Topological Descriptor for Oxygens in Zeolites. Analysis of Ring

Mar 26, 2009 - Topology of zeolite nets has been studied in terms of rings. A freely available software tool for the calculation and systematic analys...
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J. Phys. Chem. C 2009, 113, 6398–6405

Topological Descriptor for Oxygens in Zeolites. Analysis of Ring Counting in Tetracoordinated Nets German Sastre* and Avelino Corma Instituto de Tecnologia Quimica U.P.V.-C.S.I.C., UniVersidad Politecnica de Valencia, AVenida Los Naranjos s/n, 46022 Valencia, Spain ReceiVed: NoVember 13, 2008; ReVised Manuscript ReceiVed: February 27, 2009

Topology of zeolite nets has been studied in terms of rings. A freely available software tool for the calculation and systematic analysis of the rings in zeolite nets is presented. Ring indices, associated to T (tetrahedral) and O atoms, are defined as a new topological concept. Ring count is also proposed as a topological descriptor of a structure which gives a fingerprint of the rings (number and size) in a zeotype. These topological concepts are linked with chemical descriptors and used together to systematize and characterize useful information on zeolites such as ring occurrence and TOT angles between different structures. Ring indices of O-sites can be employed to characterize the location of protons in acid zeolites giving a structured information on the ring environment of each active site. 1. Introduction The design of new materials within solid state chemistry is strongly based on our knowledge of the general rules which dictate order at the short and long-range in matter. Designed (hypothetical) structures can be assessed as feasible or unfeasible on a particular energy landscape, and order can be recognized as a common element of stable structures. The mathematical understanding of three-dimensional nets has allowed a more systematic classification of nets. Covalent networks, with welldefined chemical bonds, are naturally suited to the mathematical concepts of connectivity and coordination, such as those introduced by Wells.1 Later developments include the realization by Andersson et al.2 and by Nesper and von Schnering3 that zero potential surfaces in solids can be described by periodic minimal surfaces. Axiomatic theory was put forward in the first attempt to describe crystal solids as built from small units or building blocks by O’Keeffe et al. in 1978.4 More recently, chemical networks were described as periodic subdivisions of space (tiles) by Delgado-Friedrichs et al.,5,6 where tiles relate to algebraic rules through the definition of Delaney-Dress symbols. This mathematical approach allows all possible networks containing a predefined number of different tiles to be described and enumerated and has been extensively used to classifymaterialssuchaszeolitesandmetal-organicframeworks.7,8 Descriptions of structures through tilings of 3-D space by simple polyhedra (those with three edges meeting at each vertex) is the most simple case, but in certain structures this decomposition can not be achieved and the description in terms of tiles becomes more difficult. Structure taxonomy becomes numerically difficult for networks which can not be described by a few tiles, and hence other topological descriptors, equally useful to describe structures regardless complexity, are also of interest as it is the case of vertex symbols. Vertex symbols for zeolite nets were introduced by O’Keeffe and Hyde in 1997,9 where rings are the main descriptor. According to Bernal,10 rings, rather than coordination numbers,11 first applied to zeolites by Meier and Moeck12 and shortly after * To whom correspondence [email protected].

should

be

addressed.

E-mail:

by Brunner,13 should be the primary topological measure of covalently bonded networks. Rings were introduced as topological descriptors through Schla¨fli symbols by Wells1 in the 1970s, but it was not until the early 1990s that the first description of tectosilicates in terms of rings was made by Stixrude and Bukowinski,14 where a simplified treatment based on clusters of significant size allowed average ring size to be related with framework density. A study by Curtis and Deem15 showed ring histograms in real and hypothetical zeolite structures and this helped to establish, based on energetic grounds, that uncommon rings containing between 14 and 18-Si are not particularly unstable. Zeolites containing such rings are likely to be synthesized in the future if adequate structure directing agents are employed. Aspects related to stability of rings in zeotypes involve not only topological aspects but they also require the definition of a mathematical function which describes the energy of the ring in terms of how far/close is the geometry of the ring constituents (T and O atoms) from the equilibrium. Considering equilibrium values for Si-O distances and Si-O-Si angles, as well as a mathematical function of energy variation depending on these two variables, we16 studied the strain associated to rings in pure silica zeolites and found no particular ring-size (except 3-rings) associated to strain. Rather, strain is associated to particularly stressed rings regardless of their size. Small rings tend to show less variability of minimum energy conformations, and thus zeolites with a large number of small rings may have a considerable proportion of them strained, with this increasing the energy of the material. This is the case of faujasite which contains a large number of 4-rings.17,18 The knowledge of rings in a structure allows a better understanding of its properties. Brunner and Meier19 suggested a relation between smallest ring size and lowest framework density. All nets considered in this study refer to zeolite framework types compiled in the sixth edition of the Atlas of Zeolite Framework types,20,21 which includes 176 types containing between 1 and 24 different vertex symbols. Topological descriptors have been defined to characterize Si (vertices) but not to characterize O (edges). Ring indices for oxygen atoms are defined in this study from the characterization of the rings

10.1021/jp8100128 CCC: $40.75  2009 American Chemical Society Published on Web 03/26/2009

Topological Descriptor for Oxygens in Zeolites

J. Phys. Chem. C, Vol. 113, No. 16, 2009 6399 TABLE 1: Rings and Vertex Symbols in GIS and MON Uninodal Zeolite Netsa b

ring count average ring size vertex symbols average ring size from vertexc

Figure 1. Multiple rings are very common in zeolite nets and they consist on rings with at least one O-T-O triad of atoms in common. This fragment corresponds to MON net. Two O-T-O opposite paths are shown around the central T atom (highlighted). One of the paths defines a 5-ring (lower left part) while the opposite path (O1-T-O2) surrounds two 8-rings. The corresponding vertex pair (see Table 1) is therefore 5 · 82.

