Theoretical Investigation of the Effects of the Zeolite Framework on the

ARTICLE pubs.acs.org/JPCC

Theoretical Investigation of the Effects of the Zeolite Framework on the Stability of Carbenium Ions Hanjun Fang,†,‡ Anmin Zheng,*,† Jun Xu,† Shenhui Li,† Yueying Chu,†,‡ Lei Chen,† and Feng Deng*,† †

State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Center for Magnetic Resonance, Wuhan Institute of Physics and Mathematics, the Chinese Academy of Sciences, Wuhan 430071, China ‡ Graduate School, the Chinese Academy of Sciences, Beijing 100049, China

bS Supporting Information ABSTRACT: Twenty carbenium ions in various zeolite models (8T HZSM-5, 72T HZSM-5, 84T HY, and 80T Hβ) are investigated by theoretical calculation methods in order to reveal the effects of the zeolite framework on the stability of carbenium ion intermediates. Most of the carbenium ions are found to be stable in these zeolite models and exist in the form of an ion pair with the zeolite conjugate bases. The carbenium ions can also be transformed into π complexes and, in some cases, into alkoxy species if the steric constraint around the CO bond is not pronounced. It is found that zeolite framework inclusion facilitates the formation of ion pairs and concurrently can increase the relative stability of ion pairs compared to π complexes and alkoxy species no matter which effect (electrostatic stabilization or steric constraint destabilization) is predominant. It is also found that bulkier carbenium ions could be accommodated well in the zeolite frameworks with larger channels or cages, and vice versa. This is relevant to the shape selectivity of zeolites. It is shown that the energy difference between the ion pair and the π complex for the carbenium ions in the three zeolite frameworks is related to the proton affinity (PA) of the corresponding neutral hydrocarbons. In general, the larger the PA value, the more negative the energy difference, and thus the higher the stability of the carbenium ion, which is consistent with the experimental observations for many carbenium ions.

1. INTRODUCTION Carbenium ions, which contain an sp2-hybridized electrondeficient carbon center, usually serve as reaction intermediates in homogeneous liquid acid-catalyzed reactions. They can be formed through various pathways, for example, protonation of alkenes, protonation of alcohols and then elimination of a water molecule, protonation of alkanes and then dehydrogenation, halide anion abstraction from alkyl halides, skeletal isomerization, or alkylation and oligomerization of other cations (see Scheme 1). However, all earlier attempts to prove the existence of long-lived carbenium ions were unsuccessful in liquid acids, such as H2SO4, HClO4, etc., and the isolation and observation of persistent carbenium ions was a triumph of superacid solution chemistry.1,2 Likewise, carbenium ions are supposed as the intermediates in heterogeneous solid acid-catalyzed reactions, such as in zeolite catalysis.38 Once a carbenium ion is formed in zeolite-catalyzed reactions, it would interact with the anionic conjugate base of a zeolite acid site through hydrogen bonding or Coulombic interactions and exist in the form of an ion pair complex913 (see Scheme 2). In principle, an individual carbenium ion could act as either a Brønsted acid because of its potential ability to release an acidic proton and form a neutral hydrocarbon or a Lewis acid due to the central positive carbon that could be r 2011 American Chemical Society

attacked by a nucleophilic reagent. As shown in Scheme 2, the transfer of an acidic proton from the carbenium ion to a basic oxygen atom of a zeolite conjugate base leads to the formation of an adsorbed neutral hydrocarbon on the acid site, that is, a π complex; meanwhile, the central positive carbon of the carbenium ion could potentially coordinate with a nucleophilic oxygen atom of the zeolite, resulting in a covalent alkoxy species. Previous theoretical and experimental results suggested that the ion pair, π complex, and alkoxy species could act as the reaction intermediates in zeolite-catalyzed reactions, and they could transform to each other.10,1217 In addition, by comparing the relative energies of the intermediate species in zeolites, the stability of carbenium ions would be evaluated. For instance, previous density functional theory calculations on an 8T cluster model of zeolite HZSM-5 suggested that the ion pair for the 1,3-dimethylcyclopentenyl carbenium ion was 2.2 and 28.4 kcal/mol lower in energy than the corresponding π complex of the neutral 1,3- dimethylcyclopentadiene and the corresponding alkoxy species, respectively.9 Thus, the 1,3-dimethylcyclopentenyl carbenium ion was predicted Received: October 11, 2010 Revised: January 25, 2011 Published: March 24, 2011 7429

dx.doi.org/10.1021/jp1097316 | J. Phys. Chem. C 2011, 115, 7429–7439

The Journal of Physical Chemistry C

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Scheme 1. Pathways for the Formation of Carbenium Ions

