Influence of Acid Strength and Confinement Effect on the Ethylene

Article pubs.acs.org/JPCC

Influence of Acid Strength and Confinement Effect on the Ethylene Dimerization Reaction over Solid Acid Catalysts: A Theoretical Calculation Study Yueying Chu,†,‡ Bing Han,†,‡ Anmin Zheng,*,† and Feng Deng*,† †

Wuhan Center for Magnetic Resonance, State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, the Chinese Academy of Sciences, Wuhan 430071, China ‡ Graduate School, the Chinese Academy of Sciences, Beijing 100049, China ABSTRACT: The influence of both Brønsted acid strength and pore confinement effect on the ethylene dimerization reaction has been systematically studied by density functional theory (DFT) calculations. In the theoretical calculations, both stepwise and concerted reaction mechanisms are considered. It is demonstrated that the reactivity of the ethylene dimerization reaction can be significantly enhanced by increasing acid strength no matter which mechanism is included, while on the basis of activated barriers, the concerted mechanism is preferred on weak acids and two mechanisms are competitive when the acid strength increases to a medium−strong acid. Due to the pore confinement effect that can effectively stabilize the ionic transition states of the dimerization reaction, the activity of the dimerization reaction is considerably improved inside the zeolite pore. Compared with the reaction on the isolated acid sites, the transition states of the stepwise reaction are more effectively stabilized than those of the concerted reaction inside the zeolite confined pore, resulting in the former reaction being preferred when the dimerization reaction occurs inside the zeolite confinement spaces. Additionally, on the basis of the systematic investigations on the alkene dimerization reactions over zeolites with varying pore sizes (such as ZSM22, ZSM-5, and SSZ-13), it is demonstrated that ZSM-22 and ZSM-5 zeolites are effective catalysts for the ethylene dimerization.

1. INTRODUCTION Dimerization of lower alkenes to form higher hydrocarbons is one of the available routes for the production of high octane number gasoline and has attracted much attention from experimental and theoretical aspects.1 Apart from these applications in the industrial processes, alkene dimerization is also an important reaction from a fundamental viewpoint. For example, in methanol-to-olefin (MTO) conversion, alkene dimerization is an elementary reaction for the formation of active species (cocatalytic hydrocarbon pool) on zeolite catalysts.2,3 Recently, many studies have been carried out on the alkenes dimerization catalyzed by solid acids using experimental and theoretical approaches.4−9 Spoto et al. investigated the dimerization reaction of ethylene and propene on zeolite HZSM-5 by fast FT-IR spectroscopy,6 and they inferred that the dimerization reaction proceeds through two elementary steps (stepwise reaction): (1) protonation of the adsorbed alkene to form surface ethoxide, and (2) CC bond formation between the alkoxide species and the second alkene (as depicted in Scheme 1a). In addition to the stepwise reaction, a concerted route in which protonation of the ethylene CC bond and new CC bond formation occur simultaneously was also proposed for the alkene dimerization reaction (see Scheme 1b). Svelle et al. theoretically explored the alkene dimerizations through the two different mechanisms over zeolite modeled by a 4T cluster (which only represents the local active structure of solid acid site).8 On the basis of the © 2012 American Chemical Society

calculated activated barriers, it was indicative that the concerted reaction was predominant in the dimerization reaction. Namuangruk et al. also investigated ethylene dimerization by using an extended 84T faujasite zeolite model.9 On such an extended model, the activated barrier (30.06 kcal/mol) of the rate-determination step of the stepwise mechanism was much lower than that (38.08 kcal/mol) of the concerted mechanism. Therefore, it is demonstrated that the stepwise route was preferred for ethylene dimerization over zeolite catalysts. By comparing the theoretical models used in previous works, it can be seen that the 84T model adopted by Namuangruk et al. included the pore structure of the zeolite, while 4T models in Svelle’s work only contained the local active structure of Brønsted acid sites.8 It is well-known that the zeolite framework has a strong effect on the adsorption state, reaction mechanism, and reactivity of the hydrocarbon transformation.10−12 Thus, the difference in the previous studies8,9 is probably caused by the pore confinement effect imposed by the zeolite framework. As one kind of the most important solid catalysts, the zeolite catalysts own different pore structures with varying shapes and sizes that could influence the reaction in different ways.13 Therefore, it is necessary to systematically investigate the relationships between the dimerization reaction activity and the Received: March 28, 2012 Revised: May 14, 2012 Published: May 24, 2012 12687

dx.doi.org/10.1021/jp302960w | J. Phys. Chem. C 2012, 116, 12687−12695

The Journal of Physical Chemistry C

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Scheme 1. Ethylene Dimerization Reaction Mechanismsa

concerted reactions (see Scheme 1), we have studied both of them to demonstrate which one is the preferred pathway with varying acid strength. Meanwhile, in order to reveal the confinement effect of the zeolites with different pores sizes on the reaction mechanism, three types of zeolites (ZSM-22, ZSM5, and SSZ-13) were employed in this study.

