Stability and Structures of Aluminosilicate Clusters - The Journal of

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Stability and Structures of Aluminosilicate Clusters Chao-Shiang Yang, Jos
e Miguel Mora-Fonz, and C. Richard A. Catlow* Department of Chemistry, University College London (UCL), Gower Street, London, WC1E 6BT, United Kingdom ABSTRACT: We investigate the structures of stabilities of small aluminosilicate clusters using molecular simulations employing density functional theory (DFT) and the conductor like screening model (COSMO), which allow us to model clusters both in the gas phase as well as in solution. We report the relative structures and energies of clusters containing between one and six Si/Al atoms and the effect on them of the interaction with Na+ and of intramolecular hydrogen bonding. Our results reveal that with the exception of the dimer, “Lowenstein” clusters (without Al
O
Al linkage) are more energetically favorable than “non-Lowenstein” clusters (which contain such bridges) in the gas phase. The stability of aluminosilicate clusters is strongly affected by solvation, with the solvent influencing their conformations. In solution, all of the most stable clusters follow not only Lowenstein’s rule, but also Dempsey’s rule.

1. INTRODUCTION Zeolites have been widely investigated for several decades because of their specific chemical and physical properties including ion-exchange, catalysis, and sorption, which have been widely applied in several industries.1 These applications hinge on both the atomic composition (Si/Al ratio) and spatial arrangement of the zeolite framework, which in turn provide a strong motivation not only for understanding the complex mechanisms of nucleation and subsequent growth of zeolites, but also for identifying the clusters that participate in the nucleation process. As for pure silica zeolites, several experimental studies have provided information on cluster structures,2,3 and the structures and energies of several key clusters have also been obtained computationally.4
8 The investigation of aluminosilicate clusters involved in zeolite nucleation, however, is particularly difficult because of a variety of factors, and these complex aluminosilicate systems are influenced inevitably by internal and external factors: the Si/Al ratio, including the distribution of aluminum ions, the location of the extra-framework cations, and aluminosilicate
solvent (water) interactions.9,10 Several techniques have been applied recently to their study, including NMR,11,12 high-resolution transmission electron microscopy,13,14 high-energy X-ray diffraction (HEXRD),15 in situ small-angle X-ray scattering (SAXS), and wide-angle X-ray scattering (WAXS).16,17 Nevertheless, the nature of aluminosilicate clusters in solution remains poorly understood, and the nature of the formation of these clusters is relevant to aluminosilicate chemistry in general. The TO4 tetrahedron (T = Si, Al) is well-known to be the basic structural unit of aluminosilicate zeolites and is used to build a variety of clusters including four-rings, five-rings, and sixrings, which are combined together to construct different 3D channel frameworks. Because of the replacement of Si atoms by Al atoms at tetrahedral sites, aluminosilicate zeolite systems form negatively charged frameworks with compensating extra-framework cations such as Na+ ions (or in the case of acid zeolites, r 2011 American Chemical Society

a proton bonded to a bridging oxygen). For extra-framework cations, several studies have indicated that the concentration of the alkali metal indeed influences the formation of clusters in the prenucleation of aluminosilicate zeolites.18,19 Therefore, the determination of the relative location of cations in these clusters and their effect on the cluster energies is clearly of importance. In aluminosilicate zeolite systems, both Lowenstein’s rule20 and Dempsey’s rule21 constrain the distribution of aluminum. Lowenstein’s rule states that Al
O
Al linkages are forbidden in the framework of aluminosilicates. Previous computational studies have found that small clusters of the type that is postulated to form during the synthesis of aluminosilicate zeolites have lower energies for “Lowensteinian” distributions of aluminum.22 Dempsey’s rule proposes that the distance between each aluminum atom is maximized in aluminosilicate zeolites to stabilize their frameworks. The nucleation and growth of zeolites is of course effected hydrothermally, and cluster properties are strongly influenced by the interaction with water;23 inclusion of solvent effects will be essential if reliable thermodynamic parameters are to be calculated. Mora-Fonz et al.24 suggested that using the COSMO approach (discussed below) to model water in pure silicate clusters the relative strength of interactions between pure silicate clusters and water would be in the order: silicate
silicate > silicate
water > water
water. Such behavior should also influence the formation of aluminosilicate zeolite clusters. Therefore, it is evident that to investigate accurately the stability of aluminosilicate clusters in solution we must consider the role of water. In this work, we analyze a range of key aluminosilicate clusters that are both consistent and inconsistent with Lowenstein’s and Dempsey’s rules. The aim is to identify the most stable clusters both in the gas phase as well as in solution. In each case, we discuss Received: March 14, 2011 Revised: September 16, 2011 Published: September 16, 2011 24102