passing through each oxygen atom. This allows a clear distinction between the environment (size and number of rings) of each oxygen site. Rings indices for T-sites have also been defined as well as the ring counting of all of the rings in a zeolite net. 2. Topological and computational details 2.1. Rings and Vertex Symbols in Zeolite Nets. Zeolite networks have the chemical composition TX2, where T is a tetrahedral atom (mostly Si or Al) and X (mostly O22) is a bridging atom between two T atoms by forming a T-O-T linkage. T atoms are topologically surrounded (chemically bonded) by four O atoms in a tetrahedral configuration and tetrahedra are connected to each other by corner-sharing O atoms which are bicoordinated. Rings are formed by (Si-O)n (n > 2) units and we will refer to them as n-rings. Rings are only considered if they can not be decomposed into smaller rings through shortcuts (see Figure 8 in ref 14), and all throughout this study “ring” will be used as a synonym of “valid ring”. A similar definition has been given in a previous study.23 Vertex symbols for zeotypes are of recommended use by the International Zeolite Association20,21 as useful topological descriptors which provide -together with the coordination sequence- a fingerprint of a framework type. Vertex symbols in four coordinated networks are six numbers consisting on the smallest valid ring sizes corresponding to each of the six possible Oi-T-Oj (i,j ) 1-4, j > i) angles (paths) that define a ring. The shortest circuit at an angle is just the shortest path along edges of the net that starts out along one edge (Oi) of the angle and returns to the starting point along the other edge (Oj) of the angle (Figure 1). Valid rings are those which can not be decomposed into smallest rings. The six numbers obtained as indicated above should then be ordered to form the vertex index as follows: (i) the symbols for opposite pairs of angles are grouped together; (ii) subscripts indicate the number of rings of a given size at each angle (a number larger than 1 indicates the presence of “multiple rings”); (iii) the symbols are ordered, subject to the constraint (i), so that shortest rings come first.9 2.2. Classification of Rings in Zeolite Nets. A systematic ring counting in zeolites can not be based on the use of vertex symbols. The reason is that when counting rings from the vertex

GIS

MON

412 · 88 5.60 4 · 4 · 4 · 82 · 8 · 8 5.60

44 · 516 · 812 6.00 4 · 5 2 · 5 · 82 · 5 · 82 5.81

a The correct average ring size can only be obtained from ring counting and not from vertex symbols. b Corresponding to a T16O32 unit cell. Calculated with our ring counting algorithm. c The number of rings of a given size, calculated from vertex, is the number of tetrahedra multiplied by the number of rings in vertex and divided by the ring size. For example, in GIS (with a 16 TO2 unit cell), the number of 4-rings is equal to 16 × 3/4 ) 12, and the number of 8-rings is equal to 16 × 4/8 ) 8. This is coincident with the ring counting algorithm. If, on the other hand, the ring counting from vertex is used to calculate the number of 8-rings in MON (with a 16 TO2 unit cell), the result is 16 × 1/4 ) 4 (4-rings), 16 × 4/5 ) 12.8 (5-rings), and 16 × 4/8 ) 8 (8-rings), which is different from the correct values from the ring counting algorithm.

symbols, it is considered that each n-ring belongs to n vertices, and the number of rings per vertex for a given vertex is the sum of the reciprocals of the sizes of the rings at that vertex.9 This is valid for structures with at most one pair of vertex symbols including subscripts (multiple rings), but it is not valid in the general case (see explanation in Table 1). This is why we have implemented a “ring counting” procedure. A case illustration of its need appears in Table 1, showing that the MON net can not be ring-counted from vertex symbols, which give a wrong answer (5.8) compared to the correct value (6.0) given from the ring counting algorithm. Although the vertex procedure to count rings may also give correct values, as in GIS (Table 1), it is not valid in the general case. Average rings sizes calculated from vertex indices do not take into account all of the rings in the framework, although they provide a reasonable approximation in most cases. A complete counting of rings requires a specific computer algorithm able to localize all rings included in each Oi-Tx-Oj path at a fixed Tx (6 paths per Tx), and throughout every tetrahedral atom (Tx) in the structure. Each ring has to be counted with its specific multiplicity (Figure 1). Without going into programming details, our computer algorithm is based on the connectivity list of each atom obtained from the crystallographic information of the unit cell. Within a given pathdirection in Oi-Tx-Oj (r Oi-Tx or Tx-Oj f), the algorithm calculates the connections from either side of the path up the nth neighbors and detects a ring through the presence of a common atom in both paths. Further subroutines store relevant information and ensure that rings do not contain shortcuts and are not repeated. A simple illustration of the information provided by this algorithm which characterizes every ring is presented in Table 2 corresponding to faujasite. With the use of the algorithm, a unit cell (Si192O384) of faujasite is found to contain 144 4-rings, 64 6-rings, and 16 12-rings. The rings were fully characterized by their atom constituents and also bonds and angles were calculated. Another simple case is reported for all the zeolite nets containing one T-site and multiple rings (Table 3). 2.3. Definition of “Ring Index”. As explained above, the classification of rings in zeolites suggests that an index could be defined with the property of giving information about all the rings present in a structure. In this regard, a first point to take into account is the fact that rings are made of vertices (corresponding to T-atoms) and edges (corresponding to oxygen

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Sastre and Corma

TABLE 2: Rings of Faujasitea ring countb average ring size vertex symbols 4-ring TOT angles 6-ring TOT angles 12-ring TOT angles b

4144 · 664 · 1216 5.14 4 · 4 · 4 · 6 · 6 · 12 T-O1-T-O2-T-O1-T-O3 142, 143, 142, 146 T-O3-T-O2-T-O3-T-O2-T-O3-T-O2 146, 143, 146, 143, 146, 143 T-O1-T-O4-T-O1-T-O4-T-O1-T-O4-T-O1-T-O4-T-O1-T-O4-T-O1-T-O4 142, 142, 142, 142, 142, 142, 142, 142, 142, 142, 142, 142

a The values of the TOT angles correspond to the unit cell reported in the Atlas of Zeolite Framework Types (a ) 24.345 Å). Corresponding to a T192O384 unit cell.

