Tailoring nanoscopic confines to maximize catalytic activity of hydronium ions

Acid catalysis by hydronium ions is ubiquitous in aqueous-phase organic reactions. Here we show that hydronium ion catalysis, exemplified by intramolecular dehydration of cyclohexanol, is markedly influenced by steric constraints, yielding turnover rates that increase by up to two orders of magnitude in tight confines relative to an aqueous solution of a Brønsted acid. The higher activities in zeolites BEA and FAU than in water are caused by more positive activation entropies that more than offset higher activation enthalpies. The higher activity in zeolite MFI with pores smaller than BEA and FAU is caused by a lower activation enthalpy in the tighter confines that more than offsets a less positive activation entropy. Molecularly sized pores significantly enhance the association between hydronium ions and alcohols in a steric environment resembling the constraints in pockets of enzymes stabilizing active sites.

a Acidity obtained from in situ titration experiments using pyridine and 2,6-lutidine; see Experimental for details. b Values in parentheses (B,L) represent concentrations of Brønsted (1540 cm -1 , molar integral extinction coefficient of 0.73 cm μmol -1 ) and Lewis acid sites (1450 cm -1 , molar integral extinction coefficient of 0.96 cm μmol -1 ) determined from gas-phase IR measurements using pyridine at 423 K. c Recovered sample after 1 h reaction at 453 K. d Not measured. e From Clariant; 0.2-0.5 μm particle size. f Recovered sample after 1 h reaction at 423 K. g From Zeolyst; ~ 1 μm particle size. h From ref. [1]. i Recovered sample after 1 h reaction at 453 K. j A sample obtained from (NH 4 ) 2 SiF 6 treatment of an NH 4 -MFI sample (Zeolyst International, CBV3024E, Si/Al = 15) and subsequently activated (calcination at 823 K for 5 h in 100 mL min -1 synthetic air with a heating rate of 10 K min -1 ).

S1.1 A brief overview of mechanistic considerations
The intramolecular dehydration of mono-alcohols is Brønsted acid-catalyzed and is postulated to start with the quasi-equilibrated protonation of the alcoholic OH to form an alkoxonium ion, followed by elimination of water and formation of the olefin (in one or two elementary steps).
Subsequent steps (e.g., olefin desorption, 1,2-hydride shift, rehydration, isomerization and C-C coupling) are irrelevant to the overall dehydration kinetics at low conversions and remote-fromequilibrium conditions. Classically, two major elimination pathways are operative: on the E1type paths (Supplementary Fig. 11a  Any of the above situations are possible, [5] depending on the alcohol structure, nature/strength of the base, polarity of the reaction media and reaction temperature. In an aqueous solution without a base strong enough to abstract a hydron from the β-carbon and on solid surfaces with predominantly acidic properties, an E1cB mechanism is highly unlikely. These mechanistic aspects, despite being well documented in homogeneous acid-catalyzed dehydration, are examined for hydrated solid surfaces in water.

S1.2 Corrections for reverse reactions
Alcohol dehydration forming olefin and water is often a reversible reaction, for which the gasphase thermochemistry is typically known. For instance, cyclohexanol dehydration to cyclohexene and water has a standard reaction enthalpy and entropy of 43.8 kJ mol -1 and 145.4 J mol -1 K -1 , respectively. In aqueous phase, however, the lack of thermodynamic data for the partitioning of reactant and products among different phases at elevated temperatures renders the direct assessment of reaction equilibrium constants and reaction quotients rather difficult. To circumvent this problem and determine the extent of the reverse olefin hydration reaction, a small quantity (5-10 mg) of a reduced Pd/Al 2 O 3 catalyst (Pd dispersion: 11 %; immeasurable activity when used alone for dehydration at 413−473 K) was added to catalyze the rapid S31 hydrogenation of cyclohexene produced. By this means, the back reaction was essentially eliminated, leading to a predominant fraction (> 95%) of cyclohexane in the products. The turnover rates determined this way on the basis of cyclohexane formation are ca. 5-10% higher than those measured only with an acid catalyst (Supplementary Table 6 reveals that the rate of the back reaction was less than 10% of the forward reaction rate on BEA (~10% conversion), while olefin rehydration was found to occur at significant rates inside the pore of MFI (> 30% of forward rate at ~9% conversion). Thus, measured reaction rates at low conversions (< 10%) reflect the forward rates on all studied acids except for MFI where forward rates would be at least 30% higher than measured rates on account of the significant back reaction even at low conversions.

