Article pubs.acs.org/JPCA
Carbocation Stability in H‑ZSM5 at High Temperature Glen A. Ferguson,† Lei Cheng,‡ Lintao Bu,† Seonah Kim,† David J. Robichaud,† Mark R. Nimlos,† Larry A. Curtiss,‡ and Gregg T. Beckham*,† †
National Bioenergy Center, National Renewable Energy Laboratory, 15013 Denver West Parkway, Golden, Colorado 80401, United States ‡ Material Science Division, Argonne National Laboratory, 9700 South Cass Avenue B109, Lemont, Illinois 60439, United States S Supporting Information *
ABSTRACT: Zeolites are common catalysts for multiple industrial applications, including alcohol dehydration to produce olefins, and given their commercial importance, reaction mechanisms in zeolites have long been proposed and studied. Some proposed reaction mechanisms for alcohol dehydration exhibit noncyclic carbocation intermediates or transition states that resemble carbocations, and several previous studies suggest that the tert-butyl cation is the only noncyclic cation more stable than the corresponding chemisorbed species with the hydrocarbon bound to the framework oxygen (i.e., an alkoxide). To determine if carbocations can exist at high temperatures in zeolites, where these catalysts are finding new applications for biomass vapor-phase upgrading (∼500 °C), the stability of carbocations and the corresponding alkoxides were calculated with two ONIOM embedding methods (M06-2X/6-311G(d,p):M06-2X/3-21G) and (PBE-D3/6-311G(d,p):PBE-D3/3-21G) and plane-wave density functional theory (DFT) using the PBE functional corrected with entropic and Tkatchenko−Scheffler van der Waals corrections. The embedding methods tested are unreliable at finding minima for primary carbocations, and only secondary or higher carbocations can be described with embedding methods consistent with the periodic DFT results. The relative energy between the carbocations and alkoxides differs significantly between the embedding and the periodic DFT methods. The difference is between ∼0.23 and 14.30 kcal/mol depending on the molecule, the model, and the functional chosen for the embedding method. At high temperatures, the pw-DFT calculations predict that the allyl, isopropyl, and sec-butyl cations exhibit negligible populations while acetyl and tertbutyl cations exhibit significant populations (>10%). Moreover, the periodic DFT results indicate that mechanisms including secondary and tertiary carbocations intermediates or carbocations stabilized by adjacent oxygen or double bonds are possible at high temperatures relevant to some industrial uses of zeolite catalysts, although as the minority species in most cases.
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INTRODUCTION The production of renewable fuels using fast pyrolysis of lignocellulosic biomass has received a surge of interest in recent years. However, the oxygenated molecules resulting from biomass fast pyrolysis have undesirable properties that make the resulting bio-oil impractical for direct commercial use, warranting robust catalytic deoxygenation strategies.1 To that end, zeolites have emerged as a potentially attractive suite of catalysts for pyrolysis vapor upgrading2−6 in addition to their other, well-known industrial applications (e.g., in the methanolto-gasoline process and in the production of ethylene from ethanol, among others).7−11 A primary reaction that zeolites catalyze in multiple industrial contexts is dehydration of alcohols.2,12 The mechanism by which dehydration occurs in zeolites has been proposed to proceed through a number of possible pathways (as illustrated in Scheme 1 for isopropanol dehydration).10 One proposed dehydration pathway involves the formation of carbocations in analogy to reactions in acidic media.13−16 In these proposed reaction pathways, the Brønsted acid sites of the zeolite protonate an oxygen atom on the reactant molecule, © XXXX American Chemical Society
resulting in dehydration to form a water molecule and a carbocation intermediate, as illustrated in Scheme 1a.10 In another possible mechanism, the dehydration reaction proceeds through a single step with concerted hydrogen transfers, as shown in Scheme 1b, which was recently explored by Kim et al.10 In this pathway, the transition state exhibits a partial charge on the carbon, thus resembling a carbocation. Such a transition state could be stabilized in the same manner as a carbocation intermediate. To date, it has been conclusively demonstrated that cyclic hydrocarbons and those with greater than five carbon atoms exist as persistent intermediates7,17−23 while straight chains with four carbons atoms exist as transient intermediates. However, four carbon species carbocations have not been experimentally observed as persistent intermediates in zeolites.13−15,24−27 It is unclear if this is due to the absence of these species in the reaction pathways or to short lifetimes in the zeolite. Some theoretical studies have proposed that these Received: July 21, 2015 Revised: October 21, 2015