Scheme 2. Transformation of Carbenium Ions in Zeolites

to be more abundant than the neutral cyclic diene and the alkoxy species, which was consistent with the NMR experimental observations.9 Later, in order to reveal whether the tert-butyl carbenium ion is a true reaction intermediate in zeolite catalysis and to predict whether it could be detected by experiments, extensive theoretical studies were performed to evaluate the stability of the ion pair, π complex, and alkoxy species for this cation on zeolites H-mordenite,10 H-ferrierite,11,13 and HY12 from a thermodynamic and/or kinetic point of view. These studies indicated that the tert-butyl carbenium ion could be formed as an ion pair intermediate; however, the ion pair was generally the least stable species among the three intermediates. Indeed, this carbenium ion in zeolites has not been directly observed by means of experiments.1416,18 In a preliminary theoretical report, we found that the thermodynamic and kinetic stability of ion pairs increased with increasing acid strength of solid acids with respect to that of π complexes and alkoxy species.19 This is because the ionic species (i.e., ion pair) are more sensitive to acid strength than the covalent species (i.e., π complex and alkoxy species).19 Besides acidity of solid acid catalysts, the framework is another important characteristic for porous solid acids, such as zeolites. Structural, energetic, and electronic properties of a guest molecule confined within the framework of a zeolite may be different from those when the molecule is outside the framework.2023 Our previous study of the effects of framework size on the 31P chemical shift of absorbed trimethylphosphine oxide (TMPO, a basic probe molecule for characterizing the acidity of solid acids) showed that increasing the size of the zeolite model facilitated the transfer of the acidic proton from the acid site to the TMPO molecule and concurrently increased the 31P chemical shift.24 In addition, different zeolite frameworks may have different influences on the properties of confined molecules involved in reactions (i.e., intermediates and transition states) and then are responsible for their distinct catalytic selectivity.2528 In this work, we further investigate the effects of the zeolite framework on the relative stability of the ion pair, π complex, and alkoxy species for various carbenium ions that are relevant to zeolite catalysis. The stability of carbenium ions was evaluated from a thermodynamic point of view. First, we compared the results based on two cluster models of HZSM-5 zeolite (8T and

72T). The 8T cluster model only considered the local structure of the acid site and did not take the framework of HZSM-5 zeolite into account, whereas the 72T cluster model considered both the acid site structure and the zeolite framework, and thus, the effects of including and not including the zeolite framework on the intermediate species were revealed. We then investigated the effects of different zeolite frameworks on these intermediate species by comparing the 72T HZSM-5 results with those obtained from zeolites HY and Hβ, which were modeled by 84T and 80T cluster models, respectively. Finally, on the basis of the results from these three zeolites, we found a correlation between the relative stability of carbenium ions in zeolites and the basicity of the corresponding neutral hydrocarbons. The carbenium ions and the corresponding neutral hydrocarbons involved in this work are shown in Schemes 3 and 4, respectively. The carbenium ions include simple alkyl cations (1c3c), a styryl cation (4c), a cumyl cation (5c), cyclopentenyl cations (6c8c), indanyl cations (9c11c), benzenium cations (12c18c), and gem-dimethyl benzenium cations (19c and 20c). Most of them were supposed as the intermediates in zeolite-catalyzed reactions; however, only a few of them have been directly identified by various experimental techniques, such as solid-state NMR observations of 7c9c9,18,29,30 and 19c31 in HZSM-5; 8c,32 10c,30 and 11c30 in HY; and 20c33 in Hβ, and IR and/or UV/vis observations of 6c34 in HZSM-5 and HY and 16c18c35,36 in Hβ.

2. COMPUTATIONAL DETAILS HZSM-5, HY, and Hβ zeolites were represented by the 72T, 84T, and 80T models, respectively, which were extracted from their crystallographic data (see Figure 1).3739 The 72T HZSM5 model covers the intersection of 10-membered ring straight and zigzag pore channels with cross sections of 5.3 5.6 and 5.1 5.5 Å, respectively (Figure 1a). The 84T HY model includes two supercages connected via a 12-membered ring window with a free aperture of 7.4 7.4 Å (Figure 1b). The 80T Hβ model has a three-dimensional channel with 12-membered ring apertures with cross sections of 6.6 7.7 and 5.6 5.6 Å, respectively (Figure 1c). The acid site positions were chosen based on their accessibility to adsorbed molecules, and the 7430

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Scheme 3. Carbenium Ions Relevant to Catalysis in Zeolites

Si12O24(H)Al12, Si1O4(H)Al1, and Si6O11(H)Al4 sites were chosen for the HZSM-5, HY, and Hβ models, respectively.3739 The terminal Si atoms were saturated with H atoms, and the H atoms are positioned on the vector from the Si atom to the O atom that the H atom is replacing. All terminal SiH bond lengths were set to 1.47 Å. An 8T cluster was constructed from the 72T HZSM-5 model. It includes the local structure of the acid site but ignores the zeolite framework. The ONIOM(M06-2X/6-31G(d):AM1) level of theory was utilized for geometry optimizations, where the (SiO)3SiOH Al(OSi)3 and the hydrocarbon fragments were considered as the high layer while the rest as the low layer. M06-2X is a hybrid meta density functional theory (DFT) method developed by Zhao and Truhlar.40 This functional implicitly accounts for medium-range electron correlation and can describe dispersion interactions well with respect to traditional DFT methods (such as B3LYP)40,41 and hence has been applied in zeolite catalysis.4245 It has been demonstrated by Limtrakul et al. that the M06-2X method can accurately predict the adsorption structures and energies for hydrocarbon species within the zeolite channels.4245 For all the geometry optimizations, the activated central O3Si-OHAlO3 (10-atom QM (quantum mechanics) cluster) fragment of zeolite models and the hydrocarbon fragment were allowed to fully relax, whereas the other atoms were fixed at their crystallographic positions, and this treatment can avoid losing the unique structures of zeolites due to full optimizations. The optimizations on the 8T cluster were calculated at the M06-2X/ 6-31G(d) level.

