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Title Understanding Brønsted-Acid Catalyzed Monomolecular Reactions of in Zeolite Pores by Combining Insights from Experiment and Theory.

Permalink https://escholarship.org/uc/item/8bt399xt

Journal Chemphyschem : a European journal of and physical , 19(4)

ISSN 1439-4235

Authors Van der Mynsbrugge, Jeroen Janda, Amber Lin, Li-Chiang et al.

Publication Date 2018-02-01

DOI 10.1002/cphc.201701084

Peer reviewed

eScholarship.org Powered by the California Digital Library University of California DOI:10.1002/cphc.201701084 Minireviews

Very Important Paper Understanding Brønsted-Acid Catalyzed Monomolecular Reactions of Alkanes in Zeolite Pores by Combining Insights from Experiment and Theory Jeroen Vander Mynsbrugge+,[a, d] AmberJanda+,[a, e] Li-Chiang Lin,[c] Veronique VanSpeybroeck,[d] MartinHead-Gordon,[b] and Alexis T. Bell*[a]

Acidic zeolites are effective catalysts for the cracking of large trinsic rate coefficient of the reaction (kint)atreaction tempera- hydrocarbon into lower molecular weight products tures, since kapp is proportionaltothe product of Kads-H + and required for transportation fuels. However,the ways in which kint.Weshow that Kads-H+ cannot be calculated from experi- the zeolite structure affects the catalytic activity at Brønsted mental data collected near ambient temperature, protons are not fully understood.One waytocharacterize the but can, however,beestimated accurately from configuration- influenceofthe zeolite structure on the is to study al-biasMonte Carlo (CBMC)simulations. Using monomolecular cracking and dehydrogenation at very low conversion, cracking and dehydrogenation of C3–C6 alkanes as an example, conditions for which the kinetics are welldefined. To under- we review recent efforts aimed at elucidating the influence of stand the effects of zeolite structure on the measured rate co- the acid site location and the zeolite framework structure on efficient (kapp), it is necessary to identify the equilibrium con- the observed values of kapp and its components, Kads-H+ and stant for adsorption into the reactant state (Kads-H +)and the in- kint.

1. Introduction

Zeolitesare crystalline microporous aluminosilicates that are depends on the heteroatom(e.g. Al, Ti,B)[5] but not the zeolite widely used in the petroleum industry as catalysts to promote framework type[6,7] or Al location,[5] and on the spatial confine- the cracking of high molecular weightcompounds, principally ment[8–15] of the proton. The latter propertyisdefined by the alkanes, to lower molecular weight compounds required for size and shapeofthe pores and channels in the zeolite frame- gaseous and liquid fuels.[1–4] The catalytically active sites in zeo- work, which are similar in dimensions to those of reactants lites are Brønsted acidic protons that charge compensate and products and reaction transitionstates.Spatial confine- anionic sites produced by the substitution of trivalent Al for ment is also responsible forthe shape-selective properties of tetravalent Si in the zeolite framework ( Si-(OH)-Al ). The ac- zeolites.[15,16]   tivity of such sites depends on the acidity of the proton, which Studies of alkane cracking have demonstrated that while cracking occurs mainly via abimolecular mechanism at high [a] J. Vander Mynsbrugge,+ A. Janda,+ Prof.Dr. A. T. Bell conversion,amonomolecular pathway in which the alkanes Department of Chemical and Biomolecular Engineering are cracked or dehydrogenated by direct interactionwith University of California, Berkeley,CA94720(USA) Brønsted acid protons prevails at very low conversions and low E-mail:[email protected] partial pressures (Figure 1).[17,18] The latter mechanism has been [b] M. Head-Gordon Department of Chemistry showntobefirst orderinthe alkane partial pressure, and the University of California, Berkeley,CA94720(USA) reactionrate in MFI (and by extension in equally or less confin- [c] L.-C. Lin ing frameworks) has been found to be unaffected by diffusion- WilliamG. Lowrie DepartmentofChemical and Biomolecular Engineering al transport to the activesites for alkanescontainingfewer The Ohio State University than 10 carbon and typical zeolite crystallite dimensions 151 W. Woodruff Ave.,Columbus, OH 43210 (USA) of 0.1–2 mm.[19–21] For these reasons, monomolecular cracking [d] J. Vander Mynsbrugge,+ V. VanSpeybroeck Centerfor Molecular Modeling, Ghent University and dehydrogenation of alkanes are ideally suited for probing Tech LaneGhent Science Park CampusA the influence of zeolite structure (pore size and topology) on Technologiepark 903, 9052 Zwijnaarde (Belgium) the intrinsic activity and selectivity of Brønsted acid sites. [e] A. Janda+ The mechanisms by which alkane cracking and dehydrogen- Present address:Department of ChemicalEngineering ation occur are showninFigure 1. At lowconversion,both re- StanfordUniversity,Stanford, CA 94305 (USA) actions begin with adsorption of the alkane at aBrønsted acid [+] J.V.d.M. and A.J. contributed equally to this work site. Monomolecular cracking or dehydrogenation then occurs The ORCID identification number(s) for the author(s) of this article can be found under https://doi.org/10.1002/cphc.201701084. from this reactant state and, as illustrated, can to avariety An invited contribution to aSpecialIssue on Reactions in Confined of products via secondary reactions at higher conversion. Spaces Figure2illustrates the processes of alkane adsorption into the

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Figure 1. Reactionmechanisms for alkane cracking over Brønstedacid zeolites at low conversion (monomolecular reactions; blue) and high conversion (bimolecular reactions; red).

Figure 2. Schematic enthalpyand entropy landscapes illustrating the various steps in monomolecular reactions of alkanesinaBrønstedacid zeolite: the alkane adsorbs onto an active site, is converted into an and asmaller alkane(cracking, m

reactantstate and the subsequent reaction in terms of the rel- of alkane within the zeolite pores is small due to the weak in- evant changes in the enthalpy and entropy of the reactantrel- teraction of the alkane with the Brønsted acid site and the low ative to its presence in the gas phase.Since the concentration concentration of alkane within the zeolite pores,[8,22] the occu-

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pancy of these sites (qads-H +)can be described by Henry’s law: and entropy changes shown in Figure 2. To do so, experimen- tal rate data are used to determine the apparent activationen- ° ° qads-H KH-H Pa 1 thalpy and entropy(DH and DS )from the temperature þ ¼ þ ð Þ app app dependence of the measured first-order rate coefficients,kapp, [8–12,22,24–26] In [Eq. (1)], KH-H + is the Henry’s law constant for alkane ad- (e.g. an Arrhenius plot) for each reactionpathway. ° ° sorptiontothe reactant state, which is defined as any configu- Values of DH int and DS int can then be determined from ration in which an alkane C Cbond is located within 5 Š of an [Eq. (4) and (5)],asfollows: [23] À Al T-, and Pa is the alkane partial pressure. The relation- ° ° ship of K to the dimensionless thermodynamic equilibrium DH app DHads-H DH int 4 H-H + ¼ þ þ ð Þ constantfor adsorption to the reactantstate, Kads-H +,isgiven ° ° [24] DS app DSads-H DS int 5 by [Eq. (2)] ¼ þ þ ð Þ