S1.3 Secondary pathways
C-C coupling was not observed on any zeolites at conversions lower than 50%; in contrast, a control experiment using cyclohexene added in quantities corresponding to 30% dehydration conversion already showed significant C-C bond formation ( Supplementary Fig. 12). This difference suggests that the intraporous concentration of cyclohexene is low when that of cyclohexanol is relatively high, a result of competitive adsorption.

S1.4 Characterization results of solid acids
The textural (BET surface areas and micropore/mesopores volumes) and acidic properties of the studied solid acids, along with the used counterparts, are compiled in Supplementary Table 1 The titration experiments using dilute aqueous pyridine and 2,6-dimethylpyridine (2,6-lutidine) solutions yielded estimates comparable to those from gas-phase infrared measurements using the pyridinium absorption band at ~1540 cm -1 (within a factor of 1.3; Supplementary Table 1). 27 Al MAS NMR spectra have been measured for zeolites ( Supplementary Fig. 13). Note that with the exception of FAU, all the studied zeolites contain negligible to small concentrations of octahedral Al species (~0 ppm). showed unchanged activities in the consecutive run ( Supplementary Fig. 1). In contrast, Yzeolite (FAU) is known to undergo structural degradation in hot liquid water. [6,7] As a previous study [6] showed that the crystallinity, porosity and acidity of Y-zeolites (Si/Al = 14 and 41) suggests that active sites on FAU remain functionally intact within this time scale.

S1.6 Effect of the Si/Al ratio in MFI and BEA framework
Although changing the Si/Al ratio for a given zeolite framework is anticipated to affect the site- demonstrated that TOFs are nearly independent of the Si/Al ratio for aqueous-phase dehydration of cyclohexanol on HBEA. [8] The relatively weak dependence of rates (per BAS) on framework Al density and silanol defect concentration for BEA zeolites provides additional evidence that measured turnover rates in liquid water are not convoluted by coupled intracrystalline diffusion S33 phenomena of cyclohexanol (kinetic diameter ~0.6 nm) to active centers confined within HBEA channels. For HMFI zeolites where the concentration of EFAL also remained low, the TOFs (net olefin formation rates) decreased as the Si/Al ratio decreased from 45 to 15 (2.0-6.0 Al/u.c.; Supplementary Fig. 14). After correcting for a greater extent of back reaction with a higher BAS density in the MFI channel, the difference in the forward dehydration rate should be rather limited (a factor of ~2).
Given that Si/Al ratio affects the hydrophilicity/hydrophobicity of, and the spatial proximity of BAS [9] inside the intraporous environment, [10][11][12] we infer that neither of these two factors are considerably altered in the studied range of Si/Al ratio, or that they, at best, have limited impact on this reaction when operated within the zero-order kinetic regime (saturation of active sites for all zeolites except CHA) and when the nature of the active site remains unchanged. However, it is reasonable to anticipate that, for highly hydrophobic zeolites (e.g., those modified with organosilanes [13] ) where water intrusion and association with the internal BAS is strongly impeded, the active site could significantly differ from intrazeolitic "hydronium ion" as in relatively hydrophilic zeolites (as used in this work), and might be better represented by framework-bound proton which was shown to catalyze the reaction with completely different energetics (e.g., in gas-phase or neat liquid alcohol phase).

