Role of Germanium in the Formation of Double Four Rings in Zeolites

Magdalena O. CichockaYannick LorgouillouxStef SmeetsJie SuWei WanPhilippe CaulletNicolas BatsLynne B. McCuskerJean-Louis PaillaudXiaodong Zou...
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J. Phys. Chem. C 2007, 111, 3575-3583

3575

Role of Germanium in the Formation of Double Four Rings in Zeolites Preeti Kamakoti* and Timothy A. Barckholtz ExxonMobil Research & Engineering, Annandale, New Jersey 08801 ReceiVed: August 7, 2006; In Final Form: NoVember 20, 2006

In recent years, a series of novel zeolites containing double four rings (D4Rs) have been synthesized by introducing germanium into the synthesis mixture. While the structure-directing effects of Ge toward D4R containing structures are well known, little is known about the underlying chemistry. In this work, plane wave density functional theory calculations are used to characterize and rationalize the site preferences, energies, and structural changes occurring when Ge is gradually substituted into the BEC framework up to 25% loadings. The calculations show that the site preference and energies are strongly dictated by the intrinsic flexibility of a given T-O-T linkage (where T ) Si or Ge), coupled with its ability to relax to geometries preferred by Ge. Calculations on small molecular fragments are used to explore the geometric variations in Ge-substituted zeolites and provide further insight into the role of Ge in stabilizing D4R units.

1. Introduction 1.1. Background. Zeolites and other microporous materials are used commercially in technologically important processes such as catalysis, adsorption, and separation. They also offer scientists an opportunity to rationalize adsorption and catalytic findings based on structural and physicochemical characteristics.1 Researchers have been working on the design and tailormade synthesis of zeolites with unique pore topologies and functionalities for specific applications, which is still a formidable challenge. Important advances have been made in the rational design of suitable structure-directing agents (SDAs), which have a strong influence on the final structure. In addition to the SDA, the framework can be manipulated to allow bonds with different bond lengths and bond angles, which influence the relative stability of the secondary building units and drive the formation of a particular structure by increasing its nucleation rate. It has been shown that isomorphous substitution of certain elements into the framework can drive the formation of new structures with secondary building units that would have been elusive in the pure siliceous form.2-4 For example, zinc strongly directs the formation of zeolites with three-membered rings, which are otherwise extremely difficult to synthesize.5 In recent years, a series of novel zeolites containing double four rings (D4Rs) with catalytically interesting pore systems such as ISV, ITH, and BEC have been synthesized.2,4,6-9 In many cases, the synthesis was shown to depend critically on the presence of Ge in the synthesis mixture. Isomorphous substitution of Si by Ge is thought to increase the framework deformability by lengthening the T-O bond distances and decreasing the T-O-T angle and will be discussed in detail in this work.1 O’Keeffe and Yaghi10 postulated that pure Ge-zeolitic materials can be synthesized when the T-O-T angles are close to 130°, which is the preferred value for Ge-O-Ge angles in its dense tetrahedrally coordinated R-quartz form. The structure directing effects of Ge toward D4R containing structures are well-known, but little is known about the underlying chemistry. Only limited theoretical work exists to * To whom correspondence should be addressed.

understand the properties of Ge-substituted zeolites and elucidate the chemistry behind the formation of structures containing D4R units. Blasco et al.1 performed calculations using cluster models to represent the 8 T-atom D4R unit containing 0-3 Ge atoms terminated using hydroxyl groups. The relative stabilities of all models were calculated for the formation reaction of D4R units in aqueous media, as well as relative to solid SiO2 quartz and rutile GeO2 and found to increase with Ge content. Sastre et al.11 also reported stability calculations using a force-field parametrized for Si/Ge zeolites and treated the presence of F- anion and SDA molecules in the structure. The preferential location of Ge was determined by calculating relative energies of statistically sampled distributions over a wide compositional range. Such methods are extremely computationally efficient, but the results are often dependent upon the availability and quality of the force-fields used. Also, they may not capture crucial structural and energetic details that are accessible to first principles calculations. A large body of work exists in the modeling of zeolite structure and reactivity using density functional theory calculations.12-14 Cluster models are routinely used for theoretical investigations of zeolites,15-17 wherein the under-coordinated oxygen atoms of the truncated structure are saturated using hydrogen atoms. This approach can be advantageous, as zeolites often have extremely large unit cells that may prove to be computationally challenging. Full periodic calculations are an alternative to cluster models. Plane wave density functional theory (DFT) calculations take into account the long-range electrostatic contributions of the zeolite and, in general, provide a more realistic description of the physical system. However, most prior work involving periodic DFT12-14 has only focused on zeolite structures that have relatively small unit cells. Astala et al.12 used periodic DFT to study the structural and elastic properties of five all-silica zeolites: SOD, LTA, CHA, MOR, and MFI. The first four contain unit cells of 36-72 atoms, whereas MFI has a considerably larger unit cell of 288 atoms. Demuth et al.13 used DFT calculations to study Al substitution in MOR, in the H+ and Na+ form. A number of studies of chemical reactions on acid sites inside zeolites have also been performed using periodic DFT methods.

10.1021/jp065092e CCC: $37.00 © 2007 American Chemical Society Published on Web 03/01/2007

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Figure 1. Schematic of a 2 × 2 × 1 periodic superstructure of BEC illustrating the location of the double four rings (D4R), the large twelvemember ring (12MR), and an inner four-member ring (4MR). Si and O atoms are depicted as yellow balls and red sticks, respectively. This coloring scheme will be used throughout the paper.