RT It is evident from these equationsthat to determine DH° K H-H K ads-H 2 int þ  VH nH þ ð Þ ° þ þ and DS int at reactiontemperatures (>673 K) it is necessary to first determine DH and DS at reactiontemperatures. where V is thevolumecontainedwithinone mole of reactant ads-H+ ads-H H+ Until recently,[27] this has not been attempted using experimen- statespheres of radius 5 Š and n is themoles of protonsper H+ tal adsorption measurements because of the tendency of the unit mass of zeolite. Undersuchcircumstances,the apparent alkane to relocatetosiliceous parts of the framework at high rate coefficient(k )ofanelementaryreactiondepends on app temperature, and because of the occurrence of chemical reac- both the thermodynamics of the adsorption at the active sites tions at temperaturesabove 600 K.[28–30] Moreover, several (K )and the intrinsic rate coefficient (k )[Eq. (3)]:[9,24]  ads-H+ int theoretical studies have shownthat the distribution of ad- kapp K ads-H kint 3 sorbed alkanes within the pores of azeolite changes with the  þ ð Þ adsorption temperature, and consequently any insights To improveoverall performance, and select or design the gleaned from low temperature adsorption experiments are un- optimal catalystfor aspecific chemical transformation, it is im- likely to be transferrable to reactiontemperatures.[24,28–31] To portanttounderstand how the environment enclosing the overcome these concerns, Janda et al. have developed atheo- acid sites affects the enthalpy (DH)and entropy(DS)changes retical approach based on configurational-bias Monte Carlo associated with the differentsteps illustrated in Figure 2. The (CBMC) simulations using the Widom particle insertion method effects of the environment on the kinetics can then be exam- for determining the enthalpy (DHads-H+)and entropy(DSads-H +) ined in terms of local variations amongsites in different parts changes for adsorption of gas phase alkanes into reactant- of aparticularzeolite framework (e.g. channels vs. cages), or in state configurations at reactiontemperature (773 K).[9,24, 32] terms of globalvariations among sites in entirely different These values of DHads-H+ and DSads-H+ can then be used to ex- ° frameworks (e.g. MFI vs. TON vs. MWW). In the former case, it tract the intrinsic enthalpy and entropy of activation, DH int ° is necessary to discernthe location of the active sites in a and DS int,from the apparent enthalpy and entropy of activa- ° ° given zeolite,while in the latter,itisimportant to base the tion, DH app and DS app,determined from experimental activa- comparison on rate data that are representative of all parts of tion energies and rate coefficients.[9,24] the framework, that is, with active sites located at avariety of To determine DHads-H + and DSads-H +,the reactantstate is de- crystallographic locations. In this Minireview we will review the fined as the ensembleofconfigurations in which an alkane C À literatureonmonomolecular cracking and dehydrogenation of Cbond is located within 5 Š of an Al T-atom.[23] This distance is alkanesinzeolites, and demonstrate how theoretical simula- in line with the Al-C distances obtained from DFT calculations tions can supplement experimental measurements to examine for alkanes adsorbed at Brønsted sites in H-MFI and from mo- the influenceofthe location of Al atomsinagiven zeolite lecular dynamics simulations for alkanesadsorbed in CHA re- [24,28] framework and the effect of the overall framework structure ported in the literature. Values of DHads-H+ and DSads-H+ de- on the values of kapp and its components, Kads-H+ and kint.This rived from CBMC simulations are in good agreement with discussion will focus primarilyonthe monomolecular cracking those obtainedfrom adsorption experiments at 300–400 K, and dehydrogenation of alkanesover H-MFIand other zeolites and at higher temperatures, the simulations also properly cap- with similar pore sizes but differing in the size and prevalence ture the tendency of alkanes to redistribute to less confining of cages. parts of the zeolite pore system (e.g, channels vs. cages).[24]

This redistribution affects the values of DHads-H+ and DSads-H+ as well as their variation with the chain length of the alkane,as 2. Experimental Studies of Reaction at discussed in Section 2.3. Brønsted Acid Sites 2.1. Determination of Activation Parameters from 2.2. EffectsofActive Site Location Experimentally Measured Rate Coefficients Janda and Bell have investigated the rates and activation pa- To understand the influence of zeolite structure on cracking rameters of n-butane cracking and dehydrogenation for a and dehydrogenation it is necessary to determine the enthalpy series of commercial H-MFI samples with different Si/Al

ChemPhysChem 2018, 19,341 –358 www.chemphyschem.org 343  2018 Wiley-VCH Verlag GmbH &Co. KGaA, Weinheim Minireviews ratios.[22] As discussed below,bysampling zeoliteswith arange MAS NMR spectroscopic techniques, together with theoretical of the Si/Al ratio, arange of the Al distribution among crystal- work, have provided strongevidencethat the distribution of lographically distinct T-sites is also effectively sampled,allow- Al is nonrandom and depends on the conditions of the synthe- ing characterization of the dependence of the kinetics on sis.[49,50] Although in most studies only the non-randomness of active site location. H-MFIexhibits twelve crystallographically the Al distribution has been demonstrated, some authors have distinct T-sites, which when occupied by Al can result in reported the distributions of protons amongst qualitatively dif- Brønstedacid sites that are located within the straight or si- ferentparts of the zeolite pore system. Bhan et al.[41] have in- nusoidalchannels, or at the channel intersections.[33] By ex- ferred the distribution of protons among the 8-ring side pock- tendingthe CBMC approaches developed by Swisher et al.,[23] ets and 12-ringmain channels of H-MOR using in situ IR spec- Janda and Bell have found that the thermodynamics of n- troscopyofadsorbed alkanes. In addition, Deˇdecˇek et al.[36–40] butaneadsorptioninthe reactant state vary among the differ- have inferred the locations of pairs of Al atoms (those close ent T-sites. Because the range of values observed for the ap- enough to compensate adivalent cation)within MFI using UV/ ° ° II parentactivation enthalpy and entropy(DH app and DS app)ex- Visiblespectroscopy of Co -exchanged MFI samples. By decon- ceeded the range of values observed for the enthalpy and en- volutionofobserved UV/Visible spectra,the authors have infer- tropy of adsorption (DHads-H+ and DSads-H +)amongstthe 12 T- red the distributions of Al pairs amongstraight channels, sinus- sites, Janda and Bell inferred based on eqns. 4and 5that the oidal channels and channel intersections, and demonstrated intrinsic activation parameters for n-butanecracking and dehy- that the location of the Al pairs varies systematicallywith the drogenation mustalso vary depending on the location of the Si/Al ratio and synthesis conditions. active site.[22] This conclusion raises the question of how the Using the same technique employed by Deˇdecˇek et al.,[36–40] distribution of Al atoms among T-sites varies as afunction of Janda and Bell[22] observed systematic trends in the distribution the Si/Al ratio for zeolitesofsimilarprovenance. of Al pairs compensating the divalent CoII as afunctionof While the exact crystallographic positions of the Al T-atoms the Al content (Figure 3.a and 3.b) of commercial samples of and their charge-compensating protons in the zeolite frame- MFI, all obtained from Zeolyst. As the number of Al atoms per work cannot be determined experimentally,XRD,[34,35] UV-visi- unit cell increases, alarger fraction of CoII (and, thus, of Brønst- ble,[36–40] infrared,[41] EXAFS,[42] and 29Si[43–45] and 27Al[40,42, 46–48] ed sites in the original sample) are located at the channel in-

Figure 3. a) Experimental UV-visible spectrum for a(Co,Na)-MFIsample, numerically smoothed for ease of visualization. b) Plot of the distributionofCoII among straightand sinusoidal channels and intersectionsasafunction of Al atomsper unit cell in H-MFI.c)First-orderrate coefficientsofmonomolecular cracking and dehydrogenation of n-butane as afunction of Al atomsper unit cell in H-MFI.d)Selectivities for monomolecular n-butane reactions as afunc- tion of Al atoms per unit cell in H-MFI. Data for MFI-15(M), which was treated with EDTA, are indicatedwith hollow symbols. Adapted with permission from Ref. [22].Copyright (2013) American Chemical Society.