Supplementary Note 2. Thermochemical analysis of adsorption measurements
When pores are fully occupied, the adsorption of cyclohexanol from dilute aqueous solution will result in displacement of intraporous water molecules out of the pores, which can be written as a reversible exchange process between the interfacial monolayer and the bulk phase: The cycle in Supplementary Fig. 18 is dissected into the following steps (dashed arrows): ( however, is not reported. For a number of alcohols (C 2 -C 4 aliphatic alcohols), the temperature dependences correspond to -ΔH = 53−65 kJ mol -1 for K H . [15] Thus, we used 57 kJ mol -1 as the mean value of the temperature dependence for Step 1. The entropy associated with this step would be 152 J mol -1 K -1 . Enthalpy and entropy changes in this step are not zeolite-dependent properties.
(Step 2: K 2 , ΔH 2 , ΔS 2 ) Next, water in the zeolite pore desorbs and the zeolites are brought from a wet state (immersed in an aqueous solution) to a dry state. The enthalpy and entropy changes for the reverse of this step approximately equal the sum of adsorption enthalpy/entropy of water into zeolitic voids (-m×ΔH/S ads,g,water ), which is zeolite-dependent, and hydration enthalpy/entropy of external surfaces (-ΔH/S hydration,ext ), which is supposedly similar for different zeolites studied in this work. Detailed results will be shown in a following contribution.
(Step 4: K 4 , ΔH 4 , ΔS 4 ) In this step, the external surface of the zeolite is hydrated/wetted (ΔH/S hydration,ext ) and a fraction of gaseous H 2 O molecule ((m-n)×ΔH/S ads,g,water ) adsorbs inside the zeolite. The hydration enthalpy/entropy in this step fully cancels out the reverse process ("wet" zeolite to "dry" zeolite) in Step 2, while the adsorption of water partially cancels out the reverse process in Step 2. With the presence of co-adsorbed ROH, the adsorption strength and entropy of water could be somewhat different. As it is challenging to assess accurately and quantitatively the interaction between ROH and water in the pore, it is assumed that the adsorption (both enthalpy and entropy changes) of ROH and H 2 O is not affected by each other.
(Step 5: K 5 , ΔH 5 , ΔS 5 ) This step fully recovers the end state in the aqueous ROH adsorption by converting n moles of water (g) from gas to liquid, with the corresponding enthalpy and entropy changes being condensation heat of n moles of water (n×ΔH/S cond,water ) and zeolite-independent.

S36
For a given zeolite, the following relations would then result from the above decomposition of the thermochemical cycle: ΔH ads,ROH,aq = ΔH ROH,aq→g -n×ΔH ads,water,g + ΔH ads,ROH,g + n×ΔH cond,water (2) ΔS ads,ROH,aq = ΔS ROH,aq→g -n×ΔS ads,water,g + ΔS ads,ROH,g + n×ΔS cond,water where ΔH/S ROH,aq→g are enthalpy/entropy changes for bringing cyclohexanol from aqueous solutions to gas phase; ΔH/S ads,ROH,aq are enthalpy/entropy changes for adsorption of cyclohexanol from aqueous solutions into zeolite; ΔH/S ads,ROH,g are enthalpy/entropy changes for adsorption of cyclohexanol from gas phase into zeolite; ΔH/S ads,water,g are enthalpy/entropy changes for adsorption of H 2 O from gas phase into zeolite; ΔH/S cond,water are enthalpy/entropy changes for water condensation; n is the moles of water molecules replaced by 1 mole of cyclohexanol.
With  Table 1 in the main text) suggest that cyclohexanol is significantly less solvated in FAU zeolite (where there are also intraporous water and hydronium ions) than in aqueous solution.

