Î²-Scission of Olefins on Acidic Zeolites: A Periodic PBE-D Study in H

Article pubs.acs.org/JPCC

β‑Scission of Olefins on Acidic Zeolites: A Periodic PBE‑D Study in H‑ZSM‑5 Mark N. Mazar,† Saleh Al-Hashimi,‡ Matteo Cococcioni,*,† and Aditya Bhan*,† †

Department of Chemical Engineering and Materials Science, University of Minnesota, 421 Washington Ave SE, Minneapolis, Minnesota 55455, United States ‡ Department of Chemical Engineering, The Petroleum Institute, P.O. Box 2533, Abu Dhabi, United Arab Emirates S Supporting Information *

ABSTRACT: Eight β-scission modes involving C6 and C8 olefin isomers are investigated using dispersion-corrected density functional theory (i.e., PBE-D) calculations. Potential energy surfaces are evaluated within an acidic H-ZSM-5 supercell containing a single, isolated active site. Minimum energy pathways are localized using the nudged elastic band method. The relative enthalpic barriers of β-scission steps can be described by the substitution order of the carbocationic carbon atom present in the reactant and transition states. Specifically, the total charge on the hydrocarbon fragment containing the β C atom increases going from the physi- or chemisorbed reactant state to the β-scission transition state; the magnitude of this change (+0.37e−0.97e) is found to correlate nearly monotonically with the activation energy (89−233 kJ mol−1). A comparison of 1° to 3° (E1) and 3° to 1° (E2) β-scission modes as well as 2° to 3° (B1) and 3° to 2° (B2) β-scission modes reveals that the barrier heights depend on the substitution order of the β C, indicating that a subcategorization of βscission modes is required based on the substitution order of the β C atom. Isomerization reactions, which are fast with respect to β-scission, enable reactant hydrocarbons to explore and find low-barrier β-scission pathways. Selectivities predicted on the basis of the relative barrier heights of β-scission modes accessible to C6 and C8 species indicate agreement with experimental observations.

1. INTRODUCTION Reactions catalyzed by crystalline micro- or mesoporous acidic zeolite or zeotype materials1,2 are central to many processes, especially those related to the production of commodity chemicals and fuels from petroleum.3−10 In hydroconversion, acidic active sites convert alkanes and olefins into smaller hydrocarbons.11,12 The monomolecular cracking of alkanes occurs through a transition-state configuration containing pentacoordinated carbocations13,14 and has been shown to have apparent activation energies dependent on adsorption enthalpies.15,16 With respect to the cracking of olefins, product selectivities17,18 indicate that β-scission is the predominant mechanism for solid acid catalysts19−24 and that apparent activation energies depend on carbocation stabilization through increased substitution and hyperconjugation.25 Consecutive, parallel reactions, which complicate overall product distributions (e.g., oligomerization and dehydrocyclization),26 and the high rates of olefin β-scission make the experimental determination of kinetic parameters elusive. Therefore, dispersion-corrected density functional theory is used in this research to determine mechanistic details and barrier heights of individual elementary steps in the β-scission of olefins. On this basis we propose distinct relationships between the barrier height and the charge of the β C atom in the reactant and transition states. © 2013 American Chemical Society

In the gas phase, where significant steric interactions are typically absent, activation energies for the β-scission of alkyl species have been predicted with linear energy relationships involving the heat of reaction (i.e., Brønsted−Evans−Polanyi relationships).27,28 In zeolites, this linear energy relationship is destroyed by the complexity of the pore structure because the electrostatic,29,30 hydrogen bonding,31 and van der Waals32−34 interactions introduced by the zeolite vary in their relative contributions along the reaction pathway.9,25,26,35−38 At stationary points, these effects may favor the physisorbed, substituted carbocationic species over the surface-bound alkoxides.24,31,35,39−42 In this work, multiple ground-state configurations containing stabilized tertiary-carbocationic species are localized. Relative to β-scission, a feed olefin rapidly equilibrates with its protonated forms (i.e., the alkoxide and physisorbed carbocationic states)25,31 as well as its isomers (Scheme 1).9,22−25,38,40 At 510 °C over H-ZSM-5, the β-scission product distribution was found to be independent of the specific olefin isomer used in the feed; double-bond then skeletal isomers were observed.25 Typically, the result of olefin protonation is Received: April 9, 2013 Revised: October 10, 2013 Published: October 15, 2013 23609

dx.doi.org/10.1021/jp403504n | J. Phys. Chem. C 2013, 117, 23609−23620

The Journal of Physical Chemistry C

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Scheme 1. Pathways in the Brønsted Acid Catalyzed Cracking of a C6 Olefin