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Figure 1. Optimized isomers of aluminosilicate species in COSMO solution: monomer, dimers, trimers, and tetramers. In all Figures, color coding as follows: purple spheres represent the Na+ ions, the pink Al, the red O, and the white H atoms; the dashed lines represent hydrogen bonds.

the factors influencing these cluster structures and energies. Our results give considerable insight into the factors controlling the early stages of zeolite nucleation and growth.

2. METHOD We construct clusters with various Si/Al ratios and arrangements of extra-framework Na+ ions used to neutralize the negative framework of the aluminosilicate clusters. Although both the Si
Al dimer and the Al
Al dimer that we investigate have been discussed in previous studies,6 extra-framework cations have been omitted from this previous work. Clusters also have isomers that are identified by atomic arrangements of Si and Al atoms. More details of the structures investigated are given below. All calculations on aluminosilicate clusters were performed by using the DMol3 code25 based on density functional theory (DFT). A double numerical basis set plus polarization (DNP) and BLYP exchange-correlation functional was employed to optimize the original clusters in the gas phase. Although a comprehensive conformational analysis was not possible for the wide range of clusters studied, different starting configurations were used to obtain an energy minimum. These

optimized clusters were then reoptimized including the conductor like screening model26,27 (COSMO) used to simulate the solvation of the aluminosilicate clusters. In the COSMO approach, the effect of solvation is simply treated as a dielectric continuum in a self-consistent procedure, but there is no explicit water in aluminosilicate clusters during the DFT calculation. The Gibbs free energy, including the zero-point energy, and the translational, rotational, and vibrational contributions to the energy are calculated with a statistical mechanical approach for the temperatures 298 and 450 K. A number of approaches are available for calculating free energies in solution.28,29 Here the Gibbs free energy of an aluminosilicate in solution was calculated by the COSMO method at 298 and 450 K. The procedure summarized above is essentially the same as that adopted by Mora-Fonz et al.4 in their study of silica clusters, where the approach has shown to yield reliable results on the relative energies of clusters studied.

3. RESULTS AND DISCUSSION The optimized structures for clusters in the gas phase and in solution are obtained from the two types of calculation: BLYP/DNP 24103

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Figure 2. Optimized isomers of aluminosilicate species in COSMO solution: pentamers. Color coding as in Figure 1.

for the gas phase and BLYP/DNP (COSMO) for the solution, as previously described. In this study, we concentrate on the structures obtained by the COSMO method because we are mainly concerned with the properties of the clusters in solution. All optimized aluminosilicate isomers for the solution calculations are shown in Figures 1
4. We consider both open (chain) and ring clusters for species containing between one and six Si/Al atoms. Moreover, the letters “A”, “B”, and “C” indicate the number of Al atoms in these aluminosilicate clusters, i.e., 1, 2, and 3, respectively. Our calculations yield both energies and structures for the clusters investigated. We are also able to analyze the differences between their isomers. The relevant structural parameters for aluminosilicate clusters including the calculated Si
O and Al
O bond lengths, the distances between Na+ ions and the nearest oxygens, T
O
T angles and for comparison, experimental crystallographic data of zeolite A30 and zeolite X31 are shown in Tables 1
4. In addition, the relative energies of these isomers are also compared in Tables 5
8. A detailed discussion of the results for the different clusters now follows.

