Ab Initio Prediction of Proton Exchange Barriers for Alkanes at

Article Cite This: J. Am. Chem. Soc. XXXX, XXX, XXX−XXX

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Ab Initio Prediction of Proton Exchange Barriers for Alkanes at Brønsted Sites of Zeolite H‑MFI Marcin Rybicki and Joachim Sauer* Institut für Chemie, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany

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S Supporting Information *

ABSTRACT: A hybrid of high level and low level quantum mechanics (QM) methods has been employed to predict intrinsic and apparent energy barriers for the direct proton exchange mechanism of methane, ethane, propane, n-butane, and i-butane on Brønsted sites of H-MFI. The specific hybrid MP2:PBE+D2 + ΔCC implementation used is known to yield the so-called “chemical accuracy” (±4 kJ/mol). Whereas the apparent enthalpy barriers decrease with increasing C number from 104 to 63 kJ/mol, in line with the decreasing heat of adsorption, the intrinsic enthalpy barriers are constant within 124−127 kJ/mol at 500 K. For methane, ethane, propane, and n-butane, we find the expected agreement of apparent barriers with activation energies from batch recirculation reactor experiments. The activation energies derived from NMR experiments (103−113 kJ/mol) are similarly constant as the predicted intrinsic barriers but systematically lower. For i-butane the predicted intrinsic and apparent barriers for the direct proton exchange step are the same as for n-butane with deviations of 2−5 kJ/mol, while the experiments yield values that are 50−60 kJ/mol lower, far outside the estimated range of combined experimental and computational uncertainty (±14 kJ/mol). A change to the indirect proton exchange mechanism, in which a hydride ion is transferred between the alkane and a tert-butyl carbenium ion can be excluded, because we confirm previous findings that the barrier for dehydrogenation that would create a tert-butyl cation from i-butane is much too high, 188 and 132 kJ/mol for the intrinsic and apparent enthalpy barriers, respectively, at 500 K. The possible role of extraframework- and framework-bound alumina species is discussed.

1. INTRODUCTION Atomistic understanding of catalysis in general, and of heterogeneous catalysis in particular, requires detailed information about active sites and elementary reaction steps. The number of possible active sites is large and so is the number of possible reactions, adsorption/desorption and diffusion steps. Microkinetic models of the complex reaction networks are needed to examine how the elementary steps are coupled together for given reaction conditions, see, e.g., refs 1 and 2. Often rate or equilibrium constants for individual steps have not been or cannot be measured which hampers the discrimination between different mechanistic proposal/s. The example we are addressing here is alkane activation by acidic zeolites3−11 which, together with C−C bond cleavage and dehydrogenation, belongs to the three elementary steps involved in catalytic cracking of crude oil, a large-scale process in petrochemical industry. For the proton exchange, it is debated whether it occurs directly via carbonium type transition structures12 or indirectly via hydride transfer involving alkoxides or carbenium ions. 4,13 The direct mechanism,12 see Figure 1, is a single elementary step in which the proton of the Brønsted site (H+B) is directly transferred to the alkane molecule, with simultaneous transfer of one of the protons of the alkane back to the Brønsted site. The mediated mechanism4 involves two proton transfer steps. First, the Brønsted proton is transferred to an alkene molecule, © XXXX American Chemical Society

and, in the second step, the hydride ion is transferred from the nearby alkane to the alkyl cation. The alkene molecule is an impurity, formed, e.g., by dehydrogenation of the alkane, or already present in the feed. In such situations, quantum chemical calculations can play an important role and support or discourage mechanistic proposals. Quantum chemistry will be only useful, however, when rate and equilibrium constants for crucial steps can be predicted with chemical accuracy (4 kJ/mol for energies and 1 order of magnitude for rate constants). This is currently possible only for reactions with a rather limited number of atoms, but not for realistic models of catalytic reactions on surfaces or in nanoporous materials that may comprise of the order of thousand atoms. Whereas methods that are sufficiently accurate (Coupled Cluster with Single and Double and Perturbative Triple Substitution, CCSD(T))14 cannot be applied because of their exponential scaling with the system size,14,15 density functional theory (DFT) as a rule cannot be trusted to yield results within chemical accuracy limits.15−18 Here, we combine the virtues of both approaches and apply a divide-and-conquer strategy19−22 that departs from a potential energy surface obtained by standard DFT with inclusion of dispersion. The energies of the reactant and Received: October 18, 2018

A

DOI: 10.1021/jacs.8b11228 J. Am. Chem. Soc. XXXX, XXX, XXX−XXX

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Journal of the American Chemical Society

molecular dynamics (MD) simulations for small alkane molecules in H−CHA taking the full periodic structure into account. They concluded that for i-butane the proton exchange proceeds through the mediated mechanism, while for smaller alkanes the direct mechanism is more favorable. However, the type of density functionals adopted (generalized gradient approximation PW91) typically underestimates energy barriers.31 A study of ethane, propane, and butane in H-MFI considered cluster models of increasing size up to 96 T atoms (T = Si, Al) and proposed an extrapolation scheme that included effects of the cluster size, basis set, and electron correlation.32 The calculated barriers were substantially underestimated with respect to the experiment, and it remained unclear why. The most recent application of DFT to the H/D exchange of ethane, propane, i-butane and i-hexane over the H-MFI used the ONIOM scheme,33 another hybrid QM:QM implementation. Differently from the implementation used here, the low level calculations of ref 33 did not apply periodic boundary conditions but were performed on a “T72” cluster model consisting of 72 TO4 tetrahedra (T = Si, Al) with the semiempirical MNDO method, while the active site of the system was represented by a relatively small 8T cluster with the M06-2X hybrid density functional. In view of the high energy barriers obtained, the authors suggest that the direct H/D exchange mechanism is not likely for branched alkanes. They favor the mediated mechanism with alkoxyl intermediates, which are formed from olefinic impurities. In this Article, we will show that our hybrid high-level QM:low-level QM calculations yield enthalpy barriers for the direct proton exchange mechanism at Brønsted sites of H-MFI that are consistent with experimental results for methane, ethane, propane, and n-butane, but not for i-butane. For the latter, we predict barriers that are 50−60 kJ/mol higher than observed ones. We will conclude that the unusually high proton exchange activity of H-MFI toward i-butane cannot be explained by regular Brønsted sites at framework positions if alkene traces in the i-butane feed are excluded.