Supplementary Note 3. Estimation of adsorption capacity under reaction conditions
The adsorption isotherms of cyclohexanol from aqueous solutions onto zeolites HMFI45, HBEA75 and HFAU30 (number denotes measured Si/Al ratio) have been measured at various temperatures (280-353 K). Langmuir-type adsorption model, as discussed in the main text, has been applied to fit these measured isotherms to obtain adsorption constant (K ads ) and saturation uptake (q max ) at each temperature. Detailed results will be reported in a subsequent publication.
For all zeolites, the saturation uptake of cyclohexanol from aqueous solutions was remarkably lower than that measured from gas-phase adsorption (1.1, 2.2 and 2.3 mmol g -1 for MFI45, BEA75 and FAU30, respectively). This appears to reflect a significant amount of water adsorbed on these zeolites in contact with aqueous solutions. The saturation uptake of cyclohexanol increased by more than a factor of 2 from MFI to BEA, while the similar cyclohexanol uptakes on BEA and FAU likely stem from a higher fraction of volume inaccessible to cyclohexanol in FAU as well as a higher quantity of intraporous water in the more defective and hydrophilic FAU.
Next, we show how we determined adsorption capacity under reaction conditions. It was found that the saturation uptake decreased as adsorption temperature increased (Supplementary Table   4). This decrease in the saturation uptake with increasing adsorption temperature stems from the decrease in density of the adsorbate phase in the micropore (like thermal expansion of a liquid) as a function of temperature. The temperature dependence takes the form: (4) where δ is the temperature coefficient of expansion. [16] Plotting measured/regressed saturation adsorption capacity at different temperatures as a function of temperature yielded a slope (-δ) of -0.0032, -0.0032 and -0.0012 K -1 for HMFI, HBEA and HFAU zeolite samples. Having extrapolating these experimentally determined q max and K ads to reaction temperatures using the same temperature dependence as determined between 280 and 353 K, we found that the saturation uptake of cyclohexanol would decrease from 0.40 to 0.35, from 1.05 to 0.92, and from 1.26 to 1.20 mmol g -1 , for HMFI, HBEA and HFAU, respectively, S38 with temperature increasing from 433 to 473 K. Assuming that the remaining micropore volume (total V micro = 0.12, 0.20 and 0.26 cm 3 g -1 , respectively, for HMFI, HBEA and HFAU) is filled by adsorbed water (with density 0.90 at reaction temperature), the uptake of water in the pore would be 3.8±0.1, 4.0±0.2 and 6.2±0.4 mmol g -1 , respectively for HMFI, HBEA and HFAU (compared with 3.0, 1.8 and 5.9 mmol H2O g -1 at room temperature, correspondingly) at 433-473 K. Independent thermogravimetric analysis (TGA) shows that 1 g of HMFI sample stored under ambient conditions (100% RH) contains 0.042 g water, corresponding to 2.2 mmol H2O g -1 .

Supplementary Note 4. Mass fragmentation pattern analyses
For aqueous phase dehydration of perdeuterated cyclohexanol (which forms C 6 D 11 OH upon exchange with the solvent, H 2 O) that occurs along an E1-type path, the carbenium ion intermediate (C 6  , was used in our analysis, as the fragmentation mechanism for this water loss process is relatively well understood. [4] In the case of C 6 H 11 OH (molecular weight 111), the m/z 82 fragment ion can lose one more H to yield m/z 81, which is present at 10% of the intensity of the m/z 82 peak. In the case of C 6  Note that all single ion intensities have been corrected for natural abundance 13 C (e.g., fragment group m/z 90, 91 and 92). The contribution of individual fragmentation processes to overall S40 water loss has been studied thoroughly. [4] The isotopic reactant, after complete exchange of the As the reverse olefin hydration events (with a rate of r b ) occur during dehydration (r f ), the H content in the recovered alcohol increases. From the isotopomer compositions before and after reaction, the extent of back reaction (r b /r f ) can be calculated. For instance, we started with 0.1 mol L -1 reactant, which contains 0.088 and 0.012 mol L -1 for C 6 D 11 OH and C 6 D 10 HOH, respectively. If both isotopomers reacted at the same rate, which should be the case due to similarly high D contents and thus little isotope effect, the final concentrations for C 6 D 11 OH and C 6 D 10 HOH in a recovered reaction mixture, at 9% conversion on MFI, should be 0.075 and Similarly, for BEA-and H 3 PO 4 -catalyzed reactions, r b /r f = 0.10 (conversion 11%) and 0.13 (conversion 18%), respectively.

