11866
J. Phys. Chem. B 2003, 107, 11866-11870
Acid Strength of Low-Valence Dopant Ions in Microporous Zeolites and AlPOs Furio Cora` ,*,† C. Richard A. Catlow,† Bartolomeo Civalleri,‡ and Roberto Orlando‡ DaVy Faraday Research Laboratory, The Royal Institution of Great Britain, 21 Albemarle Street, London W1S 4BS, UK; 2. Dipartimento di Chimica IFM, UniVersita` di Torino, Via P. Giuria 7, 10125 Torino, Italy ReceiVed: June 3, 2003; In Final Form: July 24, 2003
Using periodic ab initio quantum mechanical calculations, we have investigated 16 low-valence dopant ions isomorphously substituted in the framework of the zeolite chabasite and of its isostructural aluminophosphate, AlPO-34. The low-valence ions are charge balanced by one acid proton. We have determined the stretching frequency of the acid OH group in each material, and examined its correlation with the structural and electronic parameters of the dopant ions. Results show that the behavior of zeolites and AlPOs is complex; optimization of their properties is suitable to combinatorial chemistry approaches, to which computational studies can make a substantial contribution.
Introduction Acid-activated reactions represent one of the pillars on which the chemical industry relies to transform raw materials, such as crude oil and natural gas, into high-added-value fine chemicals. The discovery and optimization of acid catalysts, therefore, has enormous economic importance. Crystalline materials that display surface Brønsted acidity are increasingly used as heterogeneous solid acid catalysts;1 they show several advantages over molecular acids: solid acid catalysts are easy to handle; no phase separation is required of the acid catalyst from the reaction products, and the catalyst can be restored at the end of the catalytic cycle; they avoid the problem of acidity leaching, and are environmentally friendly. Among the solid acids investigated for applications in heterogeneous catalysis, doped microporous framework materials, such as the silica-based zeolites and the aluminophosphates (AlPOs), occupy a prominent position.1,2 They combine the acid catalytic activity with an extraordinary degree of shapeselectivity enabled by the microporous nature of the solid. Transformation reactions of methanol, i.e., the methanol-toolefins (MTO) and methanol-to-gasoline (MTG) processes, are typical acid-catalyzed reactions that exploit the shape-selectivity of acid zeotypes:3 small-pore frameworks yield selectively light olefins (MTO), as the polymerization reaction stops after its first (few) steps when the product fills the microporous interstices. In medium- and large-pore materials, instead, the polymerization proceeds to a greater extent, yielding gasoline as the main product (MTG).3 H-ZSM54,5 and H-SAPO-346 are among the catalysts employed industrially for the MTG and MTO reactions, respectively. Acid protons are introduced in zeotype frameworks as chargecompensation for low-valence dopant ions. In principle, isomorphous substitution of a framework cation with any lowvalence dopant can be employed: M3+/Si4+ replacements in zeolites; M2+/Al3+ and M4+/P5+ substitutions in AlPOs, each need a charge compensation which can be accomplished by means of acid protons. Among other factors, such as framework * Corresponding author. Fax: +44-(0)20-76293569. E-mail: furio@ ri.ac.uk. † Davy Faraday Research Laboratory, The Royal Institution of Great Britain. ‡ Universita ` di Torino.