3.1. Open Chain Clusters. Here we consider the structures and energies of chain-like clusters with special attention to the effects of Al distribution. Charge neutrality is ensured for all clusters by including the appropriate number of Na+ ions. 3.1.1. Structures and Energies of Monomer and Dimers: Al(OH)4Na, AlSiO(OH)6Na, and Al2O(OH)6Na2. Al(OH)4Na, AlSiO(OH)6Na, and Al2O(OH)6Na2 are the smallest basic clusters in aluminosilicate zeolites. The relevant structures of Al(OH)4
, AlSiO(OH)6
, and Al2O(OH)62
have been reported in a previous study5 for the case of pure siliceous clusters. Here we add the counterions (Na+ ions) to neutralize these clusters and analyze the resulting structures of the solvated clusters. The Na+ ion coordinates to the aluminate monomer (Al(OH)4Na); the Al
Ot bond lengths (where t refers to the terminal
OH) vary from 1.79 to 1.82 Å; the Na+ ion is close to a pair of oxygen atoms (Na
O: 2.29 Å), and the strong electrostatic attraction between the sodium ion and oxygen atom causes the other two Al
Ot bonds to weaken. Considering now the dimers, both AlSiO(OH)6
and Al2O(OH)62
have two hydrogen bonds within each cluster. However, with the inclusion 24104

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Figure 3. Optimized isomers of aluminosilicate species in COSMO solution: hexamers. 24105

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Figure 4. (a) Optimized isomers of aluminosilicate species in COSMO solution: three-rings, four-rings, and five-rings. (b) Optimized isomers of aluminosilicate species in COSMO solution: six-rings. 24106

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Table 1. Bond Angles (degrees) and Bond Lengths (angstroms) for Optimized Isomers of Aluminosilicate Clusters in COSMO Solution (Ob = Bridging Oxygen)

a

Ref 30. b Ref 31.

of Na+ ions, there is competition in both AlSiO(OH)6Na and Al2O(OH)6Na2 between the intramolecular hydrogen bonds and the interactions with Na+ ions. In AlSiO(OH)6Na, the Na+ ion coordinates to three O atoms in the tetrahedral position, whereas a single hydrogen bond forms opposite (Figure 1). It is worth noting that the atoms, which are involved in forming the intramolecular hydrogen bond, result in the smallest O
H distance of 1.77 Å, typical of hydrogen bonding. Moreover, because of the interactions with the Na+ ion, the Al
Ob
Si angle in AlSiO(OH)6
,5 of 115° (where b refers to the bridging oxygen), also increases to 131° in AlSiO(OH)6Na. In addition, the difference in valence for Si and Al atoms results in an unequal charge distribution and, as a consequence, a large difference in bond lengths to the bridging oxygen (Si
Ob: 1.65 Å, Al
Ob: 1.83 Å). The effect of bond elongation because of the interactions with Na+ ions is also noted in Al2O(OH)6Na2 (where the Al
Ot bond is 1.77
1.82 Å). The Al2O(OH)6Na2 has two Na+ ions, where each Na+ ion is also coordinated to three O atoms in both tetrahedral positions (Figure 1) and has a stronger framework
cation electrostatic attraction, constraining the Al
Ob
Al angle to be close to 180°. Hence, on comparing with the structures of Al(OH)4
, AlSiO(OH)6
, and Al2O(OH)62
,5 it is clear that the structural conformations of Al(OH)4Na, AlSiO(OH)6Na, and Al2O(OH)6Na2 are strongly influenced by the electrostatic interactions with Na+ ions rather than the effect of intramolcular hydrogen bonds. Turning now to the free energy for the formation of both AlSiO(OH)6 Na and Al2 O(OH)6 Na 2 in the gas phase and

“COSMO” solution, the two dimerization reactions are SiðOHÞ4 þ AlðOHÞ4
Naþ f ðOHÞ3 AlOSiðOHÞ3
Naþ þ H2 O

ð1Þ AlðOHÞ4
Naþ þ AlðOHÞ4
Naþ f ðOHÞ3 AlOAlðOHÞ3 2
Na2 2þ þ H2 O

ð2Þ The condensation energies for the calculations in both the gas phase and COSMO solution are given in Table 9. In the gas phase, we note that the free energy at 298 K is
60 kJ mol
1 for the Si
Al dimer and
106 kJ mol
1 for the Al
Al dimer. The lower energy of the Al
Al dimer condensation would appear to contradict Lowenstein’s rule, but hydrothermal synthesis occurs in aqueous media and, in the COSMO solution, the free energy at 298 K is
21 kJ mol
1 for the Si
Al dimer and
16 kJ mol
1 for the Al
Al dimer. Therefore, only when considering the effect of the solvent is the energy of formation for the Si
Al dimer more favorable than that for the Al
Al dimer. The electrostatic interactions between the gasphase clusters of the charge-neutralizing Na+ ions provide a high degree of stability for the Al
Al dimer, which is greatly reduced in solution. When the temperature for dimerization is increased from 298 to 450 K, the same trend can again be observed: the Si
Al dimer is the most favorable cluster in solution. Furthermore, our values (298 K:
21 kJ mol
1, 450 K:
23 kJ mol
1) are also close to the experimental value that was obtained from solubility measurement 24107