Scheme 2. Modes of β-Scission As Defined by the Substitution Order of the Alkoxide or Carbenium Ion Present in the Reactant and Product States; Reactions Shown Indicate the β-Scission Pathways Studied in This Work

the formation of an alkoxide.24−26,30,38 In the case of chemisorbed alkoxides, the bond between the carbon atom and the framework oxygen atom (i.e., the C+−O25 bond represented in Scheme 1) elongates until C+ attains an sp2 hybridized geometry; for physisorbed carbocationic species the C+ atom is already sp2 hybridized. β-scission begins with the elongation of the bond in the β-position from C+ (α C−β C). The transition-state structure is achieved once the α C and β C atoms become fully sp2 hybridized; the result is two fragments: an olefin and another carbocationic hydrocarbon. For the new, smaller carbocation there are three possibilities (Scheme 1), each resulting in the formation of the second olefin: immediate hydrogen transfer to the zeolite, physical adsorption with subsequent hydrogen transfer to the zeolite, or chemical adsorption with subsequent β-hydrogen elimination. β-scission rates increase with the availability of isomers containing highly substituted carbon atoms, a corollary of carbon number.25 The example shown in Scheme 1 is for a Ctype β-scission, starting from and ending with a secondary carbocationic species. Weitkamp et al.43 and Buchanan et al.25 have established nomenclature to identify β-scission elementary steps according to the carbocations present at the reactant state and formed at the transition state (Scheme 2). In previous work, the relative rates of different β-scission modes have been attributed to the substitution order of the β C atom.44−46 The findings of this work confirm this assessment; however, the relative stability of the carbocationic species formed at the transition state is of greater importance, and the substitution order of the β C atom is a major factor determining the overall stability of a species. The relative stability of the reactant state, and therefore the substitution order of the C+ atom,25,42 also influences the activation energy. Each of the βscission modes shown in Scheme 2 is studied in H-ZSM-5. Alkoxide formation and olefin desorption (Scheme 1) are studied in additional pathways; as expected, both barriers are lower than that of the β-scission elementary steps. Furthermore, the order of the overall barrier heights of the β-scission modes (Scheme 2) is related to the change in charge required by the β carbon atom to undergo β-scission. This relationship is also reflected by the total charge of the cationic fragment formed at the β-scission transition state.

2. COMPUTATIONAL METHODS All atomic configurations and energies reported here were determined with periodic boundary conditions and a supercell 23610



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difference between the transition state and the minimum associated with reactants adsorbed within the zeolite. During the evaluation of reaction pathways, conformationally different product states, with energies similar to the initial one, were occasionally found. In these cases, the newly discovered conformation was independently optimized and used as the new product state, effectively eliminating chemically irrelevant rotations from the pathway.

of the full crystal structure of the MFI framework: a siliceous material with a two-dimensional pore network containing intersecting straight and sinusoidal 10-membered ring (10mr) channels. The same active site, located at one of these intersections, was used in all cases; specifically, a Brønsted acid site consisting of an aluminum substitutional impurity at the T12 tetragonal site (T-site) and a hydrogen counterion on an adjacent oxygen atom (O25). An embedded cluster (EMB) approach was employed to reduce computational costs; that is, atoms within a range of influence of the active site were allowed to move while all atoms outside this range were held fixed at their siliceous positions (i.e., XRD positions and unit cell parameters47). In a previous study, a comparison of the internal coordinates of this system with that of the purely siliceous structure revealed negligible differences outside the third shell of nearest neighbor T-sites,48 thus defining the range of influence of the active site. All of the calculations in this work were performed using the plane-wave, pseudopotential total-energy code of the QuantumESPRESSO package.49 Ultrasoft pseudopotentials were used throughout.50 The Perdew−Burke−Ernzerhof (PBE)51 generalized gradient approximation of the exchange−correlation functional was used. To improve the treatment of dispersion interactions, which are critical in the study of chemistry in zeolites,32,33 the dispersion-correction methodology pioneered by Grimme et al.52 was employed (i.e., DFT-D2). Barone et al.53 modified this sixth-order dispersion-correction term to include periodic boundary conditions and implemented it in the Quantum-ESPRESSO package. It should also be noted that the dispersion coefficients used in this work were computed from first principles based on atomic polarizability (i.e., DFTD3).54 Because of the size and dimensions of the supercell, the Γ-point was used to sample the Brillouin zone. Electronic Kohn−Sham states were expanded up to a kinetic energy cutoff of 45 Ry (612 eV), and a cutoff of 450 Ry (6120 eV) was used for the electronic charge density. Atomic configurations were localized with the Broyden−Fletcher−Goldfarb−Shanno (BFGS) method,55 and structures were considered relaxed to their equilibrium configuration when the forces on mobile atoms were below 0.001 (Ry/a0). Löwdin atomic charges were evaluated from the projection of Kohn−Sham states onto orthogonalized atomic orbitals.56 While the sum rule of the obtained occupation numbers is nearly satisfied, some deviations can be expected from the imperfect overlap between the Kohn−Sham and the atomic orbital basis sets.57 The climbing-image nudged elastic band (CI-NEB) method58−61 was used to find minimum energy pathways (MEPs) and localize transition-state (TS) geometries. Rudimentary initial guess pathways were determined by interpolation of the internal coordinates (i.e., bond lengths, bond angles, and dihedral angles between atoms) and improved through NEB calculations using cluster models of the zeolite framework. The framework models encompassed three tetrahedra (3T) and consisted of the Al atom, the bridging oxygen atoms involved in the reaction, and their corresponding Si atoms (i.e., Si−O25−Al−O26−Si). Oxygen atoms at the edge of each cluster were replaced with hydrogen atoms along the same bond vector and at a distance of 1.472 Å; this distance was determined from optimization of SiH4 at the same level of theory. Final minimum energy pathways were found by continuing the NEB calculations using the EMB method. Activation energies determined from these MEPs correspond to the energy