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likely to exhibit both of these interactions, this is a possible source of significant error. Embedding methods using semiempirical and molecular mechanics do not capture the longrange electrostatic effects and may fail to include local steric effects depending on the size of the high-level region chosen for the embedding method. Periodic DFT using GGA with a planewave basis set (which we denote as “pw-PBC”) suffers from a lack of van der Waals (vdW) interactions and may suffer from noncanceling self-interaction errors.13−15,24−26,33−35,39 It is possible to use van der Waals corrections to improve the vdW forces for pure GGA functionals, resulting in significant improvement of the total energy. The computationally expensive MP2:DFT method34,35,39 overcomes these limitations and is likely an excellent estimate for carbocation energies in zeolites but is exceptionally expensive and not widely available, making it impractical for routine calculations. To date, the MP2:DFT method has only been applied to tert-butyl carbocation calculations.34,35,39 However, recent exchangecorrelation functionals, such as M06-2X,40 may also be able to accurately describe carbocation stabilities in zeolites at a significantly reduced computational cost using embedding methods. Of note, previous work on carbocation stability relative to the corresponding alkoxide by Fang et al. included 20 ion pairs in HZSM-5, HY, and H-BEA zeolites.33 This study used the ONIOM embedding method with the M06-2X functional for the high level and AM1 for the low level. In this work, stable cations were not found for the ethyl and isopropyl cations, but a minimum was found for the tert-butyl cation. Using the MP2:DFT method, Tuma et al.34,35,39 confirmed that the tertbutyl cation is a minimum on the potential energy surface (PES) and is metastable relative to the alkoxide for H-FER zeolite. The tert-butyl cation has been observed in the H-ZSM5 zeolite using NMR spectroscopy.41 Carbocations would be thermodynamically favored at higher temperatures due to entropic stabilization. At moderate temperatures (0 °C), small linear carbocations are unlikely to be found in zeolites with the possible exception of the tert-butyl cation. However, it is still possible that at the high temperatures (500 °C) found, for example, in catalytic upgrading of biomass pyrolysis vapors, a small percentage of highly reactive carbocations may be present as reaction intermediates, but it is unclear if these species exist in sufficient concentrations to be kinetically relevant. To that end, in this study, we use DFT calculations to determine which carbocation species can exist in sufficient quantities to be significant at pyrolysis reaction conditions. We also examine if ONIOM embedding methods can accurately capture the energy differences between carbocations and alkoxides using the M06-2X and PBE-D3 functionals. Our results indicate that only the tert-butyl cation and cations stabilized by functional groups adjacent to the positively charged carbon will be present at high temperature. No ONIOM methods tested could find minima for the primary carbocations. Some secondary and tertiary carbocations were minima with embedding methods. The relative energy between the carbocations and the alkoxides differs between the embedding methods used and the pw-PBC method. The differences range between 0.23 and 14.30 kcal/mol depending on the molecule, the model, and functional chosen for the embedding method. Several possible mechanisms exist for dehydration reaction of zeolites. Other possible intermediates are possible including protonated alcohols that can undergo E1- and E2-like
Scheme 1. Three Possible Dehydration Reactions of Isopropanol to Propene and Watera
a
In addition to the concerted mechanism shown in (b), it is also possible for the reaction to occur through an elimination-type mechanism with the hydroxyl group as the β-hydrogen acceptor.