ChemPhysChem 2018, 19,341 –358 www.chemphyschem.org 344  2018 Wiley-VCH Verlag GmbH &Co. KGaA, Weinheim Minireviews tersections relative to the more confining straight and sinusoi- demonstrated that the zeolite synthesis method strongly af- dal channels. The spectroscopic technique developed by Deˇde- fects the distribution of Al atoms within various zeolites. Goun- cˇek et al.[36–40] and appliedbyJanda and Bell[22] cannot be used der and Iglesia have also reported variations in both the rate to infer the locations of isolated (i.e. non-paired) Al atoms. coefficients and selectivities of monomolecular reactions of However,asnoted in Ref. [22],the distributions of isolated and propaneover commercial H-MFI samples differing in the Si/Al paired Al sites would have to be strongly anti-correlated in ratio.[8] Although these authorsdid not observe any systematic order for the distribution of Al pairs to not reflect qualitatively trendsincatalytic behavior over the narrower range of Al con- the distribution of isolatedAlatoms, and of Al atoms in gener- tent investigated, the observeddifferences suggest that differ- al, among the different pore environments. ences in Al siting andpossibly underlying differences in intrin- The increase in the fraction of Al pairs located at intersec- sic kinetics may influence the differences in kinetics among the tions discussed above was found to coincide with ageneral in- H-MFI samples. ° crease in the apparent activation parameters (DH app and Rather than investigate the distribution of Al within H-MFI ° [22] DS app), in the turnover frequencies forboth cracking and de- as afunctionofSi/Al ratio, as was done by Janda and Bell, hydrogenation (Figure 3c), and in the selectivity for dehydro- Gounderand Iglesia[8] characterized the distributionofprotons genationversus cracking as well as for terminal cracking versus among the 8-ring side pockets and 12-ringmain channels of central cracking (Figure 3d).[22] From these observations and H-MOR by deconvolutionofthe infrared bands corresponding the above-mentionedCBMC-calculated variation in adsorption to the OH stretching vibrations of protons in each location.[41] thermodynamics among the 12 T-sites, Janda and Bell pro- Using this information, they wereable to calculate the rates posed (using eqns. 4and 5) that the changes in the apparent and selectivities of dehydrogenation and cracking of propane ° ° activation parameters (DH app and DS app)are at least partly and n-butanefor each of these environments in H-MOR. Goun- driven by underlying changes in the intrinsic activation param- der and Iglesiaattributed differences in the rates and selectivi- ° ° eters (DH int and DS int)with changes in the confinementof ties among the 8-ring side pocketsand 12-ringchannels to dif- Brønstedprotons.Consistent with this proposal,inmore ferencesinactivation entropyand to the relative stabilities of recent work Bucˇko and Hafner have found, using molecular dy- different transition states (referenced to the gasphase) corre- ° namics simulations, that DS int for propane cracking differs sig- sponding to each reactionpathway within these environ- nificantly between the 12-ring channels and 8-ring side pock- ments.[8] Specifically,they concluded, similartoJanda and ets of H-MOR.[29] Bell,[22] that later transition states such as dehydrogenation are As discussed in Ref. [9],the conclusion of Janda and Bell[22] preferred at lessconfining locations such as the 8-ring side that confinementinfluences the apparent activation parame- pockets versus the 12-ringchannels. Gounder and Iglesia[8] also ° ° ters (DH app and DS app)ofalkane cracking and dehydrogena- used previously reported adsorption data obtainedatroom tion has been reported in anumber of previous studies. How- temperature to infer that the intrinsic activation energies for ever,the conclusion of Janda and Bell that confinementalso the two pore environments are the same within error and that ° influences the intrinsic activation parameters (DH int and kapp is dominated by the influence of the entropy of the transi- ° DS int)contrasts with the previous conclusions, asdiscussed tion state relative to its presence in the gas phase. Unlike ° [8,10–12,25,26] [22] [8] below,that the intrinsic activation enthalpy (DH int) Janda and Bell, Gounder and Iglesia did not implicate dif- ° [10,12, 13] and entropy(DS int) are independent of the Brønsted ferences in intrinsic activationparameters in explaining differ- acid site confinement. The reasons given by Janda and Bell for ences in kinetics among the 8-ring side pockets and12-ring the observed increase in the activation parameters as the frac- channels, and intrinsic activation parameters were implicitly ° ° tion of sites located at intersectionsversus channels increases (for DS int)orexplicitly (for DH int)concluded to be the same were connected to differences in transition-state geometries, for the two locations. discussed furtherinSections 2.4 and 3and calculated using We suggest that there are two possible reasonsfor this dis- density functional theory.The resultsofthe DFT calculations crepancy.The first is relatedtothe methodofcalculation em- demonstrate that cracking transition states occur earlier along ployed by Gounder and Iglesia[8] to determine intrinsic activa- ° the reaction coordinate relative to dehydrogenation transition tion parameters. The value of DH int was determined by these states,[51] which Janda and Bell suggestcauses the intrinsic free authors using eqn. 4together with adsorption data measured ° energy barrier DG int for dehydrogenation transition states to at room temperature for the 8-ring side pockets and 12-ring be lowered in less confining pore spaces relative to those for channel locationsusing geometrical arguments. It is possible cracking transition states. that, as aresult of the uncertainty introduced by this method [22] ° The observations of Jandaand Bell contrast with earlier re- of estimation, to afirst approximation the values of DH int ap- ports by Haag and Dessau, who found no systematic variation peared to be within experimental error for the two environ- of the activity per Al atom for the overall rate of consumption ments. of n-hexaneinH-MFI over awide range of Si/Al ratios.[52–54] Asecond possible reason for the different conclusions of This difference may be aconsequence of aconstant Al distri- Gounder and Iglesia[8] versus Janda and Bell[22] is that the range bution in the zeolite samples used by Haag and Dessau result- of confinements represented by the 8-ring side pockets and ing from differences in the synthesis procedure used to pre- 12-ring main channels of MOR are small enough such that dif- ° ° pare the zeolite samples used by the two sets of authors.As ferences in DH int and DS int among the two locations are in- mentioned above,anumber of previous studies,[36–50] have significant.Consistent with the conclusions of Gounder and Ig-

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[9] lesia, in our recent work (cf. Section 2.4) we found that differ- Figure 4shows the CBMC-calculated values of DHads-H + and ° ° ences in the values of DH int and DS int among zeolite struc- DSads-H+ as afunction of temperature for the adsorption of pro- tures having similar levels of average confinement are within pane, n-butane, n-pentane and n-hexaneinH-MFI.[24] The solid experimental error.However,asdiscussed in section 2.4, when curves represent the resultsofCBMC simulations in which the zeolite structures having awide range of the confinement of Al atom is placed at either the T9 (upper solid curves) or the

Brønstedprotons is sampled, and accurate values of DHads-H+ T4 (lowersolid curves) site in the MFI unit cell, and represent and DSads-H+ calculated using CBMC simulations at reaction those sites for which the magnitudes of DHads-H+ and DSads-H+ ° ° temperature are used to determine DH int and DS int,trends in are the smallest (forT9, located at the channel intersection) ° ° DH int and DS int with respect to confinement become appar- and the largest (for T4,located in the sinusoidal channel). The ent. dottedcurves, which represent the Boltzmann averagedvalues

of DHads-H+ and DSads-H + for azeolite in whichthe Al is evenly distributed between the two sites, indicatethat alkanes adsorb 2.3. EffectsofAlkane Chain Length primarily in the channels at ambient temperature, and redis- Janda et al.[24] have also investigated the effectsofthe chain tribute towards the more spacious intersectionsathighertem- length of n-alkanes on cracking kinetics within H-MFI using a peratures. For n-butane, the relative probability of the alkane combination of previously reported experimental apparent ac- adsorbing at T9 versus T4 changes smoothly by afactor of 6  tivation energies and rate coefficients[55] to calculate the intrin- in moving from 275 to 773 K.[24] Additionally,the dependences sic activation parameters for propanethrough n-hexane. Inde- of DHads-H+ and DSads-H+ on alkane chain length are expected pendentQM/MM calculations were also performed for the T-12 to be weakerfor intersections versus channels. This proposal is site of MFI, located at the intersection of the straight and si- based on the observation of Eder and Lercher[56] that the slope nusoidalchannels. To extract intrinsic activation parameters of aplot of DSads-H+ and DHads-H+ is larger for more confining from experimental data, the authors developed and employed zeolite structures.Asaresult, the dependence on chain length ° ° atwo-step CBMC approach to calculate enthalpies and entro- of DH int and DS int extracted from eqns. 4and 5using DHads- pies of adsorption of n-alkanes from the gas phase to the reac- H+ and DSads-H + determined at 773 Kisexpected to differ from tant state at reactiontemperature (773 K). They then used that found using experimentaladsorption data measured at these values together with [Eq. (4) and (5)] to determine the in- 300–400K.[57] trinsic activationparameters forthe overall consumption of The relocation of the adsorbed alkane to less confining each alkane, normalized by the number of C Cbonds.[24] The spaces at high temperature and the consequences for DH À ads-H+ advantage of the CBMC simulations is that they properly ac- and DSads-H+ are expected to be even more pronouncedinma- count for the changes in the distribution of alkane amongst terials with more heterogeneous pore systems.[24] As an exam- differentenvironments in the zeolite at high temperature and ple, Figure 5shows the distribution of n-butane at 50 Kand they also account for the greater number of configurations ex- 773 Kinthe zeolite H-MWW,which consists of sinusoidal chan- plored by the alkane in the vicinity of the active site at high nels and super cages.[31] At 50 K, the alkane is localized to the temperatures.[24,28–31] most confining part of the zeolite in the vicinity of the acid

Figure 4. Plots of a) enthalpy changes DHads-H+ and b) entropy changes DSads-H+ for the adsorption of propane(black triangles), n-butane (red triangles), n-pentane(blue triangles)and and n-hexane (green triangles) from the gas phaseonto BrønstedprotonsinH-MFIwith one Al per unit cell obtained using CBMCsimulations. The upperand lower solid linescorrespond to Al locatedonly at T9 and T4, respectively. The dashed lines representthe Boltzmann weighted averages of DHads-H+ and DSads-H+ for Al distributed evenly between T9 and T4. Adapted with permission from Ref.[24].Copyright (2015) American Chemical Society.