Rozanska et al.14 reported calculations for step-by-step alkylation of benzene with propene in mordenite using cluster and periodic calculations. The cluster calculations yielded qualitatively different reaction energy diagrams due to their inability to account for long-range framework effects. The aim of this work was to obtain fundamental insight into the role of Ge in stabilizing structures containing D4R units. This is envisioned to be a starting point for investigating ways of synthesizing zeolites with unique topologies via substitution of additives present in the synthesis mixture into the framework. Such topologies include structures containing building units such as three-member and double for rings, and involve the formation of relatively acute T-O-T angles. Additionally, the insight gained from this work may be applied toward the screening of other substituents as alternatives to Ge. Plane wave DFT calculations were used to characterize and rationalize the site preferences, energetics, and structural changes occurring when Ge is gradually substituted into the zeolite lattice. The zeolite chosen for this work was BEC, which is also known as polymorph C.4,6 BEC has a unit cell consisting of 32 T-sites and 64 O atoms for a total of 96 atoms per unit cell, thereby making it a computationally feasible system. It also exhibits a diverse range of ring types and secondary building units, and this facilitates the study of the relative behavior of Ge substitution into various types of secondary building units in the lattice. Finally, the existence of experimental data makes it possible to compare and validate our results qualitatively and quantitatively, where possible. 1.2. BEC Structure. Zeolite Beta, which is widely used as a solid catalyst in petroleum refining,18,19 petrochemistry, and fine chemical production is a highly faulted intergrowth of two polymorphs, A and B, which are commonly found in 60:40 ratio.19 Newsam et al.20 described a hypothetical framework, denoted as polymorph C, also known as BEC, which could be generated from polymorph A by the recurrent application of a shear operation along the a and b axes. The resulting structure has a three-dimensional system of 12-member rings (12MR) that intersect perpendicularly. Furthermore, BEC contains two D4R cages as secondary building units per unit cell. A schematic of BEC is presented in Figure 1. Recently, Corma et al. successfully synthesized this structure by using Ge from both fluoride4 and fluoride-free6 systems over a wide range of Ge

Kamakoti and Barckholtz loadings. The presence of fluoride in the synthesis mixture was found to strongly accelerate the crystallization kinetics.6 A schematic of the BEC structure illustrating various aspects of the structure is presented in Figure 1. This structure consists of three crystallographically unique T-sites and seven types of unique O atoms. The D4R cages consist entirely of T1 sites, as shown in Figure 2a. A total of sixteen T1 sites, labeled 1-16, form the D4R cages and are bonded to oxygen atoms O3, O4, O5, and O6. Sites 1-8 and 9-16 each form a D4R unit with different orientations as shown in the figure. As shown in Figure 2b, there are eight T2 sites, labeled a-h, located adjacent to the D4R cages. Each T2 site is connected to two T1 sites via O5. They also connect two T3 sites via O2. Eight T3 positions, labeled A-H, form two single four-member rings (4MR) in the unit cell formed by O1 and O7, presented in Figure 2c. X-ray powder diffraction (XRD) analysis of the calcined sample8 (Si:Ge ) 1.8:1) and a Rietvald refinement of the crystal structure gave a space group of P42/mmc. Refined Ge occupations for each T-site were obtained on a relative basis as a function of the total Ge content in the calcined BEC sample. At loadings greater than 3 Ge per unit cell, the Ge population at T2 was small, but not negligible. For a Ge content of less than approximately 25% of the T-sites, the Ge population was found to grow more steeply at site T1 than at T2 and T3 sites, which indicated the preferential occupation of T1. At higher concentrations, T2 and T3 populations were found to rapidly increase. The above analysis of the XRD data provides information about the overall substitution of Ge atoms in T-sites but not about its distribution in the D4R cages. When fluoride is used in the synthesis of the BEC, there is strong evidence that the F- anions are located in the D4R cages. 19F MAS NMR spectroscopy is very sensitive to the F- anion environment and provides evidence to the heterogeneous nature of the D4R composition and can give valuable information on the chemical and geometrical environment around it.9 Sastre et al.8 performed 19F MAS NMR spectroscopy to obtain a distribution of Ge atoms among the cages. The incorporation of Ge into the D4R sites was estimated using the relative intensities of the 19F resonance signals. Using models to estimate Si/Ge ratios in the D4R cages that were consistent with the NMR spectra, the authors concluded that Ge was progressively incorporated into a D4R to reach ∼3-4 atoms per cage. A further increase in Ge content favored the substitution into other crystallographic sites. 2. Methods 2.1. Density Functional Methods. All periodic calculations were performed using the Vienna ab initio simulation package (VASP).21,22 The total energy was calculated by an iterative solution of the Kohn-Sham equations of density functional theory. Electron exchange correlation effects were described using the local density approximation (LDA).23 As described below, this approach has been found to accurately reproduce the structural properties of various dense 4-fold coordinated silica and germania polymorphs.24 The calculations were performed with a plane-wave basis set using the projectoraugmented wave method (PAW) originally developed by Blo¨chl25 and recently adapted by Kresse and Joubert.26 The plane-wave kinetic energy cutoff was set to 400 eV. Total energy calculations were performed with the residual minimization method for electronic relaxations accelerated using the Methfessel-Paxton Fermi-level smearing with a width of 0.2 eV. A Monkhorst-Pack mesh with a 6 × 6 × 6 k-grid was used for silica and germania polymorphs, whereas a single Γ point was

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Figure 2. Three different views of the BEC unit cell illustrating the different types of T and O sites in the framework. Si atoms are represented as yellow balls, and O atoms as red sticks. T1, T2, and T3 sites are labeled 1-16, a-h, and A-H respectively, while oxygen atoms are labeled O1-O7. (a) Sketch highlighting the two D4Rs present in the unit cell, the T1 site, and oxygen atoms O3-O6 associated with the D4R. The T1 sites are labeled 1-16. (b) Sketch highlighting T2 sites labeled a-f, and associated oxygen atoms O2 and O5. (c) Sketch highlighting T3 sites within 4MR labeled A-H and associated oxygen atoms O1, O2, and O7.