Supplementary Note 5. Derivations of rate expressions for different reaction pathways
In homogeneous acid-catalyzed alcohol dehydration in water, we suggest that the reaction starts with the association of hydronium ion (active site) with alcohol, which is effectively a displacement reaction of a H 2 O molecule by an alcohol in the first solvation shell of the hydronium ion (equation (5)).
Under reaction conditions, this association step is considered rapid enough to be treated as quasiequilibrated, with a thermodynamic constant K L,a (where the subscript "L" stands for the liquid phase, and "a" stands for association). For simplicity, we represent the hydronium ion as Solving the above equation gives: , , The next step, proton transfer from water cluster to ROH, is required to weaken the C-O bond and prepare the intermediate for cleavage. For this rapid step, we have: Thus, Mechanistic considerations diverge after the protonation step. For Supplementary Fig. 11(a) and (b), two subsets of classical stepwise E1-type mechanism, by applying steady-state assumption to the solvated carbenium-ion intermediate, , we have (refer to Supplementary Fig.   15 for the meaning of rate and equilibrium constants for individual elementary steps): (10) The expression for TOF is (equal to that of the fourth step): Replacing the term for , we have: We consider that in dilute acid solutions, H 2 O is the most likely base, when there is no external base added, that is abundantly present. For zeolites, intraporous water is most likely the base that deprotonates the carbenium ion intermediate. Note that showing water as the product in C-O bond cleavage and as the base in the deprotonation step, as shown below (cf. Supplementary Fig.   15), does not change the TOF expression.
Two extreme scenarios exist for E1-type mechanisms. In one, i.e., Supplementary Fig. 11(a), the microscopic reverse of C-O bond cleavage has a much higher free energy barrier than the deprotonation step such that k C-H >> k r , the TOF expression is simplified to: The same rate expression would arise if the C-O bond cleavage were assumed to be irreversible and rate-determining. In this case, only secondary KIE is anticipated as none of the equilibrium and kinetic constants relate to a step where C-H bond is formed or cleaved.
At the other extreme, k C-H << k r , the TOF expression is simplified to: Provided that the TS for C-H bond cleavage (k C-H ) occurs late (product-like) along the reaction coordinate, primary KIE is anticipated in this case.
For a classical concerted E2-type path, i.e., Supplementary Fig. 11(c), the expression for TOF is (refer to Supplementary Fig. 15 for the meaning of rate and equilibrium constants for individual elementary steps): Replacing the term for , we have: Note that the [C 6 H 11 OH] term in rate expressions in Supplementary Fig. 11 corresponds to the association complex. So the equations derived above are identical to those shown in the main text.
It has been demonstrated from isotope experiments (see main text) that the prevalent dehydration mechanism is of predominant E1 character with the C β -H bond cleavage as the kinetically relevant step, for aqueous phase dehydration of cyclohexanol catalyzed by both dilute homogeneous acids and acidic zeolites. Therefore, equation (15) would be the appropriate rate expression.

S45
For homogeneous acid catalyzed dehydration, TOF ratios at different alcohol concentrations can be used to determine K L,a (equation (18)). The results are shown in Supplementary Table 8 of our previous work [2] and discussed in Supplementary Note 8. ,

Supplementary Note 6. Analysis of kinetic isotope effects
For dehydration of cyclohexanol (C 6 H 11 OH and C 6 D 11 OH), the measured isotope effects (IEs) on the reaction rates reflect the effects of H/D identity on the individual rate and equilibrium constants, as shown below: where According to Lowry and Richardson, [17] for a step involving the re-hybridization of α carbon from sp 3 to sp 2 in the TS, the IE value can be estimated by the following equation for K 2 : [17] , , exp . (20) where υ P is the vibrational frequency of an C-H bond of the product state (carbenium ion) and the υ R is the vibrational frequency of the corresponding C-H bond of the reactant state (protonated alcohol). For sp 3 hybridization on the α carbon of the protonated alcohol and sp 2 hybridization on α carbon of the carbenium ion, the υ R is ~1350 cm -1 and the υ P is ~800 cm -