short-chain (4 carbons or fewer) carbocations exist as reaction intermediates in the recent literature.28−32 Alternatively, other species, alkoxides, have been observed as persistent intermediates in zeolites for short chain species, i.e., fewer than five carbon atoms.13−15,17−20,24−27 The mechanisms that form alkoxides would follow a stepwise pathway, as illustrated in Scheme 1c. In this mechanism, shown for isopropanol, dehydration occurs while forming a carbon−oxygen bond to the zeolite framework,11,27 in this case an ethyl group bound to the oxygen site in the framework. The presence of these intermediates would indicate a stepwise mechanism in Scheme 1c. Mechanisms that exhibit carbocations are thought to exhibit significantly faster rates than those that go through stable alkoxide intermediates.13−15,24−27 From these data, one could conclude that at low temperatures that can be experimentally explored17−20 short-chain carbocations are not present as part of the reaction mechanism. This does not preclude the formation of carbocations as metastable, highly reactive intermediates at the elevated temperatures (∼500 °C) found in catalytic fast pyrolysis and other industrial applications of zeolites. At high temperatures (∼500 °C), carbocations would be entropically stabilized and would be expected to have a greater population than at lower temperatures. However, the difficulty in experimental detection at elevated temperatures warrants the use of quantum mechanical calculations to determine if these species exist and if they can play a role in dehydration mechanisms in zeolites. Previous first-principle calculations have shown that alkoxides are more stable than carbocations, with the exception of the tert-butyl cation both using 0 K conditions and using entropic corrections for 298 K.13−15,25−27,33−35 These studies have employed models consisting of small clusters treated with density functional theory (DFT),36 embedding methods using DFT with semiempirical methods or molecular mechanics, 13,14,25,26,28−31 periodic DFT, 6,37,38 and the hybrid MP2:DFT method at 298 K.34,35,39 With the exception of the lattermost, these model−method combinations exhibit significant approximations for carbocations relative to alkoxides. Specifically, cluster models do not capture the steric and longrange electrostatic effects present in zeolites. As zeolites are B
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The Journal of Physical Chemistry A mechanisms as detailed in work of Kostestkyy et al.42 Understanding how these relate to carbocations requires a more detailed knowledge of the PES than is contained here and will be the subject of future studies. The work herein is to determine if unstabilized carbocations are reasonable intermediates at high temperatures (500 °C) and if ONIOM models are reasonable for predicating the existence of these species.
accurate. Consistent with previous work,33 the results using the less computationally intensive M06-2X/6-311G(d,p):PM6 model chemistry did not result in minima for most the carbocation species, which was also found by Fang et al. using M06-2X/AM1.33 The QM/QM model was chosen as the least computationally intensive embedding method that may have the possibility of capturing the part of the interactions present in the pw-PBC or large basis set calculations. The atoms in the region calculated using the more accurate method (model system or high level) contain the substrate molecules and a 5T cluster, which constitutes the T12 site (substituted by an Al atom), a Brønsted acid site proton, and the nearest four silicon sites around T12. The atoms in the region calculated using the less expensive method (low level) contain 309 atoms. All atoms in the high level layer were relaxed while the atoms in the low level were fixed at their crystallographic positions. Additional models with different numbers of T sites, i.e., 8T, 12T, and 22T clusters, were used to investigate the effect of model size on the stability of the cation using the tert-butyl cation. Models of these structures can be seen in Figure SI 1 of the Supporting Information. The tert-butyl species is the largest cation studied, and it has the greatest potential to interact with atoms outside the local 5T environment of the acid site. Specifically, the 8T cluster model included an additional three silicon sites around the tert-butyl cation. The 12T cluster consists of one entire 10member ring (10-MR) surrounding the cation and the 22T cluster consists of two 10-MRs. In the second 22T cluster model (22T_96atoms), an additional 38 atoms in the low level around the tert-butyl cation were also relaxed, resulting in a total number of 96 flexible atoms, while in the first 22T cluster model, only the atoms in the high level (58 atoms) were relaxed. Minima were verified as having all positive frequencies. All embedding calculations used Gaussian09 suite of programs.67 The optimization procedure for the primary carbocations was as follows; starting structures, taken from PBC calculations, were optimized using the 5T model. These optimization resulted in alkoxides. A second attempt was made using constrained optimization of the carbocation molecules followed by full optimization of the 5T model with the carbocation that also resulted alkoxide formation. The third attempt at finding a stable minimum was to move the carbocations as far away as was reasonable from the T12 site prior to optimization. These optimizations resulted in spontaneous hydrogen transfers to the zeolite or interaction of the carbocation with the low level of the ONIOM layer. Finally, the high-level region of the ONIOM model was systematically increased from 5T to 8T, 12T, and 22T prior to optimization. These final optimizations also resulted in alkoxides for the primary carbocations. Therefore, we have concluded, using these ONIOM models, the minima on the PES for primary carbocations either do not exist or are too shallow to reasonably locate. The Boltzmann distribution was used to determine the relative population of the carbocation to alkoxide by calculating the ratio of probabilities for each energy state using eq 1 represented as a percentage.