2. COMPUTATIONAL METHODS It was demonstrated that the Brønsted acidity could be mimicked by tuning the terminal SiH bonds of zeolite models in theoretical calculation.21−28 In this work, we used an 8T HZSM-5 cluster model with different peripheral SiH bond lengths to represent a series of isolated acid sites with different acid strengths. In the calculations, the 8T model was cut out of the crystallographic structure of the HZSM-5 zeolite,29 and the Al12O24HSi12 site was used to represent the Brønsted acid site (Figure 1). All terminal

a

(a) Stepwise mechanism; (b) concerted mechanism.

zeolite pore in order to find the proper pore structure for effective dimerization of ethylene. On the other hand, the influence of acidity on alkene dimerizations has also been extensively explored by experimental methods. Dutta et al.4 have investigated the oligomerization of ethylene on various solid acids with different acid strengths, such as HZSM-5, Ni-SAPO-5, HPW/HZSM-5, NiSO4/ZSM-5, NiSO4/γ-Al2O3, and KPW (potassium salt of tungstophosphoric acid). They found that the conversion was remarkably improved on the strong HPW/HZSM-5 acid catalyst. A similar trend was also observed by Sohn et al. who investigated the dimerization reactions on a series of metal oxide catalysts with different acid strength.14−18 Based on the experimental results, it was revealed that the reactivity of the dimerization reaction increased with the increase of acid strength. However, it is not clear whether a quantitative relationship between acid strength and reaction activity is present. With regard to the acid strength−activity relationship, experimental data usually afford a qualitative result and are unable to offer the detailed interpretation of the origin of catalytic reactivity. As the supplementary means of experimental approach, theoretical calculation can offer an atomiclevel description of a complete reaction mechanism, including the structures and energies of the adsorption state and the transition state (TS).19,20 Moreover, the reaction rate constants also can be derived through the transition-state theory (TST) calculation, which can be compared with experimental results directly. Although theoretical calculations have been carried out on the alkenes dimerization catalyzed by zeolite catalysts with medium acid strength,8,9 the relationship between acid strength and reaction activity in the whole acid strength range (from weak, medium−strong, and strong to superacid) is still lacking. In this work, taking the acid strength and the confinement effect of solid acid catalysts into account, the mechanism and the reactivity of ethylene dimerization on Brønsted acid sites were theoretically investigated. Since two different mechanisms are involved in the dimerization reaction, namely, stepwise and

Figure 1. Representations of ZSM5, SSZ-13, and ZSM-22 framework structures by 72T, 74T, and 66T cluster models and the 8T ZSM-5 cluster model. The 8T cluster in the extended cluster models represented as ball and stick view was treated as the high-layer atoms during the ONIOM calculations.

hydrogen atoms in the cluster were defined to be located at a distance rSiH away from the corresponding silicons during calculations, so that each SiH bond is oriented along the direction toward the neighboring oxygen atom. As such, Brønsted acid sites with different acidic strengths can readily be represented by varying the rSiH value in the 8T cluster model. The calculations were performed using B3LYP hybrid density function with 6-31G(d, p) basis sets. The boundary SiH3 groups of the cluster model were fixed, while other atoms of the acid site model and the organic fragment were allowed to relax during the structure optimizations. In the calculation, the activated barrier (Eact) is calculated as the single-point energy difference between the absorption complex and transition state 12688