TABLE 1: Lattice Parameters and Average Geometrical Parameters for Silica and Germania Polymorphs Calculated Using DFT Using PAW-LDA and PAW-GGA and Corresponding Experimental Data28-33 lattice parameters a, c (Å) polymorph R-SiO2 R-cristobalite β-tridymite R-GeO2 rutile-GeO2

DFT-LDA 4.92, 5.39 4.98, 6.92 5.19, 8.49 4.90, 5.70 4.42, 2.90

DFT-GGA 5.11, 5.57 5.11, 7.11 5.25, 8.91 5.11, 5.81 4.55, 2.99

average T-O bond length (Å) expt 5.4028

4.91, 4.97, 6.9230 5.06, 8.2827 4.98, 5.6432 4.40, 2.8631

used for the zeolites. A few calculations using a 2 × 2 × 2 k-grid were performed for pure siliceous and representative BEC configurations substituted with one and two Ge atoms. The difference in the total energies computed using a Γ point and 2 × 2 × 2 k-grid were found to be less than 2 kJ/mol. The relative energies between configurations at a given composition using at both levels were nearly identical, thereby validating the use of a single k-point for all calculations reported in this work. Geometric relaxations were performed using a conjugate gradient algorithm until the forces on all unconstrained atoms were less than 0.04 eV/Å. Structural optimization was performed as follows. The crystal structure of BEC was fully optimized in the purely siliceous form using the P42/mmc space group, as reported in literature.8 First, the lattice parameters and atomic positions were optimized in a series of fixed volume calculations. The addition of Ge to the framework will result in a volume expansion of the framework due to its larger ionic radius. Furthermore, to complicate matters, the optimal cell volume and resulting energy could vary slightly depending upon the location of Ge atoms in the configurations considered. Because this work is mainly focused on low Ge loadings, it is reasonable to assume that the relative energies between different configurations and local geometries in the vicinity of a Ge atom at a given composition will not change upon incorporating volume expansion. This has been verified for low Ge loadings up to three atoms. For the sake of computational efficiency and consistency, for all remaining calculations involving framework substitution of Ge, the lattice parameters, and cell shape were held fixed, while allowing all internal coordinates to relax completely. For nearly all calculations below, energies are reported as kJ/mol on a unit cell basis. The only exceptions are energies of silica and germania polymorphs, which are reported on a

average T-O-T bond angle

DFT-LDA

expt

DFT-LDA

expt

1.61 1.61 1.56 1.76 1.88

1.61 1.60 1.59 1.72 1.89

143.3 145.3 179.7 125.3 114.9

143.7 146.5 180.0 130.3 114.9

kJ/mol on a per T-atom basis, which enables comparison between systems with different numbers of T-sites. Cluster calculations were performed using the Gaussian 98 software package.27 Geometry optimization was performed with the B3LYP hybrid density functional and the 6-31G(d) basis set. Further calculation details are presented in upcoming sections. 3. Results 3.1. Benchmarking Calculations. Prior to modeling the BEC zeolite, a suitable exchange-correlation functional, plane wave cutoff energy, and other parameters required to obtain accurate results must be chosen. To validate these choices, we calculated the structural properties of dense silica and germania phases with relatively small unit cells and performed a comparison with prior experimental values. First, the volume and geometry optimization of three SiO2 phases (R-quartz, R-cristobalite and β-tridymite) and two GeO2 phases (R-quartz and rutile) were performed. Each phase was optimized using both the LDA and GGA PW9124 functional, and the PAW basis set. Consistent with previous theoretical work, a better agreement was found between the geometries obtained using LDA and experimental data,28-33 and hence, the LDA functional was chosen for all future calculations. A summary of these results using PAW-LDA is presented in Table 1. A satisfactory description of the geometries does not guarantee that calculations reproduce the energies correctly. This issue was addressed by calculating the relative stabilities of the above dense polymorphs of silica and germania. The relative stabilities of R-cristobalite and β-tridymite referenced to R-quartz were 4.6 and 6.5 kJ/mol of SiO2, respectively. These values are somewhat higher than the corresponding experimental

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TABLE 2: Average Si-O-Si Bond Angles, ∠(Si-O-Si), Bond Lengths, d(Si-O), for Each Type of Crystallographic Oxygen Atom in BEC, Range of Observed O-Si-O Bond Angles, ∠(O-Si-O), and Si-Si Distances, d(Si-Si) oxygen

d(Si-O), Å

∠(Si-O-Si)

