Proton Mobility in Chabazite, Faujasite, and ZSM-5 Zeolite Catalysts

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J. Phys. Chem. B 2001, 105, 1603-1613

1603

Proton Mobility in Chabazite, Faujasite, and ZSM-5 Zeolite Catalysts. Comparison Based on ab Initio Calculations Marek Sierka and Joachim Sauer* Humboldt-UniVersita¨ t zu Berlin, Institut fu¨ r Chemie, Arbeitsgruppe Quantenchemie, Ja¨ gerstrasse 10-11, D-10117 Berlin, Germany ReceiVed: NoVember 7, 2000

Ab inito predictions of the proton-transfer reaction rates in chabazite, faujasite, and ZSM-5 zeolites are presented. The reaction studied, a proton jump between neighboring oxygen atoms of the AlO4 tetrahedron, defines proton mobility in an unloaded catalyst. Classical transition state theory is applied, and the potential energy surface is described by the QM-Pot method. The latter combines a quantum mechanical description of the reaction site with an interatomic potential function description of the periodic zeolite lattice. At room temperature, the calculated rates vary over a broad range of 10-6 to 105 s-1, depending on the zeolite type and the particular proton jump path within a given zeolite. Proton tunneling effects appear to be negligible above room temperature. The calculated reaction barriers vary between 52 and 106 kJ/mol. While in all three zeolites both low and high barriers exist, the special structural features of the zeolite frameworks allow the prediction that the proton mobility is generally lower in chabazite and faujasite than in ZSM-5, in agreement with experimental data. Three structure factors determine the height of the barriers: (i) stabilization of the proton in the transition structure by interactions with neighboring oxygen atoms, (ii) local framework flexibility, which allows for narrowing of the O-Al-O angle without too much energy penalty, and (iii) overall flexibility of the zeolite lattice. The first two factors explain that proton jumps occurring between oxygen atoms in six-membered aluminosilicate rings have the lowest barriers. Jumps between oxygen atoms in four-membered rings and oxygen atoms in open zeolite channels or cavities have high barriers. The larger overall flexibility of the ZSM-5 lattice makes barriers for jumps occurring within a ring of a given size in ZSM-5 generally lower than in chabazite and faujasite.

1. Introduction Zeolites are an important class of shape-selective acidic catalysts used in various processes of the petrochemical industry. Their activity is due to Brønsted acidic sites, tSi-O(H)-Alt, called bridging hydroxyl groups (Figure 1). Although catalysts of different framework structure have these active sites in common, they may show very different catalytic performance.1-3 Understanding the origin of these differences is vital for designing new and more efficient catalysts. Among the measures of acidity used to characterize and to compare the sites in different zeolites are the energy of deprotonation (proton affinity) and the heat of ammonia adsorption. While the former is only indirectly accessible by experimental means (via correlation with IR frequency shifts), the latter can be measured by microcalorimetry or by temperature programmed desorption. A previous computational study reached the conclusion that these two measures may rank different zeolites in different order.4 Both of them are static properties, i.e., they are defined in terms of reaction energies. Another way of characterizing the acidic proton is looking at dynamic processes involving this proton. The simplest of such processes is the proton jump between neighboring oxygen atoms of the AlO4 tetrahedron (Figure 1). Experimentally, proton jumps have been studied using various variable temperature 1H NMR techniques.5-9 Table 1 summarizes energy barriers derived from NMR experiments for two * Corresponding author. E-mail: [email protected].

Figure 1. Brønsted acidic site in zeolite and the proton jump reaction.

TABLE 1: Proton Jump Barriers, ∆E‡ (kJ/mol), Inferred from 1H NMR Experiments at Temperatures T (K) zeolite

∆E‡

T

Si/Al

ref

faujasite

21-42 61 78 45 18 11 17-20

293-673 298-658 610-640 298-658 370-420 298-373 298-473

1.2, 2.6 3 2.4 38 35 21 12-53

5 6 7 6 7 8 9

ZSM-5

industrially used catalysts, faujasite and ZSM-5. The broad range of experimental energy barriers, 21-78 kJ/mol for faujasite and 11-45 kJ/mol for ZSM-5 zeolite, points to the large uncertainty of experimental values and underlines the need for theoretical predictions. Some of the experimental data suggest that proton mobility is higher in the ZSM-5 zeolite than in faujasite.6,7 This study makes ab initio predictions of rate constants for proton jump processes in the protonated forms of chabazite (HCHA), faujasite (H-FAU), and ZSM-5 (H-MFI) zeolites. Classical transition state theory10 (TST) is used, which needs the energies and harmonic vibrational frequencies of the initial

10.1021/jp004081x CCC: $20.00 © 2001 American Chemical Society Published on Web 02/03/2001

1604 J. Phys. Chem. B, Vol. 105, No. 8, 2001 and final states, as well as the transition structures. For molecules in the gas phase, the computational techniques of ab initio quantum chemistry yield these data with high accuracy. Application of these methods to elementary reaction steps on the surface of industrially important catalysts such as zeolites is hampered by the size of their unit cell, which may contain several hundred atoms. We cope with this complication by using a technique which limits the quantum mechanical treatment to the reaction site but combines it with an interatomic potential function treatment of the whole periodic structure (QM-Pot).11,12 It accounts for both the structural constraints imposed by, and the long-range potential due to the periodic zeolite lattice at modest computational expense. The QM-Pot method proved successful in studies of the site and framework dependence of reaction energies related to zeolite acidity such as the energy of deprotonation13-16 and the heat of ammonia chemisorption.4,17,18 A recent extension allows localization of transition structures in extended systems in general and in zeolite catalysts in particular.12 Here we apply the QM-Pot technique to evaluate stationary points relevant to the proton jump reaction. Preliminary reports have been already published for the QM-Pot predictions of proton jump reaction barriers in H-CHA and H-FAU zeolite12,19 but did not include the coupled cluster energy corrections and vibrational frequency calculations necessary for rate constant evaluation. Theoretical calculations related to the proton mobility in zeolite catalysts have been so far limited to gas-phase cluster model calculations. Using free cluster models, Sauer et al. predicted a proton jump barrier in zeolites of 52 ( 10 kJ/mol.20 Recently, calculations using partially constrained cluster models have been made for faujasite.21,22 After including our QM-Pot estimates of the long-range corrections in H-FAU,19 these authors arrived at a barrier of 97 kJ/mol (corrected for zeropoint vibrational energy). The estimated proton jump rate was 0.2 s-1 at 300 K. This rate includes a correction factor due to proton tunneling calculated from the zero-point energy corrected barrier and the harmonic frequencies for the transition structure. From the Arrhenius fit of the rate constants at different temperatures, corrected for tunneling effects, an effective proton jump barrier of 60 kJ/mol was obtained. The conclusion was reached that proton jump barriers derived from experimental mobility data are underestimated when tunneling is neglected. Our computational study is the first that compares proton mobility in different zeolite structures and takes the full periodic crystal structure into account, both with respect to the longrange interactions and structure constraints imposed by a flexible lattice. This allows for the first time an examination in detail of different proton jump paths within a given structure and a comparison of different zeolite structures with respect to proton mobility. We are able to identify three structural features that determine the heights of the barriers and explain why the barriers are generally lower in ZSM-5 than in chabazite and faujasite. This article is organized as follows. First, the periodic models for zeolite catalysts examined are presented, and computational details are given. Because the experimental proton jump barriers are not accurate enough to assess the accuracy of our calculations, we carefully examine the convergence of our combined QM-Pot method toward the full periodic quantum mechanical limit. We also provide an estimate of the remaining uncertainty of the calculated proton jump barriers on the basis of an analysis of the sources of computational errors. For the same reason, in the first part of the Results and Discussion section, we show that the results for the initial and final states of the reaction are in agreement with what is experimentally known about Brønsted

Sierka and Sauer

Figure 2. Fragment of chabazite lattice and numbering of oxygen sites. For simplicity, oxygen atoms are omitted.

