Predicted Effects of Site-Specific Aluminum Substitution on the

J. Phys. Chem. B 1997, 101, 9943-9950

9943

Predicted Effects of Site-Specific Aluminum Substitution on the Framework Geometry and Unit Cell Dimensions of Zeolite ZSM-5 Materials† Gabriele Ricchiardi|,‡ and John M. Newsam* Dipartimento di Chimica IFM, UniVersita’ di Torino, Via P. Giuria 7, I-10125 Torino, Italia, and Molecular Simulations Inc., 9685 Scranton Road, San Diego, California 92121-8752 ReceiVed: June 30, 1997; In Final Form: September 7, 1997X

The nature of the distribution of aluminum over the framework cation sites in aluminosilicate zeolites is known to influence the catalytic properties. Simulation is here used to probe how particular Al T-site substitution patterns are manifested in the framework geometry and unit cell dimensions of ZSM-5 (MFIframework), arguably the most technologically important zeolite. Aluminum was substituted in turn onto each of the 12 crystallographically distinct T-sites in the MFI-framework. The corresponding anionic framework charge was compensated either by a nonframework tetrapropylammonium cation (TPA+) or by introducing a proton at each of the four apical oxygen atom positions in turn for each of these 12 T-site choices. Each of these 12 (TPA+) or 48 (H+) configurations was optimized at constant pressure to a zeroforce, energy minimum configuration using a validated molecular mechanics force field. The manner in which the observed structural changes scale with the extent of Al substitution on each site was evaluated. Comparisons with available experimental data in the literature indicate that the Al distribution in real materials is, at least, moderately disordered. This is consistent with the similar Al site substitution energies found for the different T-sites in the present and previous simulation results.

Introduction The nature of the distribution of aluminum over the framework cation sites (T-sites) in aluminosilicate zeolites is known to influence their catalytic performance. ZSM-5, a synthetic zeolite currently accessible over a framework composition range 8 < Si:Al < ∞, with Si:Al ) 25-100 being typical, is arguably the most technologically important zeolite, with applications ranging from p-xylene production to the conversion of methanol to gasoline.1 The general framework structural characteristics of ZSM-5 (MFI-framework) and the closely related purely siliceous material silicalite are well-known. Silicate tetrahedra are interlinked to form 4-, 5-, and 6-rings in characteristic pentasil cages and chains. The chain interconnections define a two-dimensional system of 10-ring channels, straight along [010], but sinusoidal along [100]. The crystallographic symmetry is typically orthorhombic, Pnma, but a change in temperature or nonframework sorbate configuration can lead to subtle symmetry distortions. Reasonably accurate determinations of the crystal structures of a series of MFI- framework materials have been reported.2 At the low aluminum concentrations typical of ZSM-5 it has proved as yet impossible to measure the distribution of aluminum over the set of 12 crystallographically distinct T-sites in the structure of orthorhombic symmetry. Powder X-ray diffraction experiments have yielded no direct information on aluminum placement and large, quality single crystals are readily available only for more siliceous compositions. Close to a pure SiO2 composition the 29Si NMR spectrum can be obtained at exquisite resolution, resolution that allows careful study of the temperature dependence of the framework structure and symmetry and the comparable changes that accompany the introduction of particular sorbates.3 However, as soon as even small amounts of aluminum are present in the framework, the † Dedicated to Sir John Meurig Thomas on the occasion of his 65th birthday. * Corresponding author. Molecular Simulations Inc. Email: [email protected]. | Present address: Humboldt Universita ¨ t, Institut fu¨r Chemie, Ja¨gerstr. 10/11, D-10117 Berlin, Germany. Email: [email protected]. ‡ Universita’ di Torino. X Abstract published in AdVance ACS Abstracts, November 1, 1997.