O1 O2 O3 O4 O5 O6 O7 ∠(O-Si-O) d(Si-Si) Å

1.62 1.60 1.61 1.60 1.59 1.61 1.59 107.6-111.6 2.99-3.12

161.0 153.8 153.6 147.2 144.3 138.2 159.2

enthalpies at room temperature34 of 2.8 ( 2.2 kJ/mol and 3.2 ( 2.6 kJ/mol, respectively. The results also correctly predict that the rutile germania phase is more stable than the R-quartz phase by 41.8 kJ/mol. No relevant experimental value was found for comparison. 3.2. BEC Structure Optimization. The optimized cell parameters for the pure siliceous BEC from PAW-LDA calculations were found as a ) 12.62 Å and c )13.08 Å. A summary of geometric parameters for the pure siliceous form is presented in Table 2. Also shown are the observed ranges for the O-T-O angles and T-T distances. As experimental data is unavailable for the pure siliceous form, a specific comparison between calculations and experiment is not possible. Polymorph C has been synthesized in the pure germanate form.35 Although the T-atom topology is the same, the structure has a unit cell described using point group symmetry distinct from that of BEC, resulting from Ge-induced structural distortions toward longer T-O bond lengths and smaller T-O-T angles. The unit cell of Ge-BEC has 256 T-atoms, making it a computationally challenging system and, therefore, has not been studied in this work. Instead it will be used to understand and rationalize the evolution of geometry at higher Ge loadings. In the following sections, the siting of Ge was probed for a series of loadings ranging from nGe ) 1(4%) up to nGe ) 8(25%), where nGe is the number of Ge atoms present in the unit cell. 3.3. Ge Substitution in BEC. 3.3.1. Single Ge Atom Substitution. First, a single Ge atom was substituted into the unit cell at either the T1, T2, or T3 site. Ge was found to have the lowest energy at the T1 site of the D4R cage, whereas T2 was found to be 6.4 kJ/mol less stable than T1. Finally, substitution at T3 affiliated with an inner 4MR ring corresponded to the least stable configuration having 13.1 kJ/mol higher energy than T1. For each site, all optimized T-O bond lengths, T-O-T angles, as well as ranges of O-T-O bond angles and T-T distances corresponding to the nearest neighbor O atoms and average values over the entire framework are presented in Table 3. Substitution of Ge results in an elongation of bond lengths toward the Ge-O bond length computed in R-GeO2 of 1.76 Å. Although there is a slight variation in the T-O bond lengths, the differences are insufficient to rationalize the energy difference between the three sites. The O-T-O bond angles remain similar to those observed in the pure Si BEC and close to the tetrahedral angle of 109.5°. The Ge-Si distances for Ge substitution in T1 and T2 remain similar to the Si-Si distances observed in the pure siliceous structure. For a Ge atom substituted in T3, the Ge-Si distances shift toward higher values ranging from 3.19 to 3.27 Å, in comparison to Si-Si distances which ranged from 2.99 to 3.12 Å in Si BEC. However, it can be seen that substitution of a single Ge atom has the greatest effect on the T-O-T angles, compared to other geometrical parameters.

The results show that all T-O-T bond angles in the vicinity of the Ge atom had a tendency to decrease, albeit to different extents depending upon the O atom bonded to the Ge. Not all oxygen atom sites are the same with respect to the deformability of the T-O-T bond angle. A qualitative estimate of this can be obtained by calculating the deviation of the T-O-T bond angle from the Ge-O-Ge bond angle of 125° as computed previously for GeO2 quartz. From Table 3, we find that ∠(T-O6-T) relaxes to the lowest observed value of 130.4°. Similarly, ∠(T-O3-T) and ∠(T-O5-T) relax substantially from initial values of 153.6° and 144.3° to 138.0° to 131.7°, respectively, approaching values close to 125°, which is the calculated T-O-T angle of R-quartz GeO2. The large decrease in T-O-T angles indicates that these are deformable linkages. Conversely, ∠(T-O4-T), which is also a part of the D4R cage, appears to resist deformation as it changes by only 0.4°. Changes in these bond angles will have important consequences at higher loadings. Analogous to the above reasoning, site T2 has two favorable T-O5-T and two unfavorable T-O2-T linkages. Substitution in T3 results in T-O-T angles that are unsuitable for Ge occupation and is thus the highest energy configuration. T1 is the most favored binding site because three out of four T-O-T linkages are deformable and amenable to Ge substitution. The simple picture that emerges from this analysis is that the substitution energy of Ge is a function of the number of deformable T-O-T linkages and their ability to deform toward values suitable for Ge atoms. To test the validity of this hypothesis, it is necessary to examine the stability and structure at higher Ge loadings, as will be discussed in the following sections. 3.3.2. Two Ge Atom Substitution. Total energies were calculated for various configurations consisting of one Ge atom located at a T1 site and a second Ge atom at each of the other possible T1, T2, and T3 sites in the unit cell. Additionally, we performed a few calculations to verify that Ge substitution in entirely T2 and T3 sites is relatively energetically unfavorable. For the remainder of this work, the subscripted notation Tc1-c2-c3...cn is used to describe a particular configuration of n Ge atoms per unit cell. This is not to be confused with T1, T2, T3 and sites O1 through O7 which are used to describe the type of crystallographic site. Here, c1 through cn denote the locations of each Ge atom, consistent with the labels described in Figure 2. A plot of relative energies referenced with respect to the lowest energy configuration obtained is presented in Figure 3. For substitution exclusively in T1 sites, T1-7 consisting of two adjacent Ge atoms connected by O6 was found to have the lowest energy, whereas T1-2 with two adjacent Ge atoms connected by O4 was the least energetically favorable. Interestingly, Ge substitution in T1-5 with sites located on the longest diagonal in the D4R, which is often assumed to be the most energetically favored configuration in the literature,1,8 was ∼4.9 kJ/mol higher in energy than T1-7. A few configurations involving one Ge atom at a T2 site were found to be comparable in energy to substitution entirely within the D4Rs. As discussed below, both factors above will have important consequences at higher loadings. Optimized geometrical parameters for several representative sites are presented in Table 4. Similar to the nGe ) 1 results, the framework energy is a function of the ability of T-O-T linkages to relax toward lower angles (∼125°). First, the geometries of the highest and lowest energy configurations with Ge atoms entirely within one D4R (i.e., T1-2 and T1-7) are contrasted. The crucial difference