Figure 1. Direct proton exchange mechanism. R1, R2, or R3 are alkyl groups or hydrogen atoms. The oxygen positions at which the proton is located may be different in the initial and the final structures.

transition structures are refined by wave function-type electron correlation calculations14 for the reaction site. Specifically, we use second order Møller−Plesset perturbation theory (MP2), and coupled cluster with single and double substitution as well as triple substitution treated by perturbation theory (CCSD(T)).14 For a key reaction of the zeolite-catalyzed methanol-toolefin process, the methylation of small alkenes,23,24 as well as for adsorption of small alkane molecules on Brønsted sites in zeolites,25 results have been obtained that agree within chemical accuracy limits with experiment. We employ this hybrid high-level QM:low-level QM approach19−22 (QM = quantum mechanics) to predict chemically accurate enthalpy barriers for proton exchange between methane, ethane, propane, as well as n- and i-butane with selected Al−O(H)-Si Brønsted acid sites in zeolite H-MFI (ZSM-5).26 In addition to the intrinsic enthalpy barriers, ΔH⧧intr (see Figure 1), enthalpies of adsorption, ΔHads, will be calculated which allows predictions of apparent barriers, ΔH⧧app, which are often the measured quantities. From recent work of Tuma and Sauer,27 hybrid QM:QM results are available for intrinsic and apparent enthalpy barriers for proton exchange between methane and Al−O(H)-Si Brønsted sites at different crystallographic positions of different zeolite frameworks (CHA, FAU, FER, and MFI).28 The conclusion was reached that variations of apparent energy barriers across different frameworks and different Al positions are largely determined by energies of adsorption whereas the intrinsic barriers show little variation. The calculated intrinsic and apparent energy barriers (at 0 K) were between 134 and 141 kJ/mol and 105 and 118 kJ/mol, respectively, and consistent with experimental results available for faujasite, ferrierite, and ZSM-5.3,5,29 Quantum chemical calculations had been performed on the alkane activation problem before, but they remained inconclusive because either too small models had been adopted12,29−31 or methods had been used that are known not to yield chemical accuracy. Bučko et al.30 carried out

2. METHODS AND MODELS 2.1. Periodic Models. We adopt the H-MFI model of Tuma and Sauer.27 It was constructed from the orthorhombic unit cell of the pure silica MFI framework. The optimization using the PBE functional34 resulted in a, b, and c lattice constants of 2022.4, 1998.0, and 1347.8 pm, respectively. By substitution of selected silicon atoms with aluminum and addition of a charge neutralizing proton, a unit cell of the HAlSi95O192 composition was obtained (Al/ Si ratio of 1/95). The orthorhombic structure of the MFI framework consists of 12 symmetry-inequivalent T atom positions. We consider the Brønsted site with Al in T7 position and the proton at O7 which is bound to Si in T8 position, the so-called Al7−O7(H)−Si8 site. This is the “regular” site which was found to be energetically most stable35 and has been adopted in previous studies.27 Our PBE+D2 calculations (see below) confirm that this site is 3 kJ/mol more stable than the Al12−O24(H)−Si3 “intersection” site which we do not consider because for methane in H-MFI no significant differences of energy barriers or adsorption energies were found between these two Tsites.27 The T7 Al-site is part of a 10-membered TO4-ring of a straight channel, but it is close to the cage formed by the intersecting straight and zigzag channels (see Figure 2). Since at the T7 site the proton can sit on either of the O7, O17, O22, or O23 atoms (O16, O11, O17, and O18, respectively, according to IZA recommendations),28 there are six possible proton exchange pathways. Since previous work on B


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Figure 2. H-MFI model with the Al7−O7(H)−Si8 Brønsted site. Color code used within this publication: silicon, yellow; aluminum, gray; oxygen, red; hydrogen, white; carbon, black. All graphical representations were prepared with the Jmol package.36 methane showed that the only effective exchange path is the one involving the O7 and O22 sites,27 this path will be investigated here. 2.2. DFT Calculations. The systems under consideration consist of about 300 atoms per unit cell, and DFT calculations were performed with periodic boundary conditions using the Vienna Ab Initio Package (VASP),37,38 version 5.3.5. The latter is a plane-wave code that uses the projector-augmented wave (PAW) method39 to describe core electrons. We use a kinetic energy cutoff of 400 eV and perform Γ-point calculations. We apply the PBE exchange-correlation functional,34 together with the D2 dispersion term;40 see refs 24 and 41 for previous works using these settings. The SCF energy convergence criterion was 10−7 eV, and structure optimizations were considered converged when the maximum force acting on the atoms was less than 10−4 eV/Å. The stationary points were subsequently characterized as minima or saddle points by normalmode analysis. Harmonic vibrational energies were determined from mass-weighted Hessian matrices, which were calculated numerically using central finite differences with Cartesian displacements of 0.02 Å. 2.3. Hybrid QM:QM Calculations. The mechanical embedding scheme we use partitions the whole system (S) into the inner and the outer region. For zeolites, cutting out the inner region creates dangling bonds, which we saturated with H atoms as link atoms. The inner part together with link atoms form the cluster (C). The total hybrid energy of the system, EHL:LL(S), is obtained as follows:42,43 E HL:LL(S) = E HL(C) + E LL(S) − E LL(C)

