyl group becomes nearly parallel with that of the benzene ring. The MP2 structure of bu-1h-b is actually almost indistinguishable from the B3LYP structure of the transition state for breaking the C1C7 bond and forming the C6H6/C4H9þ complex A1 (see below). For completeness, we have also calculated all the transition states for proton walk along the benzene ring and the barriers in each direction. The energies of the above-mentioned species have been calculated with the B3LYP/6-311þþG(d,p) methodology and the composite model chemistry CBS-Q (Gaussian keyword CBS-QB3). The results are displayed in Table 1 and the graphic in Figure 13. Agreement with the well-known para/ortho directing property of a tert-butyl group is seen. π-Electron Complexes. In addition to the above species, several stationary states corresponding to ion π-electron bonded complexes have been found. There are two C6H6/C4H9þ complexes. They will be termed A1 and A2 in the following. There are also two C6H7þ/C4H8 complexes, in the following called B1 and B2. In addition, several transition states corresponding to formation of the above complexes and reactions between them were found; see below. Figure 5 depicts the complex A1. This is also the complex found by Heidrich.19 The structures found in the two cases are

TS-12 TS-23

-389.681054 -389.679207

59.0 63.8

-388.982790 -388.980472

43.0 49.1

TS-34

-389.679706

62.5

-388.980637

48.7

Barriers for Hydrogen Shifts C1 to C2

C2 to C1

C2 to C3

C3 to C2

C3 to C4

C4 to C3

28.4b

54.4

59.2

45.3

44.0

62.5

15.4c

38.4

44.5

32.0

31.6

48.7

a

TS-MN: The transition state for proton shift between carbon M and N. b Calculated with B3LYP, kJ mol-1. c Calculated with CBS-QB3, kJ mol-1.

Figure 5. The structure of a π-electron complex C6H6/t-C4H9þ, termed A1. This is the only kinetically stable π-electron complex.

visually quite similar, and they both have Cs symmetry with C1, C4, C7, and C8 in the symmetry plane. The corresponding benzene ring and tert-butyl group C-C bonds are virtually identical in the two cases. However, the distance between the benzene ring and the tert-butyl cation is markedly different; B3LYP gives a much larger separation. The benzene ring and tert-butyl group separation as represented by the C1C7 distance given by B3LYP is 3.510 Å, while Heidrich’s MP2-based result is 3.109 Å. Figure 6 shows the tert-butyl cation/benzene complex, A2. This structure was surprising, but it represents a potential energy surface minimum, although the minimum is very shallow and the barrier for converting it to A1 is very low (see below). This complex is less strongly bound than A1. Generally speaking, the benzene ring and the tert-butyl group are further apart even 3108



Figure 6. The structure of a π-electron complex C6H7þ/iso-C4H8, termed B1.

Figure 7. The structure of a π-electron complex C6H7þ/iso-C4H8, termed B2.

though the shortest Htert-butylCbenzene in A2 has only increased from 2.44 Å in A1 to 2.54 Å in A2. Figures 7 and 8 show the complexes B1 and B2. These complexes can clearly be considered to consist of an isobutene molecule and a benzenium ion. Complexes of this kind were also observed by Berthomieu et al.11 They carried out semiempirical computations with the fragments (C6H7þ and C4H8) frozen at their equilibrium geometries. The most important geometric characteristics of B1 and B2 are seen from the figures. The geometries of the isobutene and benzenium parts are almost the same as in the separate constituents, but the isobutene double bond is lengthened from 1.335 Å in the free isobutene molecule to 1.357 Å in the complexes, and the C4-H9 bond is 1.180 Å in the complexes and only 1.11 Å in an isolated benzenium ion, thus showing a fairly strong interaction between the two moieties. The barriers for converting these complexes into A1 are, as shown below, very small. The energies of the species A1, A2, B1, and B2 as obtained with the B3LYP/6-311þþG(d,p), CBS-QB3, and G3 (G3B3) methodologies are displayed in Table 2. A1 is by far the most stable π-electron complex. Transition States. Transition state geometries and energies have been found and calculated for the reactions: (1) Breaking of the C1C7 bond in bu-1h-b and formation of complex A1, in the table designated as TS(1Hb-A1). (2) The transition from B1 to A1 (or vice versa) where there is a transfer of a proton between the benzene ring and the butyl group, designated as TS(B1-A1).