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COMPUTATIONAL DETAILS The stability of noncyclic carbocations resulting from dehydration reactions in H-ZSM-5 (MFI framework) was determined by calculating the carbocation energy relative to the corresponding alkoxide. The base unit cell for the MFI framework contains Si96O192 atoms resulting in a neutral system. To introduce a Brønsted acid site, a silicon atom was substituted with an aluminum atom at the T12 site,36,43 which is claimed to be the most common site for aluminum substitution. The resulting negative charge was balanced by adding a proton on the adjacent oxygen to maintain a neutral system. In this work, the dehydration (or any other reaction that may have a carbocation or alkoxide as an intermediate) is assumed to follow Scheme 1a,c where the intermediate is either the carbocation or the alkoxide in the sinusoidal channel of HZSM5. Models with and without a water molecule were examined to determine if the explicit inclusion of a water molecule in the zeolite cavity is a possible source of error, but no significant differences were observed. The position of the adsorbate was optimized in the zeolite cavity starting from the conformation in previous work.10 Kohn−Sham DFT solved using a plane-wave basis with periodic boundary conditions was implemented in the Vienna Ab initio Simulation Package (VASP) 5.3.5.44−47 The ion− electron interactions were described using the PAW potentials48,49 with an energy cutoff of 400 eV. The generalized gradient corrected PBE functional was used for all periodic calculations. PBE functionals were found to accurately reproduce experimental binding energies for alcohols.50 The unit cell was relaxed to 20.01 Å × 19.74 Å × 13.14 Å with Γpoint sampling. Optimizations were carried out until the forces were below 0.05 eV/Å. The van der Waals forces were calculating using the method of Tkatchenko and Scheffler as implemented in VASP.51−53 The Γ-point phonon dispersions were calculated using the force constants found by numerically differentiating the forces using a two-point finite difference (displacement of 0.015 Å) for a subset of the model including the reactant molecule, the aluminum and silicon atoms proximate to the reactant, and the oxygen atoms bound to these species. Resulting second derivatives were used to verify minima. Free energies include the entropy corrections calculated using standard approximations and zero-point energies calculated from the frequencies. All embedding calculations were performed using the twolayer ONIOM QM/QM scheme. The values for the embedding method54 were calculated using both the (M06-2X/6-311G(d,p):M06-2X/3-21G)40,55−62 and the (PBE-D3/6-311G(d,p):PBE-D3/3-21G//M06-2X/6-311G(d,p):M06-2X/321G)63,64 model chemistries.65 The M06-2X model chemistry was found to have a mean unsigned error of 1.61 kcal/mol compared to CCSD(T) corrected MP2 at the infinite basis set limit for model zeolite systems.66 The value of the latter method was to test the difference between the functionals used for embedding and pw-PBC while the more accurate metahybrid GGA M06-2X functional is expected to be more
pi /pj = e(ϵj − εi)/ kT
(1)
In eq 1, pi and pj are the probability of states i and j and ϵi and εj are the energies of states i and j. This equation yields the relative percentages of alkoxodes and carbocations. C
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RESULTS AND DISCUSSION The intermediates of alcohol dehydration by zeolites are water and either a carbocation or alkoxide. For short-chain (3−4 carbons) carbocations, it is possible that additional functional groups on the molecule can stabilize a carbocation. To explore this possibility, the carbocations and corresponding alkoxides were calculated for the following species: ethyl, acetyl, propyl, isopropyl, allyl, butyl, sec-butyl, and tert-butyl, with the carbocations shown in Figure 1. The intramolecular con-
Figure 1. Connectivity for the carbocation species calculated inside the zeolite cavity geometries constructed from the pw-PBC optimized geometries.