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upon increasing rSiH from 1.30 to 2.50 Å, the DPE value of the isolated Brønsted acid sites decreases gradually from 309.28 to 251.64 kcal/mol, covering the typical solid Brønsted acid strengths from weak (rSiH = 1.30−1.47 Å), medium−strong (rSiH = 1.75 Å), and strong (rSiH = 2.00−2.25 Å) to superacid (rSiH = 2.50 Å).25,38,39 In the following, we will use these models to investigate the influence of acid strength on alkene dimerization with two different mechanisms. 3.2. Influence of Acid Strength on the Reactivity of Ethylene Dimerization. 3.2.1. Stepwise Mechanism. For the stepwise mechanism, as depicted in Scheme 1a, one ethylene molecule is initially adsorbed on the Brønsted acid site, and then, an ethoxide species is formed through a carbenium ion TS. Subsequently, another ethylene molecule interacts with the ethoxide intermediate to generate butoxide. Figures 2 and 3 illustrate the transition-state structures for the dimerization reaction catalyzed by Brønsted acid sites with strengths varying from weak to strong to superacid. When the first step (step 1) of the reaction occurs under a weak acid strength (such as the acid strength of HZSM-5; DPE = 300.17 kcal/mol; rSiH = 1.47 Å), the double bond of C1C2 is elongated to 1.396 Å in the transition state (TS1, Figure 2b) from 1.330 Å in the gas state, indicating that the C1C2 double bond is nearly converted into a single bond. Moreover, the acidic proton H1 is partially transferred to the C1 atom of ethylene, which is evidenced by the O1H1 (1.419 Å) and C1H1 (1.251 Å) distances. Simultaneously, the C2 atom of ethylene is moving closer to the O2 atom of the cluster model (rC2O2 = 2.205 Å), leading to the formation of a C2O2 bond (or ethoxide). Further progress of the stepwise mechanism (step 2) leads to the formation of butoxide. In this step, the C2 atom of ethoxide approaches the C3C4 double bond of another ethylene, and a new CC bond is formed. The relevant transition states (TS2) of this step are displayed in Figure 3. It is observed that the C2H5+ fragment moves far away from the acid site with the C2O2 distance stretching to 2.411 Å in the transition state. Simultaneously, a new CC bond will be formed with a C2···C3 length of 2.341 Å (Figure 3b). As shown in Table 2, the acid strength can affect the structures of the transition states (TS1 and TS2). For example, in the protonation reaction of ethylene (TS1), the stretching degree of the double bond decreases gradually (rC1C2 from 1.396 to 1.388 Å), and the distance between the C2 and the O2 atoms is getting longer and longer (rC2O2 from 2.166 to 2.496 Å) with increasing the acid strength from weak to strong to superacid (see Table 2 and Figure 2). In TS2, increasing acid strength will result in a decrease of the O2···C2 distance (ethoxide complex) from 2.451 to 2.175, and the distance between C2 (ethoxide) and C3 (alkene) is elongated from 2.295 and 2.611 Å (see Table 2 and Figure 3). Figure 4 depicts the energy profile of ethylene dimerization catalyzed by Brønsted acid sites with varying acid strengths, and the corresponding activated barriers (Eact1, Eact2) are listed in Table 2. The activated barriers are 21.04 and 29.12 kcal/mol for TS1 and TS2 steps under the acid strength of HZSM-5 (DPE = 300.17 kcal/mol; rSiH = 1.47 Å). As listed in Table 2, both of the activated barriers reduce significantly with the increase of acid strength. As the acid strength increases from weak (DPE = 309.28 kcal/mol; rSiH = 1.30 Å) to medium−strong (DPE = 284.14 kcal/mol; rSiH = 1.75 Å) to strong (DPE = 271.04 kcal/mol; rSiH = 2.00 Å) to superacid (DPE = 251.64 kcal/ mol; rSiH = 2.50 Å), Eact1 decreases from 21.49 to 19.35 to 17.29 to 12.62 kcal/mol, respectively, while Eact2 decreases from

of the guest−host (alkene−zeolite) systems, that is, Eact = ETS − Eads. It is well-known that the confinement effect from the zeolite pores should have significant effect on the reaction pathways;9 therefore, it is necessary to theoretically investigate the dimerization mechanisms confined inside the zeolites with varying pore sizes. Foster and co-workers have demonstrated the diameter Di (Å) of the maximum included sphere in a zeolite framework could estimate the zeolite pore volume (pore volume = 4/3π (Di/2)3) more exactly.30,31 Based on their results, the SSZ-13, ZSM-5, and ZSM-22 zeolites possess varying Di values that are 7.31, 6.30, and 5.65 Å respectively. Herein, we used the extended 74T, 72T, and 66T models to represent the SSZ-13, ZSM-5, and ZSM-22 zeolite structures to explore the pore confinement effect of the zeolite frameworks (see Figure 1). In the theoretical calculations for the extended zeolite model, the terminal SiH was fixed at a bond length of 1.47 Å, oriented along the direction of the corresponding SiO bond. The combined theoretical model, namely, ONIOM (B3LYP/631G(d,p):MNDO) was applied to predict the geometries of various adsorption structures and transition states. To preserve the integrity of the zeolite structure during the structure optimizations, only the (SiO)3SiOHAl(SiO)3 active center and ethylene molecule in the high-level layer were relaxed while the rest of atoms were fixed at their crystallographic locations. Then, the single-point energy calculations were further refined at the level of B3LYP/6-31G(d,p). Furthermore, the single-point energies at the level of B97D/ 6-31G(d,p) Grimme’s functional that includes dispersion interaction were also calculated.32,33 The frequency calculations were performed at the same level as geometry optimizations to check whether the stationary points found exhibited the proper number of negative frequencies. Only one negative frequency would be observed for transition-state points and none for minima. All the geometry optimizations and frequency calculations were performed using the Gaussian 09 package.34