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Figure 5. Heat maps showing the distributionofCatoms of the terminal C Cbond of n-butane interacting via this bond with aBrønsted acid site at site T4 À in MWW,obtained from CBMC simulations at 50 Kand at 773 K. At 50 K, butane is predominantly adsorbed inthe sinusoidal channel, while at 773 K, adsorp- tion in the supercage is favored for entropic reasons. Framework atoms outsidethe plane represented in the heat maps have been omitted for clarity.The color scale represents the percentageofconfigurations in which the Catom is found within asquare with side length 0.05 Š projected onto different planes. Adapted with permission from Ref. [31].Copyright (2017)American Chemical Society.

° site, while at reaction temperatures (773 K), the alkane explores Different conclusions regarding the variation of DH int and ° alarger volume as it moves into the 12-ring supercages. Classi- DS int with chain length are reached when values of DHads-H+ cal extrapolationofvaluesofDHads-H + and DSads-H+ to tempera- and DSads-H+ determined from room temperature adsorption ° ° tures of cracking, or treating these values as temperature-in- measurements are used to extract DH int and DS int.Inearlier variant,does not properly account for such temperature-de- work, Bhan et al.[57] used such adsorption data[58] to calculate ° pendentchanges in the siting of the alkane andinthe con- Kads-H+,and then DS int from absolute rate theory (using inde- ° comitant change in the dependence of DHads-H+ and DSads-H+ pendentvalues of DH int obtained from Ref. [55]), from the on chain length.[56,57] same rate coefficients and activation energies[55] used by Janda [24] On the basis of their calculations of DHads-H+ and DSads-H+ et al. Using this method of analysis, Bhan et al. observe,as from CBMC, Janda et al. suggestthat the experimentally ob- do Janda et al.,that an increase in the intrinsic rate coefficient served increase in the apparent rate coefficient for n-alkane with chain length drives an increase in the measuredrate coef- cracking with increasing chain length in H-MFI is mostly due to ficientfor n-alkane consumption over MFI. However,because the increase in the intrinsicrate coefficient kint [see Eq. (3)] and, of the different dependences of DHads-H + and DSads-H + on chain to alesser extent, the increase in the correspondingequilibri- length for the room temperature data versus for the CBMC-cal- um constant Kads-H+ for adsorption of the alkane into the reac- culated values, adifferent trend emergesfrom each study for [24] ° ° tant state. The increase in the intrinsic rate coefficient for how DH int and DS int depend on chain length. cracking with chain length in MFI is attributed primarily to a In amore recent experimental study,Lietal.[27] have report- ° ° ° ° decreaseinDH int,and DS int is found to be relativelyinsensi- ed trends in DH int and DS int with respect to alkane chain tive to chain length. In support of these conclusions, inde- length in MFI that are qualitatively similartothose reported by pendentQM/MM calculations reported in the same work pre- Bhan et al.,[57] Li et al. use infrared operando to ° dict aslight decrease in DH int with chain length and no de- infer the coverage of Brønsted acid sites at reaction conditions ° pendence of DS int on chain length. based on the perturbation of the zeolite OH stretching band

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1 ° at 3600 cmÀ ,whichiscaused by the specific interaction of al- ed by Li et al. The absolute values of DH int for each alkane are kanes with protons. From measurements of the coverage of also within experimental error between the two studies. protons as afunction of temperature and pressure, Li et al. cal- Although the above discussion shows that the absolute ° ° [27] culated thermodynamic adsorption parameters at reaction values for DH int and DS int obtained by Li et al. do not differ conditions. Intrinsic rate coefficients and activation parameters significantly from those reportedinour recent work,[24] it is still were then determined by using these data together with ap- notable that Li et al. observe adifferent trend in intrinsic activa- parentrate coefficients for monomolecular cracking obtained tion parameters with respecttochain length. One possible at the same time as the adsorption measurements. reason for this difference is the fact that different zeolite sam- [57] [27] ° Similar to Bhan et al., Li et al. conclude that DH int is ples wereused to obtain the rate data from whichLietal. and nearly constant and that kint increases due to an increase in Janda et al. extracted intrinsic activation parameters. It is im- ° ° DS int with chain length, although the values of DS int that Li portant to consider this possibility because the Al distribution et al. obtain are less positive, and the trend with chain length amongst differentparts of the framework (e.g. channels vs. in- significantly weaker,than those reported by Bhan et al. Li et al. tersections) may differ between the two samples. This may ° ° thus conclude that monomolecular cracking rates of different lead to different trends in DH int and DS int with respect to ° ° n-alkanes are controlled by the value of DS int,while DH int is chain length. For example, our independent QM/MM calcula- constant both for the overall rate of cracking and for individual tions[24] for the T12 site in MFI (located at the channel intersec- ° C Cbonds. As discussed below,the different conclusions tions) predict that DH int decreases slightly with chain length, À [24] ° reachedbyLietal. versusJanda et al. can be attributed to while DS int does not vary systematicallywith chain length. Al- severalpossible factors, and demonstrate that the dependen- thoughthis finding is consistent with the trend that we have ° ° ces of DH int and DS int on chain length requirefurtherinvesti- observed using previously reported experimental rate data gation in order to establish whether the magnitude and direc- combined with CBMC simulations, it is possible that different ° ° tion of these dependences are general,orare afunction of relationships of DH int and DS int to chain length would be ob- zeolite properties such as the Al distribution and confinement. tained for Al T-sites located in other parts of the zeolite frame- We first examinethe explanations of Li et al.[27] for the differ- work. Achange in this relationship with achange in confine- ° ° ent trends in DH int and DS int with respect to chain length ment would be qualitatively consistent with the observation of that they report versus those reportedbyJanda et al.[24] Li Eder and Lercher[56] that the strength of the correlation of et al. attributethe different trends primarilytothe failure of DSads-H+ and DHads-H+ for n-alkanes adsorbed in agiven zeolite the CBMC simulations of Janda et al. to account for depends on the confinement. bondinginteractionsbetween the alkane and proton. We note Finally,itisworth noting that the findings of Bhan et al.[57] that the force field we have employed does account for such are sensitive to the methodwith whichexperimentaladsorp- ° ° interactions. Specifically, the parameters for Oatoms bonded tion dataare used to extract DH int and DS int from measured to Brønsted protons were modified to reflect the specific inter- rate data. As discussed in Ref. [24] two sets of experimentalad- action of the alkane with the proton. These modified parame- sorptiondata[58,59] are reported in the literature for the same ters were used for one of the four atoms bondedto zeolitesample used by Narbeshuber et al.[55] to obtain the orig- each Al T-site. Therefore, we believe that it is unlikely that a inal experimental rate measurements. Bhan et al. obtained ° failure to account for hydrogen bondingbetween the zeolite DS int from the measuredrates and activation energiesofNar- [55] and reactant alkane contributes significantly to the different beshuberetal. by using values of DHads-H+ and DSads-H+ re- ° ° [58] trends with chain length obtained for DH int and DS int in our ported by Eder et al. to calculate equilibrium constants for work versusthat of Li et al. adsorption, Kads-H+ .From values of kapp reported in Ref. [55] kint Li et al.[27] also report asystematic difference between the was then determined using eqn. 3and the calculated equilibri- ° ° absolutevalues of DS int that they obtain relative to the values um constants, and DS int was extracted from kint using absolute [24] ° reportedbyJanda et al. (see Ref. [27],Table 4), with most of rate theory andindependentvalues of DH int reportedin the values reported by Li et al. being more positive than those Ref. [55].This method of analysis to the finding of Bhan ° ° reportedbyJanda et al. The magnitude and direction of this et al. that DH int is constant while DS int increases strongly difference, however,appears to be aconsequence of the fact with chain length. ° that Li et al. have not treated our reported values of DS int as Adifferent conclusion is reached if values of DHads-H+ and [58] [59] being corrected for the number of C Cbonds in the alkane. DSads-H+ reported by Eder et al. or by De Moor et al. are À ° ° This correction is implicit to the fact that we have normalized used to extract both DH int and DS int from the experimental all rate coefficients by the number of C Cbonds (see Ref.[24] rate data using eqns. 4and 5(i.e. without using independent À ° Table 4heading,and Ref. [27],p.4545). Not accounting for this valuesofDH int taken from Ref. [55]). Using the adsorption normalization causes Li et al. to overestimate the differences data reported by De Moor et al.,the same trendsasthose ob- ° between our reported values of DS int and theirs.When it is servedbyJanda et al. using CBMC-calculated adsorption data ° ° correctly assumed that our reported valuesfor DS int are cor- are observed—that is, that DH int decreases with chain length ° ° [24] rected for the number of C Cbonds, our values of DS int are while DS int is invariant with chain length. Using the adsorp- À ° within experimental error of those reported by Li et al. This tion data of Eder et al. resultsinaweakincreaseofDS int with ° [24] conclusion is based on reported 95 %confidenceintervals re- chain length and adecrease of DH int with chain length. On ported by Janda et al. and on twice the standard errors report- the basis of the above discussion, it can be seen that the