S1089-5647(97)02110-X CCC: $14.00

resolution is degraded and the spectra of aluminosilicate MFIframework materials afford insufficient definition to allow information about aluminum site preference to be extracted; this resolution loss reflects that aluminum atoms that are second neighbor to a central 29Si nucleus have a significant effect on its chemical shift.3,4 These experimental challenges, combined with the importance of aluminum site placement, have created a significant opportunity for modeling and simulation. Several groups have attempted to compute the relative site substitution energies for aluminum into each of the crystallographically distinct T-sites5-9 with both classical and quantum mechanical methods. In fact, over the last two decades, quantum mechanical computations on cluster models with this objective serve as a good illustration of the steadily increasing sophistication in simulations, made possible by hardware and methodology improvements. A more recent study9 employs semiempirical methods applied to calculations on discrete clusters with up to some 50 atoms. These types of cluster calculations appear to be converging, perhaps unsteadily, on a picture of quite similar thermodynamic site substitution energies for each of the different T-sites, although, as discussed below, the siting of the charge-compensating acidic proton can have a significant effect on the lattice energy and framework geometry. The cluster calculations yield, subject to some simplifying assumptions, relative T-site aluminum substitution energies computed (1) for the thermodynamic equilibrium state, (2) at zero K, and (3) for models devoid of nonframework species other than Brønsted acid functions. Zeolites are, however, metastable materials crystallized hydrothermally under kinetic control, and if, as indicated by the most recent calculations, the relative T-site substitution energies for the different sites are not grossly disparate, the actual aluminum distributions in real materials will be determined by the particular conditions of synthesis. As the mechanisms of zeolite synthesis at the molecular level remain obscure, we especially need an experimental indicator of which sites are actually adopted by aluminum in real MFI-framework materials. The unit cell dimensions of quality ZSM-5 materials can be measured by powder X-ray diffraction almost routinely to an © 1997 American Chemical Society

9944 J. Phys. Chem. B, Vol. 101, No. 48, 1997

Figure 1. T-site numbering in the asymmetric unit of the MFIframework (orthorhombic description). The mirror plane generating the asymmetric unit of the monoclinic structure contains the oxygen atoms labeled with *.

accuracy of (0.005 Å or 0.05° (some 0.02%). The character of the changes in the unit cell dimensions that accompany framework T-atom substitution are known to depend on the framework topology (e.g. ref 10) and might be presumed to depend on the Al T-site substitution pattern. We present here an attempt to relate changes in the unit cell dimensions, macroscopic observables, to particular patterns of local T-site substitution by aluminum in a zeolite framework using a reasonably well-established molecular mechanics method. 2. Methodology 2.1. Model Construction. Initial crystallographic coordinates for representative instances of the MFI-framework were taken from ref 11 (orthorhombic silicalite) and ref 12 (monoclinic silicalite). Crystallographic coordinates were used as starting points, but no constraints were imposed during the simulation, so that the simulated structures depend only on the applied force field and not on the initial geometries. The independence of results from the initial geometry was checked on various representative models. Models were constructed by an Al-forSi substitution at one of the crystallographic positions in the asymmetric unit, application of the symmetry operators, and then conversion to the triclininc, P1, description. There are 12 nonequivalent T-sites in the orthorhombic structure and 24 in the monoclinic case. The substitution of Al onto each of these was accompanied by placement of a proton at one of the four oxygen atoms of the [AlO4]- tetrahedron, thus giving 48 and 96 different Al/H substitution configurations in the orthorhombic and monoclinic structures, respectively. Models with 4 (corresponding to Si:Al ) 23) and 8 (Si:Al ) 11) Al atoms per unit cell were generated by substitution in the unique T-sites of the monoclinic and orthorhombic structures, respectively. These ordered substitution models were the basis for investigating the relationship between Al substitution position and the cell parameters. Models containing 1 and 2 Al per unit cell were also built for some substitution sites, to investigate further the scaling of substitution energy with Al content. Models containing 4 Al and 4 tetrapropylammonium (TPA+) cations as counterions per unit cell were also studied. Although the monoclinic structure was conveniently used in the generation of the initial structures, the results will be discussed in terms of the 12 distinct T sites of the orthorhombic structure. In fact, no significant differences were observed for sites which are inequivalent in the monoclinic structures yet mirror-related in the orthorhombic structure. The T-site numbering scheme is shown in Figure 1. 2.2. Parametrization of the Interatomic Interactions. A validated molecular mechanics force field of high-quality, cff91_czeo,13-15 was used in all the calculations. The force