type and dopant concentration, the resulting acidity depends primarily on the type of low-valence dopant employed.7 The number and strength of the acid sites available can be controlled by controlling the type and content of dopant ions during the synthesis. Defining a scale of relative acidity for the possible dopants, and correlating the acidity with the chemical composition, would be very useful in optimizing the activity and/or selectivity of the catalysts without extensive testing of each dopant type. Comparative experimental studies have been reported on dopant effects, which explore possible correlations of the catalytic activity for isostructural frameworks with the dopant type. Correlations have been proposed between the acid strength and the ionic radius7 and with the electronegativity8 of the dopant, and with the TO ˆ HT′ angle of the protonated oxygen (OH) with its nearest neighbor ions T and T′ in the framework.9,10 Comparing the properties for all possible dopant ions, however, is very challenging for experimental studies, owing to the influence of ill-controlled quantities in the catalyst after preparation and activation: isomorphous substitutions of low-valence ions are often energetically unstable and difficult to achieve; and the use of stoichiometric amounts of different dopant ions during the synthesis may result in different concentrations of dopants in framework and extraframework positions in the final product. Moreover, other active defect centers may be created in the catalyst, and the interaction between defect centers in the same region of the catalyst may alter their activity. Comparative experimental studies, therefore, are always limited to only a subset of the possible low-valence ions allowed by the framework stoichiometry. The application of computer modeling techniques is very powerful in such a case: all the above variables can be easily controlled in a modeling study of the solid. Although calculations consider an idealized description of the acid catalyst, they enable us to compare the properties of different isomorphous dopants in the same framework type, excluding the influence of all the other factors that are always present in experimental studies. Modeling represents therefore an ideal tool to define a relative scale of acidity for different dopant ions, and to grade their catalytic activity. To achieve this goal, we have studied a set of 16 low-valence dopant ions, isomorphously substituted for Si, Al, or P, in an isostructural polymorph of silica and AlPOs. We have chosen
10.1021/jp035553l CCC: $25.00 © 2003 American Chemical Society Published on Web 10/04/2003
Acid Strength of Dopant Ions in Zeolites and AlPOs
J. Phys. Chem. B, Vol. 107, No. 43, 2003 11867
Figure 1. Structure of a 2+ dopant ion, charge compensated by an acid proton, replacing a framework Al3+ ion in AlPO-34, described using periodic boundary conditions.
the chabasite framework type, with its analogue AlPO-34; this structure combines a direct relevance to catalysis with a relatively small unit cell, composed of 36 ions in the undoped framework, which makes the study feasible on a routine scale with accurate ab initio quantum mechanical (QM) calculations. Given the importance of acid zeotypes in heterogeneous catalysis, the acid OH site associated with low-valence dopant ions has been characterized with a variety of computational techniques, including isolated11 and embedded12-14 QM clusters, supercell techniques,15-19 and force field methods.20 Previous computational studies, however, are limited to the Al3+/Si4+ replacement in zeolites (chabasite in our work), and Si4+/P5+ in AlPO-34, which are extended here to a greater range of dopants, including several open-shell transition metal ions. Method In our computational study of the low-valent ions, we used the supercell approach, with one dopant ion per crystallographic unit cell of the host chabasite or AlPO-34 frameworks, composed of 36 ions (with stoichiometry T12O24, where T ) Si, Al, or P). The doped framework is described using periodic boundary conditions s a model that provides a correct description of the crystalline environment of the active site, including the Madelung field and the structural strain caused by the crystalline matrix on the substitutional ion. Even at the high level of doping used in our calculations, the dopant ions are separated by ∼10 Å from each other, and can be considered as non-interacting. In this work, we examine the properties of the following lowvalence dopants: B3+, Al3+, Ga3+, Co3+, and Fe3+/Si4+ in chabasite; Be2+, Mg2+, Ca2+, Sr2+, Cr2+, Mn2+, Fe2+, Co2+, Ni2+, and Zn2+/Al3+, and Si4+/P5+ in AlPO-34. The low-valence ions are charge-compensated by protonating one of the framework oxygens that is nearest neighbor to the dopant (the structure of a 2+ ion in AlPO-34 is illustrated in Figure 1). Not all the dopant ions, investigated in our computational work, have yet been successfully introduced experimentally in microporous zeolites and AlPOs, which is the case, for instance, for the Sr2+/Al3+ and Co3+/Si4+ substitutions. We have, however, examined them computationally, with the aim of extending the range of dopants considered and of highlighting the possible trends in the calculated properties as a function of the chemical features of the dopant ions. Since the list of dopants examined includes several openshell transition metal ions, we performed our calculations with an (unrestricted) Hartree-Fock (HF) Hamiltonian, which employs the exact expression of exchange forces, which is