3. RESULTS AND DISCUSSION We introduce a nomenclature used to identify the different states of the studied pathways. Multiple pathways were studied for some β-scission modes (Scheme 2); reactant (r), transition (ts), reaction intermediate (ri), and product (p) states are identified according to their respective reaction pathways. For example, the transition state of the second B2-type β-scission pathway (B2-2) is denoted as B2-2.ts. The reactant state of the first, and sometimes the only, investigated pathway of each mode was achieved using the same procedure. The optimization of these reactant states began with the cationic carbon atom in an sp3 hybridized geometry and a starting C+−O25 distance close to that of a single bond (∼1.52 Å); that is, a configuration close to that of an alkoxide was chosen as the initial guess. For tertiary species, it is not uncommon for the cationic carbon to become sp2 hybridized, losing its σ-bond with the zeolite in the optimized state. Investigation of a different pathway of the same mode sometimes necessitated an alternate reactant state; in these cases, the new reactant state was optimized starting from a conformational isomer of the first. The initial guesses for the product states were constructed from their corresponding reactant states by breaking the appropriate bonds and setting up the cationic species in an alkoxide configuration at the O26 atom; the O26 atom was used for the product state because pathways with hydrocarbons beginning and ending on adjacent, bridging oxygen atoms have been shown to have lower enthalpic barriers.44 The O25 atom protrudes into the straight channel and the O26 atom into the sinusoidal one, ensuring that the β-scission step takes place within the intersection of the two channels. The studied elementary steps include the protonation of 4methyl-2-pentene to form an alkoxide, the rotational isomerization of a highly branched C8 tertiary-carbocation (3,5dimethyl-3-hexyl-carbocation), twelve β-scission elementary steps across eight modes, and β-hydrogen elimination from 2propoxide (Scheme 1). At the stationary states, the C−O bond lengths are characteristic of the substitution order of the cationic carbon atom (i.e., C+ in the reactant state or β C in the transition state); a range of 1.52−1.54 Å is found for primarycarbocations, 1.57−1.59 Å for secondary-carbocations, and 1.69−5.98 Å for tertiary-carbocations. Each pathway will be separately discussed in the following sections. 3.1. A-Type (3° → 3°). Two pathways involving conformational isomers of the most branched C8 tertiary-carbocation (A1 and A-2) were investigated with respect to the A-type βscission mode (Figure 2). In A-1, the relative atomic positions of the carbocationic fragment resulting from β-scission are generally maintained (Figure 1a); this is not the case in A-2, in which the carbocationic fragment resulting from β-scission performs an umbrella-like inversion about the β C atom (Figure 1b). 23611



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Figure 1. Categorization of the β-scission step according to the behavior of the carbocationic fragment. (a) Rotation and translation or (b) umbrella-like inversion. In (a), the shaded “side” of the carbocationic fragment faces the species to which it binds throughout the reaction; in (b), the light and shaded side switch.

Designated as the A-1 reactant state (A-1.r), the optimization of the alkoxide-like initial guess (2,4,4-trimethyl-2-pentoxide) resulted in a tertiary-carbocation (2,4,4-trimethyl-2-pentylcarbocation) with no chemical bond to the zeolite. In this case and others involving stabilized tertiary-carbocations, the four Al−O bonds were nearly equal in length (∼1.72 Å) and the anionic charge was delocalized. Two C4 fragments, isobutene and a tertiary-butoxide, resulted from the optimization of the product state (A-1.p). During NEB calculations, a reaction intermediate containing a stabilized tertiary-butylcarbocation was found (A-1.ri); the β C atom in this state, as in the A-1.ts1 and A-1.ts2 transition states, was sp2 hybridized. The major difference between A-1.ri and the two transition states is the rotation of the tertiary-butyl-carbocation within the sinusoidal channel. The activation energy to overcome the βscission transition state (A-1.ts1) is 115 kJ mol−1, while the barrier to form the A-1.p tertiary-alkoxide from the A-1.ri tertiary-carbocation is 63 kJ mol−1. Although the A-1.ts2 and A1.p configurations are very similar with a flat energy landscape between them, the discovery of the carbocationic reaction intermediate indicates that this β-scission mechanism follows an SN1 inversion mechanism; that is, the nucleophilic substitution (A-1.r → A-1.ts1 → A-1.ri) is unimolecular, requiring only the presence of the A-1.r tertiary-carbocation. From the elongation of the β-bond (A-1.r) to the formation of the A-1.p tertiaryalkoxide, the fragment containing the β C atom effectively rotates and translates, maintaining relative atomic positions (Figure 1a). The reactant state (A-2.r) was localized through the ∼180° rotation of the A-1.r hydrocarbon about its length and subsequent optimization. As in the A-1 pathway, a reaction intermediate containing a stabilized tertiary-butyl-carbocation was found in A-2; the primary difference between the two states consists of a rotation of the isobutene. The formation of the tertiary-butoxide is not studied in this case because the barrier to rotate isobutene, a small neutral species, is likely negligible in comparison; that is, the tertiary-butoxide formation step of A-1 (A-1.ri → A-1.ts2 → A-1.p) is an appropriate extension from the similar reaction intermediate of A-2 and therefore the A-2 reaction intermediate terminates the A-2 pathway (A-2.p). The combined pathway (Figure 2) involving the A-2 β-scission step and the tertiary-butoxide formation step (A-2.r → A-2.ts → A2.p → A-1.ri → A-1.ts2 → A-1.p) differs from that of A-1 in that the carbocationic fragment formed during β-scission undergoes an umbrella-like inversion (Figure 1.b) rather than rotation and translation. The “side” of the tetrahedron facing the species to which the β C atom is bound (i.e., either the α C atom or the O26 atom) switches in A-2, but not in A-1. The activation energy of A-2 (92 kJ mol−1) is 23 kJ mol−1 lower than that of A-1 (115 kJ mol−1), illustrating that species