Figure 3. Fragment of faujasite lattice and numbering of oxygen sites. For simplicity, oxygen atoms are omitted.

sites in H-CHA, H-FAU, and H-MFI zeolites. The second part then deals with the transition structures, reaction barriers, and TST reaction rates for proton jumps in these zeolites. The importance of proton tunneling in the context of our results is also considered. We compare our QM-Pot results with the free cluster calculations of Fermann et al.21,22 and with available experimental data. Finally, the dependence of the proton jump barriers on the structural parameters of the zeolite catalysts studied is discussed. 2. Periodic Zeolite Structures The periodic models for zeolite structures contain always one Al atom per unit cell. The acidic forms of a particular zeolite are created by adding a proton to one of the four oxygen atoms of the AlO4 tetrahedron. These periodic models are described below. H-Chabazite (H-CHA). Figure 2 shows the framework of zeolite chabazite.23 It consists of a network of double sixmembered aluminosilicate rings (hexagonal prisms) connected by four-membered rings. All tetrahedral atom positions are crystallographically equivalent and there are four distinct oxygen positions.24 We use a unit cell consisting of 37 atoms, HAlSi11O24.12 Hence, the Si/Al ratio is 11. H-Faujasite (H-FAU). Figure 3 shows the faujasite framework.25 In this structure, sodalite units are connected by double six-membered aluminosilicate rings (hexagonal prisms). All tetrahedral atom positions are equivalent, and there are four crystallographically distinct oxygen positions. The full unit cell of faujasite consists of 576 atoms and belongs to the Fd3m space group.26 We consider a smaller rhombohedral cell containing 145 atoms, HAlSi47O96. Hence, the Si/Al ratio is 47. H-ZSM-5 (H-MFI). Figure 4 shows the framework of zeolite ZSM-5, which consists of straight channels (direction [010]) and intercrossing sinusoidal channels (direction [100]).27 Silicalite, the all-silica form of ZSM-5, is known to occur in two forms: orthorhombic with space group Pnma, which is stable above 340 K,28 and monoclinic with space group P21/ n.1.1, which is stable below this temperature.29 In the orthor-

Chabazite, Faujasite, and ZSM-5 Zeolite Catalysts

J. Phys. Chem. B, Vol. 105, No. 8, 2001 1605 TABLE 2: Cluster Models Used for QM-Pot Calculations zeolite H-CHA H-FAU H-MFI

Figure 4. Fragment of ZSM-5 lattice, location of the T7 site, and numbering of oxygen sites. For simplicity, oxygen atoms are omitted.

hombic form, there are 12 crystallographically distinct tetrahedral atom positions.28 For our studies, we chose the Al atom located in the crystallographic position T7, which was found energetically to be preferable in previous studies.30,31 The unit cell of ZSM-5 used in this study contains 289 atoms, HAlSi95O192. The Si/Al ratio of this model is 95. 3. Computations 3.1. QM-Pot Method. The QM-Pot method used11,12 partitions the whole system (S) into two parts, the inner part (I) containing the reaction site and the outer part (O). The inner part is treated by quantum mechanics (QM). The outer part and all the interactions between the inner and outer parts are treated by a parametrized interatomic potential function (Pot). If chemical bonds exist between the inner and outer parts, the partitioning leads to dangling bonds, which are saturated by terminating atoms,32 called link atoms. The link atoms and the atoms of the inner part form the cluster (C). The QM-Pot energy of the whole system, EQM-Pot(S), is defined by the subtraction scheme

EQM-Pot(S) ) EQM(C) + EPot(S) - EPot(C)

(1)

where EQM(C) and EPot(C) are the QM and Pot energies for the cluster only, respectively, and EPot(S) is the energy for the whole system calculated at the interatomic potential function level. The calculations are performed using the QMPOT program12 which is an implementation of the QM-Pot method. As interatomic potential functions, we use shell-model ionpair potentials33 parametrized on density functional results for protonated forms of zeolites.15 The empirical valence bond (EVB) approach is employed to connect the analytical potential functions valid in the reactant and product valleys such that an approximate description is also obtained for the transition region. This is achieved by a coupling term, for which parameters have been derived from quantum mechanical calculations on small molecular models in our previous work.12,15 All potential function calculations employ the GULP program.34 The electrostatic energy is evaluated by the standard Ewald summation technique. For the summation of short-range interactions, a cutoff radius of 10 Å is chosen. The QM calculations use the density functional (DF) method and employ the TURBOMOLE program.35,36 The B3LYP exchange-correlation functional37,38 is applied, which proved superior compared to other functionals, especially with respect to structural parameters.39 DF calculations of Hessian matrixes are performed with the GAUSSIAN94 program.40 We adopt the fully optimized basis sets from the group of Ahlrichs,41 double-ξ basis sets for silicon, aluminum, and hydrogen, and a triple-ξ basis set for the oxygen atoms. Polarization functions are added to all atoms with exponents 0.35 (Si), 0.3 (Al), 1.2

structure optimization/ vibrational analysis 3T (H9Si2AlO10) 4T (H9Si3AlO12) 8T (H13Si7AlO22) 5T (H13Si4AlO16) 16T (H23Si15AlO43) 18T (H25Si17AlO48)

single-point energy periodic structure 23T (H23Si22AlO57) 25T (H31Si24AlO65)

(O), and 0.8 (H). This combination is labeled T(O)DZP. The numerical integrations use grid 3 from ref 36. The periodic structure of a particular zeolite is first optimized under constant pressure conditions applying the shell-model potential alone. The cell parameters corresponding to the protonated form of a zeolite with the lowest energy are chosen and used for the constant volume EVB and QM-Pot calculations for all other proton positions and transition structures. The following optimization strategy is adopted.12 First, minimizations and transition structure searches are made using the EVB potential only, and an exact Hessian matrix is calculated at each iteration. Starting from a reasonable structure guess, the calculations usually take less than 30 cycles to converge. Second, QMPot optimizations are performed using initial structures and Hessian matrices obtained from EVB calculations, as described in ref 12. We apply the following convergence criteria: the maximum energy change is 2.7 × 10-5 eV, the maximum gradient component 1.0 × 10-2 eV/Å, and the maximum displacement component 1 × 10-3 Å. At the end of each QMPot optimization, the exact Hessian matrix is evaluated, and a vibrational analysis is performed to ensure that a stationary point of the correct order is found. Structure optimizations do not apply symmetry constraints, i.e., the P1 space group is assumed. 3.2. Cluster Models. We perform QM-Pot calculations embedding QM clusters of different sizes, summarized in Table 2. Three different cluster sizes are defined for different purposes. In the following, the notation n-membered aluminosilicate ring means that n TO4 tetrahedra (T ) Si, Al) form the respective ring. (i) For H-CHA, the QM cluster models used in QM-Pot structure optimizations and Hessian matrices calculations consist of three and four TO4 units (3T and 4T models, panels a and b of Figure 5).12 A detailed description of the calculations on H-CHA is given in ref 12. (ii) For QM-Pot optimizations of H-FAU, we use a cluster model that consists of eight TO4 tetrahedra and is built of three joined four-membered aluminosilicate rings (Figure 5c). We label this cluster model 8T. Note that in previous QM-Pot studies,12,19 this cluster model was labeled 4T3. The QM-Pot structure optimizations of H-MFI use cluster models that consist of 5 TO4 tetrahedra (5T model, Figure 5d). The advantage of the 8T and 5T cluster models is that their position in the lattice is independent of the proton position, and thus, their absolute energies can be directly compared. We perform full QM-Pot structure optimizations using these clusters for all stationary points relevant for proton jumps. For the equilibrium structures, we calculate QM-Pot Hessian matrices analytically and perform vibrational analysis. (iii) To monitor the convergence of the reaction barriers and energies calculated with the QM-Pot method with respect to the cluster size, we perform single-point calculations using larger cluster models. For H-FAU, these models consist of 23 TO4 units (23T model, Figure 6a), while for H-MFI, they consist of 25 TO4 units (25T model, Figure 6b). In two cases where

1606 J. Phys. Chem. B, Vol. 105, No. 8, 2001

Sierka and Sauer

Figure 5. 3T (a), 4T (b), 8T (c), and 5T (d) cluster models used for QM-Pot structure optimizations and calculations of vibrational frequencies.

