Computer simulation of zeolite structure and

Faraday Discuss., 1997, 106, 79È92

Computer simulation of zeolite structure and reactivity using embedded cluster methods Paul Sherwood,a* Alex H. de Vries,a Simon J. Collins,a Stephen P. Greatbanks,b Neil A. Burton,b Mark A. Vincentb and Ian H. Hillierb* a CCL RC Daresbury L aboratory, Daresbury, W arrington, UK WA4 4AD b Department of Chemistry, University of Manchester, Manchester, UK M13 9PL

The use of bare cluster models to understand the nature of zeoliteÈsubstrate interactions may be improved to take account of the environment of the BrÔnsted acid site. We consider two models for introducing the electrostatic e†ects of the zeolite lattice. The Ðrst involves generating a specialised correction potential by Ðtting a non-periodic array of ca. 60 point charges to the di†erence between the bare cluster and periodic potentials. The second starts by Ðtting a periodic array of atomic charges to the potential of the inÐnite lattice and then builds up a classical cluster of ca. 2000 atoms into which the QM cluster is embedded. Such embedded cluster calculations, employing a T3 cluster, with electron correlation at the density functional theory level, are described, to model the interaction of water at a BrÔnsted acid site. Structures of the waterÈzeolite complex, and associated vibrational frequencies and 1H NMR shifts are calculated and compared with calculations of bare clusters of varying size and with experimental data. We then describe a mixed quantum mechanicalÈmolecular mechanical (QMÈMM) model derived by combining charges from the second model with a standard aluminosilicate force Ðeld. We report preliminary results on the e†ect of embedding on the energetics of a prototypical hydrocarbon cracking reaction ; the methyl-shift reaction of a propenium ion coordinated to the acid site.

The importance of zeolites in many industrial catalytic processes has prompted continuing studies to understand the relationship between their structure and reactivity. A particular area of study has been the interaction of substrates with a BrÔnsted acid site, central to many reactions catalysed by zeolitic aluminosilicates, such as the cracking of hydrocarbons and the conversion of methanol to gasoline.1 Recently, there have been many examples of the functionalisation of zeolites by the exchange of protons by metal ions, leading to a range of catalytic applications such as the decomposition of nitrogen oxides over Cu-exchange zeolites.2 Interactions occurring at BrÔnsted acid sites have been explored by a range of experimental techniques, particularly NMR and IR spectroscopy, in an attempt to clarify the nature of the adsorbed substrate, with particular emphasis on the degree of proton transfer from the zeolite to the substrate. In parallel with these experimental studies, there have been continuing theoretical and computational developments in order to achieve the necessary realism to model the often quite subtle features of the zeoliteÈsubstrate interaction. The accurate modelling of these interactions is particularly challenging as the catalytic activity and selectivity arise from a number of di†erent factors, including local 79

80

Simulation of zeolites using embedded cluster methods

structural e†ects on acidity, the level of aluminium substitution, the zeolite pore structure, chemical impurities and extra-framework ions. The most commonly used computational strategy is to employ clusters of varying sizes to represent the active site of the zeolite,3h5 and to use standard electronic structure methods, available in a number of commercial packages, to model the adsorbateÈzeolite system. These models typically include two or three tetrahedral (T) atoms (Si, Al) and the bonds cleaved to generate the cluster are terminated by adding additional monovalent atoms, typically hydrogen. A drawback of these bare cluster models is that they omit long-range electrostatic e†ects and fail to include the geometric and electronic environment of the BrÔnsted site speciÐc to a particular zeolite. These problems can, in principle, be addressed by the use of substantially larger clusters and studies using clusters up to T46 have been carried out.6,7 However, the routine use of ab initio quantum chemical methods is computationally prohibitive for systems of this size. A more realistic way of modelling the catalytic reaction, which avoids these problems, is to employ methods that can treat periodic systems, and to use these to model periodic supercells involving the active site and substrate. Such a strategy will often necessitate the use of quite large unit cells and hence may also be computationally prohibitive. However, such a strategy has been employed using periodic calculations based upon both a gaussian basis8 and a plane wave expansion within a density functional theory (DFT) formalism.9 The latter approach has been particularly useful in view of the ease of calculation of energy gradients allowing, in principle, both stationary structures to be obtained and molecular dynamics (MD) simulations to be performed.