Ricchiardi and Newsam field belongs to the “class II” family,16 and is derived from fits to potential energy hypersurfaces calculated ab initio for molecular models.17 The energy functional form is a Taylor expansion in the internal coordinates, including diagonal and cross-terms with Coulombic and 6-9 dispersive attractive/ repulsive terms added. The parametrization of the TPA+-containing structures required empirical modification of the published force field. The net -1 charge per aluminum on the zeolite framework was distributed evenly over the AlO4- tetrahedron (decreasing the Al charge by 0.5e and increasing the negative O charge by 0.125e). TPA+ intramolecular and TPA+-zeolite parameters were taken from the cff91 force field.15 The net charge on the TPA ion was +1. This choice of formal charges in describing the TPA-zeolite interaction contrasts with the low formal charge values used in the intrazeolite force field, but it is necessary to correctly reproduce the order of magnitude of the host-guest interaction energies. Long-range Coulombic interactions were summed using the Ewald method18 (with an accuracy of 0.0025 kcal mol-1 on the electrostatic energy), while 10 Å cutoffs were adopted for van der Waals interactions. 2.3. Optimization Methods. The model structures were optimized by means of constant pressure lattice energy minimization with respect to Cartesian atomic coordinates and cell parameters using the Discover 3.2 package.15 Cell parameter optimization was performed with the method by Parrinello and Rahman.19 A series of algorithms was used for minimization, including an initial steepest descent stage followed by a conjugate gradient stage converging to within the final mean square derivative threshold of 0.001 kcal mol-1 Å-1. The efficient Newton-Raphson algorithm was avoided because of instability when applied to the adopted energy expression (see below). Periodic boundary conditions were applied using the explicit image convention. Optimization of many models was complicated by the presence of multiple local minima, necessitating use of differing minimization protocols and controls (the geometrical features responsible for this complexity are discussed below). For cell distortions, the stability of the solution was tested initially by two methods: (a) randomization of atomic coordinates (0.00.2 Å random shifts), or (b) random cell distortions (max. 0.5 Å, 2.0°) followed by a fresh minimization. Neither of these methods was able to detect new minima with different cells, nor did either lower significantly the energy of high-energy structures suspected to contain residual strain. A dynamical simulating annealing protocol, consisting of a series of molecular dynamics runs at successively decreasing temperatures, followed by minimization was found to be most effective. (Annealing procedure: Initial temperature 800 K, final temperature 200 K, temperature step -100 K. For each temperature: 1000 1 fs MD steps in the NPT ensemble. Temperature controlled by velocity scaling. Then, energy minimization as described above.) This protocol was able to successfully locate lower energy configurations for most high-energy structures. 2.4. Model Analysis. Model construction, visualization, and analysis were performed using InsightII, DeCipher, and various crystallographic and analytical programs in the Solid-State suite.15 This program suite allows model building, manipulation, measurement, and spreadsheet property tabulation, in addition to the range of necessary display functions. 3. Results 3.1. Optimization Methods. The nature of the molecular mechanics force field used in these simulations13,14 is such that discontinuities in the energy surface are expected for some

Site-Specific Aluminum Substitution

J. Phys. Chem. B, Vol. 101, No. 48, 1997 9945 TABLE 1: Normalized Relative Al Substitution Energies, kcal mol-1 per Al Atoma

Figure 2. Apical oxygen atom motion in the zeolite framework resulting from concerted motions of relatively rigid TO4 tetrahedra.