TABLE 1: Relative Energy (E, in kcal/mol), Equilibrium Bond Distances (R, in Å), and Angle (Al-OH-Si in °) around the Acid OH Group, and OH Stretching Frequencies (νOH in cm-1) for Al-chabasite and H-SAPO-34, Protonated at Sites O1 and O3 (sites are labeled as in ref 17) E R(OH-H) R(Si-OH) R(Al-OH) Al-OH-Si νOH DFT [15] 0 DFT [17] 0 HF, this work 0 expt [23,24]
H-SAPO-34, Protonation Site O1 0.970 1.762 1.763 0.973 1.782 1.828 0.948 1.761 1.804
H-SAPO-34, Protonation Site O3 DFT [15] 1.0 0.970 1.777 1.779 DFT [17] 2.1 0.976 1.792 1.828 HF, this work 0.8 0.949 1.768 1.818 H-Al-chabasite, Protonation Site O1 DFT [15] 0 0.972 1.680 1.838 DFT [17] 0 0.974 1.702 1.904 HF, this work 0 0.949 1.689 1.899 expt [23,24] H-Al-chabasite, Protonation Site O3 DFT [15] 2.1 0.972 1.697 1.857 DFT [17] 1.4 0.975 1.714 1.938 HF, this work 1.6 0.949 1.687 1.894
132.6 130.7 128.0
3870 3765 4186 3625
131.9 138.8 128.9
3865 3726 4127
132.8 132.9 128.0
3845 3747 4141 3603
134.4 135.2 128.0
3840 3733 4135
important for a correct representation of the unpaired electrons. We used the latest version of the CRYSTAL code,21 which includes the analytical evaluation of gradients. For each of the defect centers investigated, we have performed a full geometry optimization, to determine the equilibrium structure. The acidity properties are calculated for the equilibrium structure of each ion; for computational convenience, we chose to screen the relative strength of the acid sites by calculating their OH stretching frequency, νOH. Both acidity and νOH depend on the strength of the OH bond, and these two observables are often assumed to correlate:19 a stronger OH bond results in a higher value of νOH and a weaker acid strength of the site. Of course, νOH is also observable by IR measurements on the solid acid catalysts. In this respect, we know that the HF Hamiltonian employed in our calculations overestimates the calculated stretching frequencies, by ∼12% compared to experiment. This error, however, is systematic s a feature that has given rise in the literature to the habit of scaling the calculated HF value of frequencies by a “golden factor” of 0.89.22 We do not plan here to compare our calculated frequencies with experiment, but only to compare the calculated value of νOH for the different dopant ions, to grade their acidic strength. We shall not, therefore, scale the calculated values of νOH. The values of νOH reported in Tables 1 and 2 have been obtained, for the equilibrium structure of each ion, by calculating numerically the dynamical matrix at the Γ point of reciprocal
11868 J. Phys. Chem. B, Vol. 107, No. 43, 2003
Cora` et al.
space. Diagonalization of the dynamical matrix yields the phonon spectrum of the system, in the harmonic approximation, from which we have derived νOH. Basis sets and computational tolerances employed are the same as described in references 15 and 16. Results and Discussion Previous computational studies have been dedicated to characterizing the geometry, energetics, and OH stretching frequencies of H-SAPO-34 and Al-doped chabasite.11-20 A full comparison of our results with these works will be given in a forthcoming paper; here we limit the discussion to a comparison of our calculated data with those of references 15-17 which have been obtained with periodic QM methods (HF here, and DFT in refs 15-17), and hence use the same model of the solid adopted here. Results are summarized in Table 1. The agreement is good: the geometric details of the acid sites show that the bond distances of the protonated oxygen OH to its nearest Al and Si ions of the framework are longer than those of the nonprotonated oxygens, and that the Si-OH-Al angle is smaller (by ∼20°) than the other T-O-T′ angles in the framework. Furthermore, all the computational works predict the framework oxygen labeled as O1 as being the stable protonation site; the calculated value of νOH in H-SAPO-34 is higher than in Alchabasite, also in agreement with experiment.23,24 The difference in νOH calculated here at the HF level is, as expected, larger than experimental and DFT values. The higher value of νOH in H-SAPO-34 compared to Al-doped chabasite suggests a lower acid strength of the former material. This result is confirmed by calculations on the adsorption of methanol in the two systems,15 which shows that the Al-doped chabasite framework is deprotonated in the presence of one CH3OH molecule, and hence is a stronger acid than H-SAPO-34 that is not deprotonated in the same conditions. To test the stability of our geometry optimization and numerical frequency calculation procedures, we performed the structural optimization of H-SAPO-34, protonated at the O1 site, from three different starting structures. The final geometries differ by (0.0002 Å in the O-H, OH-Al, and OH-Si bond distances, 0.1 kcal/mol in the energies, and 10 cm-1 in νOH, which represent the numerical error bars in our calculations.