Embedded cluster models In other areas of condensed-phase modelling, particularly solvation studies and enzyme catalysis, hybrid methods are widely employed.10h12 Here, the reactive centre is described using a full QM treatment, and the more distant environment, which takes no direct part in the chemical reaction, is described at a much lower level of theory, often with a quite simple force Ðeld. The success of such hybrid methods naturally depends upon the use of an appropriate level of theory to describe the reactive centre, and the accurate description of both the electrostatic and other non-bonded interactions between the two regions, as well as the proper treatment of the junction between the two regions. In view of the polar nature of zeolites and other micro- and meso-porous materials, it is particularly important to model correctly the electrostatic environment of the active site resulting from the surrounding three-dimensional structure. We have suggested that a Ñexible and computationally economic way of achieving this is to use an embedded cluster model to study zeoliteÈsubstrate interactions.13 Here the cluster is embedded in an array of point charges which are chosen to model the electrostatic environment of the periodic lattice. However, since the formal atomic charges used in aluminosilicate force Ðelds are chosen to reproduce structural rather than electrostatic data, such charges may be inappropriate for use in embedded cluster models of zeolites. Indeed, oxygen charges vary from [0.26 for the CFF force Ðeld of Hill and Sauer,14 and [1.1 in the rigid ion model of van Beest et al.,15 to the formal [2.0 charge of the shell model of Catlow et al.16 One approach that we have used both to model the environment of the cluster and to correct for termination e†ects, is to derive a set of formal point charges by a leastsquares Ðt involving the electrostatic potential (ESP) of the inÐnite 3D lattice, calculated at the HartreeÈFock (HF) level.13,17 Here the di†erence between the ESP of the cluster and of the inÐnite lattice in the region of the BrÔnsted acid site is Ðtted to a point charge potential to obtain point charges (potential-derived charges, PDC). This approach, which we henceforth label as model 1, has been validated by comparison with adsorp-

P. Sherwood et al.

81

tion energies calculated at the full, periodic supercell level. Furthermore, when compared to full periodic results, indications are that our simpler description is competitive with more sophisticated embedding techniques.18 Although these charges which are derived from such a Ðtting technique, do reÑect the periodic nature of the lattice they need not be atom centred, and the individual values have no physical signiÐcance. Indeed, even if they are atom centred, atoms of the same type will have di†erent formal charges associated with them, depending upon the actual cluster chosen in the Ðtting procedure. Thus, they are unsuitable for inclusion in a general hybrid QMÈMM method, where a complete force Ðeld is used to model the non-QM region. Furthermore, in the spirit of using general force Ðelds, it may be advantageous if such atomic charges were transferable between zeolites. We have, therefore, explored the use of an alternative strategy for obtaining PDC.19 Here formal atomic charges are derived for a periodic siliceous structure which reproduce the ESP for the same periodic structure calculated at the HF level. We have derived PDC for eight periodic siliceous zeolite systems by reference to ESPs from periodic HF calculations. Using a separate charge for each crystallographically unique atom, it was possible to Ðt the potential outside the van der Waals surface to within an RMS deviation of ca. 4 kJ mol~1. Fitted charges spanning [0.8 to [1.0 for oxygen, and 1.6 to 2.0 for silicon, were obtained when Ðtting to STO 3G calculations. Subject to the constraint that a common charge be assigned to all atoms of a given type, the RMS error in the point charge potential may rise as high as ca. 10 kJ mol~1 and a signiÐcant reduction in the magnitude of the charges, relative to the unconstrained case, is observed. For Ðtting to an STO 3G ESP, a single assignment of an oxygen charge of [0.78 is suggested, whereas for a larger basis (6-21G*) a reduction in the compromise oxygen charge to ca. [0.6 is found. Once these periodic atomic charges, capable of reproducing the quantum periodic potential have been obtained, they may be used to construct a Ðnite set of point charges which, after treatment for termination e†ects, form the basis for embedded QM cluster models. We will describe a simple scheme of this type, referred to below as model 2. The advantage of both such embedded models is that the electrostatic e†ect of the PDC may be directly included in the one-electron Hamiltonian of conventional electronic structure codes, allowing for the location and characterisation of stationary structures, and for the calculation of molecular properties. However, there are some additional complications that need to be addressed. In view of the lack of van der Waals interactions with the non-QM region, geometric constraints must be imposed on the QM cluster to prevent the generation of unrealistic stationary structures. This has implications for the subsequent optimisations and calculation of vibrational frequencies, to be discussed later. Here, we describe embedded cluster calculations, based upon both approaches, to obtain PDCs. We discuss their use to model the interaction of water with a BrÔnsted acid site, focusing on the prediction of substrate binding energies, vibrational frequencies, and 1H chemical shifts.