transient geometries that the system may adopt during minimization. These arise from the form of the torsional terms in the energy expression, which are coupled with angular terms that accommodate substantial flexibility. In addition to the ill definition of the dihedral angle when one of the involved angles approaches 180° that can be handled straightforwardly, a discontinuity may also result as a torsional angle switches from 0 to 180° when an angle value changes across the linear, 180° configuration. This behavior can be avoided by additional switching functions in the energy expression,20 but it does not, in any event, alter the final result of the minimization, since 180° T-O-T angles are not expected in the optimized, zeroforce structures, but only in structures that are transient during minimization or dynamics. Newton and Newton-Raphson minimization algorithms using analytical second derivatives resulted in oscillatory behavior for all structures showing T-O-T angles near 180°; the conjugate gradient algorithm, however, achieved satisfactory convergence for these same structures. Further complexity in the crystal structure energy surface derives from two distinct internal degrees of freedom. First, motion of hydrogen atoms perpendicular to the Si-O-Al plane yields two distinct shallow minima for symmetrical out-of-plane positions. However, since the differences in local structure and energy for the two configurations are small, this behavior does not significantly affect the substitution energy or final framework geometry. Second, and more importantly, differing apical oxygen atom configurations give rise to different local minima. Although the framework topology strongly constrains the T-atom positions, concerted motion of the coupled TO4 tetrahedra allow the oxygen atoms considerable positional freedom in the structure, as demonstrated for several zeolites by molecular dynamics simulations21 and structural studies (e.g. ref 22). The oxygen atoms track on approximately ellipsoidal paths centered on the T-T axis (Figure 2). Certain of the minima that arise from these particular degrees of freedom, such as those that involve oxygen atoms protruding toward dense regions of the lattice rather than toward adjacent voids, are easily noted as local minima. Other local minima are less obvious as such, resulting from a complex interplay of the rotations of many tetrahedra. It is remarkable that, while in framework structures built with only four- and six-membered rings there is usually only a single low-energy oxygen atom configuration, that is then uniquely populated at low temperature, for pentasil frameworks there are usually many different oxygen atom configurations that have similar energies. We interpret this behavior in terms of “odd-membered ring frustration” resulting from competing geometrical constraints. As in other “frustrated” systems, such as triangular spin-lattice systems, the optimization problem can be approached by techniques such as simulated annealing, use of neural networks, etc. The concept of “odd-membered ring frustration” and the number of different structures of similar energy that result may have significant implications in, for example, crystallographic structure analyses. The simple molecular dynamics simulated annealing procedure we evolved to use here was able to consistently locate

Alb

OHc

4 Al-Hd

1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 6 7 7 7 7 8 8 8 8 9 9 9 9 10 10 10 10 11 11 11 11 12 12 12 12

1 15 16 21 1 2 6 13 2 3 19 20 3 4 16 17 4 5 14 21 5 6 18 19 7 17 22 23 7 8 12 13 8 9 18 25 9 10 15 26 10 11 14 22 11 12 20 24

13.60 20.12 16.05 13.11 4.18 7.06 10.82 17.61 6.55 19.36 11.18 5.35 27.34 12.12 15.71 7.62 8.58 5.05 15.32 0.00 11.69 13.22 9.91 13.11 6.68 0.40 14.53 20.82 8.89 8.32 13.94 20.27 17.18 10.43 15.07 6.63 16.01 23.56 10.36 5.33 17.79 8.23 26.26 7.88 12.28 9.56 10.69 9.87

4 Al-TPAe 12.10

7.52

8.85

6.77

5.12

12.47

7.76

4.33

4.57

0

3.06

8.22

8 Al-Hf

clusterg

12.72 18.75 12.34 19.05 5.83 5.14 9.95 18.35 4.99 15.55 6.56 6.61 39.17 11.43 15.42 9.34 8.10 4.77 17.73 0.00 9.01 9.35 8.37 9.11 * * * * 7.40 7.54 15.27 25.21 * * * * * * * * 15.68 8.37 25.21 6.71 * * * *

12.57 26.66 13.73 10.54

9.24 4.18 12.12 0.00

8.89 13.18 12.93 9.59

a Normalized substitution energies, as kcal mol-1 per Al atom, for the substitution of Al/H and Al/TPA into the different MFI framework sites are given relative to the lowest energy value for each series. b Tsite. c OH-site number. d Structures with 4 Al and H+ per unit cell. e Structures with 4 Al and TPA+ per unit cell. f Structures with 8 Al and H+ per unit cell (structures labeled with * would contain anti-Loewenstein Al-O-Al bridges and were not computed. g Cluster models built as in ref 9.

lower energy configurations from many of the high-energy structures initially found, and the results presented are those obtained via this route. 3.2. Aluminum Site Substitution Energies. Constant pressure lattice energy minimizations based on molecular mechanics force fields give access to the relative energies of different structures, provided they contain the same number of atoms and the same atom connectivity, i.e., the same number of terms of each type in the energy expression. (This is true for molecular mechanics forcefields, since some of the terms have a zero value with physical meaning (e.g. vdW and Coulombic terms), while others have an arbitrary zero corresponding to the optimal geometry for the corresponding internal coordinate.) The relative Al-for-Si substitution energies normalized to a per Al atom basis, which can be regarded as a measure of the relative stabilities of the structures if entropic differences are, as is reasonable, assumed to be small, are listed in Table 1. These normalized substitution energies for structures containing 4 Al

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Figure 3. Relative, normalized substitution energies, kcal mol-1 per Al atom, for the substitution of Al/H+ and Al/TPA+ into the different MFIframework sites (numbering as in Figure 1, Table 1). Energies are displayed relative to the lowest value for each series. For Al-H substitution, there are four points per T-site corresponding to the four oxygen atoms bonded to Al that can bear the acidic proton. No dynamical simulated annealing was used for structures containing 8 Al per unit cell (see text).