Figure 2. Reaction mechanisms and energy profiles (kJ mol−1) for the A-type β-scission of two conformational isomers of a tertiarycarbocation (2,4,4-trimethyl-2-pentyl-carbocation). Five elements are involved: silicon (yellow), aluminum (black), oxygen (red), carbon (gray), and hydrogen (white).

not forming chemical bonds with the framework can access pathways with lower barriers for β-scission through conformational isomers achieved by rotation; the rotation of a C8 tertiary-carbocationic species was addressed further in the context of B2-type β-scissions. The elementary step resulting in tertiary-butoxide formation (A-1.ri, A-1.ts2, A-1.p) is endothermic (62 kJ mol−1), indicating here that the tertiary-butyl-carbocation has a lower energy than the tertiary-butoxide. An ONIOM(B3PW91/6-31G(d,p):MNDO) investigation of H-MOR using multiple cluster sizes also found positive heats of reaction (∼ 38 kJ mol−1).36 However, an ONIOM(MP2/6-31G(d,p):MNDO) 3T:84T study of the tertiary-butyl cation in H−Y, a framework with large ∼12 Å internal cages, reports tertiary-butoxide to be 40− 51 kJ mol−1 more stable than tertiary-butyl-carbocation.31 The large difference in adsorption enthalpy across frameworks is indicative of the increased coordination between the carbocationic species and the framework in H-ZSM-5 and HMOR compared to H−Y and illustrates that the stability of a carbocationic species at an energy minimum can be dramatically changed relative to its corresponding surface alkoxide. This assertion is in agreement with findings in the literature,31,32,34,38,62,63 showing that dispersion interactions stabilize carbocationic states at energy minima to an extent greater than at transition states. 3.2.1. B1-Type (2° → 3°). In the β-scission of C8 olefins, one B1-type pathway was investigated (Figure 3). β-scission of the secondary-alkoxide (4,4-dimethyl-2-hexoxide) reactant state (B1.r) results in two fragments: a C3 (propene) and a C5 (1,1dimethyl-1-propoxide); in this instance no reaction intermediate containing a physisorbed tertiary-carbocation was found. A comparison of this pathway with the A-type pathways shows that the adsorption energy of the reactant hydrocarbon is a factor in determining the barrier height; the activation energy 23612



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carbocationic fragment resulting from β-scission in the B2-1 pathway maintains its general structure through rotation and translation (Figure 1a). The A-2 and B2-2 pathways also share similar mechanisms: the carbocationic fragment resulting from β-scission in B2-2 is inverted about the β C atom (Figure 1b). Unlike the A-type pathways, the formation of surface-bound alkoxides in the B2-type pathways occurs in a single step, making them bimolecular (i.e., SN2). In addition to the two B2type β-scission elementary steps, one additional step was studied (B2-0): the rotational isomerization of the tertiarycarbocationic hydrocarbon that takes place between the B2-1.r and B2-2.r states. In B2-1, overcoming the activation energy (171 kJ mol−1) for the β-scission of the 3,5-dimethyl-3-hexyl-carbocation (B2-1.r) results in C5 (pentene) and C3 (2-propoxide) fragments. The B1-type β-scission also forms C3/C5 fragments, but with an 18 kJ mol−1 higher barrier; this is explained by both the ∼20 kJ mol−1 higher adsorption energy of the B1.r secondary-alkoxide compared to that of the B2-1.r tertiary-carbocation and by steric hindrance from the ethyl substituent at B1.ts. As in A-2, the reactant state of the second pathway (B2-2.r) is derived from the ∼180° rotation of the B2-2.r hydrocarbon about its length. The resulting conformation is 37 kJ mol−1 higher in energy than B2-1.r and has an α C−β C bond vector that points almost directly at the O26 atom. Although forming the same products as in B1, the B2-2 activation energy is the lowest among any β-scission elementary step (89 kJ mol−1) and significantly lower than that of B2-1 (171 kJ mol−1). The minimum energy pathway (B2-0) corresponding to the rotational isomerization of B2-1.r to B2-2.r was found (Figure 4). The activation barrier (64 kJ mol−1) is noted to be 25 kJ mol−1 lower than that of B2-2, indicating that rotational isomerization is fast compared to β-scission steps and that the B2-2 pathway is favored over the B2-1 pathway. As in the A-2 pathway, the ease of rotation that tertiary-carbocationic reactants afford allows β-scission to proceed through preferred pathways; for B2-2, that is a SN2 reaction (i.e., single step) with umbrella-like inversion. 3.3. C-Type (2° → 2°). Three C-type β-scission pathways (C-1, C-2, and C-3) were studied with C6 species. Each begins from one of two conformational isomers of 4-methyl-2propoxide that are separated in energy by 22 kJ mol−1 (Figures 5 and 6) and ends with two C3 fragments. The lower-energy reactant state was used in the C-1 pathway (C-1.r) while the higher-energy reactant state was used in both the C-2 and C-3 pathways (C-2.r = C-3.r). The difference between these conformational isomers is in the position of the β C atom; d(β C−O26) is 4.45 Å for C-1.r and 3.66 Å for C-2/3.r, meaning that the extent to which the hydrocarbon occupies the sinusoidal channel in C-2/3.r is greater than that in C-1.r. In addition to the three C-type β-scission pathways, the olefin protonation reaction (C-0) resulting in the low-energy conformation of 4-methyl-2-propoxide was also investigated (C-0.p = C-1.r). At the reactant state (C-0.r), the Brønsted proton is equidistant to the two carbon atoms of the double bond (1.94 Å) of the 4-methyl-2-propene olefin. The energy of physisorption is 121 kJ mol−1 and the activation energy required to form the surface-bound secondary-alkoxide (C-0.p) is 52 kJ mol−1. The C-0 pathway confirms the consensus in the literature that, relative to β-scission, adsorption and desorption (70 kJ mol−1) processes are fast.25,38,64 In the C-1 pathway, a reaction intermediate (C-1.ri) and two transition-state structures (C-1.ts1 and C-1.ts2) were localized

