Brønsted Acid Catalyzed Cyclization of C7 and C8 ... - ACS Publications

J. Phys. Chem. C 2008, 112, 12825–12833

12825

Brønsted Acid Catalyzed Cyclization of C7 and C8 Dienes in HZSM-5: A Hybrid QM/MM Study and Comparison with C6 Diene Cyclization Yogesh V. Joshi and Kendall T. Thomson* School of Chemical Engineering, Purdue UniVersity, West Lafayette, Indiana 47907 ReceiVed: December 25, 2007; ReVised Manuscript ReceiVed: June 4, 2008

We extend our previous work (Joshi, Y. V.; Thomson, K. T. J. Catal. 2005, 230, 440) on H-ZSM-5 catalyzed cyclization of C6 diene using hybrid QM/MM method by studying cyclization of C7 and C8 dienes by 1,6 ring closing mechanism at the B3LYP/6-31g(d,p):UFF hybrid ONIOM method. We find the activation barrier for C7 or C8 diene cyclization starting from secondary chemisorbed alkoxide is lower compared to that for C6 diene. This is expected according to carbenium chemistry rules, which marks secondary carbenium transition state of C7 or C8 diene more stable compared to the primary carbocationic transition state for C6 diene. The energy difference between the bare cluster (BC) and embedded cluster (EC) calculations clearly point out the shape selective exclusion of the C8+ chemisorbed alkoxides. Thus, calculated energetics evidence the C7 cyclic product as the primary product of cyclization for light alkane aromatization reaction and explains the dominance of toluene in the aromatics distribution. 1. Introduction Aromatics are the important products of the refineries and serve as the feedstock for the most of the chemical industry. Aromatics such as benzene, toluene and xylenes are in top 20 chemicals produced in the world. Currently, catalytic reformate and the pyrolysis gasoline are the important sources of aromatics for chemical process industry. However, demand for a particular aromatic component keeps changing rapidly due to the changing regulations limiting the use of aromatics in these gasoline blends. Hydrodealkylation and toluene disproportionation are the industrial processes used to control the distribution of the aromatics from a production point of view. Light alkane aromatization1 is the process by which alkanes such as ethane, propane and butane are converted into value added and easy to transport aromatics. The absence of the acyclic alkenes1 in the aromatic products make the process economically attractive as the separation costs are minimal. MFI (ZSM-5) based zeolites are the preferred catalysts for the light alkane aromatization process due to their shape selectivity and lower deactivation rates. It is well-known that initial dehydrogenation (activation) of the light alkane is the rate limiting step for aromatization.1–3 In the absence of the extraframework metals, the initial activation is mainly catalyzed by Brønsted acid sites. This reaction is less selective which brings down the overall selectivity. Hence additional dehydrogenation activity in the form of extraframework metals is needed to improve this catalyst. Ga4,5 and Pt are such metals which promote the activity and selectivity of propane aromatization. However, these metal exchanged catalysts suffer from major drawback of faster deactivation due to coking. Understanding aromatization is vital for enhancing the knowledge about coking via formation of multinuclear heavy aromatics. The aromatization reaction chemistry is extremely complicated6 as it involves complex reaction networks with different gas phase and surface intermediates. The reaction network consists of various reaction families such as (1) alkane activation * To whom correspondence should be addressed. Phone: (765) 496-6706. Fax: (765) 494-0805. E-mail: [email protected].

and dehydrogenation, (2) chemisorption of the alkene, (3) oligomerization and beta scission, (4) isomerization, (5) hydride transfer, (6) cracking, (7) disproportionation, (8) cyclization, and (9) dehydrogenative aromatization. As any intermediate along the reaction pathway can serve as the reactant or product for different reaction families, the reaction network is highly interconnected. Experimentally, it is very difficult to study thermodynamics or kinetics of any particular reaction by decoupling it from rest of the reaction network. Current experimental understanding is based on the experiments done at conditions involving lower pressures, temperatures and higher space velocity. Some of these reaction steps are derived from the knowledge based on the super acid catalyzed solution based chemistry due to the apparent super acidity of H-[Al]ZSM-5 on the Hammett acidity scale. Overall aromatics selectivity, as well as the distribution of the aromatics (B/T/X ratio), are important criteria in determining the performance of the catalyst. Hence understanding how this distribution is controlled by the kinetics, as well as thermodynamics, is critical to improve and to control the catalysts performance for the aromatization reaction. In a complex reaction network, the concentrations of the products or reactants or any intermediates are mainly influenced by the entry or exit points for that particular species in the reaction network. These entry or exit points represent the primary transformations. Transalkylation is one such reaction family which will directly influence the BTX distribution. In the absence of diffusion barriers, or at higher residence times, the distribution is driven toward equilibrium. For propane aromatization using HZSM-5 (823 K and 56% conversion), the product consists of BTX in 25:45:25 proportions. The rest of the 5% is represented by C9+ aromatics. Although toluene clearly dominates the product distribution, it is not clear how far from equilibrium this product distribution is. We also note that at 800 °K, the calculated7,8 aromatics distribution for toluene disproportionation is 32:41:23 for BTX. The similarity between these two product distributions suggests the possibility of toluene as the primary product of aromatization. In the presence of the additional dehydrogenation function in the form of the extraframework

10.1021/jp712071k CCC: $40.75  2008 American Chemical Society Published on Web 07/31/2008