Figure 4. Relative substitution energy, kcal mol-1 per Al atom, versus substitution site. Comparison of results of MNDO cluster calculations from ref 9 with the results obtained in this work for structures with 4 Al-H per unit cell.

per unit cell (for both 4 H+ and 4 TPA+ charge compensation) and for 8 Al per unit cell (H+) are plotted in Figure 3 as a function of the substitution site. The relative energy values span a range of some 30 kcal mol-1 (125 kJ mol-1, 1.3 eV) for the H+ form and some 10 kcal mol-1 for the TPA+ form, in agreement with previous work by Redondo9 and Kramer.8 Note that for the TPA+-containing structures the use of relative energies excludes the absolute value of the TPA+-zeolite interaction energy, but does reflect differences in this energy for different Al-sites. For the proton site of lowest energy for each T-site substitution position, the 4 Al-H and 8 Al-H (data in parentheses) per unit cell data show an average relative energy of 6.55 (6.79) kcal mol-1 (standard deviation: 3.82 (3.63)). The average standard deviation of energies for the different H positions for a given Al substitution site is, however, 5.74 (6.64) kcal mol-1. The energy of

substitution is thus determined more by the H position than by the Al position. Comparison with results in the literature shows agreement with the MNDO cluster calculations of Redondo et al., as shown in Figure 4. This is particularly remarkable considering the very different nature of the calculations. The results of Redondo et al. were obtained from semiempirical quantum chemical calculations with the MNDO Hamiltonian on large, but discrete, cluster models of the H-ZSM-5 substitution site and its first two neighboring shells of tetrahedra (five shells of nearest neighbors). Both shells were allowed to relax during geometry optimizations, the outer atoms being fixed at the original crystallographic positions. We believe that a key, common feature contributing to the agreement of the present results is the substantial degree of geometrical relaxation allowed, complete in the present case and spanning nearly four full

Site-Specific Aluminum Substitution

Figure 5. Comparison between relative normalized Al-TPA substitution energies (kcal mol-1 per Al atom, from this work) with earlier data for simple Al framework substitution (ref 7).

coordination shells in the former MNDO cluster calculations. Previous quantum mechanical calculations had enforced a rigid, average crystallographic geometry on the cluster or allowed relaxation only of much smaller regions. Additionally, the parameters in the cff91_czeo molecular mechanics force field used here were fitted to an energy hypersurface computed quantum mechanically. To explore the impact of the constrained degree of relaxation on the results, calculations with the force field method were repeated on clusters built and constrained as in ref 9 for T-sites 1, 5, and 9 (Table 1g). The agreement with the MNDO cluster results were not, however, improved, and we have not made any further systematic attempt to identify the source of the remaining discrepancies. We do, however, show that unit cell dimension change upon substitution has a significant but not dominant effect on the lattice energy. In contrast, the Al-site substitution results of Kramer et al.,8 in which periodic boundary conditions were applied but no counterions were introduced, are in poor agreement with the present Al-H+ substitution results, but better align, other than for site 4, with the present Al-TPA+ substitution results (Figure 5). We consider the molecular mechanics force field used in this work to be more accurate for the description of the local geometry of the highly covalent acid site than the shell model potentials of ref 8 due to the accurate sampling of the energy hypersurface upon which the present parameters are based. The inadequacy seems not to lie in the shell model itself, since a shell model potential has been recently fitted to the same data set employed for the present force field, achieving even better results.23 The generally comparable results for the structures devoid of acid sites obtained with the two quite different force fields are encouraging and imply that they both reasonably describe the mechanical effect of aluminum insertion into the framework. Discrepancies are, however, expected based on the intrinsic differences between the predicted energy surfaces and by the inclusion of the TPA+ cation in the present models. Possible scaling of the substitution energy with the aluminum content was examined by introducing 1, 2, 4, and 8 Al atoms per unit cell onto a select set of sites. The scaling behavior varies for different sites, but generally indicates cooperativity for low-energy sites (that is, the normalized substitution energy