Figure 3. Cluster models used for MP2 calculations. Different cluster models were selected to investigate “channel” (top) and “cage” (bottom) type transition structures. Link atoms are represented as white sticks. given as XTnOHmSiH, where “XT” refers to the number of TO4 tetrahedra. The subscripts nOH, mSiH refer to the number of terminating OH and SiH bonds, respectively. Obtaining reliable hybrid QM:QM results needs a careful selection of the cluster model for the high-level calculations. We designed models of increasing size for both “channel” and “cage” type transition structures (Figure S1 in the Supporting Information). Since i-butane is the bulkiest of all alkanes investigated here, we did calculations with different model sizes for this hydrocarbon only. For both energy barriers and adsorption energies, increasing the cluster size beyond 24 and 25 T atoms for “channel” and “cage” type structures respectively, does not change the hybrid results anymore (see Figure S2 in the Supporting Information). Therefore, these clusters, depicted in Figure 3, were used for all further hybrid QM:QM calculations. Our QM:QM calculations employed the MonaLisa code,44 which is the successor of the QM-POT code.43 As high-level method we use MP2, whereas low-level calculations for the host are performed with PBE+D2 with the same settings as described in the previous section. Low-level PBE+D2 cluster calculations were corrected for the BSSE errors (see next subsection for details of the BSSE correction scheme) and performed with TURBOMOLE 6.5 using def2-TZVP basis sets.45,46

(1)

To the high-level energy of the cluster, EHL(C), the energy of the full system obtained at the low-level, ELL(S), is added. The third contribution, ELL(C), eliminates approximately the double counting of the contributions coming from atoms in the inner region and artificial contributions from link atoms. Figure 3 shows the cluster models adopted to perform high-level calculations. Dangling bonds on O and Si were saturated by adding hydrogen atoms at constant bond distances of 95.3 pm (OH) and 145.5 pm (SiH) respectively.27 The composition of the clusters is C


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Journal of the American Chemical Society Equation 1 is valid also for determining the forces,45 which makes structure optimizations at the hybrid QM:QM potential energy surface (PES) possible. Tests performed for i-butane show, however, that this does not change the energy barriers and adsorption energies more than 1 kJ/mol with respect to the hybrid energies calculated at the DFT-optimized structures (see discussion in section 3.4). Therefore, in this work, we do not optimize the structures at the hybrid PES, but we calculate single point hybrid MP2:PBE+D2 energies at the PBE+D2 equilibrium structures. 2.4. Wave Function Based Electron Correlation Methods. As a high-level method we used MP2 with the resolution of identity (RI) approximation47 as implemented in TURBOMOLE 6.5.48 MP2 energies were extrapolated to the complete basis set limit using a two point extrapolation scheme49,50 with cc-pVXZ basis sets, X = T,Q.51,52 The energies used for the extrapolation were corrected for the BSSE using the counterpoise correction (CPC) scheme.53 Test calculations (see section S2 in the Supporting Information) have shown that extrapolation of BSSE corrected energies calculated with cc-pVTZ and cc-pVQZ basis sets yield energy barriers and adsorption energies within 1 kJ/mol of our best estimate for the complete basis set limit values. To apply the counterpoise procedure to adsorption complexes (structures R-a and P-a in Figure 1), we split the system into the alkane molecule and the acidic zeolite part. For the transition structure (TS in Figure 1), the system is divided into the protonated alkane and the negatively charged zeolite site. This partitioning scheme proved to work well in previous studies.23,27 To account for higher order electron correlation effects, we carried out CCSD(T) calculations using the cc-pVTZ basis set and the ricc2 program of TURBOMOLE 6.5. They could be completed for a small model of the reaction site only that is shown in Figure 4. However,

(1) PBE+D2 calculations with periodic boundary conditions (VASP) (1a) Structure optimization for minima and transition structures (1b) Harmonic wavenumber calculations for stationary points (2) Singe point MP2/CBS(T,Q) and PBE+D2/def2-TZVP calculations, both BSSE corrected, on cluster models shown in Figure 3 (TURBOMOLE). (3) Single point CCSD(T) and MP2 calculations with the ccpVTZ basis set on cluster models shown in Figure 4 (TURBOMOLE). 2.6. Enthalpy Calculations. To compare computational results with experiments, we calculated zero-point vibrational energies, ΔEZPV, and vibrational contributions to thermal energies, ΔEtherm, within the harmonic approximation56 at the PBE+D2 level (see Tables S6 and S7 in the Supporting Information). The enthalpy of processes of interest is calculated as ΔH = ΔEel + ΔEZPV + ΔEtherm + pΔV

(4)

where ΔEel is the electronic energy of the process, p stands for pressure of the system, and ΔV is the change of the volume during the process. The pΔV term is −RT for adsorption enthalpies and apparent enthalpy barriers, and 0 for intrinsic enthalpy barriers. Our best final enthalpy values, ΔHfinal (see Tables 1−3), are calculated according to eq 4 with electronic energies obtained at the hybrid QM:QM level and the remaining terms, abbreviated as (ΔH−ΔE)PBE+D2, calculated at the PBE+D2 level within the harmonic approximation:

ΔHfinal = ΔEfinal + (ΔH − ΔE)PBE + D2

(5)

57

Anharmonic calculations have shown that the harmonic approximation underestimates adsorption enthalpies of alkanes in zeolite H− CHA about 2 kJ/mol,25 and enthalpy barriers for methylation of alkenes in H-MFI about 4 kJ/mol.24

3. RESULTS AND DISCUSSION The direct proton exchange mechanism (Figure 1) involves three steps: (i) adsorption of the alkane (R → R-a), (ii) proton exchange (R-a → P-a) and (iii) desorption of the alkane (P-a → P). The full description of the process requires localization of five stationary points on the potential energy surface. The adsorption enthalpy is defined as follows ΔHads = HR‐a − HR (6) Figure 4. Cluster model (transition structure with i-butane) for CCSD(T) calculations.

where HR is the enthalpy of the reactants (unloaded zeolite plus alkane in the gas phase) and HR‑a is the enthalpy of the adsorbate complex. The intrinsic enthalpy barrier is ⧧ ΔHintr = HTS − HR‐a

our calculations performed for much bigger clusters using domainbased local pair natural orbital (DLPNO) CCSD(T) method54 implemented in ORCA program,55 version 4.0, confirm that a cluster of this size covers already all electron correlation effects which are not included in the MP2 calculations (see section 3 in the Supporting Information). The difference between CCSD(T) and MP2 electron correlation contributions obtained with the small cluster models,

where HTS is the enthalpy of the transition structure. The apparent enthalpy barrier ⧧ ΔHapp = HTS − HR

(8)

is the sum of the enthalpy barrier and the adsorption enthalpy: ⧧ ⧧ ΔHapp = ΔHintr + ΔHads

ΔCC(Csmall) = ΔECCSD(T)/cc ‐ pVTZ(Csmall) − ΔEMP2/cc ‐ pVTZ(Csmall) (2) when added to the hybrid MP2:PBE+D2 results, yields our final estimates for adsorption energies and energy barriers, ΔEfinal = ΔEMP2:PBE + D2 + ΔCC

(7)

(9)

3.1. DFT Calculations: Localization of Transition Structures. Optimization of the protonated zeolites with Al in T7 and the proton attached to the O7 and O22 atoms shows that the former structure is 8 kJ/mol more stable. Therefore, all intrinsic reaction barriers are reported with respect to the bare Al7−O7(H)−Si8 site. We distinguish two types of transition structures, namely “channel” and “cage”, see Figure 5. In the former the R1 group is pointing in the straight

(3)

It will be further referred to as hybrid MP2:(PBE+D2) + ΔCC energy. 2.5. Summary of computational protocol. To obtain our hybrid MP2:(PBE+D2) + ΔCC energies we perform the following steps: D


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channel of MFI, whereas in the latter the R1 group points in cage direction. To find transition structures for ethane, propane, n-butane and i-butane, the R1 group (see Figure 5) was substituted with −CH3, −C2H5, −C3H7 or −CH(CH3)2 groups, respectively. This way only proton exchange at primary carbon atoms is examined. Both experiments4,11 and calculations30 showed that proton exchange at the tertiary atom does not happen with i-butane. Figure 5 shows the most stable “channel” and “cage” type transition structures for the investigated alkanes. All of them were distorted along the transition mode and were subsequently optimized along the intrinsic reaction coordinate (IRC) to obtain the corresponding adsorption complexes. This way we obtained all stationary points of the proton transfer mechanism (Figure 1). The intrinsic energy barriers and adsorption energies for the lowest energy reaction pathways are collected in Table S4, and selected bond distances and angles are available in Table S5. For the n-alkanes, the “channel” type transition structures are energetically favored, whereas for i-butane the “cage” type structure is almost 10 kJ/mol more stable than the corresponding “channel” type structure. This may be explained by stronger repulsive interactions between the bulky i-butane molecule and the zeolite framework in the double 10-membered ring of the main channel compared to the cage. In contrast, due to better fitting, the attractive dispersion interaction between the alkane and the zeolite wall is larger in the straight channel, which explains the preference of the “channel” transition structures for linear alkanes.58,59 For i-butane, the proton exchange barrier at the T12 Brønsted site is virtually the same as that for the T7 site (see Table S4 in the Supporting Information, “cage” structure). This supports limiting our studies to the T7 site. Tables 1−3 include the PBE+D2 adsorption energies, intrinsic energy barriers, and apparent energy barriers, respectively for the lowest energy reaction pathways (the other pathways are described in section S5 in the Supporting Information). The apparent energy barriers of the proton exchange process are decreasing with increasing carbon number of the alkane. The intrinsic energy barrier is almost independent of the chain length. It decreases from 109 kJ/mol for methane to 104 kJ/mol for i-butane. The same observation has been made in previous theoretical studies.30,32,33,60 This is the consequence of the fact that the primary carbon atom,

Figure 5. Two distinct types of transition structures for the Al7− O7(H)−Si8 Brønsted site: the “channel” and the “cage” structures, and corresponding low energy transition structures (cut out from periodic structures) for ethane, propane, i-butane, and n-butane.