TABLE 3: Rings, Average Ring Sizes, and Vertex Symbols of All Uninodal Zeolite Nets with Multiple Rings net

ring counta

average ring sizeb

vertex symbolsc

ABW ACO AFI ANA ATO BCT DFT GIS MER MON NPO

44 · 64 · 84 412 · 812 46 · 652 424 · 616 · 896 49 · 654 42 · 68 44 · 68 · 810 412 · 88 424 · 816 44 · 516 · 812 32 · 66

6.00 6.00 5.79 7.06 5.71 5.60 6.55 5.60 5.60 6.00 5.25

4 · 6 · 4 · 6 · 6 · 82 4 · 82 · 4 · 82 · 4 · 82 4 · 62 · 6 · 63 · 62 · 63 4 · 4 · 6 · 6 · 8 4 · 84 4 · 62 · 6 · 62 · 6 · 63 4 · 62 · 6 · 6 · 6 · 6 4 · 4 · 62 · 83 · 62 · 83 4 · 4 · 4 · 82 · 8 · 8 4 · 4 · 4 · 82 · 8 · 8 4 · 52 · 5 · 82 · 5 · 82 3 · 62 · 6 · 6 · 6 · 6

a Corresponding to the unit cell as given in the Atlas of Zeolite Structure types. The respective number of TO2 units in each unit cell is 8, 16, 24, 48, 36, 8, 8, 16, 32, 16, 6. b Average ring size is calculated by a simple average from the ring count. c Vertex symbols,9 unlike ring counts, are not a new definition but they are included here in order to make clear that both topological descriptors are not related to each other.

atoms) and therefore a “ring index” needs to be defined for each type of atoms. Second, rings associated to T-atoms and O-atoms are not necessarily related as they belong to different parts of the net (vertices and edges). We define the ring index associated to an atom as the list of rings (size and number) which passthrough (contain) that atom. 3. Results and Discussion 3.1. Ring Indices in Zeolite Nets. Zeolite networks can be classified according to the ring channels present in their structure. Appendix E of the Atlas20,21 contains such classification. An interest in rings arises from the fact that their size and occurrence influences important physicochemical properties related to their microporosity; hence, applications in catalysis and separation processes heavily depend on the structure of rings. For this reason, the availability of the ring indices which associate the rings present in a structure with their atomic constituents is convenient (T- and O-atoms). To illustrate ring indices, the simple case of faujasite follows. Faujasite (FAU) contains one T-atom and four O-atoms and topologically is a simple net because it consists of a unique T-site without multiple rings (Table 2). The corresponding ring indices are listed in Table 4. In this particular case, but not in a general case, it can be seen that the ring index is a condensed form of the vertex index. The O-sites contain three rings, which is a fingerprint of a structure than can be described from packings of finite polyhedra where three polyhedra meet at an edge, and three rings meet at an edge (more details are given in the Supporting Information). Topological differences between O1-O4 (Figure 2) become clear-cut from their corresponding ring indices where it can be seen that different environments

TABLE 4: Ring Indices of Faujasite (FAU) Unique Atomsa atom

ring index

T O1 O2 O3 O4

43 · 62 · 12 42 · 12 42 · 6 4 · 62 4 · 6 · 12

a A unit cell of faujasite (T192O384) contains 192 T, 96 O1, 96 O2, 96 O3 and 96 O4 atoms. See also Figure 2.

appear for each oxygen atom. Some oxygens are associated to 4- and 12-rings (ring index 42 · 12 for O1), 4- and 6-rings (42 · 6 and 4 · 62 for O2 and O3 respectively), and 4-, 6-, and 12-rings (4 · 6 · 12 for O4). To further illustrate the concept of ring index, ring indices for all of the zeolite nets containing only one T-site and containing multiple rings in their vertex sites are included in Table 5. A simple derivation of how the ring counting can be obtained from the ring indices can be found in the Supporting Information. Ring indices, therefore, present three useful applications: (i) number of rings of each size in a net can be calculated, which we call “ring count”; (ii) average ring size of a net can be calculated; and (iii) they give the information about the topological ring environments of T- and O-sites in nets. As a particular case, the average ring size of AFI is 5.79 (see details in the Supporting Information), and this value can not be obtained from the vertex index.24 Hence, this is one of the reasons which makes the ring index a valuable tool for the topological analysis of nets. 3.2. Rings Wider than the Shortest Are Not Contained in Indices. A univocal definition of rings around a Oi-Tx-Oj path requires us to take only the shortest ring size (with its corresponding multiplicity) but wider rings around such path may also exist. This is the case, for example, of AFI net. Figure 3 shows a path for which the shortest is a 6-ring but also a 12-ring exists, and this is what we call “ring wider than the shortest”. Rings wider than the shortest do not appear in ringindices but sometimes they are of interest. In the case shown, 12-rings do not appear in the ring indices (see values for AFI in Table 5) but they are useful to characterize the AFI net in terms of porosity and catalytic activity.25 The algorithm presented contains the possibility of selecting rings of an upper limit size wider than shortest rings and this allows the study of these kinds of rings. Table 6 shows some data of 12-rings in structures AFI, ATO, and NPO which do not appear in the ring indices (nor in vertex indices) and are important from the topological and chemical viewpoints. Our software contains a switcher parameter which allows us to turn on a modified algorithm in order to take into account wider rings and include them in the ring count.