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° ° trends in DH int and DS int with respect to chain length require to the references cited above for more comprehensive discus- furtherinvestigation, in particular to shed light on how such sions. trends may varywith respect to active site confinement, and Although absolute values of the intrinsic activation parame- ° ° with the methodwith which DH int and DS int are extracted ters were not reported, Gounder and Iglesia have reported rel- from adsorption data and experimental rate data. ative values of measured activationenergies and activation en- ° tropies (DS app)for monomolecular cracking vs. dehydrogena- tion of agiven alkane on H-FER, H-MFI, H-MOR and H-FAU, and 2.4. Effect of Zeolite Topology ° ° concluded that differences in E app and DS app between reac- Severalauthors have investigated the influence of zeolite top- tion pathways are independent of the zeolite and are equal to ology on the rate of monomolecular cracking of propane[25] differences in the gas phase protonation enthalpy or entropy and n-hexane.[10,11,26] For H-FAU, H-MOR, H-BEA and H-MFI, the of the relevant C CorC Hbonds.[13,14] On the basis of this in- À À ° measured rate coefficients (kapp)for the overall rate of con- terpretation, relative values of E app and DSapp,aswell as selec- sumption of alkane werefound to increaseasthe measured tivities, would be expected to be structure-insensitive. Howev- ° activation energies (E app)decrease with decreasing pore size. er,this contradictsthe previously mentioned study of propane Additionally,ineach of these reports, the intrinsic activation and butanecracking over H-MOR by the same authors, in ° energies (E int), calculated by subtracting experimentally deter- which differences in selectivities were attributed to “location- mined adsorption enthalpies for non-specific adsorption any- specific differences” in the activation entropies for reactions where in the zeolite (DHads)measured at ambient tempera- occurring at sites in the 8-ring side pockets vs. the 12-ring tures, werefound to be independent of the zeolite, leadingto main channels of H-MOR.[8] the conclusion that higher observed cracking rates are caused Janda et al. have determined both the absolute and relative by stronger adsorption rather than by differencesinintrinsic valuesofintrinsic and apparent activation parameters for ° ° [10,11,25,26] activation parameters (i.e. DH int and DS int). Rama- alkanecracking and dehydrogenation foreight 10-ring zeolites chandranetal. later reported that aplot of DSads versus DHads differing in the shape of the channels and in the size and for n-hexane adsorption in several zeolitesshows asimilar abundanceofcavities:TON, FER, -SVR, MEL, MFI, SFV,STF,and ° [9] slope to that of aplot of ln(kapp)versus E app,obtained from MWW (Figure 6). The authors used DSads-H+,calculated using ° ° the rate data reported in Ref. [10],and concludedthat the var- CBMC, as aproxy for confinement. To extract DH int and DS int, iation in measured activation parameters among zeolitesis an improved single-step CBMC approachinvolving domain de- caused by differences in the adsorption thermodynamics, not composition of DHads and DSads (for non-specific adsorption) [12] the intrinsic kinetics. was developed in order to determinevalues of DSads-H + versus ° Using the same methodology,Kotrel et al. found that E int DHads-H+ specific to protons. Using the values of DHads-H + and for n-hexane monomolecular cracking is larger for H-MFI than DSads-H+ obtained in this manneratreactiontemperatures, the [60] ° ° for H-BEA and H-FAU. However,these authors attributed authors were abletodetermine DH int and DS int using such differencestodifferences in acidity among zeolites. It is Eqns. (4) and (5). ° noted that differences in acidity,ifpresent, would be expected Figure 7shows apparent activation enthalpies (DH app)and ° ° to influence the kinetics of monomolecular activation of alka- entropies (DS app), and intrinsic activation enthalpies (DH int) [5,6,61] ° nes based on anumber of experimental and theoreti- and entropies (DS int)asafunctionofthe entropyofadsorp- [5,7,62–65] cal studies, asubject that has recently been reviewed tion of n-butane adsorbed at an active site (DSads-H+), Boltz- by Boronat and Corma[66] and by Derouane et al.[49] This raises mann averaged over all T-sites,which describes the average the issue of whether the acidity of protons is correlated with level of confinementfor azeolite in which the Al atoms are zeolite structure and confinement, since this Minireview is fo- distributed randomly amongthe T-sites.[9] Because the Al distri- cused primarily on the effectsofstructure and confinement on bution is known to be nonrandom anddeterminedbythe Si/ alkane cracking and dehydrogenation kinetics. Several studies Al ratio and the zeolite synthesis procedure,[34–50] where possi- have concluded that the acidity is independentofthe zeolite ble the apparent activation barriers were also Boltzmann aver- structureand the locationofthe acid sites,[5–7] butisdepen- aged over multiple samples with different Si/Al ratios. As the [5] ° dent on the heteroatom (Al, B, Ti) and on the concentration overall confinementincreases (i.e. as DSads-H+ decreases), DH int [67–69] ° of framework Al atoms for lowvalues of the Si/Al ratio for and DS int for terminalcracking and dehydrogenationde- which the acidity is lower as aresult of the presence of Al crease.This observation was attributed to differences in the next-nearest-neighbor pairs. Because all of the zeolites dis- calculated geometries of the transition state,[51] which for dehy- cussed in this Minireview are aluminosilicates, and nearly all of drogenation involves nearly fully-formed products, and for the zeolite structures studied in theworks cited (with the ex- cracking more closely resembles aprotonated alkane.More ception of H-FAU) are highly siliceous(Si/Al > 8), it can be con- confining frameworks were interpreted to confine the late cluded that the acidity does not vary strongly among struc- transition state and restrict motion of the product fragments, ° ° tures and therefore should not contribute significantly to ob- causing the observed decreases in DH int and DS int.While ° served trends in kinetics with respect to confinement. Because DH int forcentral cracking does not vary significantly with ° adetailed discussion of the factors controlling Brønsted acidity DSads-H+ , DS int is lower for the most confining zeolitesbecause and its effects on monomolecular reaction kinetics in zeolites more entropy is lost upon protonation of the alkane to form is outside the scope of this Minireview,the readerisreferred the transition state. Selectivities for terminal cracking and de-

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Figure 6. Series of 10-ring zeolites differing in the shape of the channels, and in the size and abundance of cavities. Representations of zeolite frameworks were generated using the ZEOMICSweb tool.[70] The channeltopology (ring size and shape) is given in bold. Channels are shown in yellow (< 6 Š diameter) and orange(>6 Š diameter). Cages are shown as green (< 6 Š diameter), blue (6–8 Š diameter), and purple(>8 Š diameter) spheres.Reproduced with permission from Ref. [9].Copyright (2016) American Chemical Society. hydrogenation vs. central cracking were found to decrease be- tions betweenthe zeoliteand the transition state become ° cause DS int decreaseswith increasing confinement forthe more significant, and the product fragments formed can move ° ° former reactions. In summary,absolutevalues of and differen- less freely, such that DS int and DH int are relatedtoconfine- ° ° ces between DH int and DS int for different reaction pathways ment in qualitatively similarways and are therefore positively were found to be structure dependentinamanner consistent correlated.[9] This proposal contrasts with previous experimen- with the calculatedtransition-state geometries, and changes in tal studies that concluded that the intrinsic activation enthal- these parameters were found to drive observed changes in se- py[8,10–12,25,26] and entropy[10,12,13] are independentofstructure lectivity with respect to confinement. and that observeddifferences in the rate for n-alkane cracking Depending on channel topology,the measured rate coeffi- over H-MFI, H-MOR, H-BEA, and H-FAU are thuspredominantly cients (kapp)change with confinement either because of causedbydifferences in the adsorption thermodynamics ac- changes in kint or because of changes in the adsorption equilib- cording to eqn. 3. The discrepancies between the conclusions rium constant (Kads-H+). In both cases, the strong compensation of Janda et al. and the studies cited above can be attributed ° ° ° of correlated changes in DH app and DS app and in DH int and primarily to the different adsorption data sets used to extract ° ° ° ° ° DS int on the free energybarriers (DG app and DG int)at773 K DH int and DS int from apparent parameters using eqns. 4and causes changes in the apparent andintrinsic rate coefficients 5. Using previously reported apparent activation energies and with confinementtobeweak relative to the strong trendsob- rate coefficients for n-hexane monomolecular consumption served for the activation parameters. The dependence on con- over H-FAU, H-MOR and H-MFI,[10] together with adsorption finementofthe latter parameters is interpreted as described data obtained using CBMC simulations, Janda et al. found a ° ° [9] above.Asconfinement increases, energetic and stericinterac- strong dependence of DH int and DS int on confinement.