Table 1. Adsorption Energies and Enthalpies (kJ/mol) of Alkanes at the Al7−O7(H)−Si8 Site (Channel Structure), Obtained by PBE+D2 and Hybrid MP2:PBE+D2 + ΔCCa ΔEPBE+D2 ΔEMP2:PBE+D2 ΔCC ΔEfinald ΔEfinal−ΔEPBE+D2 (ΔH − ΔE)PBE+D2,323K (ΔH−ΔE)PBE+D2,500 K ΔHfinal,323Ke ΔHfinal,500Ke

methane

ethane

propane

n-butane

i-butaneb

i-butanebc

−36.9 −30.5 −0.2 −30.5 6.5 5.0 7.6 −25.5 −22.9

−52.2 −44.9 −0.3 −44.9 7.3 5.0 7.6 −39.9 −37.2

−66.5 −58.2 −0.1 −58.2 8.2 4.8 7.5 −53.4 −50.7

−79.6 −70.4 −0.1 −70.4 9.3 4.7 7.2 −65.7 −63.2

−72.3 −63.8 −0.1 −63.8 8.4 5.2 7.7 −58.6 −56.1

−72.4 −63.6 −0.1 −63.6 8.9 5.2 7.7 −58.4 −55.9

a

All values are single point energies calculated at the PBE+D2 structures. bCage structure. cStructure optimized at the MP2/cc-pVTZ:PBE+D2 level with 11T cluster (final hybrid energies calculated using MP2/CPC-CBL(T,Q):PBE+D2 method and 25T cluster). Thermal contribution and ΔCC corrections calculated for PBE+D2 structure. dEquation 3. eEquation 5. E


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Table 2. Intrinsic Energy and Enthalpy Barriers (kJ/mol) for Proton Exchange of Alkanes at the O7(H)−Al7−O22 site in HMFI (Channel Structure), Obtained by PBE+D2 and Hybrid MP2:PBE+D2 + ΔCCa ΔEPBE+D2 ΔEMP2:PBE+D2 ΔCC ΔEfinald ΔEfinal−ΔEPBE+D2 (ΔH−ΔE)PBE+D2,500K ΔHfinal,500Ke

methane

ethane

propane

n-butane

i-butaneb

i-butanebc

109.2 140.6 10.1 150.7 41.5 −23.5 127.2

105.7 134.7 10.0 144.7 39.0 −19.8 124.9

106.2 136.1 9.6 145.8 39.6 −18.9 126.9

104.4 134.9 9.8 144.7 40.3 −18.4 126.3

103.5 133.9 9.7 143.6 40.1 −19.4 124.2

104.4 133.0 9.7 142.8 38.4 −19.4 123.4

a

All values are single point energies calculated at the PBE+D2 structures. bCage structure. cStructure optimized at MP2/cc-pVTZ:PBE+D2 level with T11 cluster (final hybrid energies calculated using MP2/CPC-CBL(T,Q):PBE+D2 method and 25T cluster). Thermal contribution and ΔCC corrections calculated for PBE+D2 structure. dEquation 3. eEquation 5.

Table 3. Apparent Energy and Enthalpy Barriers (kJ/mol) for Proton Exchange of Alkanes at the O7(H)−Al7−O22 Site in HMFI (Channel Structure), Obtained by PBE+D2 and Hybrid MP2:PBE+D2 + ΔCCa ΔEPBE+D2 ΔEMP2:PBE+D2 ΔCC ΔEfinald ΔEfinal−ΔEPBE+D2 (ΔH−ΔE)PBE+D2,500K ΔHfinal,500Ke

methane

ethane

propane

n-butane

i-butaneb

i-butanebc

72.2 110.4 9.9 120.3 48.1 −15.9 104.4

53.5 90.1 9.7 99.8 46.3 −12.2 87.6

39.8 78.0 9.6 87.6 47.8 −11.5 76.1

24.8 64.5 9.7 74.3 49.5 −11.2 63.1

31.2 70.1 9.7 79.8 48.6 −11.8 68.0

32.0 69.5 9.7 79.2 47.2 −11.8 67.4

a

All values are single point energies calculated at the PBE+D2 structures. bCage structure. cStructure optimized at MP2/cc-pVTZ:PBE+D2 level with 11T cluster (final hybrid energies calculated using MP2/CPC-CBL(T,Q):PBE+D2 method and 25T cluster). Thermal contribution and ΔCC corrections calculated for PBE+D2 structure. dEquation 3. eEquation 5.

gradient approximation (GGA) type16,17 which have large selfinteraction error. 3.3. Comparison with Previous Calculations. The recent hybrid M06-2X:MNDO calculations of Zheng and coworkers33 yielded intrinsic energy barriers of 134, 139, and 130 kJ/mol for ethane, propane and i-butane respectively, which are only 7−14 kJ/mol lower than those determined in this work. This reflects the reduced self-interaction error of the M06-2X hybrid functionals (54% Fock exchange) that had been used for the reaction site. The obtained adsorption energies33 are not binding enough compared to our results, by 7, 13, and 27 kJ/mol for ethane, propane, and i-butane, respectively, most likely due to the failure of MNDO to account properly for dispersion. Due to a partial compensation, apparent energy barriers of 96, 93, and 84 kJ/mol have been obtained for ethane, propane, and i-butane, respectively,33 which deviate only 4−5 kJ/mol from our best estimate. The adsorption energies of ethane, propane and i-butane calculated as periodic MP2 estimate by Sukrat et al.,32 −30.5, −42.6, and −48.5, respectively, are much less binding than our best hybrid QM:QM estimate, −44.9, −58.2, and −63.8 kJ/ mol, respectively. Their apparent energy barriers (56, 55, 58, and 46 kJ/mol for ethane, propane, n-butane, and i-butane, respectively)32 are much lower than our final estimates and show no dependence on the number of carbon atoms. 3.4. Comparison with Experiments. 3.4.1. Uncertainty of hybrid MP2:(PBE+D2) + ΔCC Results. The approximations involved in our final hybrid QM:QM estimate imply some remaining uncertainty with respect to the CCSD(T) limit for adsorption energies and energy barriers. They cannot be precisely determined, but there are some indications based on the following effects (see Table S3 in the Supporting Information): (i) We optimize structures at the PBE+D2