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Table 2. Bond Angles (degrees) and Bond Lengths (angstroms) for Optimized Isomers of Aluminosilicate Clusters in COSMO Solution (Ob = Bridging Oxygen)

(
21.56 ( 0.29 kJ mol
1).32 It is clear that in the process of dimerization, the Si
Al dimer is indeed the key cluster in the nucleation of zeolites, and the coordinated Na+ ion is also present in this dimer. We return to cluster energies in Section 3.3. Meanwhile, we concentrate on an analysis or the structural features of the larger clusters studied. 3.1.2. Geometrical Analysis for Trimers and Tetramers. We now extend our study to Al-containing isomers for both trimers and tetramers. For trimers (Table 1 and Figure 1), we consider the two types of isomers: first those in which only one Al atom is substituted (trimer A1 and trimer A2), and second, those in which two Al atoms are substituted (trimer B1 and trimer B2). The comparison between trimer A1 and trimer A2 indicates that the variation of bond lengths and T
O
T angles depends on the arrangement of the Al atoms (the charge distribution) and the Na+ coordination. Therefore, compared with trimer A1 with, the central Al atom, the Si
Ob bond lengths of trimer A2, with the terminal Al atom, vary considerably (1.62 to 1.65 Å), reflecting its asymmetrical structure. Next, we find that when each Na+ ion is coordinated to the nearest three O atoms to form an almost cyclic structure, the changes in the T
O
T angles for trimer A1 and trimer A2 seem to be controlled by the Na+ coordination: the effect of the electrostatic attraction between frameworks and the Na+ ions causes the range of T
O
T angles to become larger in the trimers. Other almost cyclic frameworks can also be found among the tetramers, pentamers, and hexamers discussed later. Table 1 shows that the range of Al
Ob
Si angles (132
166°) of trimer A1 is generally larger than the Si
Ob
Si angle (143°) and the Al
Ob
Si angle (141°) of trimer A2. Interestingly, the relative electronic energy indicates that trimer A1 is more stable

than trimer A2 (Table 5). Considering now trimer B1 and trimer B2, the variation of T
O
T angles for trimer B1 (127
145°) and trimer B2 (129
150°) is similar, but trimer B2 is more stable than trimer B1, as might be expected from the larger Al
Al separation. Moving to the tetramers, there are six different isomers with almost cyclic structures: two isomers with one Al atom and four isomers with two Al atoms (Table 1 and Figure 1). When only one Al atom is present in both tetramer A1 and tetramer A2, we find little difference in their geometries but a greater difference in numbers of intramolecular hydrogen bonds. As previously discussed, when these clusters include the counterion, there is competition between the intramolecular hydrogen bonds and the interactions of the Na+ ions. For tetramers containing two Al atoms, various Lowenstein and non-Lowenstein structures are considered. We note that the Al
Ob
Al angles (156
161°) are much larger than other T
O
T angles (125
143°) in nonLowenstein clusters (tetramer B1 and tetramer B2), owing to the close proximity of the Na+ ions. Furthermore, the large variation in the range of Al
Ob bond lengths (1.76
1.80 Å) is due to the effect of the charge distribution of the Al
Ob
Al bond. Similar behavior can also be noted regarding the Al distribution in the larger clusters discussed below. Energetic aspects of these clusters will be considered later. 3.1.3. Geometrical Analysis for Pentamers and Hexamers. Tables 2 and 3 show that there are 15 isomers for pentamers and 22 isomers for hexamers. No more than three Al atoms can be accommodated in such clusters without violating Lowenstein’s rule, and a large number of isomers is possible when three Al atoms are present in these clusters. It is also more difficult to achieve the Na+ coordination that avoids substantial framework 24108