It is demonstrated that the combinations of the MP2:M062X theoretical method can provide a good description of dispersion interactions and the energy results.42 Therefore, all the final single-point (SP) energies were obtained at the ONIOM (MP2/6-311G(d,p):M06-2X/6-31G(d)) level of theory, where the central O3SiOHAlO3 (10-atom QM cluster) and the hydrocarbon fragments were considered at the high MP2 level and the remaining fragment was treated at the DFT level. It should be mentioned that a similar 10-atom QM cluster (SiOHAl(OSi)3) was chosen in the energy calculations of HZSM-5 systems.42 Frequency calculations were performed only for the individual carbenium ions and neutral hydrocarbons, to obtain the enthalpic term for protonation affinities (PAs) of neutral hydrocarbons. All calculations were performed using the Gaussian09 software package.46

3. RESULTS AND DISCUSSION 3.1. Stability of Individual Carbenium Ions. Protonation affinity (PA) of a hydrocarbon is the energy that is released in the protonation reaction of a hydrocarbon with a single acidic proton to form the corresponding carbenium ion (Hþ þ R f HRþ).47,48 A higher PA indicates a stronger basicity of the hydrocarbon and, in turn, suggests that it is not easy for the carbenium ion to deprotonate to form the neutral hydrocarbon. As a consequence, the higher the PA of the neutral hydrocarbon, the higher the stability of the carbenium ion in the gas phase. 7431



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Scheme 4. Corresponding Neutral Hydrocarbons of Carbenium Ions in Scheme 3

We calculated the PA values of all the neutral hydrocarbons illustrated in Scheme 4 and compared our theoretical results with the available experimental data49 and some previous theoretical results at highly accurate, but time-consuming, levels35,36,50 (see Table 1). The carbenium ions shown in Scheme 3 are the most stable protonated products of the corresponding neutral hydrocarbons. When the theoretical and experimental values are compared, it can be found that the MP2/6-311G(d,p)//M062X/6-31G(d) level of theory used herein does a reasonable job for predicting the PA values of these hydrocarbons, within a deviation of 2 kcal/mol for most of the olefinic hydrocarbons and a deviation of 4 kcal/mol for the aromatic hydrocarbons. On the basis of extensive experimental attempts and with the assistance of theoretical calculations, Haw and Nicholas predicted that the carbenium ions could be persistent in zeolites if their deprotonated neutral hydrocarbons have a PA value that is more than 209 kcal/mol.50 Neutral hydrocarbons 7h11h, 19h, and 20h have a PA value more than 209 kcal/mol, and indeed the corresponding carbenium ions, 7c11c, 19c, and 20c, have been experimentally approved to be long-lived intermediates in zeolites.9,18,3033 However, it was later reported that carbenium ions 6c and 16c18c could be also persistent in zeolites, though the PA values of the neutral hydrocarbons are less than the PA limit.35,36 Therefore, it is insufficient to only employ the PA criterion for evaluating the stability of carbenium ions in zeolites, and the environments of zeolites should be taken into account. 3.2. Effects of Zeolite Frameworks on the Ion Pair, π Complex, and Alkoxy Species. 3.2.1. 8T HZSM-5 versus 72T

HZSM-5. Table 2 summarizes the results of the carbenium ions in the 8T and 72T HZSM-5 models. It is found that carbenium ions 3c, 5c11c, and 18c20c can act as stable intermediates in the form of an ion pair in the 8T model. All attempts to obtain the minimum structures for carbenium ions 1c, 2c, 4c, and 12c17c failed. They were found to be transformed into either π complexes or alkoxy species during the geometry optimizations. In the 72T HZSM-5 model, however, carbenium ions 4c and 13c17c can exist as stable ion pairs, indicating that the zeolite framework inclusion facilitates the formation of ion pair complexes. A similar stabilizing effect for ionic intermediates by the zeolite framework was also found in the benzene alkylation reaction with ethene.51 In that work, the larger 33T HZSM-5 model is able to stabilize the protonated ethylbenzene intermediate, whereas the smaller 5T and 17T models could not.51 However, ethyl (1c), isopropyl (2c), and benzenium cations (12c) still could not exist as stable intermediates even when the zeolite framework was included, in agreement with previous theoretical and experimental results that they were not stable and existed only as transition states in zeolites.10,42,5255 This is either due to the easy accessibility of the positively charged carbon of the carbenium ion by a zeolite oxygen (for 1c and 2c) or due to the strong ability of the carbenium ion to lose an acidic proton to a zeolite oxygen (for 12c). It is also found that most of the carbenium ions could be transformed into stable alkoxy species in the 8T model with the exception of the two gem-dimethyl benzenium ions (19c and 20c). The initial alkoxy species structures for these two carbenium ions 7432