12826 J. Phys. Chem. C, Vol. 112, No. 33, 2008 Ga, initial product distribution is dominated by benzene.9 Thus a possible role of the kinetics in determining aromatics distribution can not be denied. Cyclization is one such reaction which could play an important role in governing aromatics distribution. There have been very few experimental investigations aimed at studying the cyclization reactions catalyzed by solid catalysts. Based on the role of the catalyst, cyclization reactions can be classified in to three categories. (1) Cyclization in the presence of metal oxides like Ga2O3 or ZnO2.10–14 (2) Cyclization catalyzed by the supported noble metals like Pt on Al2O3, Pt-HZSM-5.12 (3) Cyclization catalyzed by Brønsted acid sites in the zeolite. Considering strong acidity of the Brønsted acid sites in the zeolite, a mechanism based on carbenium ion chemistry has been suggested. Experimental investigations involving model reactants12,15–17 have concluded that (i) dienes or trienes are the precursor for cyclization, (ii) napthenes like cyclohexane are unlikely to be the intermediates for cyclization on monofunctional Brønsted acid zeolites, and (iii) ring closure to cyclic olefins is irreversible. These studies concluded that ring closure is less activated than other important reactions like dehydrogenation and cracking. In the gas phase the diene molecules undergo thermal rearrangements such as Cope and Claisen rearrangement via a cyclic radical-cation transition state. A recent publication18 regarding the Cope rearrangement inside the zeolite channels reports the stabilization of the radical-cation intermediate even at room temperatures. Unsaturated alkenes can undergo Diels-Alder [4 + 2] cycloaddition to form cyclohexene with reported energy barrier of 27.5 kcal/mol. A triene can undergo gas phase pericyclic reaction to form cylohexadiene. The activation barrier for this cyclization reaction was found19 to be 30 kcal/mol. Although these reactions are suspected to be taking place in the zeolite cavities, the activation barriers are higher compared to the Brønsted acid catalyzed cyclization.20 As a result, they should play a minor role in overall cyclization activity of the HZSM-5 catalyst under propane aromatization conditions. The complexity of the propane aromatization reaction mechanism6 necessitates the use of theoretical molecular modeling methods to study individual reaction steps.20–23 We started our investigation of cyclization mechanism by studying several gas phase reaction pathway.22 Our investigations lead us to three different reaction pathways for cyclization of the carbenium ion. We found that the cyclization of the protonated hexadiene follows the rules of the carbenium ion chemistry so that the classical 1,5 ring closure and ring expansion represents the least activated pathway for gas phase cyclization. We also found that 1,6 ring closure is feasible and should be investigated as a alternate mechanism. We used these gas phase cyclization results as a starting point for the Brønsted acid catalyzed cyclization using hybrid QM/MM method. For C6 diene, we found20 that the 1,6 ring closure has lower activation barrier than the 1,5 ring closure. This observation was mainly reasoned by the larger charge separation caused by the higher steric hindrance faced by the secondary carbon. The main goal of this study is to investigate the dependence of the cyclization reaction energetics on the length and structure of the hydrocarbon molecule. This will aid in better understanding of the B/T/X distribution in the aromatization products. We want to use the calculated energetic parameters for kinetic modeling of the propane aromatization using ZSM-5. In this contribution we extend our previous work of C6 cyclization by studying the 1,6 ring closure of C7 and C8 dienes. For this investigation we used a hybrid molecular modeling method (QM/MM) which combines the accuracy of electronic density functional theory with the speed of molecular mechanics. The

Joshi and Thomson

Figure 1. Zeolite clusters for T12 Brønsted Acid site (I) from MFI framework, (a) Bare Cluster (BC) with 11 T sites; (b) Embedded Cluster (EC) with total 138 T sites.

rest of this paper is organized as follows. In section 2, we present the details of our calculations. In the same section we have pointed out the specific approximations made while using hybrid methods and our efforts to overcome the inaccuracies. In section 3, we discuss the currents results regarding the 1,6 ring closure. In the same section we have drawn comparison between energetics for the C6, C7 and C8 diene. We summarize important conclusions of the paper in the section 4. 2. Details of the Calculations 2.1. Cluster Model. In the ZSM-5 crystal structure (MFI framework) there are 12 symmetrically nonequivalent tetrahedral framework positions known as T-sites. An isoelectronic substitution of the framework Si by Al- requires the charge compensating extraframework cations. These extraframework cations serve as active catalytic sites for several reactions. The catalytic sites located in the cross section of the two intersecting channels are easily accessible for larger reactant molecules. As intersection provides sufficiently large space for the molecular transformations, it is believed that the catalytic sites in the intersection are more active. Hence we have selected T12 site as the site to study cyclization as it is located right at the intersection between two channels. Electronic structure calculation of a large MFI unit cell is computationally prohibitive and hence we have resorted to a cluster approximation. For modeling large hydrocarbon molecules such as C8 dienes, we need a sufficiently large cluster to justify any sort of shape selectivity. Such a large cluster would be impractical for the intended level of theory. To overcome this problem we employ embedded cluster models.24,25 As a result, most of the calculations were performed with two types of clusters (structure I in Figure 1). One of the two clusters (Figure 1a) is built around the T12 site of ZSM-5,26 with a total of 11 T sites in the cluster. From this point onward, we will refer to this 11 T cluster as the bare cluster (BC). The 11 T bare cluster is terminated using Si-H groups with Si-H bond length of 1.4979 Å. Si and H from terminal groups are maintained at fixed Cartesian positions throughout rest of the calculations. The second cluster represents an embedded cluster (EC) model. It consists of two layers as shown in the Figure 1b. The