Topological Descriptor for Oxygens in Zeolites

J. Phys. Chem. C, Vol. 113, No. 16, 2009 6401 TABLE 5: Ring Indices of the Unique Atoms of All Uninodal Zeolite Nets Containing Multiple Rings net a

ABW ACOb AFIc ANAd ATOe BCTf DFTg GISh MERi MONj NPOk

T

O1

O2

O3

42 · 63 · 84 43 · 86 4 · 613 42 · 62 · 816 4 · 69 4 · 66 42 · 66 · 810 43 · 84 43 · 84 4 · 5 5 · 86 3 · 66

42 · 82 86 68 4 · 6 · 88 66 64 4 · 6 4 · 85 42 · 8 42 · 8 52 · 84 3 · 62

4 · 62 · 8 42 · 82 4 · 66

62 · 84

4 · 65 4 · 62 4 · 6 4 · 84 4 · 83 42 · 8 4 · 5 2 · 83 64

O4

65

4 · 67

4 · 62

65

4 · 86 4 · 83 54 · 82

4 · 83

a Composition: 8 TO2: 8 T, 4 O1, 8O2, 4O3. b Composition: 16 TO2: 16 T, 8O1, 24 O2. c Composition: 24 TO2: 24 T, 12 O1, 12 O2, 12 O3, 12 O4. d Composition: 48 TO2: 48 T, 96 O1. e Composition: 72 TO2: 72 T, 36 O1, 36 O2, 36 O3, 36 O4. f Composition: 16 TO2: 16 T, 16 O1, 16 O2. g Composition: 8 TO2: 8 T, 8 O1, 4 O2, 4 O3. h Composition: 16 TO2: 16 T, 16 O1, 16 O2. i Composition: 32 TO2: 32 T, 16 O1, 16 O2, 16 O3, 16 O4. j Composition: 16 TO2: 16 T, 8 O1, 16 O2, 8 O3. k Composition: 6 TO2: 6 T, 6 O1, 6 O2.

Figure 2. Perspective views of ring indexes associated to the unique atoms in faujasite (Table 4). Top left: T-atom showing rings 43 · 62 · 12; top-right: O1 (central atom) showing 42 · 12 rings; bottom-left: O2 (central atom) showing 42 · 6 rings; bottom-middle: O3 (central atom) showing 4 · 62 rings; bottom-right: O4 (central atom) showing 4 · 6 · 12 rings. See also Table 4.

Figure 3. Fragment of the AFI topology. Two rings around the highlighted O-T-O link can be seen: a 6-ring and a 12-ring. Of these two rings only the shortest is considered in the vertex index. A consistent definition useful for ring counting suggests to stick to shortest rings, but the possibility of counting rings wider than the shortestrings allows, in a number of cases, a better characterization of the zeolite topology.

3.3. TOT Angles and Ring Size. The algorithm presented allows the possibility to calculate the TOT angles associated to each ring size. It is not clear whether certain ring sizes are associated to the presence of certain TOT angles. This is a point which goes beyond strictly topological arguments and relates to thermodynamics. Energetically favored TOT angles depend on the chemistry of the T-atoms, and, for example SiOSi equilibrium angles are roughly 144°,26-30 while equilibrium GeOGe tends to be about 130°.31-33 In Si,Ge-zeolites, TOT positions restricted to be lower than ∼140° will preferentially be occupied by Ge rather than Si.34-40 Sticking to the most usual case of zeolite nets as silicates, computational chemistry studies indicate SiOSi angles of 130°, 143°, 147°, and 149° in 3- to 6-rings respectively according to a study by van Santen et al. 41

based on clusters whose terminating atoms are not subjected to constraints of nets; and similar conclusions can be drawn from the study of Kudo et al.,42 although in this study the results depend strongly on the symmetry of the ring. Our geometric study has been performed by taking the geometries and symmetries from the CIF files provided by the International Zeolite Association.21 A further analysis is presented in the Supporting Information by minimizing such structures with a forcefield under SiO2 composition and keeping the symmetry. Our algorithm allows to study in detail the TOT composition of rings of different sizes. Just for the sake of analysis we choose a subset of the zeolite nets whose largest channel contains 10rings, and we analyze all TOT angles according to the rings they belong to. Table 7 shows the range of values (minimummaximum) found in each case. It is clear that 3-rings are characterized by very low values of TOT angles, but further than that, it is not easy to establish trends in larger rings since in all cases values in the range 140-180° can be found. A graphical representation of the individual values of all TOT angles can be seen in Figure 4 (bottom) which indicates that TOT angle values between 130-180° can be found in 4-, 5-, 6-, 8-, and 10-rings. 7- and 9-rings show a narrower span due to the smaller sampling as they are less usual rings, but in any case they also show a considerable variety: 140-160°. TOT averages (Figure 4, top) give a less blurred picture and they are calculated as follows. For each individual ring, the average of the n TOT angles of a n-ring is calculated and plotted. It may -incorrectly- be thought that only 3-rings bear TOT angles close to 130°, and because of that it might seem surprising that there are some 10-rings whose average TOT angles are below 140° (Figure 4, top). They correspond to structures WEI (average TOT in 10-rings equal to 137°) and OBW (average TOT in 10-rings equal to 131°), and these structures also contain 6and 8-rings with average TOT values below 140°. Another interesting finding from Figure 4 (top) is the fact that maximum average TOT values increase in 4-, 5-, and 6-rings, which seems to be in agreement with previous findings.41,42 Larger rings such as 8- and 10-rings do not show the same trend of increasing maximum average TOT value and in fact, such rings (specially 8-rings) seem to contain TOT values close to the (SiOSi) equilibrium value (ca. 145°) which justifies the large occurrence