Hybrid QM–MM models Since the atomic charges from model 2 have been chosen to generate accurate electrostatic interactions, it is reasonable to assume that they may serve as a suitable atomic charge model for use in a classical force Ðeld for zeolite modelling, allowing the development of QMÈMM models that can treat both the electrostatic interactions and the mechanical Ñexibility of the zeolite lattice. To date, no zeolite force Ðeld based on such a PDC charge model has been derived. We discuss mixed QMÈMM results using the following three models for the QMÈMM coupling, similar to those of Bakowies and Thiel.20

82

Simulation of zeolites using embedded cluster methods

(1) Mechanical embedding, where the QMÈMM interactions are the classical bonded and non-bonded forces. (2) Electrostatic embedding, where the electrostatic potential due to the MM region is included in the electronic Hamiltonian of the QM region, allowing QM polarization. (3) MM polarization, where the electronic response of the MM region is modelled by coupled atomic polarizabilities in part of the MM region. We have explored these schemes based on combining Ðtted atomic charges with a standard aluminosilicate force Ðeld (CFF),21 and used them in a preliminary study reported here, of the so-called methylÈshift reaction in a propenium ion over an acid site in zeolite Y. The non-classical, cyclic propenium transition state structure in this reaction has been proposed by Sie22 as an alternative to earlier suggested pathways in hydrocarbon conversion reactions over zeolite sites.

Computational details In the models used here, H-terminated T3 clusters based upon zeolite Y were chosen in view of the number of experimental studies involving the interaction of small substrate molecules with this zeolite. All PDC models were obtained using a periodic HF calculation, at the 3-21G level, of zeolite Y in which the aluminium sites were replaced by silicon, allowing the sodium counterions to be neglected. PDC model 1 A hydrogen-terminated T3 cluster, Si O H , was excised from the zeolite Y structure, 3 periodic 4 8 the di†erence in the ESP between the structure and the cluster was Ðtted to obtain the PDC, as described in ref. 13. PDC model 2 The PDC used in model 2 were again obtained using an HF 3-21G periodic calculation on a purely siliceous zeolite Y structure. The oxygen and silicon charges which best reproduce the quantum mechanical ESP were found to be [0.92 and 1.84, respectively. However, these charges, which are appropriate for an inÐnite periodic system must be modiÐed for use in our cluster model. This is accomplished by introducing, and treating, two boundary regions, the inner QMÈMM boundary, and the outer boundary of the MM cluster. Initial modiÐcations to the atomic charges are obtained by considering the charge on a given centre to arise from a sum of terms, one for each bond formed. The atomic charges are then assigned automatically, in a bond increment manner, based on connectivity, such that a silicon with only two bonds would have a charge of 1.84/2, i.e. 0.92. To correct for the loss of the long-range Madelung potential, we consider a wholly classical cluster, compare the ESP in the interior of the cluster with that from the inÐnite array of periodic charges, and correct the former by addition of further charges outside the cluster. The values of these additional charges are derived by least-squares Ðtting to the di†erence potential, by direct analogy with the PDC scheme of model 1. Fig. 1 illustrates the steps involved, comparing the periodic HF results [Fig. 1(a)] with the potential from the periodic point charges [Fig. 1(b)]. When the Ðnite cluster is terminated as described above the resulting potential in the interior of the cluster [Fig. 1(c)] is essentially identical to that of the periodic point-charge array ; the residual error is shown in Fig 1(d). To treat the boundary between the QM and MM regions, we Ðrst adjust the charges on the MM junction atoms using the bond charge-increment model described above. However, the problem of unrealistic electrostatic interactions between the MM junction and QM termination atoms remains. To overcome this we have chosen to redistribute

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83

Fig. 1 Electrostatic potentials of the silicate : (a) periodic HF 3-21G calculation ; (b) Ðtted periodic point-charge potential ; (c) potential due to the corrected classical cluster (model 2) ; (d) di†erence between the two potentials (b) and (c). Contours for (a), (b) and (c) at 12.5 kJ mol~1, (d) at 2.1 kJ mol~1.