Brønsted Acid Catalyzed Cyclization of C7 and C8 Dienes innermost layer, called ‘model geometry’, consists of the 11 T sites and hydrocarbon species treated with more accurate level of theory. These 11 T sites are the same T-sites from the bare cluster calculations. The outer layer consists of 127 T sites located symmetrically around inner 11 T cluster. Thus, in total, the embedded cluster (EC) consists of 138 T sites. This cluster represents the complete intersection of the straight channel and sinusoidal channel, which is important in order to account for the shape selective effects of the zeolite cavities. This large cluster is classically termed as the ‘real geometry’. The outer layer of the embedded cluster is terminated with Si-H bonds with Si-H distance fixed at 1.47 Å. Hence forward the embedded cluster results are referred by ‘EC’ and bare cluster results are referred by ‘BC’. 2.2. Theory Details. The embedding scheme used for the hybrid method is a two layer ONIOM27 method. It is a simple extrapolation scheme which makes use of two levels of theories, namely high level and low level. We have employed density functional theory as the high level of theory. The density functional consists of Becke three parameter28 hybrid exchange functional, with the Lee, Yang and Parr correlation functional29 termed as B3LYP. The basis set used for higher level theory is a 6-31g(d,p) double-ζ basis set.30 With the focus of the study being the activity of the catalytic site, the contribution of the BSSE to the reaction energies and activation barriers is expected to be very small. Molecular mechanics using the universal force field (UFF)31 was employed as a lower level theory. The UFF atom types for Si, O, Al were specified as Si3, O_3_z, Al3, respectively. It is well-known that for Brønsted acid catalyzed reactions in the zeolite pores, the transition states are cationic in nature.32,33 In such situations electrostatic interactions due to the zeolite cavity are important34 to ensure the accuracy of the calculations. At the same time recent studies35,36 have shown that the stabilization of the reaction intermediates (especially more cationic transition states) occurs due to short-range electrostatic interactions which polarize the C-H bonds in the hydrocarbon. Hence a large cluster37 will be sufficient to calculate the energetics accurately. Embedded cluster approximation allows us to overcome the inability of DFT in accounting stabilization due to dispersion forces. It also enabled us to account for any kind of shape selectivity for cyclization reactions inside zeolite pores. However, for the current investigation we have not considered the explicit charge embedding but rather implicit. We have justified our approach in our previous publication20 on cyclization of the C6 diene. Our preliminary investigation indicated that the implicit charge embedding, by which point charges are considered in the lower level of theory (molecular mechanics MM), did not lower the activation barrier for all the carbocationic transition states. We found20 that the energetics is very sensitive to the choice of the point charges and without rigorously defined point charges, the calculated energetics would be less reliable. The charge equilibration method (QEq), proposed by Rappe et al.,38 is a popular method for calculating the point charges for the given molecular geometry. The QEq charges parametrically depend on the geometry of the molecule and hence most of the molecular modeling packages calculate the charges based on the initial geometry. During the subsequent geometry optimization, these charges are kept fixed, so that the force minimization and the energy minimization are consistent. Because of this, if the molecular geometry changes by a large extent during optimization, the final geometry may not be consistent with the charges based on the initial geometry.

J. Phys. Chem. C, Vol. 112, No. 33, 2008 12827 For calculations presented here, we have devised a modified implicit charge embedding scheme. Under this scheme we take a converged geometry of the QM/MM calculation without charge embedding. Then we calculate the QEq charges for real and model structure of the catalyst site. For the subsequent QM/ MM geometry optimizations, we use these charges for the MM level calculations of energy and gradients by including additional Coulombic term. We have calculated and compared the cyclization energetics using all three methods, namely, a) QM using DFT; b) QM/MM (DFT/UFF) without charge embedding; and c) QM/MM (DFT/UFF) with implicit charge embedding. This comparison is reported at the end of the result section. The most of the reported energetics is calculated using first two methods. All of our calculations were done using the Gaussian03 software package.39 To carry out our modified charge embedding scheme, we used the external keyword to run separate MM level calculations. For both, the stable intermediates and the transition states, default convergence criteria of 0.00063 Å for average displacement and 0.35 kcal/Å for average gradient were employed. This convergence criterion is very stringent in the light of the assumptions and approximations involved in the cluster calculations. However, it ensures the reproducibility and reliability for future extensions and comparisons. During the normal-mode analysis, the constraint on the terminal Si and H atoms can result into the imaginary frequencies (negative force constants). For all the reaction intermediates, the absence of the imaginary frequencies was ensured after removing the contributions from the fixed atoms to the Hessian matrix.40,41 All the transition state geometries show single imaginary frequency corresponding to the eigenvector along the reaction path. This allowed us to do consistent thermochemical analysis of all the reaction paths. A transition state is assumed to represent the true reaction path only if these relaxations result into the right reactant and product geometries. 2.3. Thermochemistry. During normal-mode analysis, we find all positive force constants for the regular minima and all but one positive force constants for the transition states. For thermochemical analysis the frequencies were used without any scaling to account for anharmonicity. A zeolite cluster represents the extended zeolite lattice with practically infinite mass42 compared to the gas phase molecule (A) the rotational and translational partition function of the transition state (TS) and active site (Z) will cancel each other. The resulting rate constant has units of per second per site. Thus the expression for the rate constant reduces to

( )( )( )

† kBT QTS k) h QAQZ

Vib

1 QA

rot

1 (QA ⁄ V)

e-∆E0⁄RT

(1)

trans

with assumptions

(QTS)rot ) (QZ)rot ) 1and(QTS ⁄ V)trans ) (QZ ⁄ V)trans ) 1 (2) For the intermediates involving zeolite site (Z or TS), the contributions of the rotational and translational terms belonging to internal energy (E) are not considered while calculating H. Similarly, rotational and translational terms of entropy (S) are neglected while calculating the entropy. By assuming same partition function for intermediates Z and TS, these contributions cancel each other while taking the difference between transition state and reactant. For gas phase species (adsorbates) all terms have been accounted. These considerations ensure accurate thermochemical analysis for catalytic site located in the infinite zeolite lattice.

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SCHEME 1: Various Acyclic Reactants and Corresponding Cyclized Products Part of Current and Previous Investigation20a

Figure 2. Reaction path for 1,6 ring closure of 1,5-heptadiene (C7 diene). II - Bent conformer of physisorbed diene; III - Bent conformer of chemisorbed diene on Si03-O20-Al12; TS1 - Transition state for ring closure; IV - Methylcyclohexene carbenium ion; TS2 - Transition state for conformation adjustment; V - Chemisorbed methylcyclohexene on Si11-O11-Al12; VI - Physisorbed methylcyclohexene on Si12HO24-Al12.

a

Numbering done to indicate C1-C6 carbon atoms involved in the ring closure. It is not the numbering according to IUPAC nomenclature. The askterisks represent the location of the carbocation center.