which takes part in this reaction, has almost the same chemical environment independently of the number of carbon atoms. 3.2. Hybrid MP2:DFT+D2 + ΔCC Calculations. The hybrid MP2:DFT+D2 + ΔCC method (described in section 2.4) was used to calculate single point energies at PBE+D2 optimized structures. A test for proton exchange in i-butane with the smaller 11T embedded cluster model showed that the structure optimizations at the hybrid MP2:PBE+D2 potential energy surface affects the final results not more than 1 kJ/mol. The hybrid MP2:DFT+D2 + ΔCC adsorption energies of alkanes (Table 1) are 7−9 kJ/mol less binding than the PBE +D2 ones. The CCSD(T) correction to MP2 adsorption energies is negligible, between −0.3 and −0.1 kJ/mol. The nearly constant difference between hybrid QM:QM and PBE +D2 results shows that PBE+D2 describes the increasing dispersion contribution with increasing chain length well. Our best estimates of intrinsic energy barriers (see Table 2) are as much as 38−42 kJ/mol higher than the PBE+D2 results, and are largely independent of the number of carbon atoms in the alkane molecule. For the intrinsic barriers, all values are in the narrow range of 143−146 kJ/mol; only the value for methane is slightly larger, 151 kJ/mol. The difference between CCSD(T) and MP2, ΔCC contributes 10 kJ/mol to these barriers. For both QM:QM and PBE+D2 methods, the apparent barriers lower with the chain length of the alkane, and the one for i-butane is higher than that of n-butane. Our best estimates of apparent energy barriers (see Table 3) are uniformly higher (46−50 kJ/mol), than the PBE+D2 results. The CCSD(T) − MP2 difference contributes 10 kJ/mol to this shift. The systematic and substantial underestimation23,27 of energy barriers with PBE+D2 is typical for functionals of generalized F


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Figure 6. Comparison of hybrid MP2:(PBE+D2)+ΔCC adsorption enthalpies (all-1H isotopologue, left panel) and Arrhenius energies (ZOH/ CnD2n+2 isotopologue, right panel) of alkanes with different carbon number (black circles) with experimental adsorption enthalpy (blue diamonds) and Arrhenius energies (blue diamonds, NMR; green diamonds, batch recirculation reactor IR/MS). The solid line on the right panel presents the expected dependence of the apparent Arrhenius enthalpy on the number of carbon atoms assuming that the adsorption enthalpy of n-alkanes decreases 12 kJ/mol per addition of one carbon atom.62

Table 4. Calculated Enthalpy Barriers for Proton Exchange in the Presence of Adsorbed Alkanes (kJ/mol) Compared to Available Experimental Information observed, NMRc EA methane ethane propane n-butane i-butane

T

118 ± 95

107 108 108 50 57

± ± ± ± ±

106 77 108 24 1411

observed, MSd ΔH⧧Ta

intrinsic

ΔH⧧T,

507−556

113

130

500 507−556 457−543 423−448 354−457 273−298

103 ± 10 104 ± 7 104 47 55 ± 14

127 129 129 129 127 128

calcd

b

EA

T

ΔH⧧Ta

apparent ΔH⧧T, calcdb

129−1483 101 ± 374e 87 ± 475e

775 748 623−698 700

123−142 95 ± 3 82 ± 4

110 110 92 80

80 ± 59,10 27 ± 513

723−823 413−473

74 23 ± 5

68 70

a Derived from measured Arrhenius barriers according to eq 10. bValues corresponding to specific experimental temperatures; for values at 500 K, see Table S9 in the Supporting Information. cExperiments in sealed NMR probe. dExperiments in batch recirculation reactor, analysis of the products using mass spectroscopy (MS). eAnalysis of the products using infrared spectroscopy (IR).

T-sites), and both theory and experiments35,61−64 suggest that there is more than one type of active sites present in this material. Our calculations were performed only for Al at T7 position, which was justified by virtually the same DFT apparent energetic barriers of i-butane proton exchange on the T12 site (see Table S4 in the Supporting Information). Closer inspection of intrinsic reaction energy contributions at the two different Brønsted sites shows, however, that these energies differ of about 3 kJ/mol. We estimate, therefore, that the uncertainty associated with diversity of the active sites is about ±3 kJ/mol only. The DFT calculations show also that all Tsites of this zeolite have very similar deprotonation energies,65,66 therefore no big variation of reactivity for the other tetrahedral positions is expected. 3.4.3. Adsorption Enthalpies. Figure 6 (left panel) compares our best estimates of adsorption enthalpies with experimental values67,68 obtained at 323 K. The calculated adsorption enthalpies of methane and ethane molecules agree perfectly with the experimental results. For longer alkanes the ab initio results are underestimated to an increasing extent with the increasing chain-length of the alkane, as in the hybrid MP2:MM calculations of De Moor et al.69 This may be due to the fact that in our molecular-statistics approach we take only the structures with the lowest energy into account and assume a harmonic (or anharmonic) potential well. Structures outside this potential well (other local minima) are not accessible with increasing temperature. A better description of adsorption