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Figure 1. Zeolite models used in this work: (a) 72T (left) and 8T (right) HZSM-5 models, (b) 84T HY model, and (c) 80T Hβ model.

were found to be readily converted to ion pairs during geometry optimizations because of the remarkable steric hindrance around the CO bonds. When the surrounding framework is associated with the 72T model, this steric hindrance becomes more significant for some alkoxy species with large dimensional sizes, and it is even impossible to obtain the optimized structures of alkoxy species for the methylbenzenium ions (16c18c). With respect to energy, the ion pair, π complex, and alkoxy species for most of the carbenium ions (1c15c, and 19c) in the 72T HZSM-5 are found to be more stable than those in the 8T model. For instance, the energies of the three intermediate species for tert-butyl carbenium ion (3c) are predicted to be 9.4, 11.9, and 1.5 kcal/mol in the 8T model and become 3.2, 17.9, and 6.8 kcal/mol in the 72T model, thus decreased by 12.6, 6.0, and 5.3 kcal/mol, respectively. Figure 2 shows the optimized geometries of the ion pair, π complex, and alkoxy species for 3c in the 8T and 72T HZSM-5 models. The zeolite framework can give an additional stabilizing effect on the confined species, which is mainly derived from the long-range electrostatic and van der Waals (vdW) interactions between the zeolite framework and the hydrocarbon fragments. However, with the increase of the size of the hydrocarbon fragments, this stabilizing effect from the zeolite framework becomes less predominant and the destabilizing effect from steric constraint is increasing remarkably, such as for 16c18c and 20c. For example, the ion pair and π complex for heptamethylbenzenium (20c) in the 72T HZSM-5 model are found to be

12.3 and 30.2 kcal/mol less stable than those in the 8T model. Compared with the size of the HZSM-5 channels, these hydrocarbon fragments appear to be too bulky and suffer significant steric constraint imposed by the zeolite framework,56 which causes a strong repulsive interaction between them and eventually increases the energy of the system. For the hexamethylbenzenium ion (18c), its π complex is destabilized by 22.7 kcal/mol, whereas the corresponding ion pair is stabilized by 1.6 kcal/mol in energy in the 72T HZSM-5 model. It seems that the stabilizing or destabilizing effects imposed by the zeolite framework are different for ion pairs, π complexes, and alkoxy species. To explicitly reveal the effects of the framework on these three types of species, we calculated the difference in energy between the 72T and the 8T models, which is denoted as ΔE72T8T. As shown in Table 2, ΔE72T8T of ion pairs is always more negative than those of π complexes and alkoxy species, which means that the framework inclusion increases the relative stability of ion pairs with respect to π complexes and alkoxy species, regardless of the electrostatic stabilization effect or the steric constraint destabilization effect being predominant. In zeolites, it is mainly the negativelycharged oxygen atoms of the zeolite framework that interact with the hydrocarbon fragments. We also found that the Mulliken charges on the hydrocarbon fragments of ion pairs are generally more positive than those on π complexes and alkoxy species (see Table S1 in the Supporting Information). As a consequence, the ion pairs would be more sensitive to the zeolite 7433



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Table 1. Theoretical and Experimental Proton Affinities (kcal/mol) of the Neutral Hydrocarbons PA theorya

neutral hydrocarbon

exptlb

ethene (1h)

164.0

162.4

benzene (12h)

176.4

179.3

propene (2h)

177.7

179.6

toluene (13h)

184.0

187.4

m-xylene (14h)

190.1

193.8

isobutene (3h)

192.0

191.7

1,2,3-trimethylbenzene (15h)

192.0 (194.3c)

durene (16h) 1,3-cyclopentadiene (6h)

193.6 (195.5c) 197.1

196.4

pentamethylbenzene (17h)

200.3

203.3

styrene (4h)

201.3

200.3

hexamethylbenzene (18h)

203.4

205.7

R-methylstyrene (5h)

207.1

206.4

1-methylindene (9h)

209.7 (209.8d)

1,3,3-trimethylindene (10h)

210.9

1,3-dimethylcyclopentadiene (7h) 1-phenyl-3-methylindene (11h)

216.5 (215.6d) 216.8

1,2,3-trimethylcyclopentadiene (8h)

219.3

1,5,6,6-tetramethyl-3-methylene-cyclohexa-1,3-diene (19h)

229.4 (227.4d)

1,2,4,5,6,6-hexamethyl-3-methylene-cyclohexa-1,3-diene (20h)

233.4

a

The PA values in this work refer to the enthalpic term at 298.15 K. b Experimental data, from ref 49. c Calculated at the G3(MP2) level; see ref 36. d Calculated at the MP4/6-311þG(d)//B3LYP/TZVP level; see ref 50.