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Figure 7. Plots of a) apparent activationenthalpy versus enthalpyofadsorption, b) apparent activationentropyvs. entropy,c)intrinsic activationenthalpy versus enthalpy of adsorption and d) intrinsicactivationentropy of adsorption for n-butane monomolecular reactions at 773 K. Values of DHads-H+ and DSads- ° ° H + were determined from CBMCsimulations,and DHapp and DSapp from measured rate data. Representative 95 %confidence intervals for DH app and DS app 1 1 1 1 1 1 are 7kJmolÀ and 9JmolÀ KÀ for cracking, and 8kJmolÀ and 11 JmolÀ KÀ for dehydrogenation. Adapted with permission from Ref. [9].Copyright Æ Æ Æ Æ (2016) American Chemical Society.

3. Quantum Chemical Studies of Reactions at permitproper captureofthe effects of the zeoliteenvironment Brønsted Acid Sites on the Brønsted acid sites.[73,74] To correctly describe the crucial long-range interactions encountered by guest molecules enter- 3.1. QM/MMApproach to Describe Reactions at Active Sites ing the zeolite pores, amore comprehensive representation of Theoretical studies of chemical transformations, in which the zeolite structure is required. This can be achievedeither by bonds are broken andformed, require quantum chemical periodically repeating the complete unit cell, or by using asuf- methods to describe the electronic structure of the system. ficientlylarge clustermodel. Densityfunctional theory (DFT) calculations have becomethe In addition to large models, accurate density functionals, for workhorse of computational because of their efficient example, wB97X-D,[75,76] are required to correctly describe the scaling with the number of atoms in the system.[71,72] However, crucial non-bonding interactions encountered by guest mole- despite the ever-growing power of computers, the quantum cules entering the zeolite pores. The hybrid quantum mechan- chemicaltreatment of large systems such as zeolites still car- ics/molecular mechanics approach(QM/MM) in which asmall ries ahigh computational cost. While early studies of zeolite- region around the active site and the adsorbates are treated catalyzed reactions relied on small representations to with while the remainderofthe system is reduce the overall number of atoms,[23,62,65] these do not described with aclassical force field has enabled routine calcu-

ChemPhysChem 2018, 19,341 –358 www.chemphyschem.org 351  2018 Wiley-VCH Verlag GmbH &Co. KGaA, Weinheim Minireviews lations on zeolite systems.[77] In these simulations,the QM have shown that this increasing deviation is causedbyoveres- region is typically asmall 5T clustercomprising the Al atom timationofthe van der Waals interactions between the adsor- and its neighboringSiatoms andany guest molecules interact- bates and the zeolite by the pairwise-additive Lennard-Jones ing with the Brønsted acid site. Figure8shows such aQM/MM potentialinP1, and derived an updated set of parameters (P2) model for H-MFI with an acid sited located at the T12 position. by recalibrating its characteristic energies.[82] Using the P2 pa- The main advantage of the QM/MM approachlies in its favora- rameter set, experimentally measured physisorption and chem- ble balancebetween the computationalcost and the accuracy isorption energies can be reproduced with errors about five for parameters that depend on both aprecise description of times smaller than obtained using the P1 parameterset thechemistry occurring at the active site and the inclusion of (Figure 9).[82] the long-rangeeffects of the zeolite environment, for example, intrinsic reaction energies. Acomplete discussionofthe merits 3.2. Insights for n-Butane Cracking and Dehydrogenation and limitations of all the different model systems and electron- Kinetics from QM/MM ic structure methods that have been employed in studies of adsorption and catalysis in zeolites is beyondthe scope of this Sharada et al. have applied the QM/MM scheme to acluster Minireview.Pidko has recently given adetailed argumentation modelcontaining 437 T-atoms to investigate central and termi- of how the success of computational approaches to complex nal cracking anddehydrogenation of n-butane in H-MFI.[51] The catalytic systemssuch as zeoliteshingesonfinding the right reactions were modeled at two Al sites to investigate the ef- compromise between zeolite representationand methodaccu- fects of acid site location:AlinT12, which places aBrønsted racy.[78] We also refer the readertorecent reviews for amore acid at the intersection of the straight and sinusoidal channels, detaileddiscussion of these topics.[74,79, 80] and Al in T10, which places aBrønsted site within the sinusoi- Gomes et al. have shown that the accuracyofQM/MM ener- dal channel. Centraland terminal cracking were shown to gies is relatively insensitive to the size of the QM region, and occur through an earlytransition state in which the proton at- that convergenceofthe thermochemical properties can be tacks the C Cbond in the alkane (Figure 10.a and 10.b). Dehy- À achieved by using large clusters (>150 T-atoms)combined drogenation wasfound to proceed through alate transition [77] with large basis sets (e.g. 6–311++G(3df,3pd)). Aset of MM state in whichthe H2 is almost fully formed (Fig- parameters (P1) forthe zeolite atoms was developed by Zim- ure 10.c and10.d).[51] merman et al. to approximate adsorption energies and transi- Intrinsic activation energies calculated for reactions at the tion states obtained from full QM calculations at the wB97X-D/ T10 site are larger than those at T12 owing to differences in in- 6–31+G**level of theory.[81] However,these parameters were teraction of the substrate with the acid site as well as with the subsequently found to overestimate binding energies of alka- zeoliteframework, demonstrating that Brønsted acid sites in nes compared with experimental values, particularly for larger H-MFIare not equivalent for these reactions.[51] This conclusion adsorbate molecules such as pentane and hexane.[51] Li et al. supports the experimental observations of Janda and Bell that

Figure 8. QM/MMmodel for H-MFI based on alarge 437 T-atom cluster.Asmall sub-cluster of 5T-atoms surrounding the Brønsted acid site is treatedquan- tum mechanically,while the remainder of the modelisdescribedwith aclassicalforce field. The QM region is depicted using aball-and-stickrepresentation. Si atoms are showninyellow,Oin red, Al in pink,and Hinwhite.