J. Phys. Chem. B, Vol. 101, No. 48, 1997 9947 decreases on increasing the number of substitutions) and anticooperativity for high-energy sites. This suggests that the thermodynamic preference for certain Al/H-sites will be enhanced for increased Al content, although this indication is probably at the limits of the predictive ability of the present model. 3.3. Interesting Structures. The key factors correlating with the Al-H substitution energies are indicated to be (a) the angle of the Al-O-Si bridge bearing the acidic proton and (b) the location of this proton relative to the channels in the framework. All of the low-energy structures have relatively acute Al-OHSi angles. For the five structures with lower energy it varies from 132° to 138°, with an average value of 136°. The proton is observed directed toward an open region of the structure. Structures in which the Al-OH-Si angle adopts values closer to 180° and/or in which the proton is pointing toward dense regions of the framework are consistently of high energy. The four lowest energy structures are shown in Figure 6. The space group symmetries of the optimized structures were routinely determined automatically by the Find-Symmetry program,15 using different capture radii (i.e. the maximum distance of an atom from its exactly symmetrical position). In most cases, the symmetry was either P1, Pnma, or P21/c, as expected based on the starting structural model, but also P1h, Pc, P21, Pna21 were observed, as summarized in Table 2. Note however that the comparison of these space group determinations with those experimentally observed by diffraction is difficult, due to the fact that in our determination all atoms (hydrogens included) are weighted equally in evaluating the symmetry. Moreover, most P1 structures have cell parameters close to orthorhombic, and the low symmetry is primarily due to small differences in the geometrical degrees of freedom responsible for the multiple energy minima discussed above. The Al-O distances in the optimized models for Al-H substitution span a wide range, 1.69-2.0 Å. In the cff91_czeo force field, parametrized against first principles-derived energy hypersurfaces, the Al-OH bond can stretch and contract in a largely flat-bottomed well; the actual bond length is then strongly influenced by its framework environment through Coulombic and cross-term interactions. This significant variability is consistent with the greater ionicity of the Al-O bond relative to Si-O and with the tendency of aluminum to form stable three-coordinate species. The Brønsted acid sites in zeolites have occasionally been described in terms of a broken Si-OH‚‚‚Al bridge with a three-coordinate Lewis acid aluminum site and a silanol function whose acidity is reinforced by the interaction with the immediately adjacent Lewis acid. The present results imply a variable propensity for the different T-sites toward bridge opening. However, we stress that force field calculations of the present type have intrinsic limitations in simulating highly distorted structures and, particularly, bond breakage or formation; this last suggestion thus warrants further study. 3.4. Unit Cell Dimension Variability. The unit cell volume for H+ and TPA+-ZSM-5 samples measured experimentally is approximately 5400 Å3,24-26 substantially smaller than the values predicted by the present force field method, as expected on the basis of the force field parametrization route and the validation data.13,14 The effect of Al insertion on unit cell parameters and volumes is discussed in terms of changes relative to an unsubstituted, siliceous MFI-framework model (silicalite) subjected to the same optimization procedure (V ) 5724 Å3). Figure 7 and Figure 8 show, respectively, the simulated unit cell volumes for the different positions of aluminum substitution and unit cell volumes plotted against substitution energies. There

9948 J. Phys. Chem. B, Vol. 101, No. 48, 1997

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Figure 6. The four lowest energy structures for H-ZSM-5: (a) Al(5)/OH(21), (b) Al(7)/OH(17), (c) Al(2)/OH(1), (d) Al(5)/OH(5).

is little correlation, but for H-ZSM-5 low energy structures generally involve expanded cells, whereas for TPA+-ZSM-5 the opposite is suggested. This is not surprising considering the positive interactions between the zeolite framework and the TPA+ guest inside its channels. The presence of multiple local minima in the energy hypersurface for the crystal structure is reflected in the fact that cell parameters obtained after simple minimization differ significantly from those obtained with annealing followed by minimization. In particular, cell angles show greater deviations from orthorhombicity. The effect of Al substitution on the individual simulated unit cell parameters varies with substitution site. Expansion of the unit cell volume and individual cell parameters upon introduction of aluminum is generally observed, although for some substitution sites slight contractions are observed. An overall expansion might generally be expected given the larger expectation Al-O distance of 1.75 Å relative to Si-O, 1.605 Å. Experimentally, most aluminosilicate zeolites do show a reasonably uniform cell volume expansion with increasing aluminum content. The flexibility of the T-O-T linkage can, however, allow a more acute T-O-T angle to compensate for a larger T-O distance, depending on the framework topology. Thus some gallosilicates have smaller unit cell volumes than their aluminosilicate counterparts, despite the yet still larger Ga-O expectation bond length of 1.82 Å.10 The effects of Al substitution on the individual cell parameters can be better appreciated by considering simple averages of the results for the different substitution sites (Table 3). The a parameter is the cell length most influenced by aluminum substitution, followed by b and c, the changes in which are an order of magnitude smaller. Experimentally, it is indeed the a parameter that is observed to show most variability,26 with c