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Figure 8. The structure of a second tert-butyl cation π-electron complex, termed A2.

(3) The transition from B2 to A1 (or vice versa) where there is a transfer of a proton between the benzene ring and the butyl group, designated as TS(B2-A1). (4) The conversion between A1 and A2, designated as TS(A2-A1). The transition state geometries can be seen from Figures 912. The energies of the above species are given in Table 2, again at the B3LYP/6-311þþG(d,p), CBS-QB3, and G3 (G3B3) levels. It is noteworthy that after adding the ZPE correction, which does not, in the case of a transition state, have any contribution from the imaginary vibration, the energies of the transition states are lower than those of the complexes A2, B1, and B2. The potential energy surface (PES) barriers are smaller than the ZPE of the vibration that disappears in the transition state. Only the PES barrier for converting bu-1h-b into A1 (or vice versa) is higher than the ZPE of the vibration that is lost in the transition state. In all cases, it was checked that the transition states are really connecting the expected minima. Because A1 is the most important complex, it was considered to be of interest to look more closely on the formation of A1 from bu-1h-b via the transition state, TS(1hb-A1). To this end, a series of optimizations were run. In each case, a fixed C1C7 distance was chosen, starting with the bu-1h-b equilibrium distance. When the converged optimization was obtained, a new optimization was started with the C1C7 distance increased by 0.05 Å. The Opt(modredundant) keyword can carry this out automatically. During the first steps, until C1C7 has increased from 1.68 to 2.02 Å, the system energy increases, corresponding to a barrier 3.3 kJ/mol. This is the transition state described above, TS(1hb-A1). As the C1C7 distance increases further, the system energy falls, and, simultaneously, the C4C8 distance decreases and the tert-butyl group flattens and approaches an ordinary tert-butyl cation. During the formation of A1 from bu1h-b, the methyl group, which approaches C4, must undergo a torsion so that a hydrogen may point toward C4. This starts to take place when C1C7 is about 2.4 Å and is not connected with any barrier. When the C1C7 distance is increased further, the energy decreases until C1C7 = 3.51 Å, when the A1 structure and energy are obtained. Taking the tert-butyl group farther away leads to increased energy. Numerical tables are too detailed to give an immediate grasp of the situation. The essence of the data given in Tables 1 and 2 is therefore given as graphs in Figures 13 and 14, which also give the calculated energies for splitting tert-butylbenzenium ions into tert-butyl cation þ benzene or isobutene þ benzenium ion. Note the closeness of the CBS and G3 results. Also note that B3LYP 3109



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Table 2. Energies of the Species Treated Here at Three Different Levels of Theory energies relative to bu-4H-b/kJ mol-1

absolute energies/Eh species

B3LYP

CBS-QB3

G3B3

B3LYP

CBS-QB3

G3B3

bu-4H-b

-389.70351

-388.99918

-389.45458

0.0

0.0

0.0

bu-1H-b

-389.69185

-388.98866

-389.44372

30.6

27.6

28.5

bu-1H-b-endo

-389.68670

-388.98383

-389.43864

44.1

40.3

41.8

TS(1Hb-A1)

-389.69150

-388.98653

-389.44010

31.5

33.2

38.0 27.0

A1

-389.70404

-388.99048

-389.44429

-1.4

22.8

A2

-389.70269

-388.98592

-389.43951

2.2

34.8

39.6

TS(A2-A1)

-389.70252

-388.98614

-389.4403

2.6

34.2

37.5

C6H6 þ C4H9þ TS(B1-A1)

-389.69211 -389.68390

-388.97008 -388.96376

-389.42338 -389.41801

29.9 51.5

76.4 93.0

81.9 96.0

TS(B2-A1)

-389.68333

-388.96387

-389.41834

53.0

92.7

95.2

B1

-389.68209

-388.96134

-389.41619

56.2

99.3

100.8

B2

-389.68166

-388.96123

-389.41647

57.4

99.6

100.0

C6H7þ þ C4H8

-389.66912

-388.94716

-389.40219

90.3

136.6

137.5

Figure 11. The transition state structure for transforming the B2 complex into the A1 complex, TS(B2-A1). Figure 9. The transition state structure for breaking the C1C7 bond in bu-1h-b forming the A1 π-electron complex, TS(1hb-A1).