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TABLE 3: Geometrical Parameters for Ge Substitution for nGe ) 1 at T1, T2, and T3 in the Vicinity of the Substitution Site Including T-O-T Bond Angles and Ge-O Bond Lengths for Each Type of Crystallographic O Atom Coordinated to the Ge Atoma T1

T2

T3

oxygen

d(Ge-O), Å

∠(Ge-O-Si)

oxygen

d(Ge-O), Å

∠(Ge-O-Si)

oxygen

d(Ge-O), Å

∠(Ge-O-Si)

O3 O4 O5 O6 ∠(O-Ge-O) d(T-T), Å

1.75 1.73 1.73 1.75 104.1-112.6 3.04-3.20

138.0 147.6 131.7 130.4

O2 O2 O5 O5 ∠(O-Ge-O) d(T-T), Å

1.74 1.74 1.73 1.73 105.1-112.4 3.06-3.20

146.2 145.9 134.3 134.3

O1 O2 O2 O7 ∠(O-Ge-O) d(T-T), Å

1.75 1.73 1.73 1.72 105.0-112.5 3.19-3.27

150.6 146.1 146.3 162.8

a

Also shown are ranges of ∠(O-Ge-O) angles and Ge-Si distances, d(T-T), around each Ge atom.

Figure 3. Plot of energies for nGe ) 2 relative to the lowest energy configuration, T1-7 (Energy at T1-7 ) 0 indicated by the asterisk) for various types of sites including T1 substitution exclusively in the same D4R (T1-T1s), T1 substitution in different D4Rs (T1-T1d), 1 T1 and 1 T2 substitution (T1-T2), and 1 T1 and 1 T3 substitution (T1-T3).

between these configurations lies in the deformability difference in the bridging O separating the two Ge atoms. T1-7 consists of an extremely deformable Ge-O6-Ge linkage that relaxes from an initially low value of 138.2° to 123.8°. In contrast, T1-2 consists of a highly rigid Ge-O4-Ge linkage that remains close to the value observed in the pure silica zeolite of 147.2°. For substitution in different D4Rs, the difference in geometry between T1-14 and T1-11, which are the highest and lowest stability sites, arises entirely from the different extents to which the T-O-T bond angles can relax. Next, consider site T1-a, where the second Ge atom is located at a T2 site immediately adjacent to the other T1 position and whose energy is 5.8 kJ/mol higher than T1-7. This value is comparable to those for substitution entirely within D4R rings. An examination of the local geometry suggests that, in addition to the deformable O3, O5, and O6 linkages ∠(T-O2-T) has begun to decrease slightly. Again, we find ∠(T-O4-T) to be extremely rigid. This behavior was found to be unique to T1-a, presumably due to its position near a T1 site that renders greater deformability. Nearly all other sites consisting of one or more T2 and T3 sites were ∼8-18 kJ/mol higher in energy than T1-7. In summary, the stability for Ge substitution into a particular T-site is directly related to its ability for relaxing the adjacent T-O-T angles toward geometries preferred by GeO2, that is, smaller T-O-T angles. The most favorable T-sites are those

adjacent to the O3, O5, and O6 atoms. Further stabilization is induced when two Ge atoms are linked by any of these O atoms resulting in the formation Ge-O-Ge pairs. The simultaneous decrease in T-O-T angles and increase in T-O bond lengths allows for the T-T distances to remain nearly unchanged, relative to the pure siliceous form. Therefore, although there are local structural distortions, the overall structure and longrange order is preserved. 3.3.3. Three Ge Atom Substitution. At higher Ge loadings, the number of possible configurations increases substantially, and the calculation of all combinations becomes a formidable task. Only a sample of possible substitutions was calculated, mostly involving substitution in three T1 sites, as well as some involving substitution at a few T2 and T3 sites. A partial set of configurations and corresponding energies relative to the lowest energy configuration, chosen from a total of 33 studied configurations, is presented in Table 5. A complete dataset appears as Supporting Information. Figure 4 presents sketches of several low-energy configurations found from these calculations. The lowest energy configuration T1-7-8 corresponds to a network of 3 Ge atoms substituted at 3 corners of a D4R face formed by O3 and O6 bridging atoms. This can be broken down into three pairwise interactions of highly favorable T1-T7 substitution with Ge-O6-Ge connectivity, T7-T8 with Ge-O3-Ge connectivity, and an intermediate energy T1-T8 with Ge-O3-Si-O4-Ge connectivity. The next lowest energy configurations consist of a T1-7 pair with the third atom placed at sites T3, T6, or T14. Using a similar analysis of pair interactions, one would tentatively predict the following energetic ordering: T1-7-3 > T1-7-14 > T1-7-11 > T1-7-6, which is entirely supported with the calculations. Interestingly, another configuration identical in energy was T1-7-a or equivalently T1-7-f, consisting of two T1 and one T2 Ge atoms connected by O6 and O5 bridging atoms. The energy of configuration T1-7-A involving a single Ge atom located at a T3 site was 11.6 kJ/ mol higher than T1-7-8. In contrast, nearly all configurations involving a Ge-O4-Ge linkage were found to be intermediate or high in energy, relative to T1-7-8. Finally, the highest energy configurations are those involving Ge substitution exclusively at T2 and T3 sites. Geometric parameters for configurations T1-7-8 and T1-7-6 corresponding to the lowest and a high-energy configurations are presented as Supporting Information. The data can be interpreted in the same manner as before. For example, in the most stable energy configuration, T1-7-8, the presence of Ge-O-Ge pairs around O3 and O6 allows for maximum T-O-T bond angle deformability and elongation of Ge-O bond lengths up to 1.76 Å. A similar argument can be used to understand why T1-7-a is a favored configuration. On the other hand, T1-7-6 contains the highly rigid Ge-O4-Ge linkage, which is sufficient to counterbalance the stability gain derived from the Ge-O6-Ge linkage.