being essentially invariant. However, experiments also predict a nonnegligible expansion along b. As regards cell angles, R is the most affected by aluminum substitution in H-ZSM-5, while β and γ are insensitive to substitution. In agreement with the experiments, the presence of TPA+ also suppresses deviations of R from 90°. Preferential distortion of the angle R is significant in many respects. It is this distortion that manifests the experimentally observed orthorhombic-monoclinic (o-m) transition in silicalite and lowaluminum-content ZSM-5. Although our model does not predict the o-m transition in silicalite directly (this being also affected by the presence of sorbates and structural defects27), it nevertheless shows how stresses introduced in different parts of the structure result in preferential distortion of the angle R. The maximum distortions observed after annealing (-0.66° and 0.55°) compare well with the values reported in the literature for monoclinic ZSM-5 samples25 (while the average calculated distortion is much smaller). Examination of the geometries of these structures shows that large variations in R are accompanied by unusually long O-Al distances (broken Si-OH-Al bridges). This can be interpreted either as a limitation of the current model in describing strained structures or as a qualitative suggestion that local bond breakage might facilitate the o-m transition. The experimentally observed scaling of the a cell parameter with Al content is on the order of 0.02 Å per Al atom, which compares well with the present simulation results that range from 0.01 to 0.02 for the models with four Al per unit cell. This comparison, although approximate, suggests how accurate cell parameter measurements may yield information on preferential Al siting in the framework. However, a detailed quantitative analysis in a system as complex as ZSM-5 requires a more consistent and more complete set of experimental data. In particular, data should refer to simulation models and actual

Site-Specific Aluminum Substitution

J. Phys. Chem. B, Vol. 101, No. 48, 1997 9949

TABLE 2: Symmetry of the Optimized Structures with 4 Al Atoms Per Unit Cell, As Determined with Different Precision Criteria Ala

OHb

STc ) 0.05

STc ) 0.1

STc ) 0.2

1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 6 7 7 7 7 8 8 8 8 9 9 9 9 10 10 10 10 11 11 11 11 12 12 12 12

15 16 1 21 1 13 2 6 19 20 2 3 16 17 3 4 14 21 4 5 18 19 5 6 17 23 48 7 12 13 7 8 25 44 8 9 10 26 41 9 10 11 14 22 11 12 20 24

P1 P1 P1 P1 P21/c P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P1 P21/c P1 P1 P1

P1 P1 P1 P1 P21/c P1 P1 P1 P1 P1 P1 P1 P1h P1 P1 P21 P1 P1 P21 P1 P1 P1 P1 P1 P21/c PC P1 P21/c P1 P1 P1h P1 P1 P1 P1 P1 P1 P21/c P1 P1 P1 P1 P1 P1 P21/c P1 P1 P1

P21/c P1 P1h P21/c P21/c P1 P21/c P21/c P21 P1 P21/c P1 P21/c P21/c P1 P21/c P1 Pna21 Pna21 Pna21 P1 P1 P21/c P1 P21/c P21/c P1 P21/c P21 P21/c P21/c P21/c P1 P1 P1 P1 P1 P21/c P21/c P21/c P1 P21/c P1 P1 P21/c P1 P1 Pc

a

Figure 7. Cell volume changes versus substitution site for H-ZSM-5 and TPA-ZSM-5 with 4 Al/unit cell, relative to unsubstituted MFIframework (silicalite: V ) 5724.0 Å3) optimized under the same conditions.

Figure 8. Cell volumes versus substitution energy for H-ZSM-5 and TPA-ZSM-5 with 4 Al/unit cell. Volumes are relative to the unsubstituted MFI-framework (silicalite) optimized under the same conditions.