Table 2. Energies (kcal/mol) of the Ion Pair, π Complex, and Alkoxy Species Intermediates for Carbenium Ions 1c20c in the 8T and 72T HZSM-5 Models, and the Energy Difference between the Intermediates in the 72T Model and in the 8T Modela,b 8T HZSM-5 carbenium ion

ion pair

π complex

ΔE72T8T

72T HZSM-5

alkoxy species

ion pair

π complex

alkoxy species

ion pair

π complex

alkoxy species

ethyl (1c)

n

8.5

12.9

n

12.8

15.7

4.3

2.8

isopropyl (2c)

n

9.8

11.9

n

13.9

16.2

4.1

4.3

tert-butyl (3c)

9.4

11.9

1.5

3.2

17.9

6.8

methylphenyl (4c)

n

14.5

12.8

9.8

22.3

19.9

12.6

6

5.3

7.8

7.1 2.8

dimethylphenyl (5c)

3.7

15.8

2.1

11.6

20.8

4.9

15.3

5

cyclopentenyl (6c)

5.9

10.2

1.8

10.5

15.5

7.6

16.4

5.3

5.8

1,3-dimethylcyclopentenyl (7c)

5.0

11.4

1.8

26.4

21.0

9.0

21.3

9.6

7.2

1,2,3-trimethylcyclopentenyl (8c) 1-methylindanyl (9c)

8.7 1.2

13.0 11.7

4.4 5.0

31.9 16.8

20.5 18.9

2.8 0.8

23.1 18.0

7.5 7.2

1.6 5.8

3.0

10.7

11.9

15.6

16.6

4.1

18.6

5.9

7.8

3.1

16.3

3.7

12.3

16.7

4.3

9.2

0.4

8

1,3,3-trimethylindanyl (10c) 1-phenyl-3-methylindanyl (11c) benzenium (12c)

n

10.3

29.5

n

16.7

29.6

6.4

0.1

toluenium (13c)

n

12.2

28.6

7.6

19.0

25.0

6.8

3.6

9.5

1.2

m-xylenium (14c)

n

12.9

25.4

0.3

22.4

24.2

1,2,3-trimethylbenzenium (15c)

n

11.6

26.6

0.1

21.6

27.7

1,2,4,5-tetramethylbenzenium (16c) pentamethylbenzenium (17c)

n n

13.2 13.5

24.4 36.7

9.1 3.8

12.0 13.7

n n

10

8.8

11.7

32.9

7.2

11.0

n

1.6

22.7

1,2,2,3,5-pentamethylbenzenium (19c)

18.0

16.4

n

39.5

29.3

n

21.5

12.9

heptamethylbenzenium (20c)

14.5

15.7

n

2.2

14.5

n

12.3

30.2

hexamethylbenzenium (18c)

1.1

1.2 0.2

Energies of the intermediates are relative to the sum of the individual neutral hydrocarbons and the zeolite model. b The symbol “n” indicates that the intermediate could not exist as a stable minimum species on the potential energy surface. a

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Figure 2. Optimized geometries of the ion pair, π complex, and alkoxy species for the tert-butyl carbenium ion, 3c, in the 8T (ac) and 72T (df) HZSM-5 models. Some main interatomic distances (Å) are indicated.

framework. Such an effect has also been demonstrated in many previous theoretical studies.42,51,57,58 It was shown that, for zeolite-catalyzed reactions, considering the framework of zeolites (using larger zeolite models) generally leads to a decrease of the activation energies by 1030% compared with smaller zeolite models.42,51,57,58 The effect of zeolite frameworks on activation energies could be explained herein. As is well-known, transition states in these acid-catalyzed reactions are carbenium ion-like species and have more positive charges on the organic fragments than the reactants, which are usually physically adsorbed alkenes, alkanes, aromatics, alcohols, and alkoxy species. Therefore, the transition states would be more sensitive to the zeolite framework than the reactants, and their energy differences (i.e., activation energies) would decrease when the zeolite framework is taken into account. 3.2.2. 72T HZSM-5 versus 84T HY and 80T Hβ. To reveal the effects of the size of channels or cages of zeolites on the stability of carbenium ions, we also investigated the carbenium ions 1c11c in the 84T HY model and benzenium ions 12c20c in the 80T Hβ model and compared the calculated results with the available experimental observations. Compared with HZSM5 zeolite, HY and Hβ exhibit large cavities and pores. The results are summarized in Tables 3 and 4, respectively. In the 84T HY model, the formation of intermediates is similar to that in the 72T HZSM-5 model (see Tables 3 and 2). All the carbenium ions (1c11c) can form stable ion pair, π complex, and alkoxy species intermediates, with the exception of ethyl (1c) and isopropyl (2c), which cannot exist as an ion pair. This is due to the easy accessibility of the positively charged carbon of these two carbenium ion by a zeolite oxygen. With respect to energy, it can be seen that the energy of the π complex for the ethyl carbenium ion (1c) in the 84T HY model (i.e., the adsorption energy of the neutral ethene) was predicted

Table 3. Energies (kcal/mol) of the Ion Pair, π Complex, and Alkoxy Species Intermediates for Carbenium Ions 1c11c in the 84T HY Modela,b 84T HY ion pair

π complex

ethyl (1c)

n

10.8

20

isopropyl (2c)

n

14

17.9

tert-butyl (3c)