the convergence is not satisfactory (vide infra), we perform structure optimizations using intermediate size models consisting of 16 and 18 TO4 units (16T and 18T models). These models are designed so that they include all five- and six-membered aluminosilicate rings to which the two oxygen atoms belong that are involved in proton jump reaction. In case of H-CHA, we use energies obtained by single-point full periodic DF calculations employing the B3LYP functional on structures obtained from the QM-Pot calculations. For a detailed description of these calculations, see ref 12. The clusters representing the QM part in the QM-Pot calculation are always terminated with OH groups. Geometric constraints are applied to the terminating OH groups according to the QM-Pot scheme.11,12 Fixed O-H distances of 96.66 and 96.28 pm are used if the OH group is bonded to Si and Al atoms, respectively. These are equilibrium distances obtained by free cluster optimizations of similar cluster models.15 3.3. Convergence Studies. The accuracy of the calculated proton jump barriers depends both on how well QM-Pot results converge toward the full periodic QM limit and the intrinsic accuracy of the QM method used. To check the former factor, we evaluate proton jump barriers using single-point QM-Pot energies obtained by embedding large cluster models, 25T and 23T (see Section 3.2). These energies are calculated at the zeolite structures optimized using the smaller 8T and 5T models for H-FAU and H-MFI, respectively. Table 3 shows the depen‡ , on the dence of the calculated proton jump barriers, ∆EQM-Pot cluster size. For H-FAU the difference between proton jump barriers calculated for 8T and 23T cluster models is smaller than 6 kJ/mol. Similarly, for H-CHA, we have found previously12 that the difference between results obtained using 8T cluster models and the full periodic QM limit is smaller than 6 kJ/mol. For H-MFI, there are two proton jump paths for which the proton jump barriers changed by more than 6 kJ/mol going from 5T to 25T cluster models. These are the jumps between the O7-O23 and O17-O22 oxygen positions. In these cases, the proton jump occurs within the dense wall of the straight and sinusoidal channel, and there are probably quite strong

Figure 6. 23T (a) and 25T (b) cluster models used to evaluate final single-point QM-Pot energies.

interactions to neighboring atoms. These interactions may not be described well enough at the shell-model potential level. The improved description of interactions by the DF method when using 25T cluster models causes the change of the barrier height compared to the 5T cluster results. To answer the question if it is enough to perform single-point calculations using the large clusters or if optimization of the large clusters is required (which would be computationally very expensive), we design intermediate size models, 16T and 18T, for O7-O23 and O17-O22 proton jumps, respectively (see Section 3.2). These cluster models are obtained from the 5T models by including oxygen atoms closest to the jumping proton. We perform full QM-Pot structure optimizations using these models and finally calculate single-point energies using 25T cluster models. The barriers obtained this way (not shown in Table 3) do not differ by more than 2.0 kJ/mol from those obtained by single-point calculations on 25T models constructed directly from the structures optimized using 5T models. Thus, on the basis of the above convergence studies, we assign the uncertainty of the calculated jump barriers, connected with approximate description of the long-range effects in the QM-Pot scheme, as lower than 6 kJ/mol. In the case of the H-CHA zeolite where different types of cluster models in different configurations are used for structure optimizations12 (3T and 4T), this uncertainty manifests itself in the fact that the proton jump energies do not obey Hess’s exactly, i.e., ∆E(O1-O3) + ∆E(O3-O2) equals ∆E(O1-O2) only approximately, with an error of up to 4 kJ/mol.

Chabazite, Faujasite, and ZSM-5 Zeolite Catalysts

J. Phys. Chem. B, Vol. 105, No. 8, 2001 1607

‡ TABLE 3: Convergence of the QM-Pot Reaction Barriers, ∆EQM-Pot , and Their Long-range Corrections, ∆E‡LR, (kJ/mol) with the Size of the QM Clusters for H-FAU and H-MFI

H-FAU

H-MFI

‡ ∆EQM-Pot

jump path O3-O2 O4-O2 O1-O2 O1-O4 O1-O3 O3-O4

∆E‡LR

‡ ∆EQM-Pot

8T

23T

8T

23T

jump path

5T

66.9 71.7 98.2 100.9 105.6 109.6

67.0 72.3 96.9 94.8 106.3 108.0

7.0 14.8 20.4 13.9 16.1 15.6

1.8 10.0 16.0 -10.2 7.7 5.0

O23-O22 O17-O23 O7-O23 O7-O22 O17-O22 O7-O17

54.4 64.9 74.1 77.9 91.0 92.6

16T, 18T

65.4 83.7

∆E‡LR 25T

5T

50.9 62.1 65.5 78.4 78.8 97.1

-5.5 2.4 14.4 10.9 33.0 61.9

16T, 18T

25T

6.2

-1.7 -1.1 2.9 14.1 17.2 15.9

37.1

3.4. Long-Range Interactions. The QM-Pot reaction barrier (as well as the reaction energy) consists of two contributions16,18 ‡ ∆EQM-Pot ) ∆E‡QM + ∆E‡LR

(2)

The first one, the direct quantum mechanical contribution

∆E‡QM ) EQM(C‡)//QM-Pot - EQM(CR)//QM-Pot

(3)

is different from free space cluster results because the structures of the embedded clusters are different from those of the free space clusters due to constraints imposed by the zeolite lattice. The notation “//QM-Pot” means that the energies are evaluated for the structures obtained from combined QM-Pot calculations. Superscripts R and ‡ correspond to the reactant state and transition state (TS), respectively. The second term includes all contributions due to the interatomic potential functions

∆E‡LR ) EPot(S‡)//QM-Pot - EPot(SR)//QM-Pot EPot(C‡)//QM-Pot + EPot(CR)//QM-Pot (4) If the QM cluster is large enough to account for all structure distortions upon the reaction, the latter contribution can be considered as a correction accounting for all long-range interactions not included in the QM part. Table 3 lists also the long-range corrections to proton jump barriers, ∆E‡LR, defined by eqs 2 and 4. For all jump paths in H-FAU, the increase of the cluster size from 8T to 23T causes a decrease of the long-range corrections. The strongest decrease by 24 kJ/mol is observed for the O1-O4 proton jump. This is also the jump path with the largest change of the barrier, 6 kJ/ mol, between 8T and 23T models. For the H-MFI zeolite, the decrease of long-range correction between 5T and 25T cluster models is between 3 and 46 kJ/mol, and in the case of the O7O22 proton jump, it increases slightly by 3 kJ/mol. The large change of ∆E‡LR by 46 kJ/mol for the proton jump between O7-O17 oxygen sites may be connected with their location in a dense environment of five-membered rings in the wall between the sinusoidal and straight channels. This change of the longrange correction is almost completely compensated by an opposite change of the direct QM contribution. The total QMPot barrier changes by less than 4.5 kJ/mol. This underlines the power of the QM-Pot approach in approximating long-range effects by the embedding potential. It is remarkable that even for the largest cluster models studied, the long-range corrections remain a significant part of the proton jump barriers. The final long-range corrections for H-FAU and H-MFI zeolites using 23T and 25T cluster models are between -10 and 17 kJ/mol. The irregularity and magnitude of the long-range corrections shows that the free space cluster

Figure 7. 1T (a) and 0.5T (b) cluster models used for calculations of CCSD(T) corrections.

models, even large ones, do not provide quantitative results of proton jump reaction barriers in zeolites. 3.5. Coupled Cluster Energy Corrections. To account for the approximate treatment of electron correlation by the DF method, we calculate corrections to proton jump barriers and reaction energies using the coupled cluster method with single and double substitutions and perturbative corrections for triple excitations, CCSD(T).42 They are evaluated as single-point energies for cluster models consisting of a single AlO4 tetrahedron, denoted 1T (Figure 7a)

∆ECCSD(T) ) ∆E(1T)CCSD(T) - ∆E(1T)DF

(5)

where ∆E(1T)CCSD(T) and ∆E(1T)DF are relative energies calculated for the 1T cluster using the CCSD(T) and DF B3LYP methods, respectively. The 1T models are cut out of the zeolite structures optimized using the QM-Pot method. The CCSD(T) calculations employ Dunning’s cc-pVTZ43,44 basis sets and are performed using the MOLPRO program package.42,45,46 To further check the influence of the basis set size on ∆ECCSD(T), we perform similar calculations using even smaller cluster models, denoted 0.5T (Figure 7b), using Dunning’s cc-pVQZ basis sets.43,44 Since these calculations are computationally expensive, we made them only for the smallest and largest ∆ECCSD(T) corrections, i.e., for proton jumps between O1-O2 and O1-O4 oxygen positions in H-FAU (cf. Tables 6-8). Using the formula of Halkier et al.,47 we extrapolate the results obtained for the 0.5T model with cc-pVTZ and cc-pVQZ to the basis sets limit. We arrive at the final difference between the cc-pVTZ results and the extrapolated limit of 1.7 and 3.7 kJ/mol for O1-O2 and O1-O4 proton jumps in H-FAU, respectively. We consider these values as remaining uncertainty of our calculations. 3.6. Final Energy Differences. The final values for proton jump barriers, ∆E‡, and reaction energies, ∆E, are calculated in the following way: (i) The single-point QM-Pot energy differences calculated for the largest cluster models, i.e., 23T cluster for H-FAU and 25T cluster for H-MFI (cf. Table 3), are taken. For H-CHA, the full periodic QM results are taken from ref 12. (ii) To these energies the CCSD(T) corrections evaluated for ‡ smaller 1T cluster models (∆ECCSD(T) and ∆ECCSD(T) , eq 5) are