Figure 3. Reaction mechanism and energy profile (kJ mol−1) for the B1-type β-scission of a secondary-alkoxide (4,4-dimethyl-2-hexoxide).

(153 kJ mol−1) is 61 kJ mol−1 greater than that of the A-2 pathway. A similar increase in adsorption energy is observed; the heat of chemisorption of the B1.r hydrocarbon (176 kJ mol−1) is 63 kJ mol−1 greater than that of the heat of physisorption of the A-2.r hydrocarbon (113 kJ mol−1). Therefore, as both transition states contain tertiary-carbocations, the majority of the difference in barrier height between the A-2 and B1 pathways is attributed to the heat of adsorption; specifically, it is attributed to the substitution order of C+ atom in the reactant states. 3.2.2. B2-Type (3° → 2°). Two B2-type β-scission elementary steps involving rotational isomers of the reactant C8 hydrocarbon (3,5-dimethyl-3-hexyl-carbocation) were investigated (Figure 4). As in the A-1 pathway (Figure 2), the

Figure 4. Reaction mechanisms and energy profiles (kJ mol−1) for the B2-type β-scission of two conformational isomers of a tertiarycarbocation (3,5-dimethyl-3-hexyl-carbocation). 23613



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Figure 5. Energy profiles (kJ mol−1) for the C-type β-scission of two conformational isomers of a secondary-alkoxide (4-methyl-2-pentoxide), the protonation of 4-methyl-2-pentene, and the desorption of propene.

Figure 6. Reaction mechanisms for the C-type β-scission of two conformational isomers of a secondary-alkoxide (4-methyl-2-pentoxide).

in the β-scission of the C-1.r reactant (Figures 5 and 6). The energy required to reach the first transition state (C-1.ts1) is 173 kJ mol−1; this β-scission elementary step results in (C-1.ri) propene and a stabilized 2-propyl-carbocation. Leading up to C-1.ts1, the β C atom transitions from the tetrahedral (sp3) to the trigonal planar geometry (sp2); this action simultaneously rotates the groups attached to the β C atom, including two methyl groups. Rotation of the methyl group that is closer to propene brings one of its hydrogen atoms (H=) into proximity with the double bond (d(H=−C+) = 2.64 Å and d(H=−α C) = 2.52 Å) in C-1.ts1; at the C-1.ri stationary point, this hydrogen atom has an elongated bond with its carbon atom (1.26 Å) and is coordinated with the α C atom (1.65 Å). The activation energy to destabilize C-1.ri and overcome the second transition state (C-1.ts2) is 24 kJ mol−1 and results in 2-propoxide formation (C-1.p). The high-energy conformation of 4-methyl-2-propoxide (Figure 5) is the reactant state of the C-2 and C-3 β-scission elementary steps; in one case, the 2-propyl-carbocation resulting from β-scission forms 2-propoxide in a single step

(C-2), while the other (C-3) explores the direct formation of the second propene through hydrogen transfer from the carbocation to the zeolite (Figure 6). Unlike the C-1 pathway, no reaction intermediate was found in C-2; this is because none of the hydrogen atoms of the C-2.ts secondary-carbocation are particularly suited to coordinate with the double bond of the propene formed. In the C-1 pathway, the hydrogen atom that coordinated with the double bond of propene (H=) belonged to a methyl-group; however, H= in C-2 is a single hydrogen atom bound to the carbocationic β C (d(H=−C+) = 2.91 Å) and d(H=−α C) = 2.95 Å)). Also, there is no elongation of the β C−H= (1.10 Å) bond. The activation energy for the C-2 pathway is the lowest (161 kJ mol−1) among the C-type pathways. As there is strong evidence that doublebond and skeletal isomerizations take place at rates higher than that of β-scission,9,24,25,31,38,40 it is reasonable to assume that a conformational isomerization from C-1.r to C-2/3.r will have a relatively low barrier height and occur quickly compared to βscission. With this in mind, the C-2 pathway is another example 23614