3. RESULTS AND DISCUSSION 3.1. Acid Model. For a Brønsted acid site, deprotonation energy (DPE) is a criterion to measure the intrinsic acid strength of solid acid catalysts.35−37 It is defined as the energy required to remove the acidic proton from the acid site to form an anionic conjugate base (AH → H+ + A−), and a smaller DPE value corresponds to a stronger acidity. As shown in Table 1, Table 1. Deprotonation Energy (DPE, kcal/mol), Mulliken Charge for H1 (|e|), and Main Geometry Parameters (Bond Length, Å; Angle, deg) of Isolated Brønsted Acid Site Models with Terminal SiH Bond Lengths Increasing from 1.30 to 2.50 Å energy

a

geometry parametersa

charge

rSiH

DPE

QH1

rO1H1

rAlO1

rSiO1

1.30 1.47 1.75 2.00 2.25 2.50

309.28 300.17 284.14 271.04 260.27 251.64

0.385 0.388 0.393 0.397 0.400 0.402

0.969 0.969 0.970 0.971 0.971 0.972

1.832 1.833 1.835 1.837 1.839 1.841

1.662 1.662 1.663 1.664 1.667 1.669

130.16 130.35 130.52 130.38 129.77 128.79

Labeled atoms, see Figure 1. 12689



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Figure 2. Optimized geometries of the transition state (TS1) for the first step of stepwise ethylene dimerization on Brønsted acid site models with terminal SiH bond length rSiH: (a) 1.30; (b) 1.47; (c) 1.75; (d) 2.00; (e) 2.25; (f) 2.50 Å. Selected interatomic distances (in Å) are indicated.

Figure 3. Optimized geometries of the transition state (TS2) for the second step of stepwise ethylene dimerization on Brønsted acid site models with terminal SiH bond length rSiH: (a) 1.30; (b) 1.47; (c) 1.75; (d) 2.00; (e) 2.25; (f) 2.50 Å. Selected interatomic distances (in Å) are indicated.

Table 2. Activated Barriers (kcal/mol) and the Transition-State Main Geometrical Parameters (Å) of the Ethylene Dimerization through the Stepwise Mechanism on the Brønsted Acid Site Models with Terminal SiH Bond Distances from 1.30 to 2.50 Å activated barrier

geometry parameters (TS1)

geometry parameters (TS2)

rSiH

Eact1

Eact2

rO1H1

rC1H1

rC1C2

rC2O2

rO2C2

rC2C3

rC2C4

rC3C4

rO1C4

1.30 1.47 1.75 2.00 2.25 2.50

21.49 21.04 19.35 17.29 15.05 12.62

33.31 29.12 22.31 17.45 14.09 11.99

1.386 1.419 1.475 1.521 1.548 1.541

1.266 1.251 1.231 1.219 1.218 1.231

1.396 1.396 1.396 1.395 1.393 1.388

2.166 2.205 2.273 2.339 2.405 2.496

2.451 2.411 2.334 2.260 2.205 2.175

2.295 2.341 2.433 2.522 2.584 2.611

2.256 2.311 2.422 2.538 2.622 2.671

1.353 1.351 1.349 1.346 1.345 1.344

3.829 3.899 4.094 4.294 4.446 4.557

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bond and the formation of the CC bond occur simultaneously, producing the butoxide product without formation of the ethoxide intermediate. One ethylene is physisorbed onto the acid site to give a weak π adsorption complex, and the second ethylene molecule is weakly coadsorbed onto the π complex, and then, through a carbonium transition state (TS), butoxide is produced. By taking the HZSM-5 model (DPE = 300.17 kcal/mol; rSiH = 1.47 Å) as an example, the distances of the acidic proton (H1) to the oxygen site (O1) and the carbon atom (C1) of ethylene are 1.533 and 1.198 Å in the TS (see Figure 5b), which suggests that the acidic H1 has partially transferred to the carbon atom (C1) of the π adsorption ethylene complex. The C2 atom is attached by the π electrons of the second ethylene with bond lengths of rC2C3 = 2.651 and rC2C4 = 2.717 Å, which will result in the formation of a new CC bond. The double bonds of the two ethylene are stretched to 1.403 Å (C1C2) and 1.346 Å (C3C4) from 1.330 Å in the gas, respectively. Similar to the stepwise mechanism, the acid strength also affects the transition-state structures of the concerted mechanism. For instance, with the increasing of the acid strength, the bridging O1H bond distance gradually decreases from 1.541 Å (DPE = 309.28 kcal/mol) to 1.499 Å (DPE = 251.64 kcal/mol), and the lengths of the double bonds C1C2/C3C4 reduce from 1.405/1.347 to 1.386/1.338 Å. Figure 6 depicts the energy profile of the reaction, and the corresponding activated barriers (Eact) are shown in Table 3. The calculated activated barrier over HZSM-5 is 27.09 kcal/ mol (DPE = 300.17 kcal/mol), which is similar to that (30.35 kcal/mol) reported by Svelle et al.8 Similar to the stepwise reaction, the reactivity can also be improved with increasing the acid strength in the concerted mechanism, which is confirmed by the calculated activated barriers. As shown in Table 3, with the increase of acid strength from weak (DPE = 309.28 kcal/ mol) to superacid (DPE = 251.64 kcal/mol), the activated barrier is decreased by 17.45 kcal/mol.