3. Results and Discussions 3.1. Reactants and Products of Cyclization. In our study of cyclization, we have considered different diene molecules. All the diene molecules and their cyclized products (alkylcyclohexene) are listed in Scheme 1. We have considered only one isomer of C6 and C7 diene. For C8 diene, we have considered two isomers. The first isomer is a linear C8 diene and the other is a branched diene. A branched diene was considered to see the possible shape selective effect on the activation barrier. All these molecules show extremely large variation in terms of number of conformers. This variation is further compounded by the various adsorption geometries. These conformers can be broadly classified as linear or bent conformers for both physisorbed and chemisorbed intermediates. We focus our efforts on the bent conformers as they are the likely reactants for actual ring closure. Transformation of the linear conformers to bent ones can be achieved through simple dihedral rotations. For each reactant, we have calculated physisorbed intermediates on the Brønsted acid site. These physisorbed dienes interact with the Brønsted proton via π-electron of the CdC double bond. Physisorbed alkenes undergo chemisorption as the CdC bond is protonated. Chemisorption of short and long hydrocarbons has been extensively studied21 and will not be discussed further. To compare the energetics of the bare cluster calculation (QM) and embedded cluster calculations, we shift the energetics of the bare cluster calculation by a fixed amount so that energies of the physisorbed complex from both methods coincide. Thus, physisorbed intermediates serve as the reference to compare reaction energetics. For C7 diene, we shift the energetics for bare cluster calculations by -25.4 kcal/mol. For linear C8 diene (2,6-octadiene or octa-1,5-diene) and branched C8 diene (5-

methylhepta-1,5-diene) the shifts in the energetics are -30.3 and -19.6 kcal/mol, respectively. To study 1,6 ring closure energetics, we start with the chemisorbed acyclic alkoxides. In Scheme 1, the carbon involved in the alkoxide formation is indicated by an “asterisk”. The position of the double bond is variable as different diene isomers can form same alkoxide intermediate and vice versa. During actual reaction, the position of the double bond is highly mobile. The six carbon members of the hydrocarbon are numbered in reactant and products of 1,6 ring closure. We like to point out that the devised numbering scheme is independent of the IUPAC recommended numbering scheme (not shown in Scheme 1). 3.2. 1,6 Cyclization of C7 Diene. Our investigation of C7 diene cyclization is particularly focused on modeling a secondary alkoxide undergoing 1,6 ring closure. This reaction is different compared to 1,6 ring closure of the C6 diene, which involves primary alkoxide as a reactant. In Figure 2, we have shown the energetics of cyclization for both bare cluster (BC) and embedded cluster (EC) calculations. The physisorption energy of the C7 diene for the embedded cluster is in line with the experimental estimations. The physisorbed C7 diene interacts with the Brønsted acid site via π-bonding. The sp2 carbon atoms are located at 2.53 Å from Brønsted protons. In the BC model same distance is 2.19 Å. The van der Waal’s stabilization of the physisorbed intermediate is evidently driving force for the additional separation in case of the embedded cluster model This effect is popularly noted as curvature effect or cavity effect in the zeolite catalysis. For EC model, the bent physisorbed intermediate is oriented along the sinusoidal channel of the ZSM-5. Although physisorbed intermediates are aligned (reaction intermediate II in Figure 2) on the potential energy surface, there is a significant difference between the energies of the chemisorbed intermediates (III in Figure 2) for the two levels of calculations. The chemisorbed intermediate for the embedded cluster calculation is significantly less stable than that for the bare cluster calculation. The embedded cluster and bare cluster geometries of the chemisorbed intermediates are shown in Figure

Brønsted Acid Catalyzed Cyclization of C7 and C8 Dienes

J. Phys. Chem. C, Vol. 112, No. 33, 2008 12829 TABLE 1: Important Geometry and Charge Parameters for Chemisorbed 1,5-Heptadiene (III), TS for Cyclization (TS1) and Chemisorbed Cyclohexene (V) III a

TS1

O20/24-C1/5 1.555 (1.544) 2.453 (2.418) (Å) C1-C6 (Å) 4.168 (3.832) 3.238 (3.137) 0.351 (0.344) 0.393 (0.377) charge on C1b charge on C5b 0.067 (0.075) 0.086 (0.089) Charge on C6b -0.044 (-0.055) -0.031 (-0.030) total HC charge 0.490 (0.475) 0.775 (0.764) img. freq (cm-1) -118.2 (-134.8)

V 1.530 (1.546) 1.530 (1.552) 0.036 (0.038) 0.291 (0.294) 0.072 (0.065) 0.462 (0.466)

a Geometry parameters after ‘/’ represent structure V. b Mulliken charges of bonded hydrogens summed into carbon charge. Bracketed quantities represent bare cluster calculations and the ones without brackets represent embedded cluster calculations.

Figure 3. Reaction intermediates for cyclization of 1,5-heptadiene (C7 diene). (a) and (b) chemisorbed secondary alkoxide at Si03-O20-Al12; (c) and (d) TS for 1,6 ring closure; (e) chemisorbed methylcyclohexene at Si11-O11-Al12 for bare cluster.

3 as (a) and (b), respectively. For the EC and BC chemisorbed intermediate the C1-C6 distance is 4.17 and 3.83 Å, respectively. The larger C1-C6 distance for the EC model indicates that the chemisorbed species is oriented in cavity without any repulsion from the channel walls. Starting from the physisorbed species, the chemisorption reaction is endothermic. The endothermicity of this transformation is larger for the embedded cluster (EC 12.4 kcal/mol) compared to that for bare cluster (BC 6.2 kcal/mol). For previously reported20 cyclization of the C6 diene, this difference is smaller (EC 4.5 kcal/mol and BC 1.1 kcal/mol). It suggests that for larger hydrocarbon molecules such as C7 diene, a major fraction is in the physisorbed state. The rest of the chemisorbed intermediates represent the activated intermediates, which undergo chemical transformations. It also suggests that the embedded cluster representation of the active site is necessary to account for the shape selective exclusion or activation of the reaction intermediates. We think the moderate endothermicity of the transformation from the physisorbed intermediate to chemisorbed intermediate will be helpful in terms of overall reactivity. This expectation is in line with the Sabatier principle according to which very strong adsorption or very weak adsorption of reactant species will represent the less optimum reaction path. During the cyclization reaction, the electron deficient alkoxide carbon (secondary) is attacked by the nucleophilic terminal carbon (primary) from CdC. The reaction coordinate is defined by the decreasing C1-C6 distance and increasing O20-C1 distance (shown in Figure 3). The carbenium center moves from C1 to the C5 carbon. The activation barrier for actual 1,6-ring closure for the C7 diene is much lower than the corresponding barrier for C6 diene. For the bare cluster calculation the energy barrier for C7 diene is 9.8 kcal/mol compared to 16.9 kcal/mol for the C6 diene. A similar trend exists for the embedded cluster calculations where the activation energy compares as 7.8 kcal/ mol for the C7 diene versus 15.5 kcal/mol for the C6 diene. Thus, the overall activation barrier for C7 diene cyclization is