the charge of the junction atom amongst the adjacent MM sites, and to correct for the dipole of these charge shifts by adding a point dipole, implemented in this study by a pair of point charges, at the MM sites that receive the charge. The result of this procedure is illustrated in Fig. 2(a), which should be compared with the periodic HF result [Fig. 1(a)]. For comparison, the potential due to the bare cluster is illustrated in [Fig. 2(b)]. Energetics and spectroscopy of water adsorption Electronic structure calculations were carried out on the T3 cluster shown in Fig. 3 using these two sets of PDC. A 6-31G** and a larger basis [6-311]]G(2d,2p)] were employed and electron correlation was included using a DFT method employing a hybrid functional (B3LYP).23 In this study, we utilise a modiÐed form of the redundant coordinate optimisation technique, implemented within the Gaussian9424 package to perform constrained optimisations of the cluster within the point-charge Ðeld. In particular, we freeze the positions of the cluster-termination hydrogen atoms to lie along the

Simulation of zeolites using embedded cluster methods

84

Fig. 2 (a) Model 2, electrostatic potential for the QMÈMM cluster ; (b) potential for the bare cluster. Contours at 12.5 kJ mol~1.

crystallographic SiwO bonds at 1.48 Ó from the Si. Furthermore, the two Si atoms of the cluster are also kept Ðxed in their crystallographic positions. Thus, the AlO unit, 4 acidic proton and substrate are allowed to relax fully within a rigid zeolite framework. These constraints included modiÐcation to the cartesian to internal coordinate transformations by increasing the relative mass of the frozen atoms. Thus the vibrational frequencies reÑect an immobile framework and the constrained optimisations are, indeed, true minima in the reduced coordinate space. For PDC model 2, it was also necessary to freeze the two oxygen atoms at their crystallographic positions to maintain a reasonable SiO orientation and prevent collapse to AlO ] SiOH. We found that this 3 further constraint results in a very similar bare cluster geometry. NMR shieldings were evaluated at the optimised geometries using the HFÈ GIAO25,26 approach with the TZP basis set of Ahlrichs,27 and PDC, where appropriate. Absolute shieldings can be compared with experimental shifts using the equation d

TMS(complex)

\d ]p [p TMS(internal reference) (internal reference) (complex)

Fig. 3 Acidic cluster Si AlO H 2 4 9

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85

Fig. 4 Methyl-shift reactions over a zeolite acid site

As is usual, the substrate molecule is the internal reference from which the hydrogen shifts are measured. We use the experimental gas-phase shift of 0.73 ppm for water.28 Methyl-shift reaction We use a T3 cluster, as in the embedding calculation, but with hydrogen atoms terminating the aluminium atom (see Fig. 4) and without the geometric constraints. These calculations were carried out at a fairly low level, HF/3-21G, to explore the important features of the model. At the mechanical embedding level, we have used the aluminosilicate consistent force-Ðeld (CFF) due to Hill and Sauer21 for all zeolite interactions. The hydrocarbon fragment was uncharged, and all atoms within the QM fragment were given zero charge. Thus, there is no electrostatic interaction between the excised QM system and the MM system. The QM fragment includes terminating H atoms to replace the O atoms, bonded to the junction Si and Al atoms, constrained to lie along the QMÈMM bond. The OwSiwO angle bend is assumed to be described correctly by the QM OwSiwH force, and the Si/AlwO(MM) stretches are described by the CFF terms, constraining the Si/AlwH distances to a Ðxed length. During optimisation of the QM cluster, the surrounding MM region was allowed to relax up to three bonds from the junction region. Non-bonded frameworkÈhydrocarbon interaction parameters were the MM2 LennardJones parameters taken from an MD study of absorption of propane in all-silica zeolites by Nicholas et al.29 In calculations at the electrostatic embedding level we utilised PDC (model 2) rather than the CFF charges, with cluster-termination e†ects on the potential at the boundary of the QM region corrected using the procedures described above for model 2. Computation of the e†ects of MM polarization were computed using the wavefunction and geometry from the electrostatic embedding calculations. The representation of the MM polarizability consisted of distributed polarizabilities at both Si and O atoms. (6.434 a3 for Si, 6.074 a3 for O).30 The number of MM atoms bearing a polarizability 0 to ca. 200 to0save computer time ; however, enough polarizabilities are taken was limited into account to have converged the polarization energy (using 500 polarizabilities yielded less than 1 kJ mol~1 extra stabilization). The calculations were performed using a hybrid QMÈMM code (ChemShell) coupling the GAMESS-UK QM code31 with the MM code, DL-POLY32, modiÐed to support the CFF force Ðeld. The MM polarisation calculations were carried out at Ðxed geometries utilising the direct reaction Ðeld version of HONDO8.1.33 We have investigated the e†ects on the reaction barrier of the methyl-shift reaction in the propenium ion of a single, isolated acid site in zeolite Y at the three progressive levels of QMÈMM embedding described above. Hydrocarbon zeolite clusters of 35 a radius from the single 0 Al-substituted T site were employed.