Figure 2. Difference between the carbocation and alkoxide species using pw-PBC and the ONIOM M06-2X/6-311G(d,p):M06-2X/321G (embedding 1, blue) or ONIOM PBE-D3/6-311G(d,p):PBED3/3-21G//M06-2X/6-311G(d,p):M06-2X/3-21G (embedding 2, green) embedding methods using the 5T ONIOM model. No minima were found with embedding methods for the ethyl, propyl, and butyl carbocations.
nectivity of the carbocations shown is that in the zeolite framework after optimization. While in most cases this geometry corresponds to the gas phase geometry such as with the ethyl cation68 (Figure 1a), some species differ as is the case for the propyl cation (Figure 1c) for which the gas phase global minimum has been shown to be noncyclic69 and the butyl cation (Figure 1f) that is found to cyclize in the gas phase.32 To determine the relative stability of the intermediates, the alkoxide and ionic structures were optimized using the pw-PBC and the two QM/QM embedding methods. The relative energies were taken to be the difference of the electronic energies, ΔE = ECarbocation − Ealkoxide. While the pw-PBC methods can suffer from nonsystematic self-interaction error, data in the work by Tuma et al.39 indicate that the error for the relative minima of the tert-butyl cation and alkoxide were constant. As the errors due to self-interaction are most severe for hydrogen transfer reactions,70 the pw-PBC method including van der Waals likely results in reasonable estimates of the relative energy. The energy differences, shown in Figure 2, are the relative energies between the respective carbocation and the corresponding alkoxide species. Two embedding methods were tested: one based on the M06-2X functional and the other on the PBE-D3 functional. The PBE-D3 functional was included to test the relative difference between functionals (vide inf ra), while the more accurate meta-hybrid GGA functional M06-2X was used for reported values. The two-carbon species include ethyl (Figure 1a) and acetyl cations (Figure 1b). It is worth noting that other possible reaction pathways exist for acetic acid dehydration in zeolites. Acetic acid is the most likely source of acetyl cation in these systems.71,72 The acetyl species is, however, an excellent example of how an adjacent functional group on the molecule can influence the carbocation stability. In this case, the functional group is the oxygen atom doubly bound to the carbocation carbon. While both C2 species are minima in the dispersion-corrected pw-PBC calculations, we could not find a
minimum for the ethyl carbocation using the embedding methods in this work, whereas we did find minima for the acetyl species. The geometries for the minima of the pw-PBC structures are shown in Figure 3. The carbon−zeolite oxygen
Figure 3. Pw-PBC optimized geometry for the two-carbon species ethyl and acetyl species with both the alkoxide and carbocations shown.