Figure 4. Energy profiles for the stepwise mechanism of ethylene dimerization reaction on Brønsted acid site models with the terminal SiH bond distance varying from 1.30 to 2.50 Å.

33.31 to 22.31 to 17.45 to 11.99 kcal/mol, respectively. Obviously, in the range of acid strength from weak to medium−strong acid, Eact2 is much larger than Eact1. Therefore, the formation of the CC bond (TS2) is the rate-controlling step for the dimerization reaction. Compared with TS1, the activated barrier of TS2 decreases more sharply, and the corresponding d(Eact)/d(DPE) slopes are 0.154 and 0.385 for TS1 and TS2, respectively. Since Eact2 is more sensitive to acid strength, Eact2 is gradually close to Eact1 with a difference less than 1 kcal/mol (see Table 2) in the range of acid strength from strong to superacid. It is likely that the two reaction steps are competitive without one of them being the ratedetermination step in this acid strength range. 3.2.2. Concerted Mechanism. As shown in Scheme 1b, for the concerted pathway, the protonation of the CC double

Figure 5. Optimized geometries of the transition state (TS) for the concerted mechanism of ethylene dimerization on Brønsted acid site models with terminal SiH bond length rSiH: (a) 1.30; (b) 1.47; (c) 1.75; (d) 2.00; (e) 2.25; (f) 2.50 Å. Selected interatomic distances (in Å) are indicated. 12691



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electrostatic stabilizations and nano-size space limitations.40 The experimental and calculational results have revealed the electrostatic interactions and pore confinements of the zeolite can stabilize cationic species more effectively, which usually results in different reaction mechanisms inside the zeolite pore structure.21,41−46 In order to explore the zeolite confinement effect on the reaction mechanism and the catalytic reactivity of the ethylene dimerization reaction, the dimerization reaction pathways were investigated on an extended 72T HZSM-5 zeolite model (see Figure 1). Figure 7 displays the corresponding optimized local structures for the stepwise reaction based on the 72T model. In the protonation step, the C1C2 bond length elongates from 1.337 Å in the adsorption state (see Figure 7a) to 1.376 Å in the TS1 transition state (see Figure 7b), and the C1H1 distance is shortened to 1.303 Å. In the CC bond formation step, compared with the corresponding adsorbed structure, the C3C4 double bond and the C2O2 length are stretched by 0.014 and 0.696 Å (see Figure 7d, e). As shown in Table 4, the activated barriers calculated for the stepwise reaction are 19.62 and 17.96 kcal/mol, respectively. Compared with the simple 8T bare model, the activated barriers are diminished by 1.42 and 11.16 kcal/mol for TS1 and TS2, respectively, which suggests that, by adopting the 72T zeolite cluster model (i.e., by taking confinement effect provoked by the zeolite framework into account) during calculations, the carbonium ion TS tends to be effectively stabilized thus leading to more reliable TS structures, predicted parameters, and Eact values. This phenomenon was also found for the propene protonation and alkane hydrogen activation reactions11,47 that possess lower activated barriers in the 72T model due to the long-range electrostatic effects provoked by the zeolite framework. It is noteworthy that the activated barrier of step 2 (TS2) decreases much more than that of step 1 (TS1) on the extended 72T model. This can be explained by the charge properties of the organic fragment in the transition-state structure. Based on the 72T model calculations, TS2 possesses more ionic character than TS1, and their net charges of the organic fragments are 0.79 |e| and 0.69 |e|, respectively. It has been demonstrated by our previous investigation that the zeolite framework could increase the relative stability of the ion pair or the species holding more net charge.21 Thus, according to the calculated net charges of organic fragments, the stability of TS2 (0.79 |e|) is more sensitive to the pore of the zeolite. Furthermore, the size of the organic fragments may be another factor that results in the difference. As depicted in Figure 7, TS2 (5.80 × 4.08 × 4.01 Å3) can fit well into the 10 MR channel structure (Di = 6.30 Å) of HZSM-5 zeolite while TS1 (4.30 × 3.40 × 2.95 Å3) is too small for the zeolite pore size. Thus, the synergetic effect from both the electrostatic interaction and the pore confinement dictates the more sharp decrease of Eact2 on the 72T model. The concerted mechanism on the 72T model is also theoretically considered. Similar to the stepwise reaction, the zeolite confinement effect plays an important role in stabilizing the TS in the concerted reaction. In this case, the activated barrier of the dimerization reaction decreases from 27.09 on the 8T model (rSiH = 1.47 Å) to 22.70 kcal/mol on the extended 72T model. It have been revealed in the above section that the CC bond formation (step 2, TS2) is the rate-determination step on the 8T model (rSiH = 1.47 Å; Eact1 = 21.04 kcal/mol; Eact2 = 29.12 kcal/mol) for the stepwise reaction. However, because of