S47
where T is the absolute temperature and υ H is the vibrational frequency of the C-H bond (~2985 cm -1 ). Thus, the estimated KIE value involving the cleavage of a C-H bond is 3.2-3.6 at 433-473 K. This value is often attenuated from its theoretical maximum (in the absence of tunneling effect) as the C-H bond is often not fully broken at the TS.
The measured IEs ( Table 1 in the main text) are somewhat smaller than the theoretical maximum (3.8-4.5). This may be explained by a less than fully broken C-H bond at the TS in the deprotonation step of the carbenium ion intermediate (TS3 in Supplementary Fig. 11b). In addition, we note that Based on the measured KIEs, k 3 (C β -H bond cleavage) should be smaller than or comparable to, but cannot be considerably greater than, k -2 (C α -O bond recombination). Conceptually, the rate of olefin formation (r o ) relative to that of 18  formed during reaction) on the cyclohexyl cation. In turn, k 3 should also be comparable to, or smaller than k -2 , which would lead to overall KIEs of > 2.8.
Taken together, the foregoing analyses clearly demonstrate that k 3,H is smaller than, or comparable to, k -2,H . It can be further deduced that when k 3 is much smaller than k -2 , the measured activation energy or free energy barrier is equal to the enthalpy/free energy change from the alcohol-hydronium ion association complex to the deprotonation TS ( Supplementary   Fig. 19).
It is also important to note that in the presence of severe intrazeolitic diffusion limitations,

Supplementary Note 7. Thoughts on rational design for acid catalysts for dehydration of cyclic alcohols in aqueous phase
In this section, we provide additional remarks on the hydronium-ion catalyzed dehydration.
First, we note that in aqueous solutions, homogeneous acids with different pK a 's do not show differences in the catalytic activity for alcohol dehydration on an active site (hydronium ion) basis. This was shown for cyclohexanol in the present work, but was found to be the case also for alkyl substituted cyclohexanol (to be shown in a subsequent contribution). We believe the conclusion is even more general to other substrates, as long as the reaction is hydronium ion catalyzed. Noteworthily, Mellmer et al. recently reported that the TOF of xylose dehydration in aqueous phase was dependent on the pK a of a given homogeneous acid. [18] However, taking into account the dissociation constants of the weak acids at reaction temperatures (e.g., H 3 PO 4 , 448 K), the true TOF (normalized to hydronium ion concentration) was actually independent of the chemical identity of the homogeneous acid (strong or weak).
While the representation of hydronium-ion-type active site seems appropriate for relatively hydrophilic zeolites in aqueous phase, it may not apply to cases where intraporous water is present at much lower concentrations. The absence or very low concentrations of intraporous water has several potential consequences. First, with intraporous water sparsely present, the framework-bound proton has a higher tendency to remain as the prevalent form of BAS and exhibit a greater potential to protonate alcohol reactants, favoring the pre-equilibrium towards protonated alcohol. Second, as the intraporous concentration of water decreases, that of alcohol may increase. Due to the first two consequences, i.e., the increased alcohol concentration in the pore and the more pronounced alcohol protonation, the dominant form of adsorbed alcohol could shift from monomer to dimer, thereby opening another reaction path to olefin. [19] Finally, with the disappearance of additional solvation of intrazeolitic intermediates and transition states (TS) by water, the activation barriers and entropies would change accordingly.
HBEA zeolites catalyze cyclohexanol dehydration with TOFs several times higher in neat alcohol phase than in aqueous solutions (to be shown in another publication). If this rate enhancement reflects the intrinsic behavior of a zeolitic proton or a small hydronium ion complex (as opposed to a large hydronium ion complex as explored in this work), it would seem S50 beneficial, as a step forward, to devise synthetic strategies to contain BAS within reaction environments protected from liquid water. In the context of aqueous phase reactions, such microenvironment-engineering strategies include synthesis of zeolites in low-defect forms [18] and post-synthetic surface hydrophobization [20,21] or defect healing, [22] which have been shown to also efficiently enhance tolerance of zeolitic materials against hot liquid water.
For aqueous phase dehydration of other cyclic alcohols (alkylcyclohexanols), microporous zeolites (except for the small-pore zeolite, CHA) are also more active catalysts than homogeneous acids and mesoporous solid acids. In general, MFI is the most active zeolite catalyst on an active-site basis. The peculiarity of MFI stems from the closely similar dimensions of the pore and the solute molecule (cyclic alcohols, ~ 0.6 nm). Towards the formation of the kinetically relevant TS, the pore confines could decrease both the enthalpy and the entropy of the TS relative to the adsorbed alcohol. As a consequence, it is always the enthalpy-entropy compensation induced by the pore constraints, or in other words, the resultant Gibbs free energy barrier ( Table 3 in the main text), that dictates the catalytic performance. As a result of the unfavorable activation entropy, 2-methylcyclohexanol dehydration becomes less active on MFI than on BEA at higher temperatures (not shown in this work). A comprehensive and more quantitative evaluation of ring-substituent effects on the reaction mechanism and energetics, as well as the underlying molecular-level origins of these effects, is to be reported in another contribution.