(C−O) bond for the alkoxides is 1.53 and 1.58 Å for the ethyl and acetyl species, respectively. The ethyl carbocation exhibits a hydrogen bridge between the carbon atoms, indicating symmetric delocalization of the charge, as illustrated in Figure 1a. The positive charge in the acetyl carbocation is stabilized by the adjacent oxygen. In this structure, the acetyl CO bond distance changes only slightly from the parent structure (0.03 Å), indicating that the localized charge does not change the nature of the CO double bond. The relative energy difference D
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1.56 Å for the allyl alkoxide. As shown in Figure 4, the propyl cation cyclizes to form the cyclopropyl cation, which delocalizes the charge across multiple carbon atoms, thereby stabilizing the species.32 Cyclization is not observed in the isopropyl or allyl cation. For these molecules, the positive charge can delocalize over the molecule due to the adjacent groups, resulting in a linear species, as shown in Figure 1d,e. The stability of the propyl cation relative to the alkoxide is such that the carbocation would not be observed under hightemperature catalytic conditions. However, the isopropyl cation and allylic cations are significantly more stable. The energy differences found using the embedding method were higher than the pw-PBC method by 10.15 kcal/mol for the isopropyl cation and 3.23 kcal/mol for the allylic cation (Figure 2). These values are in reasonable agreement given the approximations of the embedding method. While at 0 °C, neither species would be observed, at 500 °C a small population of isopropyl carbocations could be found with the proportion of allylic carbocation is 1 order of magnitude lower (Table 1). The four-carbon species were also examined, including the butyl (Figure 1f), sec-butyl (Figure 1g), and tert-butyl (Figure 1h) species. Unlike previous studies,28−32 neither embedding nor pw-PBC could find a minimum for the primary carbocation. The butyl compound has been shown to form cyclic structures,31,32 but these species were not found in the constrained zeolite channel used in this study. Reported geometric values for the pw-PBC method from those previous studies have the hydrogen atoms bound to the second carbon frozen, which likely forces the geometry into an artificial minimum. In the current work, embedding methods bound the carbocation to a framework oxygen atom to form the corresponding alkoxide, while the pw-PBC calculations underwent a zero-barrier 1,2-hydride transfer to the sec-butyl cation. This transfer is an artifact of how the carbocation was constrained in the channel of this zeolite. The sec-butyl and tert-butyl cations were minima with the pw-PBC and the allDFT embedding method, as shown in Figure 5. The alkoxide C−O bond distances are within the same range as the previous systems of 1.54 Å for the butyl alkoxide and 1.57 Å for the secbutyl alkoxide. However, the tert-butyl alkoxide has a bond distance of 1.65 Å, reflecting the steric repulsion present in the system. The butyl cation delocalizes the charge by forming the bridging hydrogen in a similar manner to the ethyl cation (vide supra), as shown in Figure 1f. The difference between the secbutyl energy for the embedding methods and the pw-PBC
for ethyl carbocation and the alkoxide was 38.74 kcal/mol, favoring the alkoxide. The energy difference indicates that even at very high temperatures, the ethyl carbocation will not exist as an isolated species. For the acetyl cation, the stabilization of the oxygen charge is also reflected in the energy. The pw-PBC energies show only a 5.53 kcal/mol difference while the embedding methods show an even smaller difference of 1.15 kcal/mol. In both cases, the alkoxide is more stable than the carbocation. If entropic corrections to the pw-PBC at 500 °C are added, the difference drops to 2.31 kcal/mol (pw-PBC), as shown in Table 1. Table 1. Free Energy Differences for the pw-PBC Model 0 and 500 °C along with Their Boltzmann Population at 0 and 500 °C Using the pw-PBC
a b
cation
ΔG bond typeb (kcal/mol) 500 °C
ΔG bond typeb (kcal/mol) 0 °C
carbocation population (%) 500 °Ca
carbocation population (%) 0 °Ca
acetyl allyl isopropyl sec-butyl tert-butyl
−2.31 −14.99 −9.92 −12.45 1.15
−5.07 −19.14 −11.99 −13.61 0.69
17.80 0.01 0.14 0.03 68.24
0.01 0.00 0.00 0.00 61.27
Assumes a Boltzmann distribution based on free energy difference. Bond type Δ = GCarbocation − Galkoxide (includes ZPE).