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TABLE 6: 12-Rings of AFI, ATO, and NPO Netsa AFI: ring countb 12-ring TOT angles ATO: ring countc 12-ring TOT angles NPO: ring countd 12-ring TOT angles

46 · 652 · 122 T-O2-T-O3-T-O2-T-O3-T-O2-T-O3-T-O2-T-O3-T-O2-T-O3-T-O2-T-O3 155, 149, 155, 149, 155, 149, 155, 149, 155, 149, 155, 149 49 · 654 · 836 · 1260 T-O3-T-O4-T-O3-T-O4-T-O3-T-O4-T-O3-T-O4-T-O3-T-O4-T-O3-T-O4 143, 164, 143, 164, 143, 164, 143, 164, 143, 164, 143, 164 32 · 66 · 1220 T-O1-T-O2-T-O1-T-O2-T-O1-T-O2-T-O1-T-O2-T-O1-T-O2-T-O1-T-O2 132, 154, 132, 154, 132, 154, 132, 154, 132, 154, 132, 154

a Such rings -in these three nets- do not belong to the class of shortest rings, but a parameter can be changed in our software tool in order to account for them. The values of the TOT angles correspond to the unit cell of maximum symmetry reported in the Atlas of Zeolite Framework Types. b Corresponding to a T24O48 unit cell. c Corresponding to a T36O72 unit cell. d Corresponding to a T6O12 unit cell.

TABLE 7: Range of TOT Angles (deg) in All Zeolite Nets Containing 10-Rings as the Largest Channel Systema net AEL AFO AHT CGF CGS DAC EUO FER HEU IMF ITH LAU MEL MFI MFS MTT MWW NES OBW PON RRO SFF SFG STF STI SZR TER TON TUN WEI

4-ring 137-147 146-147 125-180 129-150 138-146 156-165 143-177 140-158 143-175 142-176 141-149 143-151 145-152 144-151 139-175 152-163 159-160 134-162 127-170 132-173 145-174 136-177 143-151 149-152 149-153 142-172 138-146

5-ring

6-ring 137-180 140-180 125-180 129-160 141-144

143-180 142-180 150-180 139-158 142-180 141-159 141-168 131-165 144-165 157-172 141-163 142-180 129-134d

142-180 159-171 142-169 141-176 141-149 144-167 134-165 146-164 157-177 141-180 142-180 134-169

127-172 133-173 140-178 134-177 141-151 149-180 142-180 150-159 133-172 130-132d

133-165 140-178 134-174 144-151 149-155 142-180 155-180 133-172 130-139

8-ring

TABLE 8: Rings and Average Ring Sizes of All Zeolite Nets Containing 10-Rings as the Largest Channel System

10-ring b

138-160 138-146 143-165 150-171 140-157 141-159c 144-148 146-165

129-160 134-164 127-172 140-172e 141-168 150-180 142-156 131-146

146-161 146-180b 125-180b 129-150 138-145 143-180 147-156 150-171 139-157 142-176 141-158 141-144 141-164 131-161 144-165 157-165 139-180 149-161 129-133 134-169 127-172 132-152 142-172 136-159 144-168 149-159 142-180 150-160 133-172 130-146

a Structures taken from the Atlas of Zeolite Framework Types. 10-rings do not appear in vertex symbols. c 9-rings. d 3-rings. e 7-rings. b

of such rings in zeolite nets. Zwijnenburg and Bell43 give average TOT values between 143 and 149 for 8-, 12-, and 16rings although in a very limited sampling, and their study suggests that rings larger than 16-rings are not particularly unstable in silica composition. A study by Akporiaye and Price44 indicates that structures with high proportion of 4-rings tend to be less stable than structures with high proportion of 5- and 6-rings. This seems to hint that 4-rings should tend to have SiOSi angles more energetic than those of 5- and 6-rings. Brunner and Meier19 suggested that a lower framework density limit exists for zeolite nets, and this limit becomes smaller as the smallest-ring-size of the net decreases. Considering the approximation that silicate zeolite structures increase their stability as the framework density increases,18,44 it can be inferred that zeolites with low smallest-

net

#TO2a

ring countb

average ring size

AEL AFO AHT CGF CGS DAC EUO FER HEU IMF ITH LAU MEL MFI MFS MTT MWW NES OBW PON RRO SFF SFG STF STI SZR TER TON TUN WEI

40 40 24 36 32 24 112 36 36 288 56 24 96 96 36 24 72 136 76 24 18 32 74 32 72 36 80 24 192 20