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3.4.2. D2-Type (2° → 1°). The D2-type β-scission of 2hexoxide results in two C3 fragments: propene and a 1propoxide (Figure 8). Out of the 12 β-scission modes reported

of the activation of low-energy reactants into higher-energy isomers that are ideal for β-scission. Of the C-type pathways, the C-3 pathway has the highest activation energy (178 kJ mol−1). At the transition state (C3.ts), one of the hydrogen atoms of the 2-propyl-carbocation is coordinated with the O26 atom (1.75 Å) and has a slightly elongated bond with its carbon atom (1.16 Å); hydrogen transfer to the O26 atom results in (C-3.p) the second propene and a Brønsted acid site (Figure 6). As long as the desorption of 2-propoxide has a lower barrier than C-2, we can conclude that C-2 is preferred over both C-1 and C-3; this pathway was studied and is denoted C-4. The reactant state of C-4 was the C-1 product state (i.e., C-4.r = C1.p). Desorption of propene through β-hydrogen elimination has an activation energy (67 kJ mol−1) that is 94 kJ mol−1 lower than that of C-2 β-scission; this propene desorption barrier is lower than that found in a (B3LYP/6-31g(d)) 10T study (92 kJ mol−1)65 as well as in a dispersion-corrected ONIOM(B3LYP/ 6-31+g(d):HF/6-31+g(d)) 8T:46T study (130 kJ mol−1).63 The reduced barrier height in this instance is the result of a hydrogen atom from the 2-propyl-carbocation coordinating with a carbon atom belonging to the double bond of propene (2.61 Å) in the transition state (C-4.ts). The activation energies of the three C-type β-scission pathways differ by just ∼17 kJ mol−1 (Figure 5). In contrast, the differences between barrier heights of pathways from the same mode are 23 kJ mol−1 for the A-types (Figure 2) and 82 kJ mol−1 for the B2-types (Figure 4). This comparison suggests that barrier heights are largely determined by the substitution order of the carbocationic carbon atom in the transition (β C) and reactant (C+) states and, to a secondary extent, by the specific mechanism within a given mode of β-scission. 3.4.1. D1-Type (1° → 2°). One minimum energy pathway was found for each of the two D-type β-scission modes and each of the reactant and product states consist of C6 alkoxide species. In the D1-type pathway (Figure 7), β-scission of the primary-alkoxide (3-methyl-1-pentoxide) reactant state results in two fragments: a C2 (ethene) and a C4 (2-butoxide). At the transition state (D1.ts), a secondary-carbocationic species is formed. Compared to other pathways forming secondary-carbocationic species, the D1-type pathway has the highest activation energy (196 kJ mol−1) because it is the only one whose reactant state contained a highly stable primaryalkoxide.

Figure 8. Reaction mechanism and energy profile (kJ mol−1) for the D2-type β-scission of a secondary-alkoxide (2-hexoxide).

in this work, this D2-type pathway has the highest activation energy (233 kJ mol−1), exceeding that of D1-type pathway by 37 kJ mol−1. This is attributed to both the stability of the secondary-alkoxide reactant state and the instability of the primary-carbocationic fragment formed during β-scission. The difference in energy between the D1.ts1 state, containing a secondary-carbocationic species and the D2.ts1 state, containing a primary-carbocationic species, is 67 kJ mol−1. Conversely, the energy difference was 30 kJ mol−1 between the D2.r1 state, containing a secondary-alkoxide, and the D1.r1 state, containing a primary-alkoxide. These observations indicate that the influence of the order of substitution of the carbocationic carbon at the transition state (β C) on the activation energies is greater than that of the order of substitution of the carbocationic carbon at the reactant state (C+). 3.5.1. E1-Type (1° → 3°). The E1-type β-scission of the C6 primary-alkoxide reactant state (3,3-dimethyl-1-butoxide) requires 144 kJ mol−1 to overcome the transition state (E1.ts), forming (E1.p) C2 (ethene) and C4 (tertiary-butyl-carbocation) fragments. As with previous pathways containing tertiarycarbocations in the transition state, the energy landscape is flat between E1.ts and E1.p. Both the D1 (Figure 7) and E1 (Figure 9) pathways contain C6 primary-alkoxides in the reactant state. Therefore, the reduced reaction barrier of E1 (144 kJ mol−1) compared to that of D1 (196 kJ mol−1) is attributed to the increased stability of tertiary-carbocationic versus secondary-carbocationic species in the transition state. β-scission in the A-1, A-2 (Figure 2), B1 (Figure 3), and E1 (Figure 9) pathways each contain a tertiary-carbocationic species in the transition state. Compared to β-scission barrier heights, one might expect their transition states to be close in total energies. The total energies of the C8 A-1.ts, A-2.ts, and B1.ts differ by less than 19 kJ mol−1; however, a direct comparison in this way is not possible with the C6 E1.ts because of the differing number of total atoms in the system. Increased dispersion interactions arising from carbon number may offer a partial explanation for the activation energy of E1 being 9 kJ

Figure 7. Reaction mechanism and energy profile (kJ mol−1) for the D1-type β-scission of a primary-alkoxide (3-methyl-1-pentoxide). 23615