Assuming a Boltzmann distribution, the population of the carbocation species at 0 °C is only 0.01% while the percentage at a catalytically relevant temperature (500 °C) is approximately 18%. This species is therefore likely to exist at catalytic temperatures in significant quantities. The stabilizing effects of the entropic contributions are due to the vibrational entropy favoring the carbocation over the alkoxide. The effect is modest at 0 °C but significant at 500 °C, temperatures exhibiting a population that if the reaction of the carbocation is facile may significantly alter the reactivity. The three-carbon molecules examined include the propyl (Figure 1c), isopropyl (Figure 1d), and allyl cations (Figure 1e). No minimum was found for the primary propyl carbocation using embedding methods, whereas the isopropyl and allylic carbocations exhibit a minimum for both the embedding and pw-PBC methods. The pw-PBC geometries are shown in Figure 4. The zeolite−alkoxide C−O bond varies from 1.51 Å for the propyl, to 1.50 Å for the isopropyl, and to
Figure 4. pw-PBC optimized geometry for the three-carbon species propyl, isopropyl, and allyl with both the alkoxide and carbocations shown. E
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Figure 5. pw-PBC geometries for the four-carbon species butyl, sec-butyl, and tert-butyl with both the alkoxide and carbocations shown.
method is 3.00 kcal/mol (Figure 2), as found for the allylic ion above. The difference for the tert-butyl cation is significantly higher at 7.38 kcal/mol for embedding methods favoring the cation, while the pw-PBC is much closer in energy at 0.23 kcal/ mol. The origin of this difference is inclusion of steric hindrance in the zeolite pore. Starting with the 5T embedded model for the zeolite, the difference between the carbocation and alkoxide species is 14.30 kcal/mol, favoring the carbocation. As more atoms are included in the quantum layer and relaxed, the value drops to 5.53 kcal/mol, favoring the carbocation, 22T 96 relaxed model shown in Figure 6 and
Based on these data, it is reasonable to consider the lower value of the pw-PBC as a better estimate of the energy difference than the embedding method. The butyl cation is unstable even at high temperature catalytic conditions and the tert-butyl cation would be the dominant species over the temperature range, as shown in Table 1. The sec-butyl carbocation would be present at 0.03%, a similar percentage to the allyl cation. Comparison of Embedding Methods to Periodic DFT Calculations. The embedding methods had absolute differences of 3.00 to 11.07 kcal/mol for the PBE-D3/6-311G(d,p):PBE-D3/3-21G//M06-2X/6-311G(d,p):M06-2X/3-21G and from 0.23 to 14.30 kcal/mol for the M06-2X/6311G(d,p):M06-2X/3-21G compared to the pw-PBC method. Using embedding methods with QM/MM or QM/QM with a semiempirical, low-level layer, we could not locate primary carbocation minima, thus suggesting that these particular embedding methods are not appropriate for the study of primary carbocations. However, these systems are not likely to be important, as carbocations energies are significantly less stable than the alkoxide by a range of 16.83−38.74 kcal/mol. For secondary, tertiary, and carbocations stabilized by adjacent functional groups (e.g., oxygen and double bonds), minima were present for the all DFT QM/QM methods. For secondary and tertiary carbocations, the differences between the two embedding methods were, in most instances, relatively modest (Table 2). The largest difference is for the tert-butyl carbocation (20.98 kcal/mol) while the smallest is for
Figure 6. ΔE between the alkoxide and the carbocation for the PBC calculation and a series of models for the M06-2X/6-311G(d,p):M062X/3-21G embedding method for the tert-butyl alkoxide and carbocation. The increasing number indicates more atoms are included in the high-level quantum region of the embedding calculation. The final 22T 96 relax also has an additional number of atoms relaxed in the low-level region of the embedding calculation.