48 · 684 · 104 48 · 684 · 104 48 · 652 · 104 420 · 640 · 86 · 104 424 · 64 · 832 · 104 42 · 524 · 84 · 108 48 · 596 · 644 · 104 · 1224 540 · 62 · 84 · 108 · 124 412 · 524 · 86 · 104 424 · 5256 · 684 · 1072 · 128 418 · 520 · 640 · 98 · 108 412 · 624 · 108 410 · 580 · 632 · 812 · 1024 44 · 588 · 636 · 1028 44 · 532 · 64 · 88 · 104 58 · 618 · 102 424 · 548 · 638 · 1018 412 · 5128 · 648 · 108 · 1240 348 · 42 · 828 · 108 412 · 628 · 84 · 1020 46 · 512 · 82 · 108 46 · 524 · 610 · 102 418 · 526 · 660 · 78 · 108 46 · 524 · 610 · 102 432 · 532 · 632 · 820 · 108 412 · 516 · 68 · 812 · 1012 416 · 548 · 656 · 1036 58 · 618 · 102 420 · 5168 · 652 · 812 · 1036 · 1212 · 164 38 · 44 · 64 · 84 · 104

6.00 6.00 6.00 5.83 6.50 6.32 6.27 6.41 5.57 6.07 6.00 6.18 6.13 6.10 5.85 6.00 5.81 6.51 5.30 7.00 6.43 5.33 5.82 5.33 5.81 6.53 6.41 6.00 6.24 5.67

a Number of TO2 per unit cell. b Some nets contain rings larger than 10, but they do not form channels.

ring tend to be increasingly unstable. The work by Brunner and Meier indicates that sufficiently low density polymorphs require the presence of 3-rings, as it is the case of RWY and ITQ-33,45 but an opposite conclusion appears in the work by Zwijnenburg and Bell,43 where an arbitrarily low density can be achieved (without 3-rings and) with a sufficiently high number of 4-rings. It is clear, therefore, that the presence of large rings does not necessarily require 3-rings, and examples of that are ETR and VFI, which contain 18-rings and whose smallest rings are 4-rings. Curtis and Deem15 studied a very large sampling of hypothetical zeolite nets and they argued that the presence of large rings does not require 3-rings. Zwijnenburg et al.46 demonstrate, within a topological approach based on polyhedra, that large rings require small rings as compensation so that the average ring size belongs to an interval of chemical stability. Our data from 10-ring-channel zeolite nets can be organized

Topological Descriptor for Oxygens in Zeolites

J. Phys. Chem. C, Vol. 113, No. 16, 2009 6403 TABLE 9: Rings and Average Ring Sizes of Selected Zeolites Belonging to the ABC-6 Family20,21,51 net

#TO2a

ring count

average ring size

CHA GME OFF ERI

36 24 18 36

427 · 66 · 89 418 · 64 · 86 412 · 66 · 83 424 · 612 · 86

5.14 5.14 5.14 5.14

a

Figure 4. n-rings are made of n-TOT links whose values for all zeolite nets containing 10-rings as the largest channels are plotted (bottom). Plot of the average of the n-TOT angles of each n-ring (top). A list of the zeolite nets considered appears in Table 7. Geometries correspond to the structures reported in the Atlas.20,21

Figure 5. Number of rings of each size throughout all of the zeolite nets containing 10-rings as the largest channel size. A list of the zeolite nets considered appears in Table 7.

according to the total number of rings of each size and the results (Figure 5) show that 10-rings (present in all structures considered) are accompanied, on average, by a large number of 6and 5-rings, and -in lower proportion- 4-rings. When considering the whole set of zeolite nets, 4-rings are the most abundant (see Figure 1 in reference 15), but when 10-ring-channel nets are considered, the 6- and 5-rings are preferred in order to compensate the 10-rings and lower the average ring size. Typical average ring sizes, as calculated from the 10-ring-channel zeolites, give values in the range 5.5-6.5 (Table 8), and this shows a preference (in aluminosilicates) of 5- and 6-rings which are believed to be the most stable in zeolite nets.28 AlPO nets (AEL, AFO, and AHT) and Co-Ga-PO nets (CGF and CGS) also show average ring sizes within this range but they are more versatile than aluminosilicates and can hold larger average ring sizes as it is the case in PON, an AlPO structure whose average ring size (7.0) is the largest among the studied (Table 8). Structures containing the smallest TOT angles (ca. 130°), away from the equilibrium in aluminosilicates, were synthesized as

Number of TO2 per unit cell.

beryllosilicate (OBW) or beryllophosphate (WEI). An early suggestion of the role of beryllium in stabilizing small (ca. 130°) BeOSi angles in minerals was already made by Downs and Gibbs in 1981.47 Examples of beryllosilicates zeotypes do not only include structures containing 3-rings, such as OSB-2,48 with topology OBW, but also structures without 3-rings such as SFH and SFN.49 These two latter topologies, not having 10-rings as their largest channels, are not included in our previous analysis, but they also deserve special attention in order to treat briefly about beryllosilicates. Zeolitic beryllosilicates are not characterized by the presence of 3-rings but rather by the presence of TOT (BeOSi) angles close to 130°. Our ring analysis shows (Table 7 and Figure 4, top) that not only 3-rings but also 6-, 8-, and 10-rings contain TOT links with angles close to 130°. Zeolite nets OBW and WEI, containing beryllium, show relatively low average ring sizes (5.30 and 5.67 for OBW and WEI respectively, as shown in Table 8) due to the presence of 3-rings; but SFH and SFN, being beryllosilicates, show average ring sizes of 6.0, with their ring counting (corresponding to 32 TO2 units) being 44 · 58 · 622 · 142. From this data, beryllosilicates seem not to present average ring sizes clearly different from those of aluminosilicates. SFH and SFN contain TOT angles below 140°, associated to 4-, 5-, 6- and 14-rings. Therefore, what these four beryllo-zeotypes (OBW, WEI, SFH, and SFN) have in common is the presence of TOT angles smaller than 140°, and such TOT angles are compatible -at least- with 3-, 4-, 5-, 6-, 8-, 10-, and 14-rings. 3.4. Related Zeolite Structures. SFH and SFN, as mentioned above, have the same ring counting and in fact they are related structures.49 Ring counting provides a new way to find related structures. The data from Table 8 shows that three other pairs (apart from SFH/SFN) contain the same ring counting: AEL/AFO, MTT/TON, and SFF/STF. In fact the latter two pairs are recognized in the Atlas20,21 as structurally related topologies. The pair AEL/AFO is not reported in the Atlas as structurally related but they are in fact related structures from the synthesis viewpoint.50 None of these three pairs can be recognized as a related pair from mathematical topological descriptors such as coordination sequences, vertex indices, or tile decomposition, and it is the ring counting which can be used as a fingerprint to help to spot topologically related zeolite nets. The ABC-6 family of zeolites has been described20,21,51 as consisting of layers of 6-rings arranged in a hexagonal array that are interconnected by tilted 4-rings in different ways. Related zeolites belonging to the ABC-6 family are CHA/GME and OFF/ERI, whose relevant topological descriptors are shown in Table 9. It can be seen that CHA and GME contain the same ring counting, and also OFF and ERI contain the same ring counting. On the other hand, the four members of the ABC-6 family considered show the same average ring size (Table 9). It is an open question to further relate these topological descriptors to characterize families of zeolites or even to discover or relate new members and families. In the present introduction to this topic it is clear that the topological