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species. The dramatic difference in barrier heights between βscission modes (i.e., E1-type and E2-type) within the same βscission group (i.e., E-type) indicates that they should be categorized differently. Out of the 12 studied β-scission pathways, the two that result in the formation of primary carbocationic species at the transition state (D2 and E2) also have the two highest activation energies. While a tertiary-carbocationic species is stabilized by its surrounding carbon atoms, the magnitude of hyperconjugation inhibits the formation of a chemical bond with the zeolite and denies these species the stability achieved by primary and secondary-carbocationic species, which do form chemical bonds with the zeolite. Therefore, the lower activation energy of E2 compared to that of D2 is attributed to the relatively lower stability of the E2 tertiary-carbocationic reactant state. 3.6. Trends in β-Scission. The barrier heights of β-scission elementary steps (Figure 11) can be generally understood according to the relative stability of carbocationic species in the reactant and transition states. Definite barrier height relationships were found by grouping pathways with respect to the substitution order (i.e., 3°, 2°, or 1°) of the carbocationic carbon atom in these states (Scheme 1). The organizing principle of the barrier height order is determined primarily from the degree of substitution of the carbocationic carbon at the transition state (i.e., β C) and, to a secondary extent, from the degree of substitution of the carbocationic carbon at the reactant state (i.e., C+). Trends in barrier height became readily apparent with respect to the substitution order of the β C atom (i.e., the carbocationic carbon atom of the transition state) when grouping β-scission elementary steps according to the substitution order of the C+ atom (i.e., the carbocationic carbon atom of the reactant state). For example, the pathways containing a tertiary-carbocationic reactant (Figure 11a, left) display increasing barrier height with decreasing substitution order of the β C atom at the transition state (A-2 ≈ B2-2 < B2-1 < E2). Grouping by secondary-alkoxide reactants (Figure 11a, center) also showed increasing barrier height with decreasing substitution order of the β C atom at the transition state (B1 < C-2 < D2). Additionally, the pathways containing primaryalkoxide reactants (E1 < D1) showed the same trend (Figure 11a, right). These findings, indicating that the substitution order of the β C atom is a major factor in determining the overall barrier height, confirm those of previous reports.25,28,42−46 Distinct trends were also found when grouping β-scission steps according to the substitution order of the C+ atom (Figure 11b). For pathways containing a primarycarbocationic transition state, the barrier height increases as the substitution order of the β C atom decreases (E2 < D2). This relationship is also found for those pathways containing a secondary-carbocationic transition state (B2-2 < C-2 < D1), but not for those containing a tertiary-carbocationic transition state (A < B1 > E1). The discrepancy is attributed to the greater chemisorption energy (30 kJ mol−1) of the C8 B1.r secondaryalkoxide versus the C6 E1.r primary-alkoxide. Therefore, the stability of the adsorbed carbocation, which is determined not only by the substitution order of the C+ atom but also by dispersion interactions, contributes significantly to the overall barrier height. Figure 11 shows that barrier heights are inextricably tied to the overall stabilization of the reactant and transition states and therefore the substitution order of both the carbocationic

Figure 9. Reaction mechanism and energy profile (kJ mol−1) for the E1-type β-scission of a primary-alkoxide (3,3-dimethyl-1-butoxide).

mol−1 lower than that of B1. Given similarly stabilized transition states, the activation energy should depend on the relative stability of the reactant states. The C8 secondary-alkoxide of B1 chemisorbed 30 kJ mol−1 more strongly (176 kJ mol−1) than the C6 primary-alkoxide of E1 (146 kJ mol−1); this is attributed to the increased bulk and, therefore, increased dispersion interactions of a C8 versus a C6 species. We note that the activation energies belonging to the set of β-scission pathways containing tertiary-carbocationic species in the transition state E1 B1 −1 −1 −1 (EA‑2 act = 92 kJ mol < Eact = 144 kJ mol < Eact = 153 kJ mol ) follow a monotonic trend with respect to the heat of adsorption −1 (ΔHA‑2 < ΔHEads1 = 146 kJ mol−1 < ΔHBads1 = 176 ads = 113 kJ mol −1 kJ mol ). 3.5.2. E2-Type (3° → 1°). The E2-type β-scission of a tertiary-carbocation (2-methyl-2-pentyl-carbocation) results in C4 (isobutene) and C2 (ethoxide) fragments. With an activation energy (200 kJ mol−1) that is 56 kJ mol−1 greater than the E1type β-scission, the barrier height of this pathway is exceeded only by that of the D2-type β-scission (Figure 10). The transition state involved the ethyl-carbocation, a highly unstable

Figure 10. Reaction mechanism and energy profile (kJ mol−1) for the E2-type β-scission of a tertiary-carbocation (2-methyl-2-pentylcarbocation). 23616



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Figure 11. Activation energies for the β-scission of C8 and C6 isomers. In panel (a), β-scission elementary steps sharing the same substitution order of the carbocationic carbon atom in the reactant state (i.e., C+) have been grouped together. In panel (b), β-scission elementary steps sharing the same substitution order of the carbocationic carbon atom in the transition state (i.e., β C) have been grouped.

Figure 12. Relationship between the activation energies of β-scission and (a) the charge of the β C atom in the reactant state and (b) the change in charge (from the reactant to transition state) of the β C atom.

carbon atoms (i.e., C+ and β C). Furthermore, the degree of substitution of these atoms can be ascertained from the reactant state alone. While a pathway containing primary-alkoxides at both the reactant and product states (i.e., 1° → 1°) is not studied in this work, our results predict such a pathway to have a barrier height greater than that of the D1-type and D2-type pathways. Several correlations are found between β-scission barrier heights and the charges of the system. The charge of the β C atom at the reactant state forms groups according to its order of substitution (Figure 12a). Additionally, nearly monotonic trends are found with respect to reactant stability within each grouping. Furthermore, barrier heights increase with the amount of positive charge that the β C atom in the reactant state requires to achieve full sp2 hybridization in the β-scission transition state (Figure 12b). The relationship is improved when considering only the pathways in which no chemical bond is formed with the zeolite but deteriorates when considering only the pathways with alkoxide reactant states. This latter point is attributed to increased steric hindrance from