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Figure 9. Adsorption energiesofguest molecules in purely siliceous MFI calculated with QM/MM(P1) and QM/MM(P2). Experimental values are shownwith 10%error bar and were derivedbyremoving zero-pointvibrational and temperature correctionsfrom experimentally measured adsorption enthalpies Æ using quasi-RRHO.[83] The connecting linesare drawntoguide the eye. Adapted with permission from Ref. [82].Copyright (2014) AmericanChemical Society.

containing 10-ring channels and differing in cavity size (TON, FER, -SVR, MFI, MEL, STF,and MWW).[31] This effort was under- taken to corroborate the conclusion of Janda et al.,who ob- served that variations in reaction rates depend not only on dif-

ferences in DHads-H + and DSads-H +,but also on differences in ° ° [9] DH int and DS int. While QM/MM calculations have provided good estimates of the intrinsic enthalpies and entropies of ac- tivationextracted from experimental rate data for MFI, extend- ing this approachtoless confining zeolitesisnot straightfor- ward, particularly for activation entropies.[31] Because quantum chemicalcalculations are very resource intensive, they are nec- essarilylimited to one (or afew) configurations of selected acid sites. However,asdiscussed above, experimentally mea- sured heats of adsorption and kinetic parameters represent en- semble averages over all possible configurations of the alkane aroundBrønsted acid protons associated with avariety of Al sites.[24] In principle, calculations should be performed for all the different Al sites within the zeolite and the Boltzmann- averaged values should be used to comparewith experimental adsorption data and rate parameters. In practice, though, re- source limitations require the selection of arepresentative T- Figure 10. Transition state geometries for central cracking,terminalcracking, site to carry out QM/MM calculations. In our recent study,[31] methylene dehydrogenation,and methyldehydrogenation in MFI, with Al placed in the T12 site. For clarity,only the atoms included in the QM region we have used CBMC-derived site-specific entropies of adsorp- [9] are shown. Si atoms are shown in yellow,Oin red, Al in pink, Cincyan, and tion (DSads-H+ ), shown by Janda et al. to provide apractical Hinwhite.[51] Figurereproduced with permission from Ref. [31].Copyright metric for confinement, in order to inform the selection of rep- (2017) American Chemical Society. resentative T-sites in the series of 10-ring zeolites.Inaddition, we ensured that the range of structuralenvironments sampled changes in the activity and selectivity of butane cracking and was representative of the changes in confinement encoun- dehydrogenation arise from changes in the distribution of Al tered by reactant and transition states (TS) in movingfrom atoms and the associated Brønsted acid sites as aconsequence zeoliteswith higheraverage confinement (i.e. lower values of [22] of changes in the Si/Al ratio of the zeolite. DSads-H+ )tozeolites with lower average confinement(i.e.

Vander Mynsbruggeetal. have conducted atheoretical highervalues of DSads-H+ ), and took into account the above- study of cracking and dehydrogenation in aseries of zeolites mentioned tendency of the adsorbed alkane to redistribute

ChemPhysChem 2018, 19,341 –358 www.chemphyschem.org 353  2018 Wiley-VCH Verlag GmbH &Co. KGaA, Weinheim Minireviews preferentially within less confining spaces (e.g. cages, if pres- ly,these authors introduced ascheme, dubbed UM-VT,in ent, rather than channels) at higher temperatures. Selection of which internal rotations are projected out of the Hessian and T-sites in this wayensures that changes in confinementoccur treated separately from the remaining vibrations, resulting in for reactant and transition states (TS) in moving from zeolites significantly improved agreement with experimental standard with higheraverage confinement (i.e. more negative values of entropies and heatcapacities for aseries of gas phase mole-

DSads-H+ )tozeolites with higheraverage confinement (i.e. less cules. The UM-VT scheme might afford similar improvements [31] negative values of DSads-H+). for zeolite systems, however, some practical limitations arise when not all atomsare chemically bonded. For loosely-bound complexes,the appropriate cutoff point for the sampling 3.3. Thermochemical Calculations along specific modes is not inherently clear.Ifthe cutoff is set and reaction kineticsinDFT studies follow too low,the mobility of the adsorbate (and thus the entropy) from anormalmode analysisonthe stationary points that cor- will be underestimated. If the cutoffisset too high, the calcu- respondtothe reactantand transition states. While activation lation will include configurations in which the adsorbate starts enthalpies are largely determinedbythe electronic energy bar- to diffuse away from the activesite, no longer occupying the rier between the reactantand transition states predictedby adsorbed state. More research is required on this particular the electronic structure method, entropies are derived from issue. Note that these concerns also apply to the approach fol- the partitionfunctions, therefore their accuracy depends on lowed by Picciniand Sauer,[89] but is not specifically addressed the appropriate treatment of the normalmodes. Treating the in their reports. low-frequency motions that correspond to translational and ro- Grimme has proposed another,more pragmatic, strategy to tationalmovements of the guest molecule relative to the zeo- address anharmonicity of low-frequency modes, using asys- lite host as vibrations under the rigid rotor-harmonic oscillator tematicinterpolationbetween aone-dimensional free rotor at (RRHO)approximationhas been shown to overestimate the low frequenciesand aharmonic oscillator at high frequen- entropylosses associated with the adsorption of the guest cies.[83] Although enthalpies are decidedly less sensitive to the molecules from the gas phase into the zeolite pores.[59,84,85] inaccurate treatmentofthe normalmodes, Li et al. have In their study of hydrocarbon adsorption in zeolites, De shown that applying the quasi-RRHO approach to evaluate Moor et al. demonstrated that the entropycannot be calculat- zero-point energies and thermal corrections can also improve ed correctly by treating the guest molecules as immobile ad- the values for the adsorption enthalpies of molecules in zeo- sorbates in the RRHO approximation, and that the remaining lites.[82] In this case, the energy contributions for all modes are mobility of the adsorbed speciesatthe active sites needs to replaced by an interpolationbetween the contributionofa be taken into account.[85] The authors suggested an alternative, harmonic oscillator and that of atranslationalorrotational mobile adsorbate calculation, which uses aso-called mobile mode.Adsorption energies calculated with QM/MM using the block analysisofthe Hessian(MBH)[86,87] to identify those low- P2 parameter set (see above)and the quasi-RRHOapproxima- frequency modes corresponding to overall globaltranslations tion agree with experimental valueswith an RMS error of 1 and rotations of the guest molecule relative to the framework. 1.8 kcalmolÀ for both nonpolar and polar molecules adsorbed Once identified, the contributions of the modes to the parti- in MFI, H-MFI, and H-BEA.[82] tion function are replaced by the correctones for translational Janda et al. have shown that the quasi-RRHO approach can or rotational motions. estimateintrinsic activation enthalpies and entropies for cen- While the MBH analysis provides an unambiguous identifica- tral and terminal cracking of propane through n-hexane in H- tion of the modes to be treated as translations or rotations, MFI in good agreement with experiments.[24] However,since the calculation of the corresponding translational entropy still this approachstill relies upon asingle geometry for both the dependsupon an ad hoc estimate of the extentofthe transla- reactantand transition state, which at finite temperature con- tional motion. Severalauthors have proposed alternative ways sists of an ensemble of similar structures with slightly different to address the anharmonicity of low-frequency modes and im- orientations, it is expected to break down for zeolites that are prove the accuracy of thermochemical calculations. Piccini and less confining than H-MFI. Since the entropy(and enthalpy) of Sauer proposed the use of fourth and sixth order polynomials the transition states will still be underestimated, apparent acti- to represent the potential energy surface of the individual vation enthalpies and entropies will be underestimated. If the normalmodes in loosely boundadsorption complexes.[88, 89] reactantand transition states undergo differing degrees of Using this method,they achieved agreement between calculat- global translation and rotation, intrinsic activation enthalpies ed and experimental adsorption free energies for methane, and entropies will also be under- or overestimated. This hy- 1 [89] ethane andpropaneinH-CHA within 3kJmolÀ . While the pothesis was confirmed in the recenttheoretical work by Van use of low-order polynomial functions is computationally ad- der Mynsbrugge et al. of butane cracking and dehydrogena- vantageous, the quality of agreement between the model and tion in 10-ring zeolites with different degrees of confine- the real potential energy surfacefor agiven system can be dif- ment.[31] Thermal corrections to the apparent enthalpies and ficult to assess. In an effort to develop amore general ap- entropies derived from CBMC simulations on the reactantstate proach,Lietal. suggested representing the potentialenergy (butane adsorbed at the Brønsted acid site), which naturallyac- surfaceofeach normalmode by interpolatingthe energies of count for anharmonic motions of the adsorbate in the vicinity aseries of geometries distorted along that mode.[90] Additional- of the activesite, were shown to enableinclusion of configura-