much lower compared to C6 diene. The primary reason for this difference is the secondary nature of the carbenium transition state. For the C7 diene, cyclization starts with the secondary alkoxide versus the primary alkoxide for C6 diene. The geometry of the chemisorbed alkoxide, TS for cyclization and the representative cyclic product is shown in the Figure 3. In Table 1, we report important geometry and charge parameters for the intermediates along the reaction path of 1,6 cyclization of the C7 diene. With a total Mulliken charge of 0.775, the transition state is clearly more cationic compared to the alkoxide like reactants or products. In the transition state geometry (Figure 3c and d) the secondary carbon (C1) positions itself between the bridging oxygen (Si03-O20-Al12) and terminal carbon. For the EC transition state the C1-C6 distance (3.23 Å) is intermediate between the chemisorbed reactant (4.17 Å) and cyclic product (1.53 Å). The imaginary freq for the transition state is small indicating a weak curvature of the reaction path. Such lower curvature is expected as the cyclization reaction path involves mostly dihedral adjustment and transition state is located in early part of the reaction path. During ring closure the C1 carbon undergoes umbrella inversion with simultaneous scission of alkoxide bond and formation of the C-C bond on the opposite side. In case of 1,6 ring closure of C6 diene the cyclic product rotates and readsorbes at Si12-O24-Al12 bridge position. While for C7 diene, the carbenium center (C5) of the cyclic product (intermediate IV in Figure 2) in proximity of the Si11-O11-Al12 bridging oxygen. However, further chemisorption is not spontaneous or downhill. After 1,6-ring closure the cyclic product undergoes a further conformational adjustment step so that it is adsorbed as a cyclic alkoxide. This conformation adjustment faces a very small activation barrier of 3.9 kcal/ mol (1.6 kcal/mol for BC). For the bare cluster the resulting product (Figure 3e) is the chemisorbed methylcyclohexene at O11 bridge positions. The corresponding species for the embedded cluster calculation is not stable, as steric repulsion destabilizes the chemisorbed species and causes it to deprotonate. The resulting 3-methylcyclohexene is physisorbed on the Brønsted acid site at the Al12-O24-Si12 bridge position. We report the energies of the physisorbed species VI in Figure 2. If we neglect the conformational adjustment after the ring closure, the barrier for the reverse reaction (staring from chemisorbed methylcyclohexene V in Figure 2) is 25.9 kcal/ mol. The exothermicity of this reaction suggests that cyclization is irreversible. The difference between the embedded cluster and bare cluster calculations suggest a large steric repulsion for the chemisorbed species compared to physisorbed species. From the reported energetics, we can conclude that the steric

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Figure 4. Reaction path for 1,6 ring closure of 2,6-octadiene (linear C8 diene). VII - Physisorbed bent conformer; VIII - Bent conformer of chemisorbed diene on Si03-O20-Al12, TS3 - Transition state for cyclization; IX - Dimethylcyclohexilium carbenium ion; TS4 - Transition state for conformation adjustment; X - Chemisorbed dimethylcyclohexene on Si11-O11-Al12; XI - Physisorbed dimethylcyclohexene on Si03-HO20-Al12.

repulsion is more for the cyclic reaction intermediate compared to the acyclic or linear reaction intermediate. 3.3. 1,6 Cyclization of C8 Dienes. As pointed out in the previous section, our cyclization study includes two types of C8 dienessa linear diene and a branched diene. For the linear diene, energetics is shown in Figure 4. The physisorption energy of the linear C8 diene (intermediate VII in Figure 4) is better represented by the embedded cluster model (EC), which was found out to be 37.1 kcal/mol. The bare cluster model calculation resulted in significantly lower physisorption energy of 6.9 kcal/ mol, as it fails to capture the stabilization due to van der Waal’s attractive forces. To compare the bare cluster model and the embedded cluster model, the reaction energetics for the bare cluster (BC) is shifted by -30.3 kcal/mol so that the energies for the physisorbed complexes coincide. In the π-complex the CdC is located at 2.19 Å and 2.4 Å for BC and EC models, respectively. Similar to C7 diene, the larger Brønsted acid and sp2 carbon separation in case of EC is driven by the curvature effect. The linear C8 diene is also aligned along the sinusoidal channel. The bent conformer of the C8 diene perfectly fits in the cross-section of the sinusoidal and straight channel. For linear C8 diene, the transformation from physisorbed diene to chemisorbed alkoxide (VI f VIII in Figure 4) is endothermic. For the embedded cluster calculation, the reaction energy is 13.4 kcal/mol (BC 6.4 kcal/mol). This suggests that, in general, for large linear dienes the chemisorbed species face more steric repulsion compared to the physisorbed species. The difference in the endothermicity of embedded cluster (EC) versus bare cluster (BC) calculation suggests that for the chemisorbed linear diene, a large part of the steric repulsion originates from the rest of the zeolite cavity represented by the molecular mechanics. As in case of C7 diene, here also we discuss the cyclization reaction starting with the bent conformer of the chemisorbed diene. The geometries of the reactant, transition state and product of the cyclization are shown in Figure 5. The C1-C6 distance for the chemisorbed intermediate in the BC and EC models are 3.97 and 4.19 Å, respectively. This observation is similar to the chemisorbed C7 diene. For C8 diene, the unadsorbed end of the hydrocarbon molecule is located in the intersection of

Figure 5. Reaction intermediates for cyclization of 2,6-octadiene (Linear C8 diene). (a) and (b) chemisorbed secondary alkoxide at Si03-O20-Al12; (c) and (d) TS for 1,6 ring closure; (e) Stable protonated dimethylcyclohexene; (f) Chemisorbed dimethylcyclohexene at Si11-O11-Al12 for bare cluster.