Figure 10. The transition state structure for transforming the B1 complex into the A1 complex, TS(B1-A1).

overestimates the barriers for hydrogen walk along the benzene ring in the tert-butylbenzenium ions and that, although B3LYP agrees well with CBS and G3 as regards the relative tert-butyl ion energies, it severely overestimates the stabilities of the complexes; that is, it strongly underestimates the energy needed to break the bond between the benzene ring and the tert-butyl group. Overview of Hartree-Fock and MP2 Computations. Although the work is concentrated around the geometries

Figure 12. The transition state structure for transforming the A2 complex into the A1 complex, TS(A2-A1).

that are obtained by the DFT method B3LYP, it was of interest to do some geometry optimizations on the complexes using the HF and MP2 methodologies. The B3LYP structures were then taken as starting points, and HF, respectively MP2, optimizations carried out. HF-based computations found the A1, B1, and B2 complexes to be stable states for the tested basis sets 6-31G(d) and 6-311þþG(d,p). The complexes were rather similar to the ones found with B3LYP, although the distance between the benzene ring and the C4 entity was much longer. Computations on the A2 3110



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between B3LYP and MP2 on this point. The PES reaction barriers predicted by B3LYP for these species are only about 1.5 kJ/mol, so these barriers are quite insignificant as compared to the relevant zero point vibrational energies. Further details are given in the Discussion.

Figure 13. tert-Butylbenzenium ion energies for the various protonation positions on the benzene ring and transition state energies (ZPE corrected) for moving the proton from one carbon to a neighbor carbon. The numbers on the abscissa show to which carbon the proton is attached, or between which atoms it is moving.

Figure 14. The energies of the π-electron complexes that have been discussed and the C1 and C4 protonated tert-butylbenzenium ions. The potential energy surface barriers for the transition states TS(B1-A1), TS(B2-A1), and TS(A2-A1) are very small and at this scale not distinguishable from the B1, B2, and A2 energies.

complex with the B3LYP structure as the starting point converged on the A1 structure with basis set 6-311þþG(d,p). However, when the smaller basis set 6-31G(d) was used, a quasi-convergence to the A2 structure was observed. The convergence criterion for forces was well within the limits, but the maximum displacement criterion was not. The optimization finally converged to the A1 structure. Corresponding MP2 optimizations on A1 with the B3LYP structure as starting point converged smoothly with only minor geometry changes; that is, the two computational methods were in essential accord. Whether A2 is a minimum point on the PS when MP2 computations are carried out depends on the basis set. Computations with the 6-31G(d) basis set converged to a retained A2 structure. When this structure was taken as starting point with the larger basis sets 6-31þG(d,p) and 6-311þþG (d,p), the optimizations were close to stop because of satisfied convergence criteria with a structure that was barely changed from the starting point. Three of the four convergence criteria set by Gaussian were satisfied. Only the maximum displacement criterion was slightly outside the limit. This shows that the A2 structure is in essential agreement also with MP2 computations. Computations on B1 and B2 converged to the A1 structure and gave no indication that B1 and B2 are stable structures within the MP2 methodology. There is, however, no serious disagreement