Table 2. Differences between the pw-PBC Method and the Two Embedding Methodsa ΔΔE (kcal/mol) cation ethyl acetyl allyl propyl isopropyl butyl sec-butyl tert-butyl
described in detail below. The previous value of 5.53 kcal/mol reported by Tuma et al. using the MP2:DFT method for the HFER zeolite indicates that significant steric repulsion is likely present.34 As the H-FER zeolite has smaller pore sizes than HZSM5, more steric repulsion would be expected. In the work by Fang et al., they calculated the energy difference for the tertbutyl carbocation and alkoxide in H-ZSM5 and reported a similar trend with a value of 9.45 kcal/mol (0.41) for the 8T model and −3.23 kcal/mol (−0.14 eV) for the 72T model.33
embedding 1
embedding 2
−4.38 0.23
−3.00 3.92
−10.38
−5.30
−3.23 −14.30
2.31 −20.75
ΔΔE = (ECarbocation − Ealkoxide)pw‑PBC − (ECarbocation − Ealkoxide)Embedding. Embedding 1 = M06-2X/6-311G(d,p):M06-2X/3-21G. Embedding 2 = PBE-D3/6-311G(d,p):PBE-D3/3-21G//M06-2X/6-311G(d,p):M06-2X/3-21G. a
F
DOI: 10.1021/acs.jpca.5b07025 J. Phys. Chem. A XXXX, XXX, XXX−XXX
Article
The Journal of Physical Chemistry A the sec-butyl carbocation (0.92 kcal/mol). These differences are lower than the differences between the embedding methods and the pw-PBC method for the same molecule with the exception of the allyl and tert-butyl species. The latter difference is likely a result of the model used. Using a 22T model results in a much smaller difference of 11.07 kcal/mol. This was also observed with embedding 1 and is likely the result of underestimated steric and hydrogen-bonding interactions, described below, rather than an intrinsic difference between the functionals used. However, these differences do indicate a modest effect of the density functional method for the embedding method that will be examined in more detail in future studies. For the tertiary species, the steric hindrance was underestimated using embedding methods. The use of embedding methods to study tertiary carbocations would require relaxation beyond the 5T model because the substrates exhibit hydrogen bonds and steric repulsion with atoms in the low level layer. As shown in Figure 6 for the tert-butyl species using embedding 1, increasing the size of the model included in the high-level region significantly reduces the difference between the embedding and pw-PBC methods. For accurate calculation of primary carbocations in H-ZSM5, pw-PBC methods are required to capture long-range electrostatic forces and shortrange steric effects. For secondary carbocations, the embedding methods provide similar results to the pw-PBC methods. The all DFT QM/QM method was sufficient for studying secondary carbocations and those stabilized by an adjacent group. Carbocation Stability at High Temperature. At low temperature (0 °C), no carbocations would exist in any significant quantity with the exception of the previously studied tert-butyl carbocation. At catalytically relevant temperatures, e.g., 500 °C, primary carbocations would not exist in significant quantities and would likely undergo 1,2-hydrogen shifts to form the secondary carbocations in the sinusoidal channel of HZSM5 or cyclization in a less confined environment. Conversely, secondary carbocations are stabilized at temperatures relevant to biomass pyrolysis vapor upgrading. Populations of isopropyl and sec-butyl would be approximately 0.01% relative to the alkoxide. While the allylic carbocation would exist at 0.01% of the population relative to the alkoxide, the acetyl carbocation would be stabilized significantly and make up ∼20% of the observed species at pyrolysis conditions. Therefore, the stability of the carbocation is dependent on the stabilization by functional groups adjacent to the site of the positive charge, the steric repulsion of the zeolite, and, as demonstrated in this study, the temperature-dependent entropic effects that are significant under catalytically relevant conditions. Because of this stabilization, some carbocations may be present in biomass pyrolysis and other industrial applications of high-temperature alcohol dehydration in zeolites and thus cannot be ruled out by their electronic energies alone. Furthermore, the intermediates in mechanisms with transition states resembling carbocations, as in the concerted mechanism shown in Figure 1c, would be stabilized under the same conditions and may also be present under high-temperature conditions.
conditions in a zeolite. To include the effects of high temperatures, entropic corrections were added to the pwPBC calculations. The results of these calculations indicate that linear ethyl, acetyl, allyl, propyl, isopropyl, butyl, and sec-butyl carbocations are not present at any temperatures, while the tertbutyl cation is the major species over the temperatures explored. At pyrolysis conditions (500 °C), the acetyl cation could be present at a 20% population relative to the acetyl alkoxide. The allyl, isopropyl, and sec-butyl cations would be present only in small amounts (