TABLE 2: Important Geometry and Charge Parameters for Chemisorbed 2,6-Octadiene (VIII), TS for Cyclization (TS3) and Chemisorbed Dimethylcyclohexene (X) VIII

TS3

O20/11-C1/5a (Å) 1.565 (1.547) 2.549 (2.372) C1-C6 (Å) 4.186 (3.972) 3.671 (3.230) charge on C1b 0.350 (0.345) 0.395 (0.356) charge on C5b 0.035 (0.032) 0.036 (0.037) charge on C6b -0.004 (-0.001) 0.011 (0.014) total HC charge 0.471 (0.481) 0.793 (0.762) img. Freq (cm-1) -80.6 (-134.2)

X 3.044c (1.624) 1.545 (1.544) 0.047 (0.083) 0.308 (0.279) 0.021 (0.018) 0.766c (0.459)

a Geometry parameters after ‘/’ represent structure X. b Mulliken charges of bonded hydrogens summed into carbon charge. c Stable carbenium ion intermediate. Bracketed quantities represent bare cluster calculations and the ones without brackets represent embedded cluster calculations.

the two ZSM-5 channels. Thereby, for EC model the larger C1-C6 distance is energetically more stable. The 1,6 cyclization is assisted by the nucleophilic attack of the secondary carbon (C6) of CdC on the carbenium center of the chemisorbed alkoxide. As shown in Scheme 1: reaction 3, formation of the covalent bond between C1 and C6 atoms places the two methyl groups at the ortho position with respect to each other. The embedded cluster calculation resulted in a cyclization activation barrier of 8.1 kcal/mol, while the bare cluster activation barrier was found to be 9.2 kcal/mol. For intermediates along the reaction pathway, we report important geometry and charge parameters in Table 2. In the transition state for cyclization, the hydrocarbon species carry significant positive charge compared to reactant or product. This transition state structure for C8 diene has similar geometry and charge as that of the C7 cyclization transition state. As a consequence of this

Brønsted Acid Catalyzed Cyclization of C7 and C8 Dienes

J. Phys. Chem. C, Vol. 112, No. 33, 2008 12831

TABLE 3: Important Geometry and Charge Parameters for Chemisorbed Branched C8 Diene (XIII), TS for Cyclization (TS5) and Chemisorbed Dimethylcyclohexene (XV) XIII a

TS5

1.579 (1.560) 2.446 (2.383) O20/11-C1/5 (Å) C1-C6 (Å) 4.606 (4.019) 3.713 (3.290) charge on C1b 0.351 (0.340) 0.394 (0.361) charge on C5b 0.093 (0.097) 0.083 (0.087) charge on C6b -0.067 (-0.067) -0.047 (-0.031) total HC charge 0.470 (0.465) 0.753 (0.756) img. freq (cm-1) -64.8 (-104.2)

XV (1.582) (1.537) (0.077) (0.281) (0.029) (0.441)

a Geometry parameters after ‘/’ represent structure XV. Mulliken charges of bonded hydrogens summed into carbon charge. Bracketed quantities represent bare cluster calculations and the ones without brackets represent embedded cluster calculations. b

similarity, the activation barriers for the two cyclization reaction paths are similar. This also points out that only the nature of the alkoxide carbon in the reactant (chemisorbed acyclic alkoxide) is important for determining the activation barrier for 1,6 ring closure. The nature of the carbon doing nucleophilic attack is not important, as the transition state geometry occurs earlier along the reaction coordinate. The transition state imaginary eigenvector indicates that the increase in the C1-O20 distance is more important reaction coordinate compared to decrease in the C1-C6 distance. For 1,6-cyclization of the C6 diene,20 we found that in TS geometry the EC results in a smaller C1-C6 distance compared to the BC representation. Based on the values reported here (Tables 1, 2 and 3), the C1-C6 distance is larger for the EC calculation compared to the BC calculation. We believe these contradictory observations could be explained based on the orientation of the hydrocarbon molecule in the transition state for cyclization. For the C6 diene, the carbon centers involved in cyclization (C1 and C6) are well inside the sinusoidal channel, while for C7 and C8 diene, the transition state orients itself in such a way that most of the hydrocarbon species lies in the intersection space of the straight and the sinusoidal pore. It is well-known that for the duel-channel system of ZMS-5 framework, the intersection of the pores has a larger cross-section compared to individual straight or sinusoidal channels. Hence, the TS for cyclization of the C6 diene is restricted by the pores, while that of the C7 and C8 dienes are not. Thus, the C1-C6 distance for C7 and C8 diene cyclization is not lowered in the EC geometry constraint. The immediate product of cyclization (intermediate IX in Figure 4) can be described as the cyclic carbenium ion without direct coordination with the bridging oxygen. The distance between the carbenium center and the framework oxygen remains 3.15 Å and 3.20 Å for BC and EC model, respectively. The conformation of the intermediate IX is such that it prevents the carbenium center from approaching the bridging oxygen Si11-O11-Al12. For the bare cluster (BC), further conformational relaxation leads to a chemisorbed alkoxide (intermediate X) at the Si11-O11-Al12 bridging position. The embedded cluster intermediate X (Figure 5) remains as a protonated carbenium ion even after a conformation adjustment. The formation of the alkoxide intermediate is unfavorable due to strong steric repulsion from rest of the zeolite cavity. Instead of the chemisorbed intermediate, it forms a stable protonated carbenium ion associated with the T12 site. The activation barrier for this conformational adjustment is just 2.9 kcal/mol (BC 3.6 kcal/mol). The resulting carbenium ion intermediates should lose a proton to form dimethylcyclohexene physisorbed (intermediate XI in Figure 4) on the Brønsted acid site at

Figure 6. Reaction path for 1,6 ring closure of branched C8 diene. XII - Bent conformers physisorbed; XIII - Chemisorbed bent conformer; TS5- Transition state for ring closure; XIV - dimethylcyclohexinum carbocation; TS6 - Transition state for conformation adjustment; XV Chemisorbed cyclohexene; XVI - Physisorbed cyclohexene on Si12HO24-Al12.