2.7

15.6

9.6

12.2 16.7

22.2 21.8

19.5 8.2

carbenium ion

methylphenyl (4c) dimethylphenyl (5c)

alkoxy species

9.5

16.9

15.5

1,3-dimethylcyclopentenyl (7c)

26.2

21.6

3.4

1,2,3-trimethylcyclopentenyl (8c)

30.3

23.8

6.1

1-methylindanyl (9c)

20

22.9

1.3

1,3,3-trimethylindanyl (10c)

18.2

22.9

3.4

1-phenyl-3-methylindanyl (11c)

27.8

22.7

10.5

cyclopentenyl (6c)

a

Energies of the intermediates are relative to the sum of the individual neutral hydrocarbons and the zeolite model. b The symbol “n” indicates that the intermediate could not exist as a stable minimum species on the potential energy surface.

to be 10.8 kcal/mol, close to the available experimental value, 9.1 kcal/mol.59 In comparison with the 72T HZSM-5 model, the bigger hydrocarbon fragments are found to be well accommodated in the 84T HY model, especially for 10c and 11c. For instance, the energies of the ion pair and π complex for the 1-phenyl-3-methylindanyl ion (11c) in the 72T HZSM-5 are predicted to be 12.3 and 16.7 kcal/mol, respectively, but decrease to 27.8 and 22.7 kcal/mol when they are trapped in the 84T HY model. Figure 3 shows the geometries of the ion pair 7435



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Table 4. Energies (kcal/mol) of the Ion Pair, π Complex, and Alkoxy Species Intermediates for Carbenium Ions 12c20c in the 80T Hβ Modela,b 80T Hβ carbenium ion

ion pair π complex alkoxy species

benzenium (12c)

n

18.0

20.3

toluenium (13c)

n

21.3

14.2

m-xylenium (14c)

0.9

24.3

11.3

2.6

26.9

11.2

1,2,4,5-tetramethylbenzenium (16c) pentamethylbenzenium (17c)

7.2 12.7

26.9 29.3

n n

hexamethylbenzenium (18c)

1,2,3-trimethylbenzenium (15c)

16.9

28.3

n

1,2,2,3,5-pentamethylbenzenium (19c) 39.3

27.9

n

41.1

27.4

n

heptamethylbenzenium (20c) a

Energies of the intermediates are relative to the sum of the individual neutral hydrocarbons and the zeolite model. b The symbol “n” indicates that the intermediate could not exist as a stable minimum species on the potential energy surface.

for 11c in the 72T HZSM-5 and 84 T HY models. It can be seen that, in the 72T HZSM-5 model, the indanyl fragment of the carbenium ion is located at the intersection of the straight and zigzag pore channels, while the phenyl-substituted group is oriented toward the direction of the zigzag channel where the 10-membered ring window (5.1 5.5 Å) is not big enough to accommodate the phenyl group. When confined in the 84 T HY model, the carbenium ion is located at the 12-membered ring window with the indanyl fragment and the phenyl-substituted group being oriented toward the two supercages, respectively. There is sufficient space to accommodate the guest hydrocarbon fragment, and thus, 11c is much more stable in the 84T HY than in the 72T HZSM-5 model. This is also in agreement with the recent results of styrene oligomerization in zeolites that the cyclic indanyl carbenium ion (11c) is formed favorably when the oligomerization reactions proceed in supercages of HY zeolite with respect to the HZSM-5 framework.60,61 However, it is found that, for the smaller tert-butyl carbenium ion (3c), the energies of the ion pair and π complex in the 84T HY model are predicted to be 2.7 and 15.6 kcal/mol, respectively, less stable (by 0.5 and 2.3 kcal/mol, respectively) than those in the 72T HZSM-5 model. Relative to the 72T HZSM-5 model, the framework of the 84T HY model is too large for the carbenium ion 3c and its corresponding neutral hydrocarbon 3h. This may result in less electrostatic attraction interactions on these confined hydrocarbon fragments, especially for the carbenium ion 3c. It has also been shown that perfect spatial constraints imposed by the zeolite framework will give the most remarkable stabilizing effect to the confined ionic species.26 In the 80T Hβ model (see Table 4), all the benzenium ions except for 12c and 13c could form a stable ion pair. The initial structures of ion pairs for benzenium and toluenium ions (12c and 13c) are found to be converted to π complexes during geometry optimization. Similar to the results obtained for the 72T HZSM-5 model, 12c14c could form stable alkoxy species in the 80T Hβ model. With respect to energy, it is clear that most of the intermediate species in the 80T Hβ model become more stable with respect to those in the 72T HZSM-5. For example, the energies of the ion pair and π complex for the hexamethylbenzenium ion (18c) in