1608 J. Phys. Chem. B, Vol. 105, No. 8, 2001 added to correct for incomplete account of electron correlation by the B3LYP functional. (iii) Finally, zero-point vibrational energies (ZPVE) are added, ∆E‡ZP and ∆EZP, for jump barriers and reaction energies, respectively, obtained from QM-Pot frequencies (cf. Tables 6-8). Note that for the proton jump barriers, the zero-point vibrational effects and the CCSD(T) corrections work in opposite directions so that the final values are close to ‡ ∆EQM-Pot . However, the two effects together may add as much as 10 kJ/mol to the difference between different paths and are by no means negligible. Considering the uncertainty of QM-Pot calculations discussed in Section 3.3 (about 6 kJ/mol) and the basis set effect on CCSD(T) energy corrections (about 4 kJ/mol), we estimate the uncertainty of our final proton jump barriers as lower than 10 kJ/mol. 4. Results and Discussion 4.1. Brønsted Sites. Before we turn to proton jump processes, we briefly discuss the results for the Brønsted site itself. Our motivation is to strengthen confidence in the method by showing that the results are in agreement with the experimental information available. Structural data and harmonic O-H stretching frequencies for different proton positions in the zeolites studied are given in the Supporting Information section. RelatiVe Stabilities. Tables 6-8 show final values for the relative energies of protons located at oxygen atoms in different crystallographic positions (proton jump reaction energies, ∆E) calculated for H-CHA, H-FAU, and H-MFI zeolites. The ZPVE and CCSD(T) corrected relative energies are between 2.6 and 12.9 kJ/mol for H-CHA, 0.5 and 18.3 kJ/mol for H-FAU, and 2.2 and 20.7 kJ/mol for H-MFI. The following order of energies emerges from our QM-Pot predictions for H-CHA: O1 < O3 < O2 < O4. The ZPVE and CCSD(T) corrections lower the energy differences by less than 2.5 kJ/ mol and do not change the order. Full periodic ab initio pseudopotential plane-wave calculations for H-CHA48,49 yield the O1-H and O3-H sites as the most stable positions, but the order of O2-H and O4-H sites in ref 49 is different from ours. Experimentally, only protonation of the O1 and O3 sites has been observed50 (note the different numbering of oxygen sites in ref 50). This is in excellent agreement with our QMPot and plane-wave predictions. For H-FAU, the following energetic order of proton locations is predicted (energies relative to the most stable position in parentheses): O1 (0.0) < O3 (9.5) < O4 (10.0) < O2 (18.3). The full periodic DF calculations of Hill et al.51 yielded slightly different relative energies, but the order is in perfect agreement with our QM-Pot results. Previous QM-Pot calculations using the HF method16 agree on the order of protonation sites, only the relative energies are slightly different. Experimental studies on a faujasite with the composition Na3H53Al56Si136O384 yielded proton occupations for O1:O2:O3:O4 of 3:1:1.6:0,52 in agreement with our QM-Pot relative energies, except for the O2 position. The experimental occupation of the O2 position may be affected by the presence of Na+ cations or the Si/Al ratio, which was much higher in the experimental sample than in the model used for the calculations. For H-MFI, the QM-Pot calculations reveal the following order of proton locations: O7 (0.0) < O17 (6.6) < O23 (18.6) < O22 (20.7). The O7 position is predicted to be the most stable proton location. This is contrary to the previous QM-Pot calculations using the HF method, which predicted O17 to be

Sierka and Sauer TABLE 4: Comparison of the Observed and Calculated O-H Stretching Frequencies (cm-1) and O-H Distances (pm) for Brønsted Sites H-FAU O1-H νOH obsd νOH calcd O-H distance νOH calcde

3623a 3626 97.50 3596

H-MFI O7-H

H-CHA H-CHA H-FAU O1-H O3-H O3-H

3610b, 3614c 3603d 3608 3606 (8) 97.64 97.63 f (3585)

3579d 3588 (8) 97.78

3550a 3563 97.94

a Ref 56. b Ref 57. c Ref 58. d Ref 50. e Ref 12. f Frequency for O17-H site.

the most stable site.4,16 There is no experimental information about preferred protonation sites in H-MFI zeolite. Not even information about preferred positions of aluminum atoms in the lattice is available. O-H Stretching Frequencies. Comparison of predicted and observed O-H frequencies is made in Table 4. Harmonic O-H stretching frequencies calculated for different proton positions in the zeolites studied can be found in the Supporting Information section. They have been obtained by the DF method for the QM clusters alone at the equilibrium QM-Pot structures found. It is known53 that such an approach can yield improved results since an improved structure is used and harmonic frequencies are, in a first approximation, determined by the structure. For H-CHA for each proton position, we use the frequencies averaged over different cluster models used in QMPot calculations and describing the same proton position (see ref 12 for details). The harmonic frequencies are scaled54 by a factor 0.9716, obtained by comparison of the DF frequencies for water and methanol with experimental values.14 We also include the calculated O-H distances in Table 4, for there is a clear correlation: the longer the O-H distance, the lower the O-H stretching frequency. The correlation coefficient is better than 0.99. For H-CHA, the experimentally observed frequencies are 3603 and 3579 cm-1 for protons at O1 and O3 positions,50 in perfect agreement with our predictions. The pseudopotential DF plane-wave calculations on H-CHA48,49 yielded O-H stretching frequencies which are generally lower than those of our results. Depending on the pseudopotential and cutoff for plane waves used, the results reported differ by 1035 cm-1, making comparison with our results difficult. Note, however, that the B3LYP exchange-correlation functional used in this study yields generally superior frequencies compared to other functionals, especially when a scaling factor is applied.39,54 For H-FAU, the full periodic DF calculations yielded harmonic O-H stretching frequencies of 3731, 3645, 3606, and 3706 cm-1 for the O1, O2, O3, and O4 sites, respectively.5l Except for O3-H, these calculations agree within 3 cm-1 with our unscaled harmonic QM-Pot frequencies. For O3-H, the deviation is larger than 61 cm-1. It has also been pointed out that these calculations yielded a much too small anharmonicity constant for the O3-H stretching vibration (ref 55, note added in proof). We suspect a numerical error in the frequency reported. For H-FAU (Si/Al ) 20.7), frequencies of 3623 and 3550 cm-1 are measured experimentally for the O1-H and O3-H groups.56 The agreement with our QM-Pot predictions is better than 13 cm-1. For H-MFI (Si/Al ) 15), only one O-H stretching band at 3610 cm-1 or 3614 cm-1 has been observed.57,58 Our QM-Pot frequency for the lowest energy O7-H site, 3608 cm-1, is closer to the experimental values than the frequency for the O17-H site, 3590 cm-1. As already mentioned, previous QM-Pot studies at the HF level found O17-H to be the most stable site.4,16 The perfect agreement with the observed frequency adds additional credit to the O7-H assignment. Apart from this difference in assignment, the

Chabazite, Faujasite, and ZSM-5 Zeolite Catalysts

J. Phys. Chem. B, Vol. 105, No. 8, 2001 1609

TABLE 5: Selected Structural Parameters (pm, deg) of Proton Jump Transition Structuresa bond distances

bond angles

zeolite

jump path

O-H

O′-H

Al-O

Al-O′

Al-H

O-Al-O′

H-O-Al-O′

free clusterb H-FAU

O3-O2 O4-O2 O1-O2 O1-O4 O1-O3 O3-O4 O23-O22 O17-O23 O7-O23 O7-O22 O17-O22 O7-O17

127.7 123.7 127.4 126.7 127.0 123.6 123.4 120.9 124.9 126.1 126.8 124.2 121.0

124.5 122.7 120.4 125.1 121.6 121.2 125.3 124.2 119.6 124.1 120.4 125.6

188.4 185.1 181.1 182.5 184.6 183.3 185.1 183.6 185.0 182.7 184.7 183.9 184.5

184.5 183.6 183.6 184.2 183.4 185.7 181.5 182.4 183.7 184.1 183.0 183.2 184.4

194.3 192.5 187.2 194.2 185.7 184.0 190.7 195.7 192.0 195.9 188.9 190.0

78.4 76.3 77.7 77.7 77.6 77.0 77.7 76.8 76.2 76.2 76.8 76.6 76.7

-0.1 0.2 -4.7 -1.3 5.9 3.8 -0.5 0.5 0.5 0.6 2.6 3.8

H-MFI

a

Data for H-CHA: see ref 12, Table 5. b Ref 21.