Figure 2. Calculated OH stretching frequency, νOH (cm-1), as a function of the electronegativity of the dopant ion, M. Circles refer to dopant ions in chabasite, squares to 2+ ions in the Al framework position of AlPO-34, and the diamond to the Si/P replacement in AlPO34.
Let us now consider the other low-valent dopant ions, which represent the novelty of the present computational work. Our systematic study enables us to investigate the possible correlations between the calculated frequencies (acidity) and, first, the atomic properties of the dopant M (ionic radius and electronegativity) or, second, the local geometrical and electronic structure of the active site in the framework (M-O and M-H bond distances, M-O ˆ H-P bond angle, electric field gradient), which have been suggested experimentally as parameters that control the acidity of the doped framework. Results are summarized in Table 2, and presented in Figures 2-4, in which we have plotted the calculated OH stretching frequency as a function of the parameters listed above. Before examining the trends, it is of interest to note that our calculations predict the Mg2+ ion in the AlPO framework to have far stronger acid properties than any of the other dopants examined, either in AlPO-34 and in chabasite. The calculated value of νOH is in fact more than 100 cm-1 lower in MgAPO34 than for any other dopant examined. This finding is supported by experimental evidence:26 MgAPO catalysts have been shown to form coke very quickly on the inner walls of the catalyst
TABLE 2: Equilibrium Structural Parameters for the 16 Low-Valence Ions Examined in Chabasite or AlPO-34a dopant chabasite Si4+ B3+ Al3+ Ga3+ Fe3+ Co3+ AlPO-34 Al3+ Be2+ Mg2+ Ca2+ Sr2+ Cr2+ Mn2+ Fe2+ Co2+ Ni2+ Zn2+ AlPO-34 P5+ Si4+
R(M-O1,3)
R(M-OH)
R(M-H)
R(OH-H)
MO ˆ HP
r
E.N.
νOH
1.612 1.369 1.689 1.762 1.829 1.797
2.485 1.899 1.992 2.066 2.049
2.803 2.418 2.523 2.612 2.579
0.943 0.949 0.948 0.948 0.948
145.7 141.9 128.0 126.2 123.6 125.8
0.42 0.23 0.51 0.62 0.64 0.63
1.90 2.04 1.61 1.81 1.83 1.88
4238 4141 4157 4195 4243
1.726 1.546 1.876 2.204 2.411 2.024 2.027 1.982 1.943 1.899 1.907
2.309 2.084 2.408 2.555 2.356 2.265 2.191 2.141 2.192 2.189
2.548 2.421 2.986 3.203 2.871 2.806 2.733 2.669 2.749 2.684
0.949 0.955 0.950 0.949 0.948 0.950 0.950 0.950 0.950 0.950
141.6 141.2 132.4 126.0 116.2 127.5 127.8 129.0 129.3 126.4 131.3
0.51 0.35 0.66 0.99 1.12 0.89 0.80 0.74 0.72 0.69 0.74
1.61 1.57 1.31 1.00 0.95 1.66 1.55 1.83 1.88 1.91 1.65
4128 4037 4140 4195 4243 4194 4157 4192 4201 4207
1.512 1.575
1.761
2.307
0.948
141.6 128.0
0.35 0.42
2.19 1.90
4186
The symbols R refer to the calculated distances in Å, as indicated; MO ˆ HP is the angle between protonated oxygen and its two nearest neighbor ions in the framework, in degrees; r is the ionic radius of the dopant ion, in Å, from ref 25; E.N. is the electronegativity of the dopant;25 νOH is the calculated OH stretching frequency, in cm-1. a
Acid Strength of Dopant Ions in Zeolites and AlPOs
Figure 3. Calculated OH stretching frequency, νOH (cm-1), as a function of the electric field gradient in the equilibrium H position, in atomic units (1 au ) 9.7174 × 1021 Vm-2). Symbols as in Figure 2.