the 72T HZSM-5 model are predicted to be 7.2 and 11.0 kcal/ mol, respectively, but significantly decreased to 16.9 and 28.3 kcal/mol in the 80T Hβ model. Figure 4 shows the optimized geometry of the ion pair for 18c in the 80T Hβ model, where it can be seen that the three-dimensional channel of zeolite Hβ is enough to accommodate the confined carbenium ion. On the basis of the results and discussion above, it could be concluded that the stability of intermediate species (especially carbenium ions) in zeolites is determined by both electrostatic and repulsive interactions between the zeolite framework and confined hydrocarbon fragments. Hydrocarbon fragments would be well fitted into the zeolite framework if the size of the hydrocarbon fragments is comparable to that of the channels or cages of the zeolites. This is also relevant to the shape selectivity of zeolites, a commonly used concept to describe how the processed intermediate molecules fit the zeolite framework.2528 Different zeolite frameworks would lead to the changes of the reaction pathway (or mechanism) for the same reactant molecule at the same reaction condition.25,27 Gemdimethyl benzenium ions (19c and 20c) are the possible intermediates of alkylation reactions of benzene (or toluene) with methanol catalyzed by zeolites.31,33 The smaller 1,2,2,3,5-pentamethylbenzenium ion (19c) has been experimentally proved to play an important role when the reaction proceeds in zeolite HZSM-5,31 whereas the larger heptamethylbenzenium ion (20c) exists as a reaction intermediate in zeolite Hβ.33 Herein, the ion pair for 19c is predicted to be much lower in energy than that for 20c when they are confined in the 72T HZSM-5 model (39.5 and 2.2 kcal/mol, respectively), and thus, the existence of 20c should be ruled out in the alkylation reactions. In the 80T Hβ model, the energy of the ion pair for 20c is predicted to be 41.1 kcal/mol, even slightly lower than that for 19c (39.3 kcal/mol). This may account for the experimental observation of 20c in zeolite Hβ.33 3.3. Stability of Carbenium Ions in Zeolites. We have compared the energies of the available ion pairs with those of π complexes and alkoxy species for all the carbenium ions in the 72T HZSM-5, 84T HY, and 80T Hβ models. Because ethyl, isopropyl, and benzenium ions (1c, 2c, and 12c) could not form stable ion pairs in these zeolite models, we will not discuss their stability. For other carbenium ions (3c11c, 13c20c), it is found that the π complexes are always more stable than the corresponding alkoxy species available (see Tables 24), and thus, the stability of the ion pairs is only compared with that of the π complexes. We calculated the energy difference between each ion pair and π complex (ΔEionπ) in the 72T HZSM-5, 84T HY, and 80T Hβ models, and correlated the ΔEionπ with the PA value of the individual neutral hydrocarbon (see Figure 5). It should been mentioned that the ΔEionπ values for 18c and 20c in the 72T HZSM-5 model are not involved due to the existence of significant steric constraints for these hydrocarbon fragments confined in the zeolite. In Figure 5, it can be seen that ΔEionπ generally decreases with the increase of PA, which indicates an increasing order of the stability of carbenium ions in the zeolites. From the thermodynamic point of view, the less the ΔEionπ, the more abundant the carbenium ion with respect to its neutral species (π complex). When taking the ΔEionπ value of 0 kcal/mol as a standard, the ΔEionπ values of 7c, 8c, 11c, 19c, and 20c are all minus (except for 11c in the 72T model), and thus, these carbenium ions would be higher in concentration than the corresponding neutral hydrocarbons. Indeed, these carbenium 7436



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Figure 3. Face views (left) and side views (right) of optimized geometries of the ion pair for the 1-phenyl-3-methylindanyl carbenium ion, 11c, in the (a) 72T HZSM-5 and (b) 84T HY models.

Figure 4. Face views (left) and side views (right) of the optimized geometry of the ion pair for the hexamethylbenzenium ion, 18c, in the 80T Hβ model.

ions have been experimentally proved to be persistent in zeolites by solid-state NMR spectroscopy, such as 1,3-dimethylcyclopentenyl (7c),9,29 1,2,3-trimethylcyclopentenyl (8c),18 and 1,2,2,3,5pentamethylbenzenium (19c)31 carbenium ions in HZSM-5; 1,2,3-trimethylcyclopentenyl (8c)32 and 1-phenyl-3-methylindanyl (11c)30 carbenium ions in HY; and the heptamethylbenzenium ion (20c)33 in Hβ. By using the same experimental approach, 1-methylindanyl (9c)30 and 1,3,3-trimethylindanyl (10c)30 carbenium ions were also confirmed to be a long-lived

intermediate in HZSM-5 and HY zeolites, respectively. Herein, the ΔEionπ value for 9c in the 72T HZSM-5 model and 10c in the 84T HY model are predicted to be 2.1 and 4.7 kcal/mol, slightly higher than the standard (0 kcal/mol). On the other hand, it is found that the ΔEionπ is much higher (more than 5 kcal/mol) for the carbenium ions 3c6c and 13c18c that indeed are transient in the reactions and have not been directly detected by solid-state NMR spectroscopy.9,14,15,18,29,30,32,55,62 Therefore, our calculated trend for the stability of various 7437



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actual effects of Lewis acid sites on the stability of carbenium ions in zeolites still need further investigations.