level, but for i-butane an optimization has been also performed at the hybrid MP2:(PBE+D2) level. The changes for adsorption energy, intrinsic barrier and apparent barrier are 0.2, 0.8, and 0.6 kJ/mol (Tables 1 and 2, cf. Supporting Information Table S3 for a summary). (ii) With respect to the MP2 cluster size, our results are converged within 1 kJ/mol (Figure S2 in the Supporting Information). (iii) As far as the basis set limit is concerned, the CPC−CBS(3,4) extrapolated MP2 adsorption energies for i-butane are compared with the CPC−CBS(4,5) MP2 results (−1.5 kJ/mol, see Table S1 in the Supporting Information). To evaluate the CCSD(T) − MP2 energy difference, ΔCC, we use a 3T cluster model only. The DLPNO implementation of CCSD(T)54 rendered it possible to employ much larger models. For i-butane, Table S2 in the Supporting Information shows a change of the CCSD(T) − MP2 of +1.4 kJ/mol when passing from the 3T model to the 25T model. Taking (i)−(iii) together for the apparent energy barriers, we arrive at an estimated uncertainty of ±2 kJ/mol with respect to the CCSD(T) limit. Since for single reference systems such as acidic zeolites, the uncertainty of CCSD(T) reaction energies is approximately 2 kJ/mol,31 the uncertainty of our hybrid electronic energies with respect to experiment is estimated to be ±4 kJ/mol, just within chemical accuracy limit. 3.4.2. Site Heterogeneity. Another source of uncertainty may be heterogeneity of the Brønsted sites. H-MFI is a zeolite which can form up to 48 different Brønsted sites (12 different G


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fair to assign error bars of ±10 kJ/mol to experimental Arrhenius activation energies. Proton exchange experiments study H/D exchange either between (per)deuterated hydrocarbons and zeolitic OH groups, ZOH/CnD2n+2, or between CnH2n+2 and deuterated Brønsted sites, ZOD/CnH2n+2. The former is the case with the NMR studies in Table 4, while the batch reactor experiments use deuterated zeolites. All enthalpy calculations reported in Tables 1−3 have been done for the all-1H systems, ZOH/ CnH2n. Table S9 compares the results for all three cases. It turns out that for the adsorption step the differences are 0.3 kJ/mol at most and, hence, can be ignored. Figure 6, left panel shows the all-1H results for the adsorption energies. For the intrinsic barriers, the deviations of the ZOH/CnD2n+2 and ZOD/CnH2n results from the all-1H values are between 2.1 and 2.6 kJ/mol. Since they agree with each other within 0.1 and 0.2 kJ/mol (only for ethane the difference is 0.5 kJ/mol), the calculated intrinsic and apparent barriers in Figure 6 and Table 4 use the ZOH/CnD2n+2 enthalpies. For the n-alkanes, Figure 6 and Table 4 show that the experimental values fall into the range spanned by the calculated intrinsic and predicted apparent barriers. The deviations of the batch reactor results for methane, ethane and n-butane are +15, +10, and −6 kJ/mol, respectively, within the error bars of experiment (±10 kJ/mol) and the uncertainty limits of our calculations (±4 kJ/mol). The barriers measured by NMR for methane, propane, and n-butane are 17, 25, and 25 kJ/mol lower than the calculated intrinsic barriers, but, within experimental error bars of ±10 kJ/mol,6,7,11 similarly constant with varying chain length. One possible reason why the measured NMR barriers are systematically lower than the calculated intrinsic ones could be that it is not just the proton exchange step that is rate determining. Differences in diffusivity can be excluded as possible cause because the self-diffusion coefficient of i-butane in silicalite-1 is about 100 times lower than that for n-butane.73 The overall good agreement for the n-alkanes fades away with i-butane. While the calculations predict an intrinsic barrier that is only 2 kJ/mol lower than for n-butane, there are two NMR experiments4,11 that report Arrhenius barriers which are 51 ± 14 and 58 (±10) kJ/mol lower than that for n-butane (Table 4). The same is true for the batch reactor experiments13 which report a drop of 54−59 kJ/mol (Table 4). These differences are far outside the estimated combined experimental and computational uncertainty range of ±14 kJ/mol for this difference. This indicates that the direct exchange mechanism is not operative for the proton exchange reaction of i-butane. 3.4.5. Alternative Mechanism. The alternative mechanism4 involves indirect hydride transfer from the i-butane molecule to a tert-butyl carbenium ion. DFT calculations for i-butane33 suggest that this step has a much lower intrinsic energy barrier (51 kJ/mol) than the direct proton exchange (128 kJ/mol).33 In both of the NMR experiments quoted in Table 4,4,11 the ibutene traces were carefully removed by catalytic hydrogenation of reactants. Formation of carbenium ions by direct dehydrogenation of i-butane is also very unlikely. The intrinsic barrier for this reaction step is as high as 180 kJ/mol as predicted by DFT. 33,76 We also investigated hydride abstraction from the tertiary C−H bond of i-butane using our hybrid MP2:PBE+D2 + ΔCC approach with the same computational settings as for the direct protonation mechanism; see the Supporting Information and Figure S4 for details.

processes for longer alkanes may require statistical averaging of possible adsorbed complexes, which could be done using molecular dynamic simulations.30,70−72 3.4.4. Proton Exchange Reaction. Enthalpy barriers calculated with transition state theory at a given temperature, ΔH⧧, relate to Arrhenius activation energies, EA, derived from data measured in a corresponding temperature range, according to56 (for details see the Supporting Information of ref 24): EA = ΔH ⧧ + nRT