during acid-activated transformations of organic reagents s a process that requires a catalyst with particularly high acid strength. When comparing the calculated values of νOH for the different dopant ions, we see from the figures that νOH does not show appreciable correlations with either the structural or the electronic properties of the active site. Of course, there is some trend between subgroups of the dopant ions, especially when we limit our attention to the closed-shell ions, such as Mg, Ca, and Sr in AlPO. Overall, however, the situation is complex, and the acid properties appear to be influenced by a combination of structural and electronic factors. In the following discussion we shall examine the dependence of the calculated νOH on the different parameters introduced earlier in the discussion and employed in Figures 2-4, to highlight the important factors that define the Brønsted acidity of doped zeotypes. No appreciable correlation between νOH and the electronegativity of the dopant ion emerges from an examination of
J. Phys. Chem. B, Vol. 107, No. 43, 2003 11869 Figure 2. This result is consistent with the molecular-ionic picture of M-O and T-O bonds in the solid (here and in the following, with T we indicate a metal ion of the host framework), that we discussed in previous publications.27-29 The results of our calculations indicate that when the oxygen ions of the framework are located between two cations with different formal charges, they form a covalent bond with the neighbor with higher charge, and an ionic bond with the neighbor with lower charge. In pure AlPOs, for instance, the P-O bonds are covalent, while the Al-O bonds are ionic; the covalence of the P-O bond is enhanced when 2+ dopant ions replace Al in the AlPO framework. Similarly, low-valence 3+ dopants in SiO2based zeolites are ionic, and increase the covalence in the bonding between their nearest neighbor oxygens and the nextnearest silicon atoms.29 The protonated oxygens responsible for the Brønsted acidity, in particular, are located between one of the host framework ions and the low-valence dopant, with which they form a long and very weak bond (see Table 2), of ionic nature. In this environment, the behavior of the OH group is dominated by the bonding of the oxygen with the framework T ion, and is only marginally affected by the type of dopant M, and by the strength and polarity of the M-OH bonds. The properties of the acid OH group, therefore, are not dictated by the (atomic) electronic properties of the dopant ion, such as its electronegativity. The low-valence dopant, i.e., the Mn+/T(n+1)+ substitutional center, corresponds to a defect with an effective negative charge of -1 in the solid. This negatively charged defect creates a Coulomb potential in the neighboring region of the solid, centered on the dopant, and which decays as r-1. The OH stretching vibration is altered by the change in the Coulomb forces; since frequencies are calculated by diagonalization of the dynamical matrix, which is the second derivative of the energy scaled by the atomic masses, the Coulomb contribution to νOH is the second derivative of the Coulomb potential, i.e.,
Figure 4. Calculated OH stretching frequency, νOH (cm-1), as a function of the structural parameters of the active site: (a) ionic radius of the dopant, in Å, (b) M-O distance, in Å, (c) M-H distance, in Å, and (d) MO ˆ HP angle (°). Symbols as in Figure 2.