Si03-O20-Al12 bridging position. The energy difference between the BC and EC calculations for the physisorbed intermediate XI is 10.8 kcal/mol, which is significantly larger than that (6.3 kcal/mol) for the physisorbed C7 cyclic product (intermediate VI in Figure 2). This again points out a clear product shape selective exclusion of C8 cyclic products. In short, the overall cyclization reaction (starting from the physisorbed acyclic diene to form physisorbed cyclic diene) is less exothermic for the C8 diene compared to the C7 diene. Thus equilibrium becomes less favorable for C8 diene cyclization. For the branched C8 diene, the energetics is reported in Figure 6 with corresponding geometries shown in Figure 7. If we compare the distance of the CdC from Brønsted proton for the BC (2.43 and 2.14 Å) and EC model (2.41 and 2.29 Å), they are similar unlike C7 diene. Comparison of bare cluster (BC) calculations indicates that the π-complex separation for branched C8 diene is larger compared to linear C8 diene. To compare energetics of the bare cluster calculations with the embedded cluster calculation, we shift the former by -19.6 kcal/mol so that the physisorbed intermediates coincide. The energetics of the cyclization pathway is reported in Figure 6. As expected, the physisorption energy of the branched C8 diene (intermediate XII in Figure 6) is lower (-28.7 kcal/mol) compared to that of the linear C8 diene (-37.1 kcal/mol). This clearly indicates that C8+ or branched C8 molecules in the medium pore zeolites, such as ZSM-5, will face size exclusion. This is in accordance with experimental observations, as C10+ hydrocarbon molecules are rarely seen for this class of catalytic reactions. Interestingly, for the branched C8 diene, the endothermicity of the transformation from a physisorbed to chemisorbed state is similar for both bare cluster (14.0 kcal/mol) and embedded cluster (13.3 kcal/mol) representations. This suggests that the bare cluster is sufficient to represent the changes in the steric interactions of the bent conformer of the branched C8 diene (Figure 7a) during chemisorption. The similar BC and EC physisorption geometries for the branched C8 diene is the other reason for the similarity in the energetics. We observe that the endothermicity of chemisorption for the dienes increases from

12832 J. Phys. Chem. C, Vol. 112, No. 33, 2008

Joshi and Thomson TABLE 4: Comparison of the 1,6-Cyclization Activation Energy Using QM, QM/MM without Charge Embedding, and QM/MM with Implicit Charge Embedding for Different Diene Molecules QM BC diene C6 C6 C7 C8 C8

details chair conformer boat conformer linear isomer linear isomer branched isomer

∆Ezpe ∆G0 16.9 17.2 9.8 9.2 7.6

17.9 18.2 9.1 9.1 6.1

QM/MM EC

QM/MM EC

∆Ezpe

∆G0

∆Ezpe ∆G0a

15.5 15.7 7.8 8.1 6.3

15.2 15.4 7.7 7.6 5.4

18.5 18.2 6.6 12.6 9.4

18.1 17.9 6.5 12.1 8.5

a Thermochemical analysis (harmonic frequencies) taken from QM/MM without charge embedding.

Figure 7. Reaction intermediates for cyclization of 5-methylhepta1,5-diene (Branched C8 diene). (a) and (b) chemisorbed secondary alkoxide at Si03-O20-Al12; (c) and (d) TS for 1,6 ring closure; (e) Stable protonated dimethylcyclohexene; (f) Chemisorbed dimethylcyclohexene at Si11-O11-Al12 for bare cluster.

C620 (4.4 and 7.2 kcal/mol) to C7 (12.4 kcal/mol) to C8 (13.4 and 13.3 kcal/mol). Large increase in the endothermicity from the C6 diene to C7 diene is due to the difference in the nature of the chemisorbed alkoxide. For the C6 diene to carry out 1,6ring closure, we need a primary alkoxide as the precursor for cyclization. It has been conclusively proven through numerous theoretical investigations20–22,35 that the primary carbon forms a more stable alkoxide bond compared to a secondary carbon, as it faces less steric repulsion from the surrounding zeolite wall. This confirms our previous hypothesis that the shape selective exclusion of larger hydrocarbons can be characterized by this endothermicity and it also explains the absence of larger hydrocarbon species (C10+) in the product distribution. The cyclization mechanism for the branched C8 diene is similar to that of the C7 diene, as the nature of the hydrocarbon backbone undergoing cyclization is same. The activation barrier for cyclization is significantly lower for both bare cluster (BC 7.6 kcal/mol) and embedded cluster (EC 6.3 kcal/mol) representations. The geometries and Mulliken charges of important reaction intermediates are reported in Table 3. The C1-C6 distance for the chemisorbed acyclic branched C8 diene is 4.02 and 4.26 for BC and EC models, respectively. As with most other cases of cyclization, the transition state is more cationic in nature compared to the reactant or the product. As in case of the linear C8 diene, on cyclization of the branched C8 diene the methyl groups located at ortho positions. The immediate product of cyclization is the stable cyclic carbenium ion. It undergoes further conformational relaxation with small activation barrier as shown in Figure 6. For the bare cluster, the resulting cyclic hydrocarbon (intermediate XV in Figure 7) chemisorbs on the Si11-O11-Al12 bridging oxygen. As in