86

Simulation of zeolites using embedded cluster methods

Computational results Zeolite–water clusters Structures and binding energies. The calculated structures are summarised in Table 1. Both PDC models and di†erent basis sets reveal the same trends. For the bare cluster there is a small increase in the OwH length due to the PDC. All calculations show a similar structure for the 1 : 1 complex with water. The water is bound as the neutral species, with a quite short hydrogen bond involving the BrÔnsted acid site, and a longer secondary hydrogen bond involving a framework oxygen atom. The e†ect of the PDC is to increase the zeolite OwH bond length, increasing the primary hydrogen-bond interaction and decreasing the secondary interaction. A similar e†ect has been found from bare cluster models, on increasing the size of the cluster. Thus, Krossner and Sauer34 studied both T3 clusters and a substantially larger model which is typical of the faujasite lattice. They found that, as the size of the model increases, the larger intermolecular distance [O(7)wH(11)] becomes longer and the shorter one [O(9)wH(3)] shortens. A comparison of the two PDC models at the 6-31G** level reveals an encouraging level of agreement between the predicted structures, with the intermolecular hydrogen bond lengths being well within 0.1 Ó. The e†ect of increasing the basis set size, investigated for PDC model 1, is to increase the hydrogen-bond lengths, an e†ect observed previously in calculations on simpler hydrogen-bonded systems. The calculated binding energies of the water molecule to the BrÔnsted acid site are given in Table 2. These values reÑect the di†erent intermolecular distances predicted by the various treatments. Thus, the e†ect of the PDC is to increase the binding energy by ca. 15 kJ mol~1 for all models considered. The binding energies are considerably smaller for the large basis set. It is of interest to note that our value for the large basis set, in the Table 1 Cluster bond lengths (Ó) and 1 :1 complexes with watera cluster

model 1 6-31G**/noneb 6-31G**/PDC 6-311]]G(2d,2p) /none 6-311]]G(2d,2p) /PDC model 2 6-31G**/none 6-31G**/PDC

complex

O(2)wH(3)

O(2)wH(3)

O(9)wH(3)

H(11)wO(7)

O(9)wH(10)

O(9)wH(11)

0.970 0.974 0.965

1.039 1.089 1.019

1.482 1.352 1.543

1.717 1.924 1.753

0.967 0.968 0.962

0.994 0.979 0.987

0.970

1.056

1.424

2.164

0.964

0.968

0.969 0.973

1.042 1.098

1.479 1.350

1.713 1.835

0.967 0.968

0.995 0.987

a See Fig. 3 for atom labelling. b Bare clusters with no point-charge Ðeld.

Table 2 Binding energies mol~1) of water model 1 6-31G**/none 6-31G**/PDC 6-311]]G(2d,2p)/none 6-311]]G(2d,2p)/PDC model 2 6-31G**/none 6-31G**/PDC