6404 J. Phys. Chem. C, Vol. 113, No. 16, 2009

Sastre and Corma

TABLE 10: Ring Indices of the O-Sites in IWW

TABLE 11: Accessibilility of the O-Sites in IWW from Data in Table 10a

O-site O1 O2 O3 O4 O5 O6 O7 O8 O9 O10 O11 O12 O13 O14 O15 O16 O17 O18 O19 O20 O21 O22 O23 O24 O25 O26 O27 O28 O29 O30 O31 O32 O33 O34

ring index 42 · 6 · 122 42 · 10 · 122 42 · 5 5 · 6 · 10 · 124 42 · 104 · 123 42 · 62 63 · 104 · 125 42 · 102 · 12 42 · 6 · 8 63 · 8 · 102 · 12 42 · 10 5 · 6 · 8 · 10 4 · 62 · 126 4 · 52 53 · 6 · 123 4 · 64 52 · 63 · 123 4 · 6 2 · 82 52 · 63 · 8 53 · 6 · 8 52 · 82 · 10 52 · 62 · 10 · 12 54 52 · 10 · 127 5 · 84 · 10 53 · 82 4 · 5 · 62 · 102 · 12 4 · 5 · 102 · 127 4 · 52 4 · 5 · 82 4 · 52 4 · 52 4 · 62 · 128 4 · 52

descriptors such as ring count and average ring size are useful quantities to study zeolite families. 3.5. Location of Catalytically Active Brønsted Sites in Zeolites. Protons are the only cations which locate in the zeolite net, with all other cations siting in extra-framework (inside channels or cavities) positions. The corresponding TO(H)T link then becomes an active (Brønsted) acid site which makes zeolites solid acid catalysts with structured active centers.52 Chemically, charge balance and energetic stability requires that the acid OH must be bonded to a Tiv-Tiii (or Tv-Tii) pair of tetrahedral atoms. A knowledge of the channel system of a zeolite net, plus an analysis of the ring indices of the O-sites can be a valuable tool to classify the accessibility of the active sites of a zeolite net. This is more evident when complex nets are to be studied, and ITQ-22 is one of such cases. Aluminosilicate ITQ-22,53 with topological code IWW, is a zeolite containing a complex system of interconnected channels made by 8-, 10-, and 12-rings, which has been used for the Brønsted acid site catalyzed xylene isomerization process.53 The unusual existence of three different ring-size channels offers a new scenario for catalytic applications where shape selectivity54-58 may allow to tailor the reaction products. IWW contains 34 different O-sites, classified as shown in Table 10. O-sites accessible from rings of the channel sizes (8-, 10-, and 12-rings) are extracted and classified according to the possibility of access from one (8, 10, and 12), two (8 + 10, 8 + 12, and 10 + 12), or three (8 + 10 + 12) channels (Table 11). The largest proportion of centers (26%) are located in the intersection between 10- and 12-rings, and this fact must be taken into account to design a catalytic application when using this material. Centres located in 12-ring channels amount 12% and

8

10

12

8 + 10

O18 O19 O20 O26 O30

O11

O1 O13 O15 O17 O33

O12 O21 O25

8 + 12

10 + 12

8 + 10 + 12

O2 O4 O5 O7 O8 O22 O24 O27 O28

O10

a O-sites accessible from several rings, of sizes x,y, are indicated as “x + y”.