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TABLE 4: Geometrical Parameters for Selected Configurations at nGe ) 2 Including Average T-O-T Bond Angles and Ge-O Bond Lengths for Each Type of Crystallographic O Atom Coordinated to the Ge Atoma T1-7

T1-a

oxygen

∠(T-O-T)

d(Ge-O), Å

O2 O3 O4 O5 O6 ∠(O-Ge-O) d(T-T), Å

138.1 148.5 131.9 123.1 101.9-103.8 3.05-3.21

1.75 1.73 1.73 1.76

T1-2

∠(T-O-T)

d(Ge-O), Å

142.1 135.6 150.6 130.0 128.6 104.3-112.7 3.04-3.22

1.74 1.75 1.73 1.74 1.75

∠(T-O-T)

d(Ge-O), Å

134.7 142.3 134.8 130.0 99.7-116.8 3.05-3.28

1.75 1.73 1.72 1.75

a Also shown are range of ∠(O-Ge-O) angles and Ge-Si distances, d(T-T), around each Ge atom in the configuration. Values in bold face indicate the presence of a Ge-O-Ge linkage.

TABLE 5: Partial List of Energies of Configurations for nGe ) 3 Relative to the Lowest Energy Configuration T1-7-8a nGe ) 3 configuration

E - Emin (kJ/mol)

nGe ) 3 configuration

E - Emin (kJ/mol)

T1-7-8 T1-7-a T1-7-14 T1-7-3 T1-14-5 T1-7-11 T5-4-2 T1-2-16 T1-3-10

0.0 1.0 4.8 5.8 6.8 7.7 9.6 11.6 12.5

T1-7-e T1-2-13 T5-2-13 T1-2-f T1-16-e T1-e-D T1-E-C TC-D-E

12.5 15.4 16.4 16.4 22.2 28.9 35.7 64.6

a These were chosen from a total of 33 studied configurations to represent the observed energy variations.

The examples presented above illustrate the effects of linkage deformability on the overall site stability. Most importantly, the results for nGe ) 3 suggest that energetic information at lower loadings and T-O-T linkage deformability can be used to qualitatively predict which configurations are most likely to be favored at higher loadings. Finally, similar to previous results, a strong tendency was observed for a pair of Ge atoms to avoid substitution adjacent to the rigid O4 atom in the D4R, as this could counteract the stability gained from other favorable Ge-O-Ge interactions in the structure. 3.3.4. Higher Ge Loadings. Using the methodology developed above, various “energetically feasible” Ge atom configurations were probed for loadings nGe > 3, as well as other configurations, to validate the above screening methodology and determine relative trends. It is important to mention that this methodology for choosing and evaluating low-energy configurations must be viewed as a reasonable initial approximation at best and not as a true predictor of quantitative energy differences, as we are only sampling a large configuration space. A summary of relative energies for various configurations at nGe ) 4-8 is presented in the Supporting Information section. Among all configurations probed at nGe ) 4, the lowest energy configuration found among our calculations was T1-4-7-8. This corresponds to Ge atoms at corners of the face consisting exclusively of two of the most deformable O linkages, O3 and O6. In contrast, configurations containing Ge atoms at the other faces of the D4R (i.e., T1-2-3-4 and T1-2-6-7) were 13.2 and 15.4 kJ/mol higher in energy, respectively. Once again, this can be understood on the basis of relative strength of the pairwise T-O-T interactions and will not be discussed further. Two interesting features emerge from these results. First, the overall energy spread between various configurations is substantially magnified with increasing Ge loading (i.e., ∼16.8 kJ/mol for nGe ) 4 and 48.4 kJ/mol for nGe ) 8). Second, the most energetically favorable configurations observed in these calculations can all be described as containing a central

Ge4 configuration T1-4-7-8, with the remaining Ge atoms substituted at other positions that enable the T-O-T bonds to relax maximally. An example of the gradual Ge occupation of sites as a function of loading from nGe ) 4-8 is illustrated in Figure 5. It is important to mention that it is highly likely that other configurations with comparable or higher energies may be found, upon a complete analysis. At each loading, a summary of the key geometrical parameters for the most stable configurations is presented as Supporting Information. When Ge is gradually incorporated into the framework, the presence of multiple Ge-O-Ge linkages eventually deforms all of the T-O-T linkages. For example, consider the configuration T1-4-7-8-14 at nGe ) 5. Here, all of the T-O4-T angles that are coordinated to the central 4 atom unit T1-4-7-8 have been deformed to lower values, whereas the ∠(Ge-O4-Si) associated with site T14 in the second D4R has a value of ∼150°. A similar behavior is observed for other linkages involving O2 and O7 bridging oxygen atoms. The other interesting feature is that at all loadings nGe > 4, the highest stability configurations consist of certain T2 and T3 sites near the central unit T1-4-7-8. This behavior can be explained using the same argument proposed previously due to deformability that is gradually induced into T-O-T linkages in the vicinity of the central unit. Although the O-T-O values at lower loadings in the vicinity of the Ge atom remained close to the tetrahedral value of 109.5°, they distort to a greater extent at loadings of nGe > 3 and can assume values ranging from ∼98° to 116°. These values are consistent with those observed in the pure germania zeolite FOS-5, as determined by XRD.35 However, this effect of Ge substitution is considerably less pronounced on the O-T-O angles, when compared with the T-O-T angle distortions. A similar effect is observed on the T-T distances, which range from 2.99 - 3.25 Å for nGe ) 8. 3.4. Zeolite Cluster Calculations. So far, plane wave DFT calculations have been used to show that the site preference and energy are strongly dictated by the intrinsic deformability of a given T-O-T linkage (where T ) Si or Ge), which is dictated by the overall lattice structure, coupled with the relaxation of T-O-T angles to those preferred by Ge. Although it is known that the presence of Ge causes more acute T-O-T angles, precise information regarding preferred geometries for Ge-O-Si and Ge-O-Ge linkages, relative to the Si-O-Si linkage, have not been calculated. A rough estimate for the Ge-O-Ge linkage can be obtained from the geometry of GeO2 quartz suggesting a value around 125°, although the same cannot be said for Ge-O-Si. In addition to finding the preferred geometry, it is also valuable to study the variation of energy as a function of geometry. Covalent bonded interactions of a silicate crystal are often treated as localized and modeled using small clusters.36-38 Little