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Table 3. Bond Angles (degrees) and Bond Lengths (angstroms) for Optimized Isomers of Aluminosilicate Clusters in COSMO Solution (Ob = Bridging Oxygen)

distortion, especially for asymmetrical clusters. As for the smaller clusters, the Na+ ion is more stable when binding with three or four O atoms when they are bonded to Al atoms rather than Si atoms as observed in crystallographic experimental data.30,31 As expected, we find that the Na+ coordination of all pentamers and hexamers has similar features. When we consider the Al
Ob
Si angle in the pentamers that contain two Al atoms, we find that the Al
Ob
Si angles of pentamer B4 are almost the same (129
130°). The location of the two Al atoms at each terminal site generates a high-symmetry structure in pentamer B4, which appears to assist the effective neutralization of the negative electronic density of Al atoms by the symmetrically distributed Na+ ions. We also find that the intramolecular hydrogen bonds tend to be symmetrical, although the effect of Na+ interactions dominates the hydrogen bonds in this framework. The highly symmetric frameworks of tetramer B4 and hexamer B3 are also similar to that of pentamer B4 (Figures 1
3). For clusters containing three Al atoms in both pentamers and hexamers, where we would expect stronger electrostatic interaction, we find that the Na+ ions occupy a large variety of sites. Similarly, larger Al
O
Al angles can be found in most non-Lowenstein frameworks in both pentamers and hexamers. Interestingly, this feature is also seen when the Al
O
Al
O
Al bridge forms in non-Lowenstein frameworks of hexamers. The range of Al
O
Al angles is

more extended than others, particularly in hexamer C9 (119
176°) and hexamer C10 (120
165°), which is due to all Na+ ions closely coordinating to O atoms, which are bonded to Al atoms. We now turn to consider clusters in which only one Al atom is substituted in both pentamers and hexamers. There is again competition between the intramolecular hydrogen bonds and the interaction of the Na+ ion in these clusters; but we find that the former is dominant. A previous study indicated that there are certain intramolecular hydrogen bonds in different pure silica clusters that strongly influence their conformations.33 The conformations with a high Si/Al ratio should also be affected by intramolecular hydrogen bonds. Compared with other aluminosilicate clusters, the Si
O
Si angles vary notably in both pentamers and hexamers with only one Al atom, as shown by the results in Tables 2 and 3. 3.2. Cyclic Clusters. Open clusters may condense to form more stable and constrained cyclic clusters, which are thought to play an important role in the nucleation process of aluminosilicate zeolites. Known zeolites are made up of various rings, especially four-rings, five-rings, and six-rings; understanding their conformation is therefore of considerable importance. In this section, possible rings are identified with different Si/Al ratios and atomic arrangements of Si and Al atoms for clusters which both do and do not accord with Lowenstein’s and Dempsey’s rule. 24109

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Table 4. Bond Angles (degrees) and Bond Lengths (angstroms) for Optimized Isomers of Aluminosilicate Clusters in COSMO Solution (Ob = Bridging Oxygen)

Table 4 shows some geometric parameters for different isomers of three-rings, four-rings, five-rings, and six-rings. Several trends regarding these cyclic isomers are the same as those for the open isomers discussed above. The results can be summarized as follows: (a) The bond length range of Si
O and Al
O is 1.62 to 1.70 and 1.74 to 1.84 Å, respectively. (b) The Al
O
Al angle in most cyclic clusters is still nearly as large as that in the open ones, reflecting the fact that Na+ ions are close to the framework. (c) The counterion Na+ tends to coordinate with three or four O atoms. We now analyze in more detail the most significant aspects of the cyclic isomer structures. The three-ring is the smallest ring in zeolites, and previous NMR studies also showed the presence of a three-ring framework in the synthesis gels for aluminosilicate zeolites;12 it is, however, rare in zeolite frameworks. We can see that in three-ring A, the Na+ ion that is closer to three axial O atoms results in near triangular coordination with a significantly smaller T
O
T angle of (122
126°) compared with the experimental data for zeolite A: 142
164°.30 The other rings including four-rings, five-rings, and six-rings are important and basic units in constructing various zeolites. It is notable that both four-ring B1 and six-ring C1 have high symmetry (Figure 4). In four-ring B1, each Na+ ion is equally bonded to four equidistant O atoms and forms square-pyramidal coordination.