Supplementary Note 8. Calculation of association equilibrium constant for the alcoholhydronium ion complex
Using measured turnover rates for homogeneous acid-catalyzed dehydration as a function of cyclohexanol concentration, the K L,a and k rds were determined. The results were shown in the Supplementary Table 8 of our previous work. [2] The enthalpy and entropy changes determined from the Van't Hoff plot of the determined K L,a were found to be -3 kJ mol -1 and 24 J mol -1 K -1 , respectively. [ These data have been presented and discussed in our recent work. [2] S52

S53
Density functional theory. Periodic DFT calculations were carried out using the CP2K code. [23] All calculations employed a mixed Gaussian and planewave basis sets. The basis set superimposition error (BSSE) derived from Gaussian localized basis set used in our CP2K calculations has been estimated to be ~3 kJ/mol. [24] Core electrons were represented with Goedecker-Teter-Hutter pseudopotentials, [25] and the valence electron wavefunction was expanded in a double-zeta basis set with polarization functions along with an auxiliary plane wave basis set with an energy cutoff of 360 eV. The generalized gradient approximation exchange-correlation functional of Perdew, Burke, and Enzerhof [26] was used. Each reaction state configuration was optimized with the Broyden-Fletcher-Goldfarb-Shanno algorithm with SCF convergence criteria of 10 -8 au. To compensate for the long-range van der Waals dispersion interaction between the adsorbate and the zeolite, the DFT-D3 scheme [27] was employed with an empirical damped potential term added into the energies obtained from exchange-correlation functional in all calculations. Important entropic contribution and zero-point energy (ZPE) corrections, which are important for zeolite-catalyzed reactions, have been taken into account. [28] More details, including the periodic structures of MFI and BEA used for calculations, can be found in our recent contributions. [2,3] Error analysis for intrinsic activation parameters. The standard errors in ΔH° ‡ and ΔS° ‡ were determined from regression analysis of the dependence of the intrinsic rate constant on temperature via the rectified Eyring equation.
ln ln The standard error in ΔG° ‡ was estimated from the quantities obtained from the sum of squares of residuals that is determined by the regression analysis of the intrinsic rate constant.
Specifically, for zeolites, TOF z = k z , according to the Eyring equation, ∆G° ‡=RTln(k B /h)-RTln(TOF z /T) Here, RTln(k B /h) is a constant, so for ∆G° ‡, the only error source is ∆ln(TOF z /T). Then, we have ∆∆G° ‡=RT*∆ln(TOF Z /T). The standard errors in ΔH° ‡ and ΔS° ‡ ( Table 3 in the main text) are bigger due to the greater uncertainty in separating ΔG° ‡ into ΔH° ‡ and ΔS° ‡ as they are derived from the slope and intercept, respectively, of the Eyring plot.