Double Four Rings in Zeolites

J. Phys. Chem. C, Vol. 111, No. 9, 2007 3581

Figure 4. Three representative configurations for nGe ) 3 having the lowest observed total energies presented in descending order of stability. Si, Ge, and O atoms are represented by yellow balls, purple balls and red sticks, respectively.

Figure 5. Sketch showing gradual Ge occupation of sites from nGe ) 4 to 8. Coloring scheme used is same as in Figure 4.

difference is thought to exist between the shapes and sizes of Si-O-Si groups in gas-phase siloxane molecules and solid silicates. Geisinger et al.36 performed molecular orbital calculations on the pure, substituted, and protonated H6Si2O7 cluster where the bond angles and lengths were systematically varied and characterized as a function of energy. This was used to explore and analyze trends in bond length and angle variations in extended structures with moderate success. These concepts were applied to perform cluster calculations on small zeolite fragments and used to address the above issues. A two T-atom cluster was carved out based on the initial BEC structure and is illustrated in Figure 6a. All of the undercoordinated O atoms were saturated using H atoms. An initial relaxation was performed, where the central bond lengths and

bond angle around the central T-atom, all of the tetrahedral O-T-O, and the O-H bond lengths were allowed to relax. During the calculation, the H-O-T angles and H-O-T-O dihedral angles were constrained, so that the H atoms would mimic the location of the T-atoms in the true extended BEC structure. A total energy scan was performed by varying the central T-O-T angle. The remaining geometrical parameters except for the H-O-T angles and H-O-T-O dihedral angles were allowed to vary with the central T-O-T angle. The ∠(T-O-T) values were varied from 120° to 180°. The entire process was performed for the H6Si2O7, H6SiGeO7, and H6Ge2O7 clusters. A plot of relative energy as a function of the central T-O-T angle for each cluster is shown in Figure 6b. For the H6Si2O7

3582 J. Phys. Chem. C, Vol. 111, No. 9, 2007

Kamakoti and Barckholtz In summary, the cluster calculations suggest that Ge stabilizes the D4R linkages at lower T-O-T angles than Si. 4. Discussion

Figure 6. (a) H6T2O7 cluster. The T (T ) Si or Ge), O and H atoms are represented using blue-gray, red, and white balls, respectively. (b) Total energy for H6Si2O7, H6SiGeO7, and H6Ge2O7 clusters as a function of ∠(Si-O-Si), ∠(Si-O-Ge), and ∠(Ge-O-Ge), respectively, ranging from 120° to 180°.

cluster, a minimum was found at ∠(Si-O-Si) ) 150.2° and d(Si-O) ) 1.63 Å. The potential energy curve is found to be relatively flat, as observed in previous studies.36 For example, the energetic penalty to form a linear Si-O-Si angle is only ∼4.4 kJ/mol. This provides a plausible explanation for the reason why the majority of silicates are formed over a wide range of T-O-T angles ranging from around 140° to 180°. For ∠(Si-O-Si) values less than 135°, the energy increases more dramatically. For the H6SiGeO7, a minimum was found at ∠(Si-O-Ge) ) 141.9° with d(Si-O) ) 1.64 Å and d(Ge-O) ) 1.75 Å. For H6Ge2O7, these values were 133.1°, 1.64 Å and 1.76 Å, respectively. The energy curve for H6SiGeO7 is already steeper than that for the above H6Si2O7, whereas the H6Ge2O7 cluster has the steepest curve. These results can be used to corroborate the above calculations on the full zeolite structure in the following manner. The first observation lies in the fact that the preferred angles for the Ge-O-Si and Ge-O-Ge angles are smaller, compared to those preferred by Si-O-Si, and this occurs around the same region where the deformation energy for pure siliceous cluster increases noticeably. In the extended zeolite, this is manifested in Ge substitution in sites where the T-O-T angles can be lowered to more acute angles. In the pure siliceous zeolite, the Si-O-Si angles range from an energetically disfavored value of 138° up to 153°. As shown by O’Keeffe,10 the T-O-T angles of a D4R unit can be reduced while maintaining regular tetrahedra, if the symmetry is reduced and the T-O-T angles are lowered to 130o. From our calculations, this is suitable for Ge-O-Si and Ge-O-Ge linkages. Finally, the plots for the H6SiGeO7 and H6Ge2O7 clusters suggest a relatively narrow stability range of T-O-T angles that are suitable for Ge substitution, and this is consistent with our calculations on the full periodic structure showing a strong preference for sites within the D4R where it is possible to achieve this geometry.