closer proximity to the zeolite pore walls. In going from the reactant to the transition state, the average change in charge of the β C atom is +0.28e; with respect to the carbocationic species present at the transition state, the averages are +0.26, +0.27, and +0.31 for tertiary, secondary, and primarycarbocationic species, respectively. In a recent computational study, Wang et al. investigated βscission modes in SAPO-34 and similar barrier heights were found.66 Specifically, the A-type barrier in SAPO-34 (93 kJ mol−1) was almost equal to the one found in this study (92 kJ mol−1). The E1-type (140 kJ mol−1) and C-type (152 kJ mol−1) barriers in SAPO-34 were also close to those reported here (144 and 161 kJ mol−1, respectively). The barrier height order of the C, D2, and E1-type β-scission modes also match that of this work (E1 < C < D2). However, the D1-type barrier in SAPO-34 (169 kJ mol−1) was 27 kJ mol−1 less than that found here (196 kJ mol−1). In another β-scission mode involving a tertiary-carbocationic reactant state, the E2-type barrier in SAPO-34 (146 kJ mol−1) was 54 kJ mol−1 less than that found 23617



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in our work (200 kJ mol−1). The differences in barrier heights may elucidate the selectivities of these two catalytic materials. Plotting charge density isosurfaces at the same level across all β-scission modes clearly shows that more facile cleavage occurs when less charge is present between the α and β carbon atoms of the reactant state (Figure 13). In A-2.r and B2-2.r, the

4. CONCLUSIONS In this work, the activation energies for twelve β-scission elementary steps were calculated using dispersion-corrected DFT. With the exception of β-scission modes involving tertiarycarbocations, the reactant and product states of each pathway consisted of surface-bound alkoxides. Rapid isomerization, protonation, and desorption relative to β-scission enable olefins to attain configurations ideal for cracking. Promotion of a lower-energy reactant state to a higher-energy conformation gives access to pathways with lower activation energies in each studied case (i.e., B2-2, A-2, and C-2). A larger change in charge of the β C from the reactant to the transition state correlates in a linear fashion with an increase of the β-scission energy barrier. The charge of the β C in the reactant state is predominantly determined by the substitution order of the β C. Therefore, the β C of E1 and E2 and similarly B1 and B2 β-scission modes have different charges in the reactant state as well as the transition state. As a result, the change in charge of the β C and the activation energy is distinct for each mode. Furthermore, lower barrier heights result from reactant states where the fragment containing the β C has a higher positive charge. For β-scission elementary steps containing the same substitution order of the β C atom, barrier heights can be predicted based on the charge on the β C atom irrespective of whether the reactant is an alkoxide or a stabilized, physisorbed carbocation. Charges as well as the substitution order of the β C and C+ atoms can be ascertained from the reactant state alone. Therefore, an informed prediction of the reactant isomer with the lowest barrier can be made based only on the number of carbon atoms. This isomer can then be optimized to compute the relevant charges so that β-scission activation energies can be predicted without the need to localize corresponding transition states.

Figure 13. Electronic charge density isosurfaces at the same level (0.2 e a.u.−3) for different β-scission reactant states.

reactant states corresponding to the β-scission elementary steps with the two lowest activation energies, the 0.2 e a.u.−3 isosurface fails to span the β-bond. However, in B1.r the isosurface does span the β-bond, and in C-2.r, the radius from the β-bond to the isosurface is larger than that in B1.r. Pursuant to this observation, the hydrocarbon is considered as two fragments throughout the reaction. In general, the activation energy is found to be lower when a greater positive charge is present on the fragment containing the β C atom (Figure 14);

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ASSOCIATED CONTENT

S Supporting Information *

Full energy profiles, atomic positions, internal coordinates, and Löwdin-derived charges for each reaction pathway. This material is available free of charge via the Internet at http:// pubs.acs.org.

Figure 14. Relationship between the activation energies and the total charge on the fragment containing the β C atom in the reactant state.

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β C fragments possessing more positive charge prior to βscission need not acquire as much charge in order to achieve the sp2 hybridization required of the β C atom in the transition state. The barrier height is, primarily, a function of the substitution order of the β C and C+ atoms of the reactant species and, secondarily, a function of the specific mechanism (e.g., different conformational isomers of the reactant state, alkoxide formation after the transition state, or direct formation of the second olefin through hydrogen transfer). On the basis of our study of a range of possible reactions on a single active site of H-ZSM-5, our results suggest that the B2type mode is preferred for C8 olefins (producing pentene and propene) and that the C-type mode is preferred for C6 olefins (producing two propene molecules); both predictions are in agreement with the product selectivity observed by Buchanan et al.25 The barrier heights determined in this work will be incorporated into a kinetic model pertaining to the transformation of methanol to hydrocarbons.

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (M.C.). *E-mail: [email protected] (A.B.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Abu Dhabi-Minnesota Institute for Research Excellence (ADMIRE), a partnership between the Petroleum Institute at Abu Dhabi and the Department of Chemical Engineering and Materials Science at the University of Minnesota, and by The Dow Chemical Company. M.C. acknowledges partial support from the NSF CAREER award, DMR 1151738. A.B. acknowledges partial support from the NSF CAREER award, CBET 1055846. We are also grateful to the Minnesota Supercomputing Institute at the University of Minnesota for providing computational resources and technical support. 23618



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Î²-Scission of Olefins on Acidic Zeolites: A Periodic PBE-D Study in H

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