TABLE 6: Proton Jump Barriers, Energies, and Their Components (kJ/mol) and Ring Sizes for Proton Jump Reaction in H-CHA Zeolitea jump path

ring size

‡ ∆ECCSD(T)

∆E‡ZP

∆E‡

∆G‡(298)

∆ECCSD(T)

∆EZP

∆E

∆G(298)

O3-O4 O1-O2 O1-O3 O3-O2 O2-O4 O1-O4

6T 8T 4T 8T 4T 4T

12.7 12.7 4.8 15.1 8.2 5.6

-11.4 -10.9 -8.9 -13.3 -8.0 -8.5

70.4 73.6 85.8 93.4 97.1 102.3

73.4 74.4 89.0 97.6 101.1 104.9

1.5 -2.3 -2.5 -0.7 1.5 -0.6

-0.4 -0.2 0.5 -0.5 0.6 0.1

4.4 9.0 5.2 2.6 5.3 12.9

7.1 7.0 6.5 1.0 5.3 10.9

a

The full QM results from ref 12, Tables 4 and 6 are used.

TABLE 7: Proton Jump Barriers, Energies, and Their Components (kJ/mol) and Ring Sizes for Proton Jump Reaction in H-FAU Zeolite jump path

ring size

‡ ∆ECCSD(T)

∆E‡ZP

∆E‡

∆G‡(298)

∆ECCSD(T)

∆EZP

∆E

∆G(298)

O3-O2 O4-O2 O1-O2 O1-O4 O1-O3 O3-O4

6T 6T 4T o.s.a 4T 4T

12.6 10.2 4.1 15.2 5.2 6.4

-11.3 -10.7 -8.2 -13.5 -8.5 -8.6

68.3 71.8 92.8 96.5 103.0 105.8

69.5 73.2 94.5 102.0 102.6 106.1

-1.3 -2.0 -3.7 -1.7 -2.4 0.7

0.1 1.0 1.1 0.1 1.0 -0.9

8.8 8.3 18.3 10.0 9.5 0.5

9.1 8.0 19.0 11.0 9.9 1.1

a

Jump occurs in “open space” (o.s.); see text for details.

predicted sequence of O-H stretching frequencies remains in perfect agreement with the previous QM-Pot studies.4,16 Particularly, the previously found decrease of O-H frequencies according to H-FAU(O1) > H-MFI > H-FAU(O3) is perfectly reproduced, in accord with experimental data. 4.2. Proton Jumps. Transition Structures. Table 5 shows the results for bond distances and bond angles for H-FAU and H-MFI. The corresponding data for H-CHA are given in Table 5 of ref 12. In the transition structures, the proton is located nonsymmetrically between two oxygen atoms approximately in the O-Al-O plane. The distortion from planar configuration, defined by the H-O-Al-O′ angle, is smaller than 6°. There is a large structure change compared to the equilibrium proton positions. The O-H distances are elongated to 119.9-128.3 pm, the Al-O(H) distances are shortened by up to 10 pm, and the Al-H distances are shortened by up to 50 pm. There is a substantial narrowing of the tetrahedral O-Al-O angle, from 95.5°-107.0° to 76°-80°. There are no systematic differences between transition structures for proton jumps in different zeolites. Proton Jump Barriers. Figure 8 shows a plot of proton jump barriers, ∆E‡, versus proton jump reaction energies, ∆E, for H-CHA, H-FAU, and H-MFI. There are two obvious conclusions: (i) In all zeolites, there are relatively low and high barriers for different proton jump paths. (ii) There is no correlation between ∆E‡ and ∆E, contrary to what has been

Figure 8. Barriers for the proton jump reaction vs relative energies of the proton positions (jump energy) for H-CHA, H-FAU, and H-MFI zeolites.

suggested for proton exchange reactions with CH4 adsorbed on Brønsted sites.59 The final, ZPVE- and CCSD(T)-corrected proton jump barriers, shown in Tables 6-8, are between 70 and 102 kJ/mol for H-CHA, between 68 and 106 kJ/mol for H-FAU, and between 52 and 98 kJ/mol for H-MFI. The free cluster result of 52 ( 10 kJ/mol obtained by Sauer et al.20 is at the lower end of the range of our QM-Pot results.

1610 J. Phys. Chem. B, Vol. 105, No. 8, 2001

Sierka and Sauer

TABLE 8: Proton Jump Barriers, Energies, and Their Components (kJ/mol) and Ring Sizes for Proton Jump Reaction in H-MFI Zeolite jump path

ring size

‡ ∆ECCSD(T)

∆E‡ZP

∆E‡

∆G‡(298)

∆ECCSD(T)

∆EZP

∆E

∆G(298)

O23-O22 O17-O23 O7-O23 O7-O22 O17-O22 O7-O17

6T o.s.a (sin.)b 6T o.s.a (str.)c 5T 5T

11.4 11.9 8.1 14.0 9.0 8.4

-10.0 -11.9 -9.4 -11.7 -8.6 -7.5

52.3 62.1 64.2 80.7 79.2 98.0

53.0 64.5 66.3 80.9 75.0 103.1

2.7 -4.0 -3.7 -1.0 -1.3 0.3

-0.2 0.7 1.7 1.4 0.4 1.0

2.2 12.0 18.6 20.7 14.2 6.6

1.9 15.0 23.9 25.8 16.9 8.9

a

Jump occurs in “open space” (o.s.); see text for details. b Jump occurs in a sinusoidal channel. c Jump occurs in a straight channel.

TABLE 9: TST Proton Jump Rates (s-1) at Different Temperatures 298 zeolite H-CHA

H-FAU

H-MFI

400

500

jump path

forward

reverse

forward

reverse

forward

reverse

O3-O4 O1-O2 O1-O3 O3-O2 O2-O4 O1-O4 O3-O2 O4-O2 O1-O2 O1-O4 O1-O3 O3-O4 O23-O22 O17-O23 O7-O23 O7-O22 O17-O22 O7-O17

8.6 × 10 5.7 × 10-l 1.5 × 10-3 4.8 × 10-5 1.2 × 10-5 2.6 × 10-6 4.0 9.1 × 10-1 1.7 × 10-4 8.2 × 10-6 6.5 × 10-6 1.5 × 10-6 3.2 × 103 3.1 × 101 1.5 × 101 4.2 × 10-2 4.4 × 10-1 5.2 × 10-6

1.5 × 9.8 2.1 × 10-2 7.1 × 10-5 9.8 × 10-5 2.1 × 10-4 1.6 × 102 2.3 × 101 3.7 × 10-1 6.9 × 10-4 3.6 × 10-4 2.4 × 10-6 7.0 × 103 1.3 × 104 2.3 × 105 1.4 × 103 4.0 × 102 1.9 × 10-4

1.3 × 1.2 × 103 l.0 × 101 7.4 × 10-1 2.5 × 10-1 9.9 × 10-2 5.1 × 103 1.6 × 103 2.4 1.7 × 10-1 2.8 × 10-1 8.8 × 10-2 8.0 × 105 2.0 × 104 1.2 × 104 1.9 × 102 1.8 × 103 1.1 × 10-1

1.4 × 7.9 × 103 9.0 × 101 7.9 × 10-1 1.3 2.1 8.3 × 104 1.8 × 104 8.7 × 102 5.3 6.2 1.3 × 10-1 1.4 × 106 2.7 × 106 3.2 × 107 9.0 × 105 4.2 × 105 2.3

9.2 × 1.0 × 105 1.8 × 103 2.1 × 102 8.2 × 101 4.6 × 101 3.3 × 105 1.2 × 105 6.4 × 102 5.7 × 101 1.4 × 102 5.3 × 101 2.0 × 107 8.7 × 105 5.7 × 105 2.7 × 104 2.2 × 105 3.8 × 101

8.0 × 105 3.9 × 105 1.2 × 104 1.8 × 102 3.1 × 102 4.5 × 102 3.2 × 106 8.7 × 105 8.1 × 104 1.0 × 103 1.8 × 103 7.2 × 101 3.0 × 107 6.3 × 107 5.7 × 108 4.0 × 107 2.4 × 107 5.3 × 102