centers located in 10-ring channels are scarce. Molecules able to diffuse selectively through 12-ring channels will undergo major reactivity than those diffusing selectively through 10ring channels. The occupation of the centers is not equally probable. Synthesis considerations teach that positively charged organic molecules acting as structure directing agents (SDA),59,60 tend to locate close to Al atoms. Calcination removes the SDA and leaves a proton nearby the Al atom. Preferential Al and proton locations based on energetic considerations dictate the proton locations in the material.61,62 Energetic considerations combined with a topological analysis may help to the design of catalytic materials for specific applications. 4. Conclusions Topological concepts are of help to understand, systematize, and analyze chemical applications of zeolite nets. Rings, classified by the number of their T (or O) constituent atoms, are an intuitive concept which allow a mutual enrichment of topology and chemistry of zeolite types. Unit cells of zeolites allow a ring counting which provides a topological fingerprint of each structure giving information about the number and occurrence of rings. Ring count also allows to find related topologies and eventually zeolites with similar synthetic routes. From the ring counting, rings passing through any T- and O-atom are located. Ring indices for T (and O) atoms are then defined by taking into account the rings passing through such atom. This new topological descriptor can be used to find the ring environment of each constituent atom in the zeotype. Geometrical analysis linked to this topological concept allows a detailed study able to relate chemical properties (such as T-O bond distances, OTO and TOT angles, T-T distances) with topological descriptors and rings in particular. Occurrence of rings in the set or specific subsets of the Atlas of Zeolite Framework types can be analyzed and classified through a large number of variables in order to find possible relations between the chemistry and topology of these materials. The concepts and algorithms presented in this study have been coded into a new version of the available Fortran software code called zeoTsites.63 Ring indices of O-sites can be used to identify and classify the Brønsted acid sites and their channel environment in zeolite nets. This can be of help in order to explain the catalytic activity of a zeolite in its protonic form. Acknowledgment. G.S. thanks Red Espan˜ola de Supercomputacio´n (RES) for making available their computational resources, and the Distributed European Infrastructure for Supercomputing Applications (DEISA) Consortium for the

Topological Descriptor for Oxygens in Zeolites provision of the ACIDFAU project. We thank two referees for insightful comments. Supporting Information Available: This includes CIF (and XTL) files of the zeolite nets used and a complete ring, geometrical, and topological analysis of all the zeotypes studied. This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) (a) Wells, A. F. Three-Dimensional Nets and Polyhedra; New York: Wiley, 1977. (b) Wells, A. F. Further Studies of Three-Dimensional Nets. Am. Crystallogr. Assoc. Monogr. No. 1979, 8. (2) Andersson, S.; Hyde, S. T.; Larsson, K.; Lidin, S. Chem. ReV. 1988, 88, 221. (3) Nesper, R.; von Schnering, H. G. Z. Krystallogr. 1985, 170, 138. (4) Hyde, B. G.; Andersson, S.; Bakker, M.; Plug, C. M.; O’Keeffe, M. Prog. Solid State Chem. 1978, 12, 273. (5) Delgado-Friedrichs, O.; Dress, A. W. M.; Huson, D. H.; Klinowsky, J.; Mackay, A. L. Nature (London) 1999, 400, 644. (6) Delgado-Friedrichs, O.; Huson, D. H. Discrete Comput. Geom. 2000, 24, 279. (7) Delgado-Friedrichs, O.; O’Keeffe, M.; Yaghi, O. M. Acta Cryst. A 2003, 59, 22. (8) Delgado-Friedrichs, O.; Foster, M. D.; O’Keeffe, M. D.; Proserpio, D. M.; Treacy, M. M. J.; Yaghi, O. M. J. Solid State Chem. 2005, 178, 2533. (9) O’Keeffe, M.; Hyde, S. T. Zeolites 1997, 19, 370. (10) Bernal, J. D. Proc. Roy. Soc. London A 1964, 280, 299. (11) Brunner, G. O.; Laves, F. Wiss. Z. Techn. UniVers. Dresden 1971, 20, 387. (12) Meier, W. M.; Moeck, H. J. J. Solid State Chem. 1979, 27, 349– 355. (13) Brunner, G. O. J. Solid State Chem. 1979, 29, 4l–45. (14) Stixrude, L.; Bukowinski, M. S. T. Am. Mineral. 1990, 75, 1159. (15) Curtis, R. A.; Deem, M. W. J. Phys. Chem. B 2003, 107, 8612. (16) Sastre, G.; Corma, A. J. Phys. Chem. B 2006, 110, 17949. (17) Petrovic, I.; Navrotsky, A.; Davis, M. E.; Zones, S. I. Chem. Mater. 1993, 5, 1805. (18) Henson, N. J.; Cheetham, A. K.; Gale, J. D. Chem. Mater. 1994, 6, 1647. (19) Brunner, G. O.; Meier, W. M. Nature (London) 1989, 337, 146. (20) Baerlocher, Ch.; McCusker, L. B.; Olson, D. H. Atlas of Zeolite Framework Types, 6th revised ed.; Elsevier: New York, 2007 (It contains 176 structures). (21) The current version of the Atlas in the web [http://www.izastructure.org] contains such list of T- and O-atoms including the coordinates according to the cif [crystallographic information file: http://ww1.iucr.org/ cif/] specification under the auspice of the International Union of Crystallography. The web version is periodically updated and it contains more structures than those in the printed edition.20 (22) S is also possible as in UCR-20: Zheng, N.; Bu, X.; Wang, B.; Feng, P. Science 2002, 298, 2366. (23) Goetzke, K.; Klein, H.-J. J. Non-Cryst. Solids 1991, 127, 215. (24) The vertex index of AFI (4 · 62 · 6 · 63 · 62 · 63), with 24 TO2/u.c. gives an incorrect counting of 24 × 1/4 ) 6 (4-rings), and 24 × 9/6 ) 36 (6rings), which in turn gives an incorrect average ring size of 5.71. This is different from the correct value of 6 (4-rings) and 52 (6-rings), which gives an average ring size of 5.79. More details in the Supporting Information. (25) Ho¨chtl, M.; Jentys, A.; Vinek, H. Appl. Catal., A 2001, 207, 397. (26) Tossell, J. A.; Gibbs, G. V. Acta Cryst. A 1978, 34, 463. (27) O’Keeffe, M.; Hyde, B. G. Acta Cryst. B 1978, 34, 27. (28) Newton, M. D.; Gibbs, G. V. Phys. Chem. Miner. 1980, 6, 221.

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