Such a highly symmetrical structure also makes the Al
O
Si angles more similar (134
138°). In six-ring C1, each Na+ ion is also arranged in a suitable position to coordinate with three or four O atoms. One is located at the central point so as to bond with O atoms in this structure, increasing the electrostatic attraction between the Na+ ion and the O atoms and decreasing the electrostatic repulsion of Na+ ions with each other. Figure 4b shows that the six-ring C1 structure is similar to the chair conformation in the same way as the most stable carbon six-ring structure. In addition, a large range of the Al
O
Si angles (125
141°) is found in the highly symmetrical six-ring C1 and in other cyclic isomers. The large distortion that occurs in cyclic clusters might be due to the closed cyclic rings being particularly constrained structures and the limited steric arrangement of the Na+ ions. Such a large range in the T
O
T angle could decrease the effect of ring strain in cyclic rings, and favor the electrostatic attraction between Na+ ions and O atoms. Once again, there is again competition between the intramolecular hydrogen bonds and the interaction of the Na+ ion in these rings. Most intramolecular hydrogen bonds in both fivering A and six-ring A with only one Al atom are arranged in an almost circular form above the plane formed by Si and Al atoms, with the Na+ ion located below. The intramolecular hydrogen bonds indeed control the conformation of rings containing few 24110

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Table 5. Relative Energies (kJ mol
1) of Aluminosilicate Isomers: Trimers and Tetramers in Gas Phase and COSMO Solution

Table 6. Relative Energies (kJ mol
1) of Aluminosilicate Isomers: Pentamers in Gas Phase and COSMO Solution

Al atoms. Furthermore, Wakihara et al.15 recently employed high-energy X-ray diffraction (HEXRD) to investigate the formation of four-rings, five-rings, and six-rings in the nucleation process of different aluminosilicate zeolites and found ring structures with sizes in the range of 3.5 and 6 Å between the most distant atoms in the rings. These results correspond closely to our calculated values of 3.31
5.86 Å for four-rings, five-rings and six-rings. In summary, the geometric parameters of Lowensteinian rings: the range of T
O bond lengths is 1.62
1.84 Å compared with 1.58 to 1.74 Å for zeolite A and 1.61 to 1.72 Å for zeolite X.30,31 The range of the T
O
T angle is 125
151° compared with 142
164° for

zeolite A and 134
144° for zeolite X. There are differences in bond angles and bond lengths in Lowensteinian clusters compared with experimental crystallographic results for zeolites. The difference in values is due to the calculated clusters being “loose” structures and not constrained as when a component of a crystal. 3.3. Relative Energies of Open Clusters. We now return to an analysis of the relative energies of the clusters depending on the number of Al atoms in these clusters and compare their energy differences in the gas phase and solution. The calculated relative energies are given in Tables 5
8. First, when only one Al atom substitutes for Si atom in these open clusters, the Al atom has a lower energy at an interior site in the 24111

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Table 7. Relative Energies (kJ mol
1) of Aluminosilicate Isomers: Hexamers in Gas Phase and COSMO Solution

cluster, both in the gas phase and in solution, which has important implications in subsequent condensations; indeed, confirmation that the ends of aluminosilicate chains in solution will be siliceous is very significant. With the Al atom located in the interior site, it is possible to form more intramolecular hydrogen bonds that can stabilize the clusters, whose stability seems not to be strongly influenced by the interaction of the Na+ ion but is greatly influenced by intramolecular hydrogen bonds. Moreover, symmetry has an interesting effect on the relative energies of these clusters. Pentamer A3 is a highly symmetric structure, where the negative charge can be distributed evenly in its framework but has a higher relative energy. Conversely, pentamer A2 with low symmetry but more intramolecular hydrogen bonds has a lower relative energy. Considering now isomers with two Al atoms in the gas phase, the most stable are found to have a maximum separation between the two Al atoms in their frameworks. These isomers such as tetramer B4, pentamer B4, hexamer B1, and hexamer B3 (the relative energies of both hexamer B1 and hexamer B3 are very similar (within 4 kJ mol
1)), as expected, have high symmetry,

less geometric distortion, and average charge distribution and are more stable than other isomers. However, the effect of solvation on these isomers causes major changes for pentamers and hexamers. The relative energies of pentamers B2 and B3 are essentially the same (