-1

101

Proton Jump Rates. Table 9 shows proton jump rates calculated using classical TST. For the zeolites studied, the rates vary between 10-6 and 105 s-l at room temperature. The uncertainty in the reaction barriers estimated as 10 kJ/mol in Section 3.6 yields an uncertainty in the TST proton jump rates of a factor of 50 at 298 K. The contributions due to the vibrational effects are small, lower than 5 kJ/mol, shown by small changes of the ∆G‡(298) values compared to the ∆E‡ values (cf. Tables 6-8). As expected from the values of proton jump barriers, the lowest jump rates are predicted for H-FAU and H-CHA zeolites and the highest for H-MFI. The TST reaction rates provide lower limit estimates for the true reaction rates due to the neglect of tunneling. However, proton tunneling is expected to be important at low temperatures only. The importance of tunneling effects primarily depends on the curvature of the barrier, controlled by the transition frequency |ω‡| ) 2π|ν‡| and, to a lower degree, on the height of barrier, ∆E‡.22 A characteristic parameter is the tunneling crossover temperature Tx, below which tunneling becomes dominant and above which tunneling becomes negligible. Using the formula of Fermann and Auerbach22

Tx )

p|ω‡F|∆E‡/kB 2π∆E‡ - p|ω‡F|ln 2

(6)

where p ) h/2π, h is the Planck constant, and kB is the Boltzman constant and from QM-Pot calculated transition frequencies, we calculate the Tx values for all zeolites studied. The results are summarized in Table 10. We find that Tx is smaller or approximately equal room temperature. The highest crossover temperature found is 320 K for the O3-O2 proton jump in H-CHA. Table 1 shows that the experiments related to the proton mobility are performed at or even above room temper-

103

104

104

TABLE 10: Absolute Values of Proton Jump Transition Frequencies, |ν‡| (cm-1), and Tunneling Crossover Temperatures, Tx (K) H-CHA jump path

|ν‡|

H-FAU Tx

jump path

|ν‡|

H-MFI Tx

jump path

|ν‡|

Tx

O3-O4 1188 278 O3-O2 1171 274 O23-O22 965 227 O1-O2 1151 269 O4-O2 1182 277 O17-O23 1128 265 O1-O3 920 214 O1-O2 1025 238 O7-O23 925 216 O3-O2 1369 320 O1-O4 1316 307 O7-O22 1151 269 O2-O4 816 189 O1-O3 919 213 O17-O22 948 221 O1-O4 796 184 O3-O4 760 176 O7-O17 806 187

ature. In fact, no detectable proton mobility in H-MFI zeolite could be observed experimentally at room temperature.5,7-9 We may then expect that proton tunneling has negligible effects on the experimental reaction rates and on the proton jump barriers derived from these rates at temperatures above 298 K. However, at temperatures below room temperature, tunneling has to be included, e.g., by the method of Fermann and Auerbach.22 Comparison with other Calculations. Fermann et al. have investigated the proton jump reaction using partially constrained cluster models consisting of three tetrahedral atoms for, what they claim, the proton jump between oxygen sites O1 and O4 in H-FAU zeolite.21,22 Their transition structure obtained by MP2 calculations is similar to our QM-Pot results (cf. Table 5). From the proton jump barriers calculated in the present work, it is, however, clear that even small changes in the geometry of the transition structure caused by zeolite lattice constraints may cause significant changes in the proton jump barriers (vide infra) and that the presence of the zeolite lattice must not be neglected. The free cluster models, even if partially constrained, are therefore of limited predictive value. After including the longrange correction derived from our preliminary QM-Pot calculations,19 Fermann et al. obtained a zero-point energy corrected

Chabazite, Faujasite, and ZSM-5 Zeolite Catalysts barrier of 97.1 kJ/mol. The value is very close to our QM-Pot result of 96.5 kJ/mol. We stress, however, that this result was obtained using corrections based on the QM-Pot calculations and that the free cluster models cannot easily capture the differences of proton jump barriers for jumps between different oxygen positions in a given zeolite and between different zeolites. The TST estimate for proton jump rate for the O1O4 positions in H-FAU at room temperature of 5.6 × 10-5 s-1 is very close to our value of 8.2 × 10-6 s-1 for the forward and 6.9 × 10-4 s-1 for the reverse proton jump rate. However, their value of the rate corrected for tunneling effects of 2.12 × 10-1 may be overestimated. This value is based on the transition frequency calculated for the gas-phase cluster model that is more than 250 cm-1 higher than the highest of our QM-Pot frequencies (Table 10). The influence of the zeolite structure, which is completely neglected in the gas-phase clusters, and particularly the interactions with neighboring atoms are very important for the transition structure, where the strong O-H bond is significantly weakened. These effects make the shape of the jump barrier in the zeolite less sharp than in gas-phase clusters. What follows is a lowering of the tunneling probability and lowering of the crossover temperature. Indeed, the Tx value based on the QM-Pot calculations for the O1-O4 proton jump in H-FAU is lower by 61 K than the value predicted by Fermann and Auerbach.22 Comparison with Experiment. The proton jump barriers inferred from 1H NMR experiments (cf. Table 1) range from 21 to 78 kJ/mol for H-FAU and from 11 to 45 kJ/mol for the H-MFI zeolite. The wide range of barriers reported already indicates that their determination meets severe difficulties. Residual amounts of small molecules such as water or ammonia, which are naturally present during the preparation of zeolites, may significantly reduce barriers for proton motion.60 Moreover, the estimates of proton jump barriers from 1H NMR experiments are based on averaging the dipolar Al-H interactions, which requires that the proton visits all four oxygen atoms of the AlO4 tetrahedron.5-9,61,62 What is then measured is the highest barrier on a minimum-energy path connecting the proton positions on all four oxygen atoms of the AlO4 tetrahedron rather than the barrier for a single-proton jump between neighboring oxygen atoms. Therefore, the experimental results cannot be easily compared with the results of our calculations. However, two experimental studies suggest a higher proton mobility for ZSM-5 than for faujasite.6,9 Our calculations support these observations due to the following reasons: (i) In H-MFI, three out of six barriers are below 68 kJ/mol, which is the lowest barrier in H-FAU. The lowest barrier in H-MFI zeolite is more than 15 kJ/mol lower than the lowest barrier in H-FAU. (ii) The experimental data for faujasite suggest that the majority of protons are at the O1 oxygen positions.52 According to our calculations, the barriers are high, between 93 and 103 kJ/mol, for all three proton jumps from the O1 position. If the 1H NMR observations are dominated by protons located initially at the O1 oxygen positions, then the observed barrier should be at least 93 kJ/mol. On the other hand, in H-MFI there exists at least one low-energy barrier (lower than 69 kJ/mol) for jumps from all four oxygen atoms around the AlO4 tetrahedron, at least for the T7 position investigated. (iii) Due to high barriers for proton jumps from O1 in H-FAU, all miniumum-energy paths connecting all four oxygen atoms of the AlO4 tetrahedron have high barriers of at least 93 kJ/mol. For H-MFI, there exists a path connecting all oxygen atoms with the highest barrier of 62 kJ/mol (for example jump from O17 to O23, from O23 to O7, and from O23 to O22). We cannot be sure that the T7 site

J. Phys. Chem. B, Vol. 105, No. 8, 2001 1611 in H-MFI chosen in this study is representative for all Al substitution sites, but we also do not have a reason to believe that the T7 position is in any way special among other possible positions. Our calculations apply to isolated Brønsted sites, i.e., a high Si/Al ratio. This type of sites dominates for Si/Al ratios above 10, typical of H-ZSM-5. For H-FAU, the Si/Al ratios are much lower and the presence of Al in next nearest neighbor positions is very likely. It remains to be examined how much this affects the proton jump rates. In any case, knowing the limiting value for isolated sites helps to separate the influence of different factors such as framework structure, Si/Al ratio, and the presence of traces of water. For H-CHA, there is no experimental data concerning proton mobility. Experimentally, it has been found that the majority of protons occupy the O1 and O3 positions.50 Our calculations predict that the highest barrier on the minumum-energy path connecting all four oxygen atoms in H-CHA is 86 kJ/mol (jumps O1-O2, O1-O3, and O3-O4). It is 7 kJ/mol lower than that in H-FAU but 24 kJ/mol higher than that in H-MFI. Hence, we predict a slightly higher or equal proton mobility in H-CHA compared to that of H-FAU but a significantly lower one compared to that of H-MFI. Role of the Zeolite Structure. The variety of zeolites structures investigated in this study allows, for the first time, for revealing possible relations between the structural parameters of a particular zeolite and the proton mobility. There is a general trend that proton jumps with high barriers have transition structures with the proton being more distorted from the plane defined by the two oxygen atoms and aluminum (H-O-AlO′ angle, cf. Table 5). We could not find any other correlation between structural parameters of the Brønsted sites or transition structures and the height of the proton jump barriers. For example, the O-Al-O angle substantially narrows in the transition structure. But speculations that the barrier height may correlate with this bond angle either in the transition structure or in the initial structure could not be confirmed. Our study points to three factors that may determine the barrier height for the proton jump reaction: (i) stabilization of the transition structure by interactions with neighboring oxygen atoms, (ii) local framework flexibility which allows the O-Al-O angle to close up to 76-80° without too much energy penalty, and (iii) overall flexibility of the zeolite lattice. We can analyze the influence of all three factors by considering the size of the aluminosilicate ring, nT, that the proton has to pass on a particular jump path. In a particular transition structure, the proton is located approximately in the plane of an n-membered aluminosilicate ring that includes both oxygen sites involved in the jump. Tables 6-8 contain these ring sizes. Figure 9 shows the dependence of the calculated proton jump barriers on the ring size, nT. For all zeolites, the proton jumps occurring within six-membered rings have the smallest barriers, while the largest barriers occur in four- and five-membered rings. Large barriers are also found when in the transition structure the proton points into “open space”, i.e., large zeolite cavities or rings of more than 8T. Obviously, the proton stabilization by neighboring oxygen atoms increase with decreasing ring size. On the contrary, smaller rings are not flexible enough to allow for an optimum relaxation, and their deformation requires more energy. Our results show that the six-membered rings have an optimum balance of the two factors and, thus, the smallest proton jump barriers. For example, H-CHA and H-FAU have a similar local structure around the AlO4 tetrahedron, built by three fused four-membered rings (cf. Figures 2 and 3). The only difference