’ DISCUSSION How well do the computational results comply with experimental data reported in the literature, and how well do they line up with previously published computational work? tert-Butylbenzenium Ions in Superacidic Solution. Olah and co-workers1 noted in their work on alkylbenzenium ions in superacidic solution two particular properties of the tert-butylbenzenium ions: (1) The protonation took place in the para position (applies to all alkylbenzenium ions). (2) Unlike the other butylbenzenium ions, which could be kept at room temperature for some time (hours), warming of a tert-butylbenzenium ion solution above -78 °C resulted in rapid cleavage whereby tert-butyl cations and benzenium ions were formed. The stability of bu-4h-b thus agrees with experiment. The computational result that bu-2h-b is only 4.7 kJ/mol higher in energy than the most stable isomer suggests that it should be possible to observe also this species by NMR spectroscopy. Farcasiu et al. were able to show the presence of the ortho protonated form of the ethylbenzenium ion in superacid solution. They found the energy to be 5.4 kJ/mol higher than that of the para protonated form.24 The computational data do not permit any detailed statements about the reactivity of t-butylbenzenium ions in superacids, but due to the high protonation activity of the acid, the reaction A-H þ C6H6 3 C4H9þ f A- þ C6H7 þ þ C4H9þ (A-H stands for the superacid) will certainly be strongly exothermic. The energy needed to break the C1C7 bond in gaseous tert-butylbenzenium ions is only 82 kJ/mol (see Table 2) so (in accord with the Hammond postulate) an activation energy considerably smaller than 82 kJ/mol is to be expected in a superacidic medium; it might well be 60 kJ/mol or less. To test this assertion, a trial run where a proton was placed 2.5 Å away from the benzene ring, over C4, in bu-1h-b was run. Upon starting a geometry optimization, formation of the separated species benzenium ion and tert-butyl cation took place in a few steps. Assuming a typical value for the pre-exponential factor, Z = 1012 s-1, and a barrier of 60 kJ/mol, the half-life of a firstorder reaction with rate constant k at -50 °C would then be τ = ln 2/k ≈ 80 s. An activation energy 55 kJ/mol would give a halflife of 5 s. The experimental observations and the computations, therefore, appear to agree well. Equilibrium of the Reaction t-C4H9þ þ C6H6 f t-C4H9 3 C6H6þ. Sen Sharma et al. studied the reaction t-C4H9þ þ C6H6 f

t-C4H9 3 C6H6þ in a mass spectrometer.5 They determined the equilibrium constant for the reaction to be 170 Torr-1 (=1.3 105 bar -1) at 305 K. The high level computations CBS-QB3 and G3B3 that are presented in this Article allow computations of the equilibrium constant because the Gibbs energies are among the computed values. When the default temperature 298 K and G3B3 are used, the reaction Gibbs energy change ΔrG° = 31.55 kJ/mol is found, giving Keq(298 K) = 3.9 105 bar-1. The van’t Hoff equation dK/dT = K 3 ΔrH°/RT2 allows an easy calculation of Keq(305 K). This correction gives Keq= 2.9 105 bar-1, which compares favorably with the experimental value 1.3 105 bar -1. (The equilibrium constant obtained with CBSQB3 is nearly an order of magnitude smaller.) The excellent 3111



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agreement between experiment and computation may, however, be somewhat fortuitous. Several of the vibrations, which contribute to the entropy part of the Gibbs energy as given by Gaussian 03, may be partially hindered rotations. This will lead to corrections of the entropy values and thus also the Gibbs energies. An in-depth analysis of this issue has not been attempted. Is There a Barrier for Addition of t-C4H9þ to Benzene? Cacace and Ciranni studied the addition of the tert-butyl cation to benzene, respectively toluene, in the presence of isobutane at near atmospheric pressure in the temperature range 273413 K.6 They found that the addition to benzene has an activation energy that is 15 kJ/mol higher than for the addition to toluene. The absolute values could, however, not be determined. They explained the presence of activation energy by assuming the reaction to take place in two steps with a primary formation of a “loose ion-molecule adduct”. Under low pressure conditions where molecular collisions are few, the primary adduct will be activated because the long-range interactions lead to translational energy, which, when the adduct forming collision takes place, is transformed into vibrations. The thus activated adduct may have an energy well above the (possible) intrinsic activation energy for transforming the adduct into a (σ-bonded) alkylarenium ion. In such a case, no activation energy is observed. The experiment took, in their case, place under atmospheric (i.e., high) pressure, so, they argued, the adduct would give off the excessive energy to interacting molecules and as a result end up being in thermal equilibrium with the surrounding molecules before forming a σ-bond to the benzene ring, and the reaction should display ordinary Arrhenius plot behavior when carried out at several temperatures. Transferred to the present computational study, this implies that the observed activation energy corresponds to the barrier TS(1Hb-A1) - A1 = 11 kJ/mol (see Table 2) when a tert-butyl cation adds to benzene (11 kJ/mol is strictly speaking the barrier at 0 K). Selective Loss of tert-Butyl Cations. It has been noted that the splitting of the tert-butylbenzenium ion in the mass spectrometer leads to C4H9þ ions and no C6H7þ ions.4,8 This is a consequence of the much higher proton affinity of isobutene relative to benzene. Table 2 shows that the energy needed to form C6H7 þ ions and isobutene is 56 kJ/mol higher than that for the reaction actually taking place. Reaction Enthalpy. There are no experimental data available that make a direct comparison between the computational results and experiment possible, but the reaction enthalpies for the following two reactions: tert-butylbenzenium cation f tert-butyl cation þ benzene or