11870 J. Phys. Chem. B, Vol. 107, No. 43, 2003 the electric field gradient (EFG) tensor, calculated in the equilibrium H position. The EFG created by a negative charge has the effect of downshifting the frequency νOH and hence of increasing the proton acidity. The influence of the EFG on the OH stretching frequency is well-known from previous computational studies on a variety of systems, including the Al3+/ Si4+ defect center in zeolites.19,30,31 In references 19, 30, and 31, the authors compared the properties of the same dopant ion (Al) in different polymorphic structures, and found a linear correlation between the calculated values of νOH and the EFG. In our work, we compare instead the calculated value of νOH for different dopant ions; in such a case, the correlation of νOH with the EFG (Figure 3) is lost. Contrary to the study of references 19, 30, and 31 in which the local structure of the defect center (Al-OH-Si) was very similar for each zeolitic structure examined, the local structural parameters of different dopant ions in the same polymorph show much more appreciable variations; for instance, we see in Table 2 that the M-H distance varies from 2.307 Å (for Si4+/P5+) to 3.203 Å (for Sr2+/Al3+). It is not surprising, therefore, that the simple correlation found in references 19, 30, and 31 is lost here. Both the Coulomb potential and the EFG generated by the chemical substitution in the framework decay on moving away from the dopant ion; we would therefore expect that the further away the acid proton is from the dopant in its equilibrium structure, the less the OH group is perturbed by the M dopant. The correlation between νOH and the M-O and M-H equilibrium distances is therefore of interest to examine explicitly. Of course, the M-O distance is also a measure of the ionic radius, r, of the M dopant. Among all the structural parameters investigated, the MH distance (Figure 4c) is perhaps the one that shows the best correlation with νOH. Zeolites and AlPOs, however, do not follow the same correlation, but rather form two distinct classes with a different shift in the calculated frequency. The dopant ions whose calculated νOH deviates most from a linear behavior as a function of the MH distance are Ca and Sr in AlPOs. These are also the biggest dopant ions examined, and cause a large structural relaxation in the AlPO framework; the equilibrium structure of Ca and Sr in the AlPO framework is therefore substantially different from that of the other dopant ions. In particular the Brønsted OH group in CaAlPO-34 and Sr-AlPO-34 points toward a second oxygen of the framework. We consider that this hydrogen bonding-type of interaction contributes to downshifting the calculated value of νOH for the Ca and Sr dopants, and explains their deviation from the correlation of the acidic strength with the inverse of the MH distance. Be2+ in AlPO-34 and B3+ in chabasite also cause a different local structure around the Brønsted OH group, as they are too small to occupy a tetrahedral framework position, and are instead stable in trigonal coordination. In the latter case, the framework is effectively broken along the bond between the dopant and the acid OH group, which contributes to increasing the M-H distance, and to decreasing the acid strength of the site, compared to the value expected on the basis of their ionic radius. From the series of comparisons discussed above, we conclude that the biggest influence on the acid strength of the doped zeolite and AlPOs is given by the ionic size of the dopant ion M. Within the structural limitations imposed by the relative size of dopant and host framework ions, smaller dopants yield shorter M-O and M-H distances in the equilibrium structure, and have lower νOH, hence are stronger acids. However, since the equilibrium local structure of the Brønsted OH group is very dissimilar among the dopant ions examined, correlating the acid