Figure 6. Energy profiles for the concerted mechanism of the ethylene dimerization reaction on the Brønsted acid site models with terminal SiH bond distance from 1.30 to 2.50 Å.

Table 3. Activated Barriers (kcal/mol) and the TransitionState Main Geometrical Parameters (Å) of the Transition States for the Ethylene Dimerization through the Concerted Mechanism on the Brønsted Acid Site Models with Terminal SiH Bond Distances from 1.30 to 2.50 Å activated barrier

geometry parameters (TS)

rSiH

Eact

rO1H1

rC1H1

rC1C2

rC2C3

rC3C4

rO1C4

1.30 1.47 1.75 2.00 2.25 2.50

29.88 27.09 22.31 18.19 14.95 12.43

1.541 1.533 1.522 1.510 1.506 1.499

1.194 1.198 1.208 1.219 1.229 1.241

1.405 1.403 1.398 1.393 1.389 1.386

2.605 2.651 2.778 2.894 3.027 3.220

1.347 1.346 1.344 1.342 1.340 1.338

3.710 3.733 3.842 3.905 3.948 4.163

One aim of this study is to determine which (stepwise or concerted mechanism) is the preferred mechanism for the dimerization reaction on solid acid catalysts. Since the reaction reactivity is controlled by the activated barriers for each mechanism, the activated barriers are used to determine which pathway is favored in the dimerization reaction. As shown in Tables 2 and 3, in the weak acid range (DPE = 309.28 kcal/mol and DPE = 300.17 kcal/mol), the activated barriers for the ratedetermination step of the stepwise mechanism (Eact2 = 33.31 kcal/mol and Eact2 = 29.12 kcal/mol) are much higher than those of the concerted mechanism (Eact = 29.88 kcal/mol and Eact = 27.09 kcal/mol), indicating the concerted mechanism prevails. This is consistent with Svelle’s work on the 4T zeolite model.8 However, as the acid strength increases to medium− strong acid strength (DPE = 284.14 kcal/mol), the activated barriers of the rate-determination steps of the two mechanisms become identical (22.31 kcal/mol), suggesting that the two reaction pathways are competitive on the medium−strong acid. After further increasing the acid strength to strong and superacid, the activated barriers of the two mechanisms are also similar with a difference less than 1 kcal/mol, implying that the two reaction pathways are probably competitive as well. 3.3. Influence of Confinement Effect on the Reactivity of Ethylene Dimerization Catalyzed by Zeolites. It is wellknown that the zeolite provides a unique environment for the transformation of hydrocarbon compounds that includes 12692



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Figure 7. Local optimized structures for the stepwise reaction on the 72T ZSM-5 model: (a) ethylene adsorption complex; (b) protonation transition state; (c) ethoxide intermediate; (d) the second ethylene adsorbed on the ethoxide; (e) CC bond formation transition state; (f) butoxide product. Selected interatomic distances (in Å) are indicated.