(kJ

92.6 105.1 64.8 79.4 102.0 114.5

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87

presence of the PDC (79.4 kJ mol~1) is close the value found for the faujasite model of Krossner and Sauer34 (73.3 kJ mol~1). Vibrational frequencies. There have been a number of calculations of vibrational frequencies of bare waterÈzeolite clusters.35h37 The vibrational frequencies that we have calculated at the various levels are shown in Table 3. The changes in these values follow the structural changes already discussed. For the bare cluster, the OwH-stretching frequency is noticeably reduced by the presence of the PDC. The e†ect of the PDC on other hydrogen atom motions (d, c) is less readily explained. Considerable changes in the vibrational frequencies of both the zeolite and substrate water are found on binding. The OwH stretching frequency of the zeolite is reduced and the other modes (d, c) are at higher energy, in line with the increase in the cluster OwH bond length and restrictions on OwH deformation upon hydrogen bonding. The e†ect of the PDC is to increase all these vibrational shifts, particularly that of the OwH-stretching frequency, which correlates with the increased binding energy predicted by the PDC models. The energies of the OwH deformation modes are relatively insensitive, both to the basis set level and to the inclusion of the PDC, being at ca. 1100 cm~1 [c(OH)] and ca. 1500 cm~1 [d(OH)]. The predicted value of the OwH-stretching frequency in the complex di†ers by nearly 1000 cm~1 for the various models used. All models predict a substantial lowering of this frequency on the inclusion of the PDC, in line with the increased hydrogen-bond strength. It is probable that the values at the 6-31G** level are too small, owing to the overestimation of the intermolecular interactions. Thus, the most realistic value that we have obtained is probably 2192 cm~1 at the 6-311]]G(2d,2p)/PDC level. It has been observed that a number of functionals used in DFT calculations predict too great a red shift in the OwH-stretching frequency of a hydrogen-bond donor on hydrogen bond formation.38 However, the functional that we have used here, B3LYP, gives a value for this frequency close to the MP2 value for the case of the water dimer,38 so that our calculation may not give a value that is unduly low. There has been considerable discussion on the interpretation of the IR spectra of waterÈzeolite complexes. The adsorption of water onto H-ZSM-539 yields two new bands at 3700 and 3600 cm~1 and three bands at 2885, 2457 and 1630 cm~1. These bands were previously interpreted in terms of an ion-pair complex involving a hydroxonium cation.39 An alternative assignment, consistent with the general theoretical conclusion that the energetically most favourable complex involves neutral water,1,34h36 with no proton transfer from the zeolite, explains the observed bands in terms of the soÈcalled AÈBÈC pattern found for strong HÈbonded complexes.40,41 This characteristic triplet of bands is caused by resonant interactions between the OH-stretching vibration, strongly broadened by interaction with low-frequency OÉ É ÉO modes, and overtones of the bending modes of the strongly perturbed bridging OH group. The strong double maximum (AÈB) observed in the experimental spectrum39 at 2885 and 2457 cm~1 may be attributed to the zeolitic OH vibration, downshifted by the H-bond interaction and strongly broadened by coupling OÉ É ÉO modes. The splitting of this band at 2675 cm~1 arises by interaction with the second overtone of the d OH bending mode, placing the fundamental at 1350 cm~1. This can be compared with our highest level result of 1513 cm~1. The considerable red shift of the OH-stretching mode that we predict, giving a frequency of 2192 cm~1, is perhaps a little low when compared with the experimental estimate in the region 2700È2300 cm~1. More controversy, however, concerns the assignment of the experimental peak at 1630 cm~1, viewed by some workers34,35,37 as a third part of the AÈBÈC triplet. The splitting at 2000 cm~1 may be due to interaction with the second overtone of the c OH bending mode or with the c ] d combination. However, an alternative OH OH explanation36 considers such a resonance process unlikely and assigns this peak to the HwOwH deformation mode of the absorbed water. Our highest level results place the

88

cluster

model 1 6-31G**/none 6-31G**/PDC 6-311]]G(2d,2p)/none 6-311]]G(2d,2p)/PDC model 2 6-31G**/none 6-31G**/PDC

complex

l[O(2) H(3)]

d[O(2) H(3)]

c[O(2) H(3)]

l[O(2) H(3)]

d[O(2) H(3)]

c[O(2) H(3)]

l[O(9) H(10)]

l[O(9) H(11)]

3803 3736 3790 3725

1057 1051 1045 1088

321È334 308È421 276È378 313È418

2516 1861 2735 2192

1516 1551 1470 1513

1113 1167 1010È1019 1101È1109

3845 3843 3863 3852

3346 3629 3391 3738

3819 3766

1050 1110

245È349 231È394

2477 1823

1490 1558

1108 1215

3851 3846

3324 3494

Simulation of zeolites using embedded cluster methods

Table 3 Harmonic vibrational frequencies for cluster and 1 : 1 complex with water (cm~1)