ChemPhysChem 2018, 19,341 –358 www.chemphyschem.org 354  2018 Wiley-VCH Verlag GmbH &Co. KGaA, Weinheim Minireviews tional effects at low computational cost.[31] If the number of lite pores, and on the location of the activesites within the [31] ° ° configurations in the transition state ensembleisroughlysimi- pores. For central cracking, values of DH app and DS app cal- lar to the number of configurations in the reactant state, the culated using the quasi-RRHO approach are underestimated, configurational contributionstothe enthalpy (DDHconfig)and especially for the less confining zeolites (Figure 11 aand Fig- entropy(DDSconfig)ofthe transition state can be estimated ure 11 b). Adding the CBMC corrections significantly improves ° ° from the difference between the values of DSads-H + at 773 K the agreement for DH app and DS app in all zeolites, which indi- calculated from QM/MM using the quasi-RRHO approachand cates that the configurational enthalpy andentropy of the those determined from CBMC simulations on butaneadsorp- transition state are fairly similar to those of the reactantstate, tion at Al in the same T-site [Eq. (6) and (7)]: consistentwith the early characterofthe central cracking tran- sition state.[51] By contrast, for dehydrogenation,adding the DDHconfig DHads-H CBMC; 773 K CBMC corrections only improves the agreement between þ ¼ ð ÞÀ 6 ° ° DHads-H QM=MM-qRRHO; 773 K ð Þ DH app and DS app from theory and experiment for the zeolites þð Þ with the mostconfining structures (Figure 11 cand Figure11d). and As the confinement decreases, theory increasingly underesti- ° mates the experimental values of DH app and, more strongly, ° DDSconfig DSads-H CBMC; 773 K DS app.This deviation is attributed to the fact that dehydro- ¼ þð ÞÀ 7 genationoccurs via alate transition state, and the CBMC cor- DSads-H QM=MM-qRRHO; 773 K ð Þ þð Þ rections derived from the reactant state fail to account for the uncorrelated rotations and translationsofthe product-like frag- 1 [31] The values of DDHconfig (10–43 kJmolÀ )and DDSconfig (62–86 ments making up the transition state. 1 1 JmolÀ KÀ )depend strongly on the shape and size of the zeo-

Figure 11. Plots of apparent activationenthalpy(a,c) andentropy (b,d) vs. adsorption entropydetermined from CBMC simulations for centralcracking (a,b) and central dehydrogenation (c,d) of n-butane at 773 K. Experimental values (red circles)are compared with theoretical values determined from QM/MM using the quasi-RRHO approach, before(black diamonds) and after (blue triangles) adding the thermal correctionsderived from CBMC simulations. Represen- ° ° 1 1 1 tative 95%confidence intervals for the experimental valuesofDH and DS are 8kJmolÀ and 11 JmolÀ KÀ .Adapted with permission from app app Æ Æ Ref. [31].Copyright(2017) American Chemical Society.

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4. Conclusions and Outlook necessaryaccuracyatareasonable computational cost. Once stationarypoints corresponding to the reactantand transition Our review shows how confinement of Brønsted acid sites in states have been identified, thermodynamic andkinetic param- zeolitescan influence the observed kinetics of monomolecular eters can be calculated from anormal mode analysis, which cracking and dehydrogenation of alkanes. The environmentof provides the contributions of the nuclear motions to the parti- the active sites varies with the distribution of the Al atoms in tion function. However,the correct treatment of the often the framework of agiven zeolite as afunctionofthe Si/Al ratio strongly anharmonic, low-frequency motions of species in the and with the overall topology of the zeolite.Tounderstand the both reactant and transition states remains achallenge. These origin of these observations, it is important to separate the motionstypically correspond to translational and rotational contributions of the adsorption thermodynamicsand the in- movementsofguest molecules relative to the zeolite host, and trinsic kinetics to the apparent kinetics. The configurational- describing them as vibrations under the rigidrotor-harmonic bias Monte Carlo (CBMC) approach described by Janda oscillator (RRHO) approximation results in overestimated entro- et al.[9,24,32] has provided acomputationally efficient tool to de- py losses of these guest molecules inside the zeolite pores scribe adsorption of gas phase alkanes into the reactant state comparedtothe gas phase. The ultimate shortcoming of this (i.e. in configurations in which the alkanes are close enough to approachisthat it relies on asingle geometry for both the re- aBrønsted acid site for cracking or dehydrogenation to occur) actant and transitionstate, which at finite temperature consist at reactiontemperatures (> 673 K), such that the correspond- of an ensembleofstructures with different orientations. If the ing enthalpy (DHads-H+)and entropy (DSads-H+ )changes can be reactantand transitionstates undergo similar motions around determined correctly and accurate intrinsic activation parame- the active site, configurational correctionsdetermined from ters can be extracted from experimental apparent activation CBMC simulations on the reactant state can be apragmatic so- parameters. lution. In the contextofmonomolecular alkane cracking and Using this approach, the intrinsic enthalpies of activation for dehydrogenation, this approach was found to work well for dehydrogenation have been found to increasewithadecrease central cracking, which proceeds throughanearlytransition in the confinement of the proton, using the entropyofadsorp- state that closely resembles the reactant, but not fordehydro- tion as aproxy for confinement.[9,24] By contrast, the intrinsic genation, whichinvolves alate transition state in whichthe activation parameters for central cracking are generally insensi- product fragments are almostfully formed.[51] The motions of tive to confinement and those for terminalcracking exhibit in- these fragments relative to each otherand to the zeolite differ termediate dependence on confinement. Progress in under- significantly from those in the reactantstate, especially in less standing the origin of these differences in sensitivity to con- confining zeolites. The treatment of such reactions, involving finementasafunctionofreactionpathway has been made such loose transition states in large-pore zeolites is achallenge using quantum chemical calculations as summarized below.In for future research efforts. In asimilarapproach to the one fol- addition, the intrinsic activation parameters for n-alkane crack- lowed by Vander Mynsbruggeetal.,[31] one might consider at- ing have been determined as afunction of chain length for tempting to derive configurational corrections for reactions MFI.[9,24] Adecrease of the intrinsic activation energy was with alate transition state based on the productstate instead found to drive an increase of the rate coefficient with chain of the reactant state. While this maycertainly be possible in length while the intrinsic activation entropy was invariant with some cases,this is not an option in the case of alkane dehy- chain length, afinding that is consistentwithindependent drogenation, since the interaction of the alkene formed in this QM/MM calculations. However,more recent experimental reactionwith the acidsite cannotbedescribed with the classi- work[27] in which different conclusions have been reached dem- cal force fields used in CBMC simulations,and afirst principle onstrates that the variationofactivation parameters with chain approachisrequired. rapidly undergo protonation, length is not fully resolved. Further investigation is necessary even at low temperatures, and the nature of the intermediates in order to determine whether the dependence of these pa- formed under reactiontemperatures remains unclear.Recent rametersonchain length is general or is afunction of confine- studies using ab initio molecular dynamics have shown that al- ment. Of note is that understanding the structure and chain kenes interacting with Brønsted acid sites can form a p-com- length dependence of intrinsic activation parameters has been plex, acarbeniumion or acovalently bound alkoxide, depend- enabledbythe abovementioned Monte Carlo technique, ing on the temperature, the chain length of the alkene and which allows intrinsic barriers to be extractedfrom measured the degree of branching.[91,92] barriers correctly by providing enthalpy and entropyofadsorp- The products formed immediately after crossingthe transi- tion to the reactant state at the temperature of the reaction. tion state for alkane cracking or dehydrogenationare metasta- This method of analysis leads to different conclusions regard- ble intermediates that are separated from more stable species ing the structure dependence (or lack thereof)ofintrinsic acti- by relatively small barriers that are easily overcome at reaction vation parameters than those previously reported, which were temperatures. Zimmerman et al. have employed quasi-classical calculated from measured activation barriers and experimental trajectory simulations with initial nuclear velocities derived adsorption data obtained at room temperature.[8,10–13,25,26] from the QM populations of the vibrationalmodes in the tran- Hybrid quantum mechanics/molecular mechanics(QM/MM) sition state at reaction temperatures to investigate the non- calculations on large cluster modelshave enabled the compu- equilibrium pathways through which the carbenium inter- tationalstudy of reactions occurring at active sites with the mediates formed by the protonation of C Cbonds in n-pen- À

ChemPhysChem 2018, 19,341 –358 www.chemphyschem.org 356  2018 Wiley-VCH Verlag GmbH &Co. KGaA, Weinheim Minireviews tane evolve into avariety of cracking products.The prevailing Conflict of interest pathways, which ultimately determine the experimentally ob- served product selectivity for n-pentane cracking in H-MFI, The authors declare no conflict of interest. were shown to deviate significantly from the potentialenergy surfaceat0Kobtainedfrom static electronic structure calcula- Keywords: activation enthalpy · activation entropy · tions.[93] More recently,Gomes et al. demonstrated similar dif- adsorption · confinement · zeolites ferences between product distributions predicted from static and dynamic pathways for the zeolite-catalyzed methylation of ethene and propene by methanol.[94] With the increasing availability of more powerful computers, [1] A. Corma, Chem. Rev. 1995, 95,559–614. severalresearch groups have started to explore the use of ab [2] M. Guisnet, J. P. 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