Cora` et al. properties with a single structural parameter related to the chemical nature of the dopant does not appear satisfactory. Subsets of dopants do exist, whose acid strength correlates with the chemical nature of the dopant; however, extension of the study to a wider range of low-valence dopant ions shows that the correlation within the subsets is fortuitous, and not the result of a law with general validity. Our results do not therefore support a simple correlation between the acid strength of doped zeolites and AlPOs with either ionic radii,7 electronegativity,8 or bond angles9,10. For the first time such an extensive set of dopant ions in a single framework type has been examined in a consistent way. Results, however cannot be simply rationalized; the complex behavior displayed by zeolites and AlPOs makes an optimization of their properties more suitable for a combinatorial approach, to which computational studies of the type reported here can make a substantial contribution. Acknowledgment. We thank our colleagues at the Royal Institution and at the University of Torino, in particular, G. Sankar, J. M. Thomas, I. Saadoune, and R. Dovesi, for valuable discussions and assistance in the calculations. F.C. acknowledges grants from EPSRC and the Royal Society to support this work. References and Notes (1) Thomas, J. M. Sci. Am. 1992, 286, 82. (2) Thomas, J. M. Angew. Chem., Int. Ed. 1999, 38, 3588. (3) Sto¨cker, M. Microporous Mesoporous Mat. 1999, 29, 3. (4) Weisz, P. B. Pure Appl. Chem. 1980, 52, 2091. (5) Weisz, P. B.; Haag, W. O.; Lago, R. M. Nature 1984, 309, 589. (6) Vora, B. V.; Marker, T. L.; Berger, P. T.; Nilsen, H. R.; Kvisle, S.; Fuglerud, T. Stud. Surf. Sci. Catal. 1997, 107, 87. (7) Hocˇevar, S.; Batista, J.; Kaucˇicˇ, V. J. Catal. 1993, 139, 351. (8) de las Pozas, C.; Lopez-Cordero, R.; Gonzalez-Morales, J. A.; Travieso, N.; Roque-Malherbe, R. J. Mol. Catal. 1993, 83, 145. (9) Nur, H.; Hamdan, H. Mater. Res. Bull. 2001, 36, 315. (10) Rabo, J. A.; Gajda, G. J. Catal. ReV. Sci. Eng. 1989, 31, 385. (11) Sauer, J. Chem. ReV. 1989, 89, 199. Sauer, J. In Modelling of Structure and ReactiVity in Zeolites; Catlow, C. R. A., Ed.; Academic Press: London, 1992; p 183. (12) Bra¨ndle, M.; Sauer, J. J. Am. Chem. Soc. 1998, 120, 1556. (13) Sierka, M.; Sauer, J. Faraday Discuss. 1997, 106, 41. (14) Treesukol, P.; Lewis, J. P.; Limtrakul, J.; Truong, T. N. Chem. Phys. Lett. 2001, 350, 128. (15) Shah, R.; Gale, J. D.; Payne, M. C. Chem. Commun. 1997, 131. (16) Shah, R.; Gale, J. D.; Payne, M. C. Phase Transitions 1997, 61, 67. (17) Jeanvoine, J.; A Ä ngya´n, J. G.; Kresse, G.; Hafner, J. J. Phys. Chem. B 1998, 102, 5573. (18) Haase, F.; Sauer, J. J. Am. Chem. Soc. 1995, 117, 3780. (19) Ugliengo, P.; Civalleri, B.; Zicovich-Wilson, C. M.; Dovesi, R. Chem. Phys. Lett. 2000, 318, 247. (20) Jackson, R. A.; Catlow, C. R. A. Mol. Simul. 1988, 1, 207. (21) Saunders, V. R.; Dovesi, R.; Roetti, C.; Orlando, R.; ZicovichWilson, C. M.; Harrison, N. M.; Doll, K.; Civalleri, B.; Bush, I.; D’Arco, Ph.; Llunell, M. CRYSTAL2003 user’s manual; University of Torino: Torino, 2003. (22) Scott, A. P.; Radom, L. J. Phys. Chem. 1996, 100, 16502. (23) Smith, L. J.; Cheetham, A. K.; Marchese, L.; Thomas, J. M.; Wright, P. A.; Chen, J.; Gianotti, E. Catal. Lett. 1996, 41, 13. (24) Smith, L. J.; Davidson, A.; Cheetham, A. K. Catal. Lett. 1997, 49, 143. (25) Lide, D. R., Ed.; CRC Handbook of Chemistry and Physics, 75th ed.; CRC Press: Boca Raton, 1994. (26) Lischke, G.; Parlitz, B.; Lohse, U.; Schreier, E.; Fricke, R. Appl. Catal. A: General 1998, 166, 351. (27) Cora`, F.; Catlow, C. R. A. J. Phys. Chem. B 2001, 105, 10278. (28) Cora`, F.; Catlow, C. R. A.; D’Ercole, A. J. Mol. Catal. A: Chem. 2001, 166, 87. (29) Cora`, F.; Catlow, C. R. A. J. Phys. Chem. B 2003, 107, 11861. (30) Sastre, G.; Lewis, D. W. J. Chem. Soc., Faraday Trans. 1998, 94, 3049. (31) Lewis, D. W.; Sastre, G. Chem. Commun. 1999, 349.