sizes on the dimerization reaction in detail, the dimerization reaction mechanisms confined inside three zeolites (SSZ-13, ZSM-5, and ZSM-22) with varying pore sizes are investigated. It was demonstrated by Limtrakul’s works that the weak dispersion interactions between adsorbed molecules and the zeolite framework play an important role in the reactions inside the zeolite pore structures.9,48−50 Compared to the conventional DFT functional, the B97D method can provide an accurate and reliable calculation for the dispersion energies, and it has been extensively used to theoretically predict the energy parameters of molecules and reactions confined inside zeolite.12,51,52 On the basis of the calculations at B97D level, Corma et al. have explained the origin of the active sites in zeolite mordenite that can effectively catalyze the methanol carbonylation reaction.51 The calculated activated barriers by the B97D method are 16.36 and 13.60 kcal/mol and 16.96 kcal/mol for the stepwise and concerted mechanisms, respectively, for ZSM-5 zeolite (see Table 4). For comparison, the corresponding values obtained by the B3LYP method are 19.62 and 17.96 kcal/mol and 22.70 kcal/mol. Obviously, inclusion of the noncovalent interaction results in a decrease of the activated barriers by approximately 2−8 kcal/mol for the ethylene dimerization over the three zeolites (see Table 4). In the following, we will discuss the influence of pore size on the ethylene dimerization reaction based on the energy data calculated by the B97D functional. The pore size of the three zeolites follows the order SSZ-13 (Di = 7.31 Å) > ZSM-5 (Di = 6.30 Å) > ZSM-22 (Di = 5.65 Å).30,31 If the dimerization reaction follows the stepwise mechanism, as shown in Table 4, the calculated activated barriers at the B97D level are 18.10 and 16.36 kcal/mol, 16.36 and 13.60 kcal/mol, and 13.58 and 15.30 kcal/mol for TS1 and TS2 inside SSZ-13, ZSM-5, and ZSM-22, respectively. The corresponding activated barriers at the B97D level are 18.56, 16.96, and 17.82 kcal/mol for the concerted mechanism inside the three zeolites. Obviously, the activated barriers of the

Table 4. Activated Barriers (kcal/mol) for the Ethylene Dimerization through the Stepwise and Concerted Mechanisms on SSZ-13, ZSM-5, and ZSM-22 Zeolite by B3LYP and B97D Functionals stepwise

concerted

zeolite

Di (Å)

method

Eact1

Eact2

Eact

SSZ-13

7.31

ZSM-5

6.30

ZSM-22

5.65

B3LYP B97D B3LYP B97D B3LYP B97D

20.45 18.10 19.62 16.36 16.17 13.58

21.81 16.36 17.96 13.60 19.10 15.30

26.48 18.56 22.70 16.96 24.90 17.82

the zeolite confinement effect, the stability of TS2 (17.96 kcal/ mol) is considerably enhanced with respect to TS1 (step 1, 19.62 kcal/mol). Thus, in contrast to the reactions on the isolated acid sites, step 1 is the rate-determination step inside the HZSM-5 pore structure. Furthermore, due to the stabilizing effect of the zeolite confinement pore, the dominant mechanism is also altered. For the 8T bare model (rSiH = 1.47 Å), the concerted mechanism is preferred. However, when the pore structure of the zeolite is considered in the calculations, the stepwise mechanism is predominant in the dimerization reaction as the activated barrier of the stepwise mechanism (Eact1 = 19.62 kcal/mol for rate-determination step) is lower than that of the concerted reaction (Eact = 22.70 kcal/mol). On the basis of the calculational results, it is demonstrated that the zeolite confinement pore cannot only affect the stabilities of the transition states but also the reaction pathway of the dimerization reaction. Therefore, the different reaction mechanisms were obtained on isolated acid sites and acid sites confined inside the zeolite pores.8,9 3.4. Influence of Pore Size on the Reactivity of Ethylene Dimerization. In order to reveal the effects of pore 12693



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Figure 8. Pore confinement effect of zeolites on the transition state (TS2) of CC bond formation for the stepwise reaction.

mol). Compared with the larger cage of SSZ-13, the perfect-fit pore structure of ZSM-5 (Di = 6.30 Å) provides an ideal electrostatic stabilization of TS2, resulting in a lower activated barrier (13.60 kcal/mol). However, for ZSM-22, the inadequate volume (Di = 5.65 Å) makes TS2 suffer from strong repulsive interactions imposed from the zeolite framework. As a result, the corresponding activated barriers Eact2 increases in the small channel of ZSM-22 (15.30 kcal/mol). As shown in Table 4, for the stepwise reaction, the activated barriers of the rate-determination step predicted on ZSM-5 (16.36 kcal/mol) and ZSM-22 (15.30 kcal/mol) are lower than that on SSZ-13 (18.10 kcal/mol), indicating that the dimerization reaction can be more effectively catalyzed by the zeolites with relative small pore sizes. As mentioned above, the pore structures of ZSM-22 and ZSM-5 are well-fit for transition states TS1 and TS2, respectively, resulting in lower activated barriers and higher activities of the dimerization reaction on these two zeolites. For the concerted mechanism, due to the well fit of the transition state (TS, ca. 5.68 × 4.74 × 3.70 Å3) inside the ZSM5 pores (Di = 6.30 Å), the activated barrier is the lowest (16.96 kcal/mol, see Table 4) among the three zeolites. Therefore, the activated barrier data demonstrate that the dimerization reaction could be most effectively catalyzed by the ZSM-5 zeolite if it follows the concerted mechanism.