ðIÞ

tert-butylbenzenium cation f isobutene þ benzenium ion ðIIÞ which represent possible reaction products after breaking the C1C7 bond may, indirectly, be compared to experimental results. (The difference in reaction enthalpies of reactions I and II equals the difference in proton affinities between isobutene and benzene.) This requires that the thermodynamic data, ΔfH°, for isobutene, benzene, and tert-butylbenzene as well as the proton affinities of the same compounds are available. These data exist except for the proton affinity of tert-butylbenzene. The lacuna is undoubtedly caused by the easy cleavage of this ion.

Table 3. Calculated and Experimental Proton Affinities of Some Alkylbenzenes

benzene toluene

a

PA(calc)a/

PA(exp)/

PA(exp) -

kJ mol-1

kJ mol-1

PA(calc)

746.7 781.8

750.4 784.0

3.7 2.2

ethylbenzene

786.2

788.0

1.8

isopropylbenzene

789.1

791.6

2.5

tert-butylbenzene

792.0

G3 calculations.

Hehre et al. estimated the proton affinity of tert-butylbenzene on the basis of comparisons between computed and experimental proton affinities of similar alkylbenzenes.25 Available computational resources at the time required the level of theory to be very low. Also, since that time, the absolute proton affinity scales have undergone several adjustments. It was therefore necessary to reevaluate the tert-butylbenzene proton affinity, following a similar procedure. The proton affinities of benzene, toluene, ethylbenzene, isopropylbenzene, and tertbutylbenzene have been calculated with the high-level G3 methodology (which is known to produce quite accurate proton affinities), and the computed values were compared to the accepted experimental values from the NIST webbook.26 The results are displayed in Table 3. The differences (experimental calculated) between experimental and computed proton affinities are small and cluster closely to their mean value, 2.2 kJ/mol. Because the calculated value for tert-butylbenzene is 792.0 kJ/mol, it may be concluded that PA tert-butylbenzene ¼ 2:2 þ 792:0 kJ=mol ¼ 794:2 kJ=mol is a trustworthy proton affinity. The proton affinity PA of a compound X is defined by PA X ¼ Δf H°ðXÞ þ Δf H°ðHþ Þ - Δf H°ðXHþ Þ The enthalpy of formation of any of the ions occurring in reactions I and II is therefore given by Δf H°ðXHþ Þ ¼ Δf H°ðXÞ þ Δf H°ðHþ Þ - PA X The experimental reaction enthalpies of reactions I and II can therefore be calculated from the available data. The published ΔfH° values for isobutene, benzene, and tert-butylbenzene are, in the same order, -17.9, 82.8, and -22.7 kJ/mol.26 The experimental proton affinities of isobutene and benzene are 802.1 and 750.4 kJ/mol.26 Utilizing these values and the value 794.2 kJ/mol found above for tert-butylbenzene, the reaction enthalpies for reactions I and II are: Δr H°I ¼ 79:7 kJ=mol Δr H°II ¼ 131:4 kJ=mol The corresponding theoretically derived values at 0 K are seen from Table 2 to be 81.9 and 137.5 kJ/mol. When G3 computations are carried out, enthalpies at 298 K are also obtained. They have not been tabulated here, but when they are used, the theoretical reaction enthalpies for reactions I and II at 298 K 3112