Figure 5. Energy difference between the ion pair and π complex for various carbenium ions (ΔEionπ, kcal/mol) as a function of the protonation affinity (PA, kcal/mol) of the corresponding neutral hydrocarbons.

carbenium ions is in a good agreement with the NMR experimental observations. Nevertheless, it has been reported that the methylbenzenium ions, such as 16c18c, could be stable in Hβ zeolite and detected by UVvis and IR spectroscopy.35,36 Meanwhile, the cyclopentenyl carbenium ion (6c) has also been demonstrated to be stable in HZSM-5 and HY zeolites by IR spectroscopy.34 Herein, the ΔEionπ values are predicted to be 19.7, 16.6, and 11.4 kcal/mol for 16c18c in the 80T Hβ model, and 5.0 and 7.4 kcal/mol for 6c in the 72T HZSM-5 and 84T HY models, respectively. Compared with the stable carbenium ions that have been observed by solid-state NMR spectroscopy, these carbenium ions are considerably higher in energy, and appear not to be persistent as long-lived intermediates in the zeolites. We suppose that the observation of these carbenium ions is, in part, due to the shorter time-scale of UVvis and IR spectroscopy in comparison with solid-state NMR spectroscopy. Sauer and co-workers have recently studied the conversion of the tert-butyl carbenium ion (4c) into neutral isobutene (4h) and alkoxy species in H-ferrierite zeolite.13 They predicted that UV/vis spectroscopy would detect this carbenium ion, though its half-life was estimated to be only 59 μs.13 In addition, the acidity of zeolites may play an additional role in stabilizing the carbenium ions. The authors in ref 35 mentioned that the co-presence of Lewis and Brønsted acid sites in dealuminated zeolite Hβ could also be responsible for the observation of the hexamethylbenzenium ion (18c).35 In our previous studies, by using 1H DQ-MAS NMR experiment and theoretical calculation, we revealed that the Lewis acid site (extraframework Al) is in proximity to Brønsted acid sites in dealuminated zeolites, which results in a synergy effect that can enhance the acid strength of Brønsted acid sites.63,64 Recently, we also theoretically demonstrated that strong Brønsted acid strength could increase the thermodynamic and kinetic stability of carbenium ions with respect to neutral hydrocarbons and alkoxy species.19 Therefore, the presence of Brønsted/Lewis acid synergy probably leads to the decrease of the ΔEionπ values and thus the increase of the stability of carbenium ions. However, the

4. CONCLUSIONS In this work, the effects of the zeolite framework on the stability of carbenium ions have been theoretically investigated. The results based on the 8T and 72T HZSM-5 models indicate that zeolite framework inclusion favors the formation of ion pairs and concurrently leads to an increase of the relative stability of ion pairs compared to π complexes and alkoxy species no matter which effect (electrostatic stabilization or steric constraint destabilization) is predominant. This may account for the reason that larger zeolite models usually lead to a decrease of activation energy in comparison with smaller zeolite models in many previous theoretical works. In comparison with the 72T HZSM-5 model, the 84T HY and 80T Hβ models exhibit a much better accommodation for bulkier hydrocarbon fragments, especially bulkier carbenium ions. Hydrocarbon fragments would be preferentially fitted into the zeolite framework if the size of the hydrocarbon fragments is comparable to that of the channels or cages of zeolites. The calculated energy difference between ion pairs and π complexes in the three zeolite frameworks is found to be correlated to the PA value of the individual neutral hydrocarbons, and this relation is in line with the experimental observations for many persistent carbenium ions in zeolites. ’ ASSOCIATED CONTENT

bS

Supporting Information. Mulliken charges on the hydrocarbon fragments of the intermediate species in the 8T and 72T HZSM-5 models and all Cartesian coordinates and absolute electronic energies of the intermediate species in this paper. This material is available free of charge via the Internet at http://pubs. acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected] (A.Z.), [email protected] (F.D.). Fax: þ86-27-87199291 (A.Z. and F.D.).

’ ACKNOWLEDGMENT We are very grateful for the support of the National Natural Science Foundation of China (21073228, 20933009, and 20773159). We also thank Shanghai Supercomputer Center (SSC) for their support in computing facilities. ’ REFERENCES (1) Olah, G. A. Angew. Chem., Int. Ed. Engl. 1995, 34, 1393. (2) Olah, G. A.; Prakash, G. K. S.; Molnar, A.; Sommer, J. Superacid Chemistry, 2nd ed.; Wiley & Sons, Inc: Hoboken, NJ, 2009. (3) Corma, A. Chem. Rev. 1995, 95, 559. (4) van Santen, R. A.; Kramer, G. J. Chem. Rev. 1995, 95, 637. (5) Haw, J. F.; Nicholas, J. B.; Xu, T.; Beck, L. W.; Ferguson, D. B. Acc. Chem. Res. 1996, 29, 259. (6) Kazansky, V. B. Catal. Today 1999, 51, 419. (7) Haw, J. F. Phys. Chem. Chem. Phys. 2002, 4, 5431. (8) Boronat, A.; Corma, A. Appl. Catal., A 2008, 336, 2. (9) Haw, J. F.; Nicholas, J. B.; Song, W. G.; Deng, F.; Wang, Z. K.; Xu, T.; Heneghan, C. S. J. Am. Chem. Soc. 2000, 122, 4763. 7438


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Theoretical Investigation of the Effects of the Zeolite Framework on the

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