stepwise mechanism are always smaller than those of the concerted mechanism for the zeolites. This indicates that the stepwise mechanism is predominant for the ethylene dimerization reaction inside the zeolite pores, being consistent with the dimerization reaction inside the HY zeolite reported by Limtrakul et al.9 It has been demonstrated by our previous works that intermediates and transition states can be effectively stabilized if the size of the hydrocarbon fragments is comparable to the pore size of the zeolites.21 The activated barriers have revealed that the stepwise reaction is predominant in the dimerization. Thus, in the following, the influence of the pore sizes on the stepwise reaction is discussed in detail. The estimated dimensions of TS1 and TS2 are approximately 4.30 × 3.40 × 2.95 Å3 and 5.80 × 4.08 × 4.01 Å3, respectively. Compared with the pore sizes of SSZ-13 (Di = 7.31 Å), ZSM-5 (Di = 6.30 Å), and ZSM-22 (Di = 5.65 Å), the dimension of TS1 is smaller than the pore size of the three zeolites. Therefore, TS1 should be most stabilized inside a zeolite with the smallest pore size. As shown in Table 4, the activated barrier of TS1 decreases from 18.10 kcal/mol for SSZ-13 to 16.36 kcal/mol for ZSM-5 to 13.58 kcal/mol for ZSM-22. In the ZSM-22 zeolite with the smallest pore size, the electrostatic interaction becomes predominant, and the stabilizing effect from the zeolite framework becomes pronounced. Compared with SSZ-13, ZSM-5, and ZSM-22, the large supercage (Di = 11.18 Å) of the HY zeolite cannot effectively stabilize the transition state, resulting in a large activated barrier (30.6 kcal/mol) for the protonation step.9 For the CC bond formation step that is associated with TS2, the activated barrier Eact2 decreases from 16.36 kcal/mol for SSZ-13 (Di = 7.31 Å) to 13.60 kcal/mol for ZSM-5 (Di = 6.30 Å). However, as the pore size further decreases to Di = 5.65 Å (ZSM-22), it is noteworthy that Eact2 does not decrease but increases to 15.30 kcal/mol. Our previous work has demonstrated that the stability of the transition state in the zeolites was determined by both electrostatic and repulsive interactions between the zeolite pores and confined hydrocarbon fragments. When the guest molecule is larger than the pore size of the zeolite, the stabilizing effect from the zeolite framework would become less predominant, and the destabilizing effect from steric constraint will increase remarkably.21 Figure 8 shows the confinement effect of the zeolite pores on TS2. The estimated dimension of TS2 is approximately 5.80 × 4.08 × 4.01 Å3. For the SSZ-13 zeolite, its cage (Di = 7.31 Å) is too big to provide an effective electrostatic stabilization, leading to a higher activated barrier (16.36 kcal/

4. CONCLUSION Our theoretical calculation results demonstrate that the acidic property and pore confinement of solid acid catalysts are two main factors that affect the dimerization reaction mechanism and catalytic activity. On the basis of the calculational activated barriers, it is revealed that the reactivity of dimerization can be increased by increasing the acid strength no matter which mechanism is considered. It is noteworthy that the reaction mechanisms are governed by the acid strengths of catalysts. As such, the concerted mechanism is favored on weak acids. However, as the acid strength increases to medium−strong acids, the two mechanisms become competitive. On the other hand, the calculational results also demonstrate that the zeolite pore can effectively stabilize the ionic transition state; the reactivity of the dimerization reaction occurring inside the zeolite pore is significantly enhanced relative to the reactions on the isolated acid sites. On the basis of the systematic investigations on the zeolites with varying pore sizes, it has revealed that ZSM-22 and ZSM-5 are effective catalysts for the ethylene dimerization reactions as their pore sizes are well-fit for the dimension of the transition states that are 12694



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effectively stabilized by the zeolite framework. The present results might provide a theoretical guide for the design, modification, and application of solid acid catalysts in the petrochemical industry.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (A.Z.); [email protected] (F.D.). Fax: +86-27-87199291 (A.Z.); +86-27-87199291 (F.D.) Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (21173255, 21073228, 20933009, and 20921004). The authors are grateful to Shanghai Supercomputer Center (SSC, China) for their support in computing facilities.

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Influence of Acid Strength and Confinement Effect on the Ethylene

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