the case of the C7 diene, for the branched C8 diene, we did not find a stable chemisorbed intermediate in our embedded cluster calculation. 3.4. Charge Embedding and Thermochemical Analysis. In this study we have considered the effect of charge embedding on the cyclization energetics. In Table 4 we present a comparison of the activation barriers for the cyclization step, i.e. chemisorbed diene giving first cyclic product. As pointed out previously, we carry out this comparison for C6, C7 and C8 dienes using three methods: (1) model cluster using QM [B3LYP/6-31g(d,p)] level of theory (2) ONIOM calculation using hybrid QM/MM [B3LYP/6-31g(d,p):UFF] method without charge embedding (3) ONIOM calculation using hybrid QM/ MM [B3LYP/6-31g(d,p):UFF] method with implicit charge embedding. We point out that the activation barriers decrease uniformly when we move from method 1 to method 2. This is in accordance with our previous observation20 that the transitions states are farther away from the zeolite wall (near the center of the zeolite cavity). As a consequence, they are better stabilized by the van der Waal’s forces compared to the chemisorbed reactants very close to the zeolite walls. This has been classically termed43 the ‘confinement effect’ or ‘surface curvature effect’.44,45 Same curvature effect leads to increasing distance of the physisorbed species from the Brønsted acid site while increasing physorption energy calculated using embedded cluster (EC). We also report the free energy barriers for these reaction steps calculated at STP (temperature 298.15 K and pressure 1 atm.). The free energy barriers for cyclization of the C7 and C8 dienes are lower compared to those for C6 dienes. This clearly suggests that the cyclization of C7 and C8 dienes is more facile compared to that of C6 diene. Other important factors to consider are the concentration of the diene inside the zeolite pores, and the endothermicity of chemisorption. For the propane aromatization reaction, the concentration of C6 species is expected to be higher than that of C7 species merely because of the fact that higher hydrocarbons are generated from oligomerization of the smaller species. The concentration of the parental acyclic dienes should decrease from C6 to C7 to C8. With all this in consideration, we conclude that for light alkane aromatization the major fraction of the cyclic product originates from the cyclization of C7 diene. The methylcyclohexane should dehydrogenate subsequently to form toluene. There is experimental evidence46 that benzene is not the primary aromatic product for aromatization reactions. Subsequently, benzene is formed by disproportionation of higher aromatics. These results have been used in the microkinetic model for propane aromatization using HZSM-5, recently put forth by Bhan et al.6 The relative activation barriers obtained from these calculations were able to explain the observed aromatic distribution through a rigorous microkinetic model.6 In the last column of Table 4, we report the activation barriers after accounting for implicit charge embedding. We observe

Brønsted Acid Catalyzed Cyclization of C7 and C8 Dienes that for the C6 diene, implicit charge embedding leads to an increase in the activation barrier by about 2.5 kcal/mol. Similarly, for the C8 diene the increase in activation energy is about 3 to 4.5 kcal/mol. While for the C7 diene the activation barrier decreases by about 1 kcal/mol. This clearly indicates that the implicit charge embedding is not consistent, as the expected stabilization of the cationic transition state is not observed consistently. Similar conclusions were drawn by Boronat et al.35 regarding semiempirical methods used as the lower level theory. 4. Conclusions From our investigation into the cyclization mechanisms of C7 and C8 dienes, using hybrid QM/MM methods, the following conclusions can be drawn: The larger olefins such as C7 and C8 dienes show negative reaction energy for transformation from the physisorbed state to the chemisorbed alkoxide. The endothermicity of these reactions increase with increasing carbon number (C6 to C8) of the diene. This indicates that for larger hydrocarbons, a very small fraction will be present as the chemisorbed alkoxide. The endothermicity of the chemisorption should serve as a criterion for the shape selective activation (when the endothermicity is moderate) or shape selective exclusion (when endothermicity is very high). We find the hybrid QM/MM calculation is a more accurate method for calculation of this endothermicity, which could serve as a physical basis to explain the absence of the larger hydrocarbon (C10+) in the product distribution. By comparing the 1,6-cyclization activation barriers of the C6, C7 and C8 dienes, we conclude that cyclization of the C7 and C8 dienes is much more facile than that of the C6 diene. This follows the rules of the carbenium ion chemistry, which state the stability of the carbenium ion increases in the order of primary < secondary < tertiary. The cyclization transition state for the C6 diene has primary carbenium ion nature (or sterically hindered secondary for 1,5 ring closure) while, for C7 and C8, it has secondary carbenium character. Thus, stability of the transition state transpires into lower cyclization barriers for C7 and C8 dienes. Our calculations suggest that toluene is the primary aromatic product for HZSM-5 catalyzed aromatization, which is in agreement with several experimental observations. Acknowledgment. This work was supported by the U.S. Department of Energy (DOE), Office of Basis Sciences (grant DE-FG02-03ER-15466). Computational resources were obtained through a grant (MCA04N010) from the National Computational Science Alliance and through supercomputing resources at Purdue University. We thank Prof. W. Nicholas Delgass and Gowri Krishnamurthy for discussions on zeolite catalyzed hydrocarbon chemistry. Supporting Information Available: This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Doolan, P. C.; Pujado, P. R. Hydrocarbon Process. 1989, 68, 72. (2) Gnep, N. S.; Doyemet, J. Y.; Seco, A. M.; Ribeiro, F. R.; Guisnet, M. Appl. Catal. 1988, 43, 155. (3) Mole, T.; Anderson, J. R.; Creer, G. Appl. Catal. 1985, 17, 127. (4) Kitagawa, H.; Sendoda, Y.; Ono, Y. J. Catal. 1986, 101, 12. (5) Fricke, R.; Kosslick, H.; Lischke, G.; Richter, M. Chem. ReV. 2000, 100, 2303. (6) Bhan, A.; Hsu, S.-H.; Blau, G.; Caruthers, J. M.; Venkatasubramanian, V.; Delgass, W. N. J. Catal. 2005, 235, 35.

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