P. Sherwood et al.

89

c mode at 1105 cm~1 and the HwOwH deformation at 1634 cm~1, consistent with OH both explanations. The two high-energy bands, observed at 3700 and 3600 cm~1 can be assigned to the OH stretch of the free proton and the H-bonded proton, respectively, calculated to occur at 3852 and 3738 cm~1 at our highest level. The corresponding values calculated in the absence of the PDC, 3863 and 3391 cm~1 are quite close to the MP2 values of Krossner and Sauer34 (3740, 3328 cm~1) and show the improved agreement obtained by inclusion of the PDC. 1H NMR shifts. The experimental NMR data, for loadings of one water molecule per bridging hydroxy group, are reported to be 6.2 ppm (H-Y),42 4.3È5.8 ppm (H-Y),43 7.1 ppm (H-ZSM-5)44 and a broad peak at 7 ppm (H-rho).45 For model 1, all calculations predict an average shift in the range 7È9 ppm, with the value being larger when the PDC is included (see Table 4). Thus, on inclusion of the PDC, the shift of the zeolitic hydrogen increases, and that of the water proton involved in H bonding decreases, in line with the increase in the primary H-bonding interaction, and the decrease in the secondary H bonding upon inclusion of the PDC. A similar though considerably smaller e†ect was observed by Krossner and Sauer,34 when bare clusters of di†erent sizes were studied. Thus, since comparison with experiment is not helpful in assessing the relative quality of the results from model 1, results for model 2 are not presented. Methyl-shift reaction Table 5 summarises the results for the methyl-shift reaction on zeolite Y at the three di†erent levels of embedding. Activation barriers were obtained for the propoxide(I)È transition state (TS) (barrier I) and propoxide(II)ÈTS (barrier II) processes in zeolite Y, propoxide(I) and propoxide(II) being the minima in which a CwO bond is formed on either side of the Al (see Fig. 4). The O atoms involved are the O(1) and O(4) zeolite sites. For the gas-phase calculations, the barrier is 316 kJ mol~1, and no distinction can be made between the two minima. The e†ects of mechanical embedding on the geometries of the minima and the TS connecting them (see Fig. 5) are shown in Table 6. Looking closely at these gas-phase and embedded structures it can be seen that the conÐning of the acid site reduces the OwAlwO angle and pushes the propenium ion into the cage. The propenium ion is further encouraged into the cage by the Van der Waals forces of the surrounding cage (zeolite hydrocarbon non-bond interactions). The e†ects of the relaxation of the zeolite cage (MM energy) is seen to also reduce the barrier. The p-bond in the minima puts more constraints on these structures than on the loose TS structure, thus putting the minima at a disadvantage. If the QM contribution to the energy of the embedded clusters is compared with the energy of the corresponding gas-phase systems it can be seen that the energy cost of deforming the QM cluster to Ðt the zeolite backbone is greater for the minima than for the TS. The resulting stabilisation of the TS (by 55 kJ mol~1 relative to minimum I and 93 kJ mol~1 relative to Table 4 H O 1H NMR shieldings 2 d(ZOH) da(H O) db(H O) 2 2 model 1 6-31G**/none 6-31G**/PDC 6-311]]G(2d,2p)/none 6-311]]G(2d,2p)/PDC

14.0 17.9 12.4 16.0

a Hydrogen bonded. b Free hydrogen.

8.1 6.0 7.5 4.4

1.6 3.3 1.4 3.2

ave. 7.9 9.1 7.1 7.9

Simulation of zeolites using embedded cluster methods

90

Table 5 Energies, activation barriers (kJ mol~1) and dipole moments (D) of the QM cluster for methyl-shift reaction in propene on a zeolite acid site at di†erent embedding levels model

energy

propoxide I

TS

propoxide II

barrier I

barrier II

gas phase mechanical

totala totala QMa MMa,b ZÈ(C,H) non-bond l (D) totala QMÈMM elecc QMÈMM pold

0 0 0 0 [12 6.3 0 [93 [30

316 247 261 [6 [20 10.9 253 [103 [45

0 55 38 9 [4 6.1 68 [100 [33

316 247 261 [6 [8

316 192 223 [15 [16

253 [10 [15

185 [3 [12

electrostatic polarised

a Energies for propoxide I, propoxide II and TS given relative to propoxide I. b Excluding the zeoliteÈhydrocarbon non-bonded interaction [ZÈ(C,H) non-bond]. c Electrostatic interaction between the DPC representation of the embedded QM cluster and the MM point charges. d Interaction of the DPC representation of the embedded QM cluster with the distributed polarizabilities on the MM atoms.