The Journal of Physical Chemistry A are 85.0 and 139.4 kJ/mol. The quite satisfactory agreement between the experimental and the computational reaction enthalpies is an indication that the computed energies of the investigated species are quite reliable. At the same time, Table 2 shows that reaction energy calculations based on B3LYP are rather inaccurate. Comparison with Earlier Computational Work. An early study of the tert-butylbenzenium system was carried out by Berthomieu et al.11 Because of the lack of sufficiently powerful computers at that time, the computations were carried out at a low level of theory, mostly with semiempirical methods. Preliminary computations on isopropylbenzenium at the HF/631G(d,p)//HF/3-21G level showed a reasonable agreement between the ab initio and the semiempirical methods. When searching for stable complexes, each of the parts in C6H6/C6H7þ or C4H9þ/C4H8 were kept with a fixed geometry, and only the relative positions of the two parts were allowed to vary. Therefore, the computations only showed that there is an attraction between the two parts in the pairs C6H7þ/C4H8 and C6H6/ C4H9þ, which turns into a repulsion at short distances. Because of the fixed geometry of the constituents, formation of tertbutylbenzenium ions could not take place. A possible formation of an alkylbenzenium ion if the geometric constraints were lifted was not investigated. Despite the computational shortcuts, there seems to be a fair qualitative agreement between their results and some of the results obtained here. A complex corresponding to A1 in this Article and several complexes of the B-type (C6H7þ/C4H8) were found. They were called R- and β-complexes. No geometry data were given, but from the figures a similarity is seen. Given the low level computational approach, the energies of both the R- and the β-complexes are surprisingly similar to the energies presented here in Table 2. Heidrich has also studied the tert-butylbenzenium ion system.19 This work was carried out at a higher level of theory, MP2/6-31þG(d,p), which was also used for geometry optimization. Some comparison with the present work regarding geometric details was given in the Results. A main point is that Heidrich found a stationary point on the potential energy surface corresponding to A1 in this Article, and a transition state between the π-electron complex and a species corresponding to bu-1h-b of this Article. The other tert-butylbenzenium ions were not looked for. In this Article, all energies are given relative to the lowest energy in the system, bu-4h-b. In Heidrich’s case, the starting point was separated benzene molecules and tert-butyl cations. The energies are therefore not directly comparable. However, if the energies of the relevant species, bu-1h-b, TS(1h-A1), and A1, are recalculated relative to the separate entities C6H6 þ C4H9þ, comparisons between the two sets of results may be given. See Table 4. It is seen from the table that there are differences, but on the whole, the lower level MP2 has produced results that line up fairly satisfactorily with the high level G3B3 and CBS-QB3 computations. Some minimum points on the PES that have been found in the present work do not appear to be minima within the MP2 methodology. It is seen from Table 2 that although the complexes A2, B1, and B2 represent clear minima on the PES within the B3LYP scheme, the PES values for the transition states are so little higher than the minimum values that the barrier may be surmounted at all temperatures. The zero point energy of the

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Table 4. Energiesa of Key Species As Given by MP2 and the Composite G3 and CBS Methods Relative to the Energy of C6H6 þ t-C4H9þ bu-1h-b

a

TS(1h-A1)

A1

Heidrich (MP2)

-58.0

-50.4

-55.9

this paper (G3)

-53.4

-43.9

-54.9

this paper (CBS)

-48.8

-43.2

-53.6

kJ mol-1.

translational vibration is higher than the potential surface barrier. The two computational methods therefore agree that there is only one stable π-electron complex in this system. It is, however, worth pointing out that because there are no forces acting on the structures A2, B1, and B2, such states are likely to persist for some time. Heidrich found that the tert-butyl cation in the complex A1 can rotate essentially freely over the benzene ring. The TS for rotating the tert-butyl cation about an axis parallel to the 6-fold benzene axis was found to have a barrier 0.2 kJ/mol, essentially the same result has been found here. Besides the structure A1, a similar structure is obtained by rotating the benzene ring moiety 30° about the 6-fold axis while keeping the C4H9þ moiety fixed. The energy of this structure is 0.05 kJ/mol higher than A1. Both structures display a vibrational frequency of less than 25 cm-1, indicating an essentially free internal rotation. In the present case, where the main objective is to study the tert-butylbenzenium system and look for possible differing outcomes depending on whether DFT-B3LYP or MP2 are used for exploring the geometries that are encountered, it is gratifying that the two methodologies agree that there is one and only one πelectron complex that may be termed a stable complex. The other minima on the PES that are found from B3LYP are so shallow that their transformations into the A1 complex proceed without barrier when the zero point vibrations are taken into consideration. Even if one, in the present case, does not find any disagreement between the two methodologies, it is felt that it still may be better to start the exploration of similar systems with a DFT-based technique. The PES appears to be more “wobbly” when studied by DFT-B3LYP than by MP2 computations and thus find more local minima. If B3LYP finds a minimum that does not have physical significance, this will be disclosed by higher level methods, whereas such states may be completely missed if the study is based on MP2. Whether these structures are of importance or not will not be an issue because they may not be discovered. This is exemplified by our previous study of the ethylbenzenium ion system where MP2 failed to find a stable ethene/benzenium ion complex.17,18 Can the A1 Complex Be Observed Experimentally? If the calculated barrier for transforming A1 into bu-1h-b (12 kJ/mol) is not a severe underestimate, the lifetime of the A1 complex may be very short unless the temperature is very low. Whether it is best formed, experimentally, from bu-4h-b via bu-1h-b or by addition of C4H9þ to benzene or by adding C4H8 to a benzenium ion is not part of this discussion. However, if a system contains a reasonable fraction of A1, it should be possible to show its presence by IR spectroscopy. The evaluation of the Hessian allows calculation of the IR spectrum. The spectral part 2500-3250 cm-1 (i.e., the CH stretching mode region) for A1, bu-4h-b, bu-1h-b, tert-butylbenzene, the benzenium ion, and the tert-butyl cation is shown 3113