1612 J. Phys. Chem. B, Vol. 105, No. 8, 2001

Sierka and Sauer 5. Summary

Figure 9. Dependence of the proton jump barriers on the ring size nT for H-CHA, H-FAU, and H-MFI zeolites (o. s. ) open space; see text for details). For simplicity, only the barriers for forward proton jumps are used.

is that the eight-membered aluminosilicate ring in H-CHA is replaced by six-membered ring in H-FAU. The two zeolites show a very similar pattern of the proton jump barriers. For both zeolites, proton jumps occurring within the four-membered aluminosilicate rings have the highest barriers. The lowest ones occur within the six-membered ring of the hexagonal prism, i.e., the O3-O4 jump in H-CHA and the O3-O2 jump in H-FAU. The stabilization by neighboring oxygen atoms is clear considering O1-O2 and O3-O2 jumps in H-CHA and O1O4 and O4-O2 jumps in H-FAU zeolite. The O1-O2 jump in H-CHA and O1-O4 jump in H-FAU involve both one oxygen of the four-membered ring in a hexagonal prism and one oxygen of the four-membered ring not in a hexagonal prism. The difference is that in H-CHA this jump occurs within the eight-membered ring while in H-FAU it occurs in the open space of the faujasite supercage with a large separation of the proton to neighboring oxygen atoms. Due to stabilization by neighboring oxygen atoms of the eight-membered ring in H-CHA, the jump barrier for O1-O2 is lower by 23 kJ/mol than that for the O1-O4 jump in H-FAU. On the other hand, the O3-O2 jump in H-CHA occurs between oxygen atoms that are members of the eight-membered ring. The O4-O2 jump in H-FAU is analogous, except that the jump occurs now within the six-membered aluminosilicate ring. Due to larger stabilization caused by the closer contact to oxygen atoms, the jump barrier for the O4-O2 jump in H-FAU is lower than the O3O2 jump in H-CHA by 22 kJ/mol. The higher flexibility of five-membered rings is confirmed in H-MFI, where the jumps occurring within five-membered rings have generally lower barriers than jumps within four-membered rings in H-CHA and H-FAU zeolites. The importance of overall lattice flexibility is illustrated by H-MFI, which, for example, manifests itself in the orthorhombic-monoclinic phase transition.29 The higher proton jump barriers in H-CHA and H-FAU zeolites compared with H-MFI are connected with the lower flexibility of their lattices due to the presence of annealed four-membered rings. Further confirmation comes from the jumps occurring within six-membered rings in H-MFI, which have generally lower barriers than analogous jumps in six-membered rings in H-CHA or H-FAU. Also, the two jumps occurring in the “open space” of the sinusoidal and straight channels in H-MFI have lower barriers than that of the corresponding O1-O4 jump in H-FAU.

Proton jumps between neighboring oxygen atoms of an AlO4 tetrahedron in the proton forms of the zeolites chabazite, faujasite, and ZSM-5 are investigated. This reaction defines the proton mobility in an unloaded catalyst and is the simplest dynamic process involving the catalytically active Brønsted sites in zeolites. To obtain information about the potential energy surface for the proton jumps, we used the QM-Pot method, which accounts for both the structural constraints imposed by and the long-range potential due to the periodic zeolite lattice. The rates for proton reactions are calculated applying classical transition state theory. At room temperature, they vary over a broad range of 10-6 to 105 s-1, depending on the zeolite type and the particular proton jump path within a given zeolite. From our QM-Pot calculations, we have also estimated the temperatures below which tunneling becomes dominant and above which tunneling becomes negligible. For all proton jumps, these tunneling crossover temperatures are lower or equal room temperature, with the highest temperature of 320 K. Hence, tunneling is not an important factor above room temperature. The final proton jump barriers including zero-point vibrational energies are between 70 and 102 kJ/mol for H-CHA, between 68 and 106 kJ/mol for H-FAU, and between 52 and 98 kJ/ mol for H-MFI. These barriers are calculated from the QMPot energies converged with respect to the size of the QM cluster and include corrections for the approximate description of electron correlation by the density functional method. While for all three zeolites studied both low and high barriers exist, the special structural features of the zeolites allow to predict that the proton mobility is lower in the zeolites chabazite and faujasite than in ZSM-5, in agreement with experimental data. Three factors are found to determine the barrier height for the proton jump reaction: (i) stabilization of the proton in the transition structure by interactions with neighboring oxygen atoms, (ii) local framework flexibility, which allows the O-Al-O angle to close up to 76°-80° without too much energy penalty, and (iii) overall flexibility of zeolite lattice. In particular, we find that proton jumps occurring between oxygen atoms in aluminosilicate rings containing six tetrahedral atoms (six-membered rings) have the lowest barriers. This is due to a fortunate combination of the first two factors. In contrast, jumps between oxygen atoms in four-membered rings and oxygen atoms in open zeolite channels or cavities have high barriers. Due to a larger overall lattice flexibility, the proton jump barriers in the same ring sizes are lower in ZSM-5 than in chabazite and faujasite. Acknowledgment. This work has been supported by the “Fonds der Chemischen Industrie” and by the “Max-PlanckGesellschaft”. Supporting Information Available: Selected computed structural parameters and scaled harmonic O-H stretching frequencies for Brønsted acidic sites in H-CHA, H-FAU, and H-MFI. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Farneth, W. E.; Gorte, R. J. Chem. ReV. 1995, 95, 615-635. (2) Schoofs, B.; Martens, J. A.; Jacobs, P. A.; Schoonheydt, R. A. J. Catal. 1999, 183, 355-367. (3) Meusinger, J.; Corma, A. J. Catal. 1996, 159, 353-360. (4) Bra¨ndle, M.; Sauer, J. J. Am. Chem. Soc. 1998, 120, 1556-1570. (5) Freude, D.; Oehme, W.; Schmiedel, H.; Staudte, B. J. Catal. 1974, 32, 137-143.