TABLE 3: Simulated Average Unit Cell Parameter Changes for H-ZSM-5 and TPA-ZSM-5 (4 Al/unit cell) H-ZSM-5 TPA-ZSM-5

a

b

c

R

β

γ

0.023 0.031

0.001 0.006

0.000 -0.016

0.036 -0.008

0.009 0.000

-0.005 0.016

Al position. b OH position. c Symmetry threshold (Å).

materials with exactly the same composition, and experimental data should be obtained by a single method on clean reproducible samples. 4. Conclusions This work presents the results of molecular mechanics calculations on the effects of framework aluminum substitution on the structures of H-ZSM-5 and TPA-ZSM-5 zeolites, employing an accurate force field derived from ab initio data. Several series of constant pressure energy minimizations have explored all the possible substitution sites and yielded relative site substitution energies and simulated cell parameters and framework geometries. Comparison with previous calculations on the same systems show (a) no correlation with early quantum mechanical calculations which assumed fixed geometries;5 (b) partial qualitative agreement with classical atomistic simulations on TPA-containing MFI-framework models based on older force fields;6 (c) no

correlation with recent calculations on H-ZSM-5 using shell model potentials, but good correlation with those results obtained for the insertion of Al in the bare lattice with no counterions;8 and (d) good agreement with semiempirical MNDO quantum calculations on large cluster models.9 The comparison of the different methods and results indicates that framework relaxation dominates the substitution energy and that much of the “stress” induced by aluminum insertion is dissipated through rearrangement of the first two shells of tetrahedra surrounding the substitution site. A nonnegligible contribution to the net substitution energy from cell relaxation is also recognized, with H-ZSM and TPA-ZSM-5 models generally showing expanded and contracted cells respectively, as compared with the unsubstituted silica MFI-framework model. The relative computed site substitution energies for H-ZSM-5 and TPA-ZSM-5 span a range of 25 and 12 kcal mol-1 respectively. For each of the 12 tetrahedral sites of H-ZSM5, the substitution energy strongly depends on which of the four different neighboring oxygens the acidic proton resides. Other than for site T1, at least one low-energy site is observed that

9950 J. Phys. Chem. B, Vol. 101, No. 48, 1997 lies no higher than 10 kcal mol-1 above the globally lowest energy configuration. The low-energy sites for the acidic site are those with more acute Si-O-Al angles in which the proton is directed toward the zeolite channels. The crystal energy surface, as described by our model, exhibits many local minima, necessitating use of a complex optimization procedure; dynamical simulated annealing was applied here. Two main structural degrees of freedom are responsible for the plethora of local minima: nonplanar AlOH-Si bridges and concerted oxygen atom motion. The local minima that derive from the concerted oxygen atom motion in the five-membered rings represent a case of frustration deriving from competing constraints, similar to that observed in spinlattice systems. The cell parameters undergo sizable changes upon H+-Al and TPA+-Al substitution for Si in the structure. These changes depend on the substitution site. On average, the cell deformations follow the trend: ∆a . ∆b ≈ ∆c, ∆R . ∆β ≈ ∆γ, in agreement with experiment. However, an in-depth quantitative comparison with experiment results is complicated by the scattering of the reported experimental data likely due to sample and methods variability and by inaccuracies in the absolute values of the simulated parameters. No evidence is found relating the observed cell parameter changes to a specific pattern or patterns of aluminum substitution, which together with the narrow range of calculated site substitution energies is consistent with a disordered distribution of aluminum over the T-sites in ZSM-5 materials. Although the experimentally observed monoclinic distortion of silicalite is not reproduced quantitatively by the models, all of the low-aluminum-content models show monoclinic distortions and the sensitivity of the cell angle R to the degree of substitution and to the presence of nonframework species is correctly described. The monoclinic distortions are, in fact, completely suppressed by the presence of the template. Acknowledgment. The MSI Catalysis and Sorption Project is supported by a consortium of industrial, academic, and government institutions; we thank the membership for their guidance and input and for many stimulating discussions. G.R. thanks MSI for support and hospitality. Supporting Information Available: Table 1S: Cell parameter changes for the 48 Al/H substitution patterns. Table 2S: Cell parameter changes for the 12 Al/TPA substitution patterns. Figure 1S: graphical display of data in Table 1S. Figure

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