Figure 15. IR spectra in the CH stretching region of the π-electron complex A1 as compared to the other species that might be present at the same time.

in Figure 15. A1 is seen to have a very intense band widely separated from the C-H vibration bands of all the other species. It should therefore be possible to monitor the presence of quite minute amounts of A1 in the tert-butylbenzenium system. The vibrational frequencies obtained from B3LYP/6-311þG(d) are known to be too high by about 3%, on average.27 The spectra in Figure 15 have not been scaled to correct this overestimation. The frequencies (wave numbers) are therefore systematically on the high side. In the experimental studies carried out by Sen Sharma et al.5 and by Cacace and Ciranni,6 tert-butyl cations were added to benzene. According to the computational results, one could also make tert-butylbenzenium ions by adding isobutene to benzenium ions. The isobutene would, without any barrier, grab the proton in the benzenium ion, forming a tert-butyl cation that might form A1, provided the excess energy could be transferred to a third species. If not, a tert-butylbenzenium ion will be formed. If the tert-butylbenzenium ion thus formed does not get rid of its excess energy fast enough, a benzene molecule and a tert-butyl cation are likely to be formed because the energy of the tertbutylbenzenium ion will be much higher than needed to split the ion into these parts. Cacace and co-workers have shown that isopropylbenzenium ions may be formed by a direct reaction between benzenium ions and propene.28 π-Complex formation was not observed.

’ CONCLUSION A computational study of the tert-butylbenzenium ion system has been performed. The structures of the various isomeric species were determined by optimizations at the B3LYP/6311þþG(d,p) level. The energies are calculated with the high level G3 (G3B3) and CBS (CBS-QB3) composite methods. There are four isomeric tert-butylbenzenium ions, depending on which carbon in butylbenzene is protonated. The structures and energies of these isomers and the barriers for their interconversion are determined. Four different stationary states on the potential energy surface, corresponding to ion/molecule π-electron complexes, have been found. The barriers for converting three of these into the fourth are, however, negligibly small (about 1 kJ/mol) as compared to the zero point energies, and after zero point energy corrections there are no barriers. Three of the complexes are thus only

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quasi-stationary states; the fourth is C6H6/t-C4H9þ complex where the tert-butyl cation is oriented essentially parallel to the benzene ring. A very similar complex has previously been predicted on the basis of MP2 computations. Comparisons on a qualitative basis between various experimental results obtained in studies on the tert-butylbenzenium ion system have been done. There is generally satisfactory agreement. The reaction enthalpy for splitting tert-butylbenzenium ions into benzene molecules and tert-butyl cations has been computed and is in good agreement with a calculation of the reaction enthalpy based on a combined series of thermodynamic measurements and proton affinities. The possibility of experimentally proving the presence of C6H6/t-C4H9þ in an experimental setup has been discussed. It is pointed out that at low temperatures the C6H6/t-C4H9þ complex may be fairly long-lived and it has an intense IR absorption at 2700-2800 cm-1, which is clearly separated from the IR bands of other species that might be present. Experimental identification should therefore be possible.

’ ASSOCIATED CONTENT

bS

Supporting Information. XYZ coordinates for the species discussed. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

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A Computational Study of tert-Butylbenzenium Ions - The Journal of

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