Chabazite, Faujasite, and ZSM-5 Zeolite Catalysts (6) Sarv, P.; Tuherm, T.; Lippmaa, E.; Keskinen, K.; Root, A. J. Phys. Chem. 1995, 99, 13763-13768. (7) Ernst, H.; Freude, D.; Mildner, T.; Pfeifer, H. In Proceedings of the 12th International Zeolite Conference; Baltimore, Maryland, July 5-10, 1998; Treacy, M. M. J., Marcus, B. K., Bisher, M. E., Higgins, J. B., Eds.; Materials Research Society: Warrendale, PA, 1999; Vol. 4, pp 2955-2962. (8) Baba, T.; Inoue, Y.; Shoji, H.; Uematsu, T.; Ono, Y. Microporous Mater. 1995, 3, 647-655. (9) Baba, T.; Komatsu, N.; Ono, Y.; Sugisawa, H. J. Phys. Chem. B 1998, 102, 804-808. (10) Eyring, H. J. Chem. Phys. 1935, 3, 107-115. (11) Eichler, U.; Ko¨lmel, C. M.; Sauer, J. J. Comput. Chem. 1997, 18, 463-477. (12) Sierka, M.; Sauer, J. J. Chem. Phys. 2000, 112, 6983-6996. (13) Sauer, J.; Schro¨der, K.-P.; Termath, V. Collect. Czech. Chem. Commun. 1998, 63, 1394-1408. (14) Sierka, M.; Eichler, U.; Datka, J.; Sauer, J. J. Phys. Chem. B 1998, 102, 6397-6404. (15) Sierka, M.; Sauer, J. Faraday Discuss. 1997, 106, 41-62. (16) Eichler, U.; Bra¨ndle, M.; Sauer, J. J. Phys. Chem. B 1997, 101, 10035-10050. (17) Bra¨ndle, M.; Sauer, J.; Dovesi, R.; Harrison, N. M. J. Chem. Phys. 1998, 109, 10379-10389. (18) Bra¨ndle, M.; Sauer, J. J. Mol. Catal. A: Chem. 1997, 119, 19-33. (19) Sauer, J.; Sierka, M.; Haase, F. In Transition State Modeling for Catalysis; Truhlar, D. G., Morokuma, K., Eds.; ACS Symposium Series 721; American Chemical Society: Washington, DC, 1999; pp 358-367. (20) Sauer, J.; Ko¨lmel, C. M.; Hill, J.-R.; Ahlrichs, R. Chem. Phys. Lett. 1989, 164, 193-198. (21) Fermann, J. T.; Blanco, C.; Auerbach, S. J. Chem. Phys. 2000, 112, 6779-6786. (22) Fermann, J. T.; Auerbach, S. J. Chem. Phys. 2000, 112, 67876794. (23) Meier, W. M.; Olson, D. H. Atlas of Zeolite Structure Types; Butterworth-Heinemann: London, 1992; pp 72-73. Available also under: www.iza-sc.ethz.ch/IZA-SC/Atlas/AtlasHome.html. (24) Calligaris, M.; Nardin, G.; Randaccio, L.; Comin Chiaramonti, P. Acta Crystallogr., Sect. B 1982, 38, 602-605. (25) Meier, W. M.; Olson, D. H. Atlas of Zeolite Structure Types; Butterworth-Heinemann: London, 1992; pp 96-97. Available also under: www.iza-sc.ethz.ch/IZA-SC/Atlas/AtlasHome.html. (26) Hriljac, J. A.; Eddy, M. M.; Cheetham, A. K.; Donohue, J. A.; Ray, G. J. J. Solid State Chem. 1993, 106, 66-72. (27) Meier, W. M.; Olson, D. H. Atlas of Zeolite Structure Types; Butterworth-Heinemann: London, 1992; pp 138-139. Available also under: www.iza-sc.ethz.ch/IZA-SC/Atlas/AtlasHome.html. (28) van Koningsveld, H. Acta Crystallogr., Sect. B 1990, 46, 731735. (29) van Koningsveld, H.; Jansen, J. C.; van Bekkum, H. Zeolites 1990, 10, 235-242. (30) Schro¨der, K.-P.; Sauer, J.; Leslie, M.; Catlow, C. R. A. Zeolites 1992, 12, 20-23. (31) Nachtigallova´, D.; Nachtigall, P.; Sierka, M.; Sauer, J. Phys. Chem. Chem. Phys. 1999, 1, 2019-2026. (32) Sauer, J. Chem. ReV. 1989, 89, 199-255. (33) Catlow, C. R. A.; Dixon, M.; Mackrodt, W. C. In Computer Simulations of Solids; Lecture Notes in Physics 166; Catlow, C. R. A., Mackrodt, W. C., Eds.; Springer-Verlag: Berlin, 1982; pp 130-161. (34) Gale, J. D. J. Chem. Soc., Faraday Trans. 1997, 93, 629-637. (35) Ahlrichs, R.; Ba¨r, M.; Ha¨ser, M.; Horn, H.; Ko¨lmel, C. M. Chem. Phys. Lett. 1989, 162, 165-169.

J. Phys. Chem. B, Vol. 105, No. 8, 2001 1613 (36) Treutler, O.; Ahlrichs, R. J. Chem. Phys. 1995, 102, 346-354. (37) Becke, A. D. J. Chem. Phys. 1993, 98, 5648-5652. (38) Lee, C.; Yang, W.; Parr, R. G. Phys. ReV. B 1988, 37, 785-789. (39) Koch, W.; Holthausen, M. C. A Chemist Guide to Density Functional Theory; Wiley-VCH: Weinheim, 2000. (40) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.; Johnson, B. G.; Robb, M. A.; Cheeseman, J. R.; Keith, T.; Petersson, G. A.; Montgomery, J. A.; Raghavachari, K.; Al-Laham, M. A.; Zakrzewski, V. G.; Ortiz, J. V.; Foresman, J. B.; Peng, C. Y.; Ayala, P. Y.; Chen, W.; Wong, M. W.; Andres, J. L.; Replogle, E. S.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Binkley, J. S.; Defrees, D. J.; Baker, J.; Stewart, J. P.; HeadGordon, M.; Gonzalez, C.; Pople, J. A.; GAUSSIAN 94, Revision B.3; Gaussian, Inc.: Pittsburgh, PA, 1995. (41) Scha¨fer, A.; Horn, H.; Ahlrichs, R. J. Chem. Phys. 1992, 97, 25712577. (42) Hampel, C.; Peterson, K.; Werner, H.-J. Chem. Phys. Lett. 1992, 190, 1 and references therein. The program to compute the perturbative triples corrections has been developed by Deegan, M. J. O. and Knowles, P. J., 1992. (43) Dunning, T. H., Jr. J. Chem. Phys. 1989, 90, 1007-1023. (44) Woon, D. E.; Dunning, T. H., Jr. J. Chem. Phys. 1993, 98, 13581371. (45) MOLPRO is a package of ab initio programs written by Werner, H.-J. and Knowles, P. J., with contributions from: Amos, R. D.; Bernhardsson, A.; Berning, A.; Celani, P.; Cooper, D. L.; Deegan, M. J. O.; Dobbyn, A. J.; Eckert, F.; Hampel, C.; Hetzer, G.; Korona, T.; Lindh, R.; Lloyd, A. W.; McNicholas, S. J.; Manby, F. R.; Meyer, W.; Mura, M. E.; Nicklass, A.; Palmieri, P.; Pitzer, R.; Rauhut, G.; Schu¨tz, M.; Stoll, H.; Stone, A. J.; Tarroni, R.; Thorsteinsson, T. (46) Lindh, R.; Ryu, U.; Liu, B. J. Chem. Phys. 1991, 95, 5889-5897. (47) Halkier, A.; Klopper, W.; Helgaker, T.; Jørgensen, P.; Taylor, P. R. J. Chem. Phys. 1999, 111, 9157-9167. (48) Shah, R.; Gale, J. D.; Payne, M. C. Phase Transitions 1997, 61, 67-81. (49) Jeanvoine, Y.; A Ä ngya´n, J. G.; Kresse, G.; Hafner, J. J. Phys. Chem. B 1998, 102, 5573-5580. (50) Smith, L. J.; Davidson, A.; Cheetham, A. K. Catal. Lett. 1997, 49, 143-146. (51) Hill, J.-R.; Freeman, C. M.; Delley, B. J. Phys. Chem. A 1999, 103, 3772-3777. (52) Czjzek, M.; Jobic, H.; Fitch, A. N.; Vogt, T. J. Phys. Chem. 1992, 96, 1535-1540. (53) Pulay, P. In Modern Theoretical Chemistry; Schaefer III, H. F., Ed.; Plenum Press: New York, 1977; Vol. 4, pp 153-185. (54) Rauhut, G.; Pulay, P. J. Phys. Chem. 1995, 99, 3093-3100. (55) Sauer, J.; Eichler, U.; Meier, U.; Scha¨fer, A.; von Amim, M.; Ahlrichs, R Chem. Phys. Lett. 1999, 308, 147-154. (56) Anderson, M. W.; Klinowski, J. Zeolites 1986, 6, 455-466. (57) Mirth, G.; Lercher, J. A.; Anderson, M. W.; Klinowski, J. J. Chem. Soc., Faraday Trans. 1990, 86, 3039-3044. (58) Beck, K.; Pfeifer, H.; Staudte, B. Microporous Mater. 1993, 2, 1-6. (59) Kramer, G. J.; van Santen, R. A. J. Am. Chem. Soc. 1995, 117, 1766-1776. (60) Ryder, J. A., Chakraborty, A. K., Bell, A. T. J. Phys. Chem. B 2000, 104, 6998-7011. (61) Mestdagh, M. M.; Stone, W. E.; Fripiat, J. J. J. Phys. Chem. 1972, 76, 1220-1226. (62) Fenzke, D.; Gerstein, B. C.; Pfeifer, H. J. Magn. Reson. 1992, 98, 469-474.