minimum II) is the main contribution to the lowering of the barrier in the embedded case. To get an impression of the e†ects to be expected by electrostatic embedding, the dipole moments of the clusters at the mechanical embedding level are also presented in Table 5. Analysis of the di†erent contributions to the barrier at the electrostatic embed-

Fig. 5 Structural parameters for the methyl-shift reaction Table 6 Optimised geometries (in Ó and degrees) for the methyl-shift reaction (see Fig. 5) using the mechanical embedding scheme. propoxide structural coordinate O(1)AlO(4) SiO(4)Al SiO(1)Al h r CXC rXAl XC

TS

gas phase

embedded

gas phase

embedded

110.6 170.6 114.2 130.1 È 1.95

92.4 133.5 124.7 128.5 È 1.90

106.4 139.6 139.2 90.1 3.37 1.79

99.5 133.8 130.1 88.6 3.44 1.80

P. Sherwood et al.

91

ding level is not as straightforward as at the mechanical embedding level. Here, we give the interaction between the QM system and the surrounding point charges by representing the QM charge distribution by the so-called dipole preserving charges (DPCs).46 The computed interactions are all attractive (by 93, 100 and 103 kJ mol~1 for the two minima and the TS, respectively) but do not di†er strongly for the di†erent points along the reaction path. The additional e†ects of electrostatic embedding on the barrier are, therefore, not nearly as large as those resulting from the mechanical constraints, lowering barrier I by 10 kJ mol~1, and lowering barrier II by 3 kJ mol~1. This barrier change is relatively insensitive to changes in the MM charges, changing by no more than 5 kJ mol~1 when the bond contribution to the oxygen charge is changed from ^0.46 to ^0.30. The build-up of dipole moment on going from minimum to TS is also expected to a†ect the MM polarization contribution to the barrier. We can estimate this e†ect by computing the interaction energy for the DPC representation of the QM region and distributed atomic polarisabilities at the MM atom sites.47 The e†ect on the barrier of the MM polarization is found to be at least as big as that of the electrostatic interaction, even though the magnitude of the interaction is signiÐcantly smaller (30È45 kJ mol~1).

Discussion We have described two alternative strategies for obtaining PDC, which can be used in a embedded cluster model of zeolite reactivity to include the electrostatic environment and to take account of termination e†ects. When used in a model of water bound to a hydrogen-terminated T3 cluster, both give very similar e†ects, as judged by predicted structures, substrate binding energies and vibrational frequencies. The inclusion of the PDC results in substantial changes in all of these three properties compared with the bare cluster results. The trends we Ðnd on inclusion of the PDC mirror those found in bare cluster calculations on increasing the size of the cluster, although the changes are in general larger than those from the cluster calculations. It is clearly computationally prohibitive to use sufficiently large bare clusters that e†ectively reproduce the results of a full periodic calculation. For example, although quite large clusters have been used to predict structures and substrate binding energies, the determination of vibrational frequencies is more computationally demanding. A computational strategy that involves a hybrid QMÈMM approach has obvious advantages and the consideration of the electrostatic potential for such a model, described in this paper, is a necessary step towards the construction of such a model. The water absorption and methyl-shift reaction show an interesting contrast in the inÑuence of the charge Ðeld in the zeolite pore. Whereas the structural changes of the water adsorbed on the site induce large vibrational frequency shifts, the structures and barriers in the methyl shift appear rather insensitive to the electrostatic Ðeld. The latter do show, however, that electronic polarization of the surroundings must also be taken into account to complete a realistic modelling of zeolite chemistry. We thank EPSRC and Shell Research and Technology Center in Amsterdam for support of this research. We would like to thank A. M. Rigby and M. V. Frash for providing gas-phase structures for, and discussions on, the methyl-shift reaction. References 1 R. A. van Santen and G. J. Kramer, Chem. Rev., 1995, 95, 637. 2 M. Iwamoto, H. Yahiro, N. Mizuno, W. X. Zhang, Y. Mine, H. Furukawa and S. Kagawa, J. Phys. Chem., 1992, 96, 9360. 3 R. A. van Santen, Stud. Surf. Sci. Catal., 1994, 85, 273. 4 U. Fleischer, K. Kutzelnigg, A. Bleiber and J. Sauer, J. Am. Chem. Soc., 1993, 115, 7833.

Simulation of zeolites using embedded cluster methods

92 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

25 26 27 28 29 30 31

32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47

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