Experimental information for BEC using XRD, electron density studies and 19F NMR has been reported in the literature,8 as discussed previously for xGe ) 0.35. Since this work focuses predominantly on lower Ge loadings, a direct comparison is not possible for the estimation of fractional occupation of each site at higher loadings. However, the DFT results are in qualitative agreement with both sets of data. Furthermore, the fluoride-free results agree with the experimental observation that Ge preferentially occupies T1 sites up to a total of 4 atoms. At loadings of nGe > 4, a selective occupation of T2 sites in the immediate vicinity of deformable Ge-O-Ge linkages was observed, and these configurations also had some of the lowest observed energies. At a loading of approximately nGe ) 7, configurations involving occupation of T2 and T3 site start to become energetically favored. Upon extrapolation to higher loadings, it is clear that the occupation of T2 and T3 atoms will increase, and this is entirely consistent with experimental observations. The configurations probed in this work are not exhaustive, although they provide insight into the onset and gradual occupation of other framework sites, as well as their location and characteristics. Recent experimental and computational studies8,9 have hypothesized that Ge atoms tend to locate as far away as possible from each other to avoid the induction of lattice strain. Forcefield calculations on BEC suggested that configurations with Ge at opposite sides were energetically preferred so as to avoid formation of Ge-O-Ge linkages. Furthermore, the study1 notes that no evidence of Ge-O-Ge linkages was observed in BEC, although a complete interpretation of the spectrum was not definitive. The above fluoride-free DFT results suggest otherwise and show that formation of Ge-O-Ge linkages around certain bridging O atoms are thermodynamically favored and is clearly not constrained by the long-range structure. This behavior is not substantially altered in the presence of fluoride anions and will be discussed in an upcoming paper.39 One possible explanation for this discrepancy could be due to the fact that Ge-O-Ge linkages in the D4R pre-nucleation building units that assemble to form the final zeolite structure are energetically disfavored compared to other configurations. Recent DFT calculations1 on D4R clusters found no energy differences between clusters with and without Ge-O-Ge linkages, and this serves to validate our results. This comprehensive work of Ge in BEC can be used to propose a possible explanation for the role behind Ge as a driving force in the formation of zeolites containing the nominally elusive D4R units. An important caveat is that these results are based on a purely thermodynamic analysis of the final structure. They do not provide any insight into the complex kinetics during zeolite synthesis. However, the agreement seen between experimental results and our theoretical calculations is quite encouraging. The energy for a Ge atom to isomorphously substitute into the framework is a function of the deformability of a T-O-T linkage. The change in T-O-T angle has a simultaneous effect on the T-O bond lengths, which increase in the presence of Ge. In contrast, O-T-O angles and the T-T distances only change slowly as a function of Ge loading. This deformability is most likely defined by the overall long-range zeolite structure. Preliminary calculations performed on several framework additives provide more insight into this observation. Two out of three types of T-O-T linkages in the BEC D4R

Double Four Rings in Zeolites unit are highly amenable to occupation by other framework substituents. This characteristic could presumably change for other Ge-containing zeolites, depending upon the relative T-O-T angle flexibilities in the framework. In addition to this intrinsic deformability, the resultant geometries must match with those preferred by Ge-O-Si and Ge-O-Ge angles, which are ∼120-135°. Increased Ge substitution induces deformability to other T-O-T linkages, as is seen upon geometric analysis of higher loading configurations. This would eventually result in a symmetry lowering of the D4R unit from Oh (cubic symmetry) to Th (tetrahedron symmetry), in agreement with the proposition made by O’Keeffe et al. previously.10 5. Conclusions A combination of DFT calculations on the periodic structure and small clusters was used to investigate the role of Ge in the formation of structures containing D4R units. The calculations show that the site preference and energies for Ge substitution are linked to the deformability of all T-O-T angles in its vicinity toward lower values. The results are in qualitative agreement with available experimental XRD and 19F NMR data. Calculations on small clusters suggest that, in contrast to the Si-O-Si linkage, Ge-O-Si and Ge-O-Ge linkages stabilize the D4R units at more acute angles. Small molecular cluster calculations of the nature described here could potentially be extended to study the effects of other framework additives. Acknowledgment. The authors acknowledge Kirk Schmitt, Karl Strohmaier, Paul Stevens, Guang Cao, and Simon Weston for helpful discussions and Jessie Vezza for help with graphics. Supporting Information Available: Energies of all studied configuration for loadings 3 e nGe e 8 of are presented. Also shown is geometrical information at each highest stability configuration for 4 e nGe e 8. This material is free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Blasco, T.; Corma, A.; Diaz-Cabanas, M. J.; Rey, F.; Vidal-Moya, J. A.; Zicovich-Wilson, C. M. J. Phys. Chem. B 2002, 106, 2634. (2) Corma, A.; Diaz-Cabanas, M. J.; Fornes, V. Angew. Chem., Int. Ed. 2000, 39, 2346. (3) Corma, A.; Diaz-Cabanas, M. J.; Martinez-Triguero, J.; Rey, F.; Rius, J. Nature 2002, 418, 514. (4) Corma, A.; Navarro, M.; Rey, F.; Rius, J.; Valencia, S. Angew. Chem., Int. Ed. 2001, 40, 2277. (5) McCusker, L. B.; Grosse-Kunstleve, R. B.; Baerlocher, C.; Yoshikawa, M.; Davis, M. E. Microporous Mater. 1996, 6, 295. (6) Corma, A.; Navarro, M. T.; Rey, F.; Valencia, S. Chem. Comm 2001, 1486. (7) Sastre, G.; Pulido, A.; Castaneda, R.; Corma, A. J. Phys. Chem. B 2004, 108, 8830.

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