(10)

where R stands for the universal gas constant and T is the absolute temperature (in K). Apparent barriers assume that the reactant is in the gas phase,24 therefore n = 1 in this case, whereas for the intrinsic barrier there is no volume work involved and n = 0. Table 4 lists the available Arrhenius energy barriers for proton exchange which originate from two types of experiments: (i) NMR, where the reaction takes place within a sealed probe (constant volume), and (ii) batch recirculation reactor experiments at constant pressure where the product concentration is analyzed using mass spectroscopy (MS) or infrared spectroscopy (IR). Tentatively, this may suggest that NMR yields intrinsic barriers since the surface coverage of adsorbed reactants (R-a) is constant and near saturation, whereas the batch reactor experiments yield apparent barriers13 assuming an equilibrium of the adsorption complex with the reactant in the gas phase. We therefore convert the experimental Arrhenius barriers into experimentally derived enthalpy barriers using eq 10, and compare them in Table 4 with hybrid QM:QM calculations for both apparent and intrinsic barriers. Figure 6 does the opposite. It compares the experimental Arrhenius activation energies with calculated intrinsic enthalpy barriers (open circles, broken line) which are directly comparable (eq 10 with n = 0). For apparent barriers, we show in Figure 6 values predicted according to ⧧ EA, T (pred) = ΔHint, T (calcd) + ΔHads,323K(expt) + RT

+ ΔT ΔHads(calcd)

(11)

to make the comparison independent of any imperfections in calculated heats of adsorption as discussed in previous sections. The last term of this equation ΔT ΔHads(calcd) = ΔHads, T(calcd) − ΔHads,323K(calcd) (12)

takes into account the fact that the heats of adsorption are usually measured at lower temperatures (298−323 K) than those at which the proton exchange experiments are performed (400−823 K). For alkanes investigated here, these corrections are independent of the chain-length, but increase from 3 to 8 kJ/mol for 500 and 800 K, respectively. Error bars on experimental activation energies are not always given, but the values obtained from Arrhenius plots, which are only linear in a limited temperature range, depend on the temperature interval chosen and have a statistical error. For example, our Arrhenius plot with the data points from Figure 7 of ref 11 (i-butane) suggests a standard deviations of about 13 kJ/mol. Error bars of at least ±5 kJ/mol have been inferred from averaging over different measurements for the same system.23 Some of the NMR experiments listed in Table 4 specify error bars of ±7 to ±14 kJ/mol.6,7,11 Hence, it may be H


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Journal of the American Chemical Society ORCID

Our best estimates for the intrinsic and apparent enthalpy barriers of dehydrogenation of i-butane at 500 K are 188 and 132 kJ/mol, respectively, much higher than the corresponding values for direct proton exchange, 126 and 70 kJ/mol, respectively. 3.4.6. Role of Extraframework Aluminum. Since our quantum chemical calculations, performed with chemical accuracy, exclude the hydride transfer mechanism for proton exchange at Brønsted sites involving carbenium ions (or alkoxides), and do not support the direct mechanism for ibutane, this raises the question if extraframework aluminum species could play a role in catalytic proton exchange. Schoofs et al. found for i-butane that “... in the absence of extra-lattice aluminium, the exchange rate is zero or very small.”13 Lercher and co-workers77 examined the effect of steaming on the activity of H-ZSM-5 catalysts. They showed that the “activity passes through a maximum for zeolites having experienced short steaming durations” and explain this by the formation of “transient partially framework-bound Al-species”.77 It is also known that CH4 splits heterolytically on aluminum oxides and forms Al-CH3. A discussion of the possible role of extraframework aluminum should also explain the difference between nbutane for which we confirm the direct H/D-exchange at zeolitic Brønsted sites and i-butane for which this is not the case. 3.4.7. Concluding Remarks. Chemically accurate ab initio calculations for the direct proton exchange at Brønsted sites of H-MFI yield enthalpy barriers that are consistent with observed ones, both in NMR (423−556 K) and batch recirculation reactor experiments (623−823K), for methane, ethane, propane, and n-butane, but not for i-butane for which the ab initio calculations yield barriers that are 50−60 kJ/mol higher than observed. Since also the indirect hydride transfer mechanism involving tert-butyl carbenium ions can be excluded and there is evidence for the involvement of extraframework and/or frameworkbound alumina species, we conclude that further clarification needs experimental studies that compare n-butane and i-butane on the same set of H-MFI samples with as much as possible control and characterization of such species.

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Marcin Rybicki: 0000-0001-9309-0495 Joachim Sauer: 0000-0001-6798-6212 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work has been supported by German Science Foundation (DFG) by a Reinhart Koselleck grant to J.S. and by the “Fonds der Chemischen Industrie”. The Norddeutscher Verbund für Hoch- und Höchstleistungsrechnen (HLRN) is acknowledged for computational grants (bec00083 and bec00160).

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/jacs.8b11228. Details on clusters models used for hybrid QM:QM calculations; details of MP2 and CCSD(T) calculations; estimate of uncertainty of hybrid MP2:PBE+D2 + ΔCC calculations; reaction barriers, adsorption energies and selected bond distances of optimized structures; hybrid MP2:PBE+D2 + ΔCC results for alkane adsorption at the Al7−O22(H)−Si11 site and for dehydrogenation of i-butane; convergence of PBE+D2 results with the cluster size (PDF) Molecular structures of the stationary points of investigated reaction pathways (CIF files) and the list of the atoms defining cluster models for the hybrid MP2:PBE+D2 calculations (ZIP)

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REFERENCES

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