New Stories of Zeolite Structures: Their Descriptions, Determinations

Review pubs.acs.org/CR

New Stories of Zeolite Structures: Their Descriptions, Determinations, Predictions, and Evaluations Yi Li and Jihong Yu* State Key Laboratory of Inorganic Synthesis and Preparative Chemistry, College of Chemistry, Jilin University, Qianjin Street 2699, Changchun 130012, China 3.1. Structures with Unprecedented Pore-Openings 3.1.1. JU-64 (JSR) 3.1.2. ITQ-40 (−IRY) 3.1.3. ITQ-51 (IFO) 3.1.4. ITQ-44 (IRR) 3.1.5. ITQ-43 3.1.6. ITQ-37 (−ITV) 3.2. Structures with Unprecedented Complexity 3.2.1. SSZ-74 (−SVR) 3.2.2. SSZ-31 (*STO) 3.2.3. ITQ-39 3.2.4. SSZ-57 (*SFV) 3.3. Structures with Intrinsically Chiral Frameworks 3.3.1. SU-32 (STW) 3.3.2. CJ-40 (JRY) 3.3.3. Linde J (LTJ) 3.4. Structures with 3-Rings 3.4.1. CJ-63 (JST) 3.4.2. PKU-9 (PUN) 3.4.3. Oxonitridophosphate-2 (NPT) 3.4.4. Be-10 (BOZ) 3.5. Future Development 4. Structure Determination 4.1. X-ray Crystallography 4.1.1. FOCUS 4.1.2. Charge-Flipping 4.2. Electron Crystallography 4.2.1. High-Resolution Transmission Electron Microscopy 4.2.2. Electron Diffraction 4.3. Computer-Aided Model-Building 4.3.1. ZEFSA II 4.3.2. FraGen 4.4. Future Development 5. Structure Prediction 5.1. A Short History 5.2. Recent Progress in ZSP 5.2.1. SCIBS and the Atlas of Prospective Zeolite Structures 5.2.2. ZEFSA II and the Database of Hypothetical Structures 5.2.3. GRINSP and the Predicted Crystallography Open Database

CONTENTS 1. Introduction 2. Structure Description 2.1. Basic Definitions 2.1.1. Framework Type Code 2.1.2. The Idealized Framework 2.1.3. Framework Density (FD) 2.1.4. Coordination Sequences and Vertex Symbols 2.1.5. Ring 2.1.6. Cage and Cavity 2.1.7. Channel 2.1.8. Effective Channel Width 2.1.9. Building Unit 2.1.10. The Largest Included Sphere and the Largest Free Sphere 2.1.11. Available, Occupiable, and Accessible Pores 2.2. New Descriptors 2.2.1. Hard Sphere Packing 2.2.2. Ring Index 2.2.3. Natural Building Unit 2.2.4. T-Ring Graph 2.2.5. Packing Unit 2.2.6. Information-Based Topological Complexity 2.2.7. Voronoi Hologram 2.2.8. Pore Size Distribution Histogram and Ray-Trace Histogram 2.3. New Methods for the Calculation of Pores 2.3.1. The Grid-Based Approaches 2.3.2. ZEOMICS 2.3.3. Zeo++ 2.4. Future Development 3. New Structures

© 2014 American Chemical Society

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Received: January 6, 2014 Published: May 21, 2014 7268

dx.doi.org/10.1021/cr500010r | Chem. Rev. 2014, 114, 7268−7316

Chemical Reviews 5.2.4. FraGen and the Hypothetical Zeolite Database 5.2.5. ZSP Using GPGPU Programming 5.3. Future Development 5.3.1. Maddox’s “Continuing Scandal” 5.3.2. Hypothetical Zeolite Databases 5.3.3. Function-Oriented ZSP 6. Feasibility of Zeolite Structures 6.1. The Feasibility of Low-FD Zeolites without 3Rings 6.2. The Feasibility of Zeolites with Unconventional Framework Elements 6.3. The Flexibility of Zeolite Frameworks 6.4. The Packing Unit Model 6.5. Local Interatomic Distances 6.6. Future Development 7. Concluding Remarks Author Information Corresponding Author Notes Biographies Acknowledgments References

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Figure 1. Number of zeolite framework types approved by IZA-SC in past years.

have led to the structure solution of many complex zeolite structures, such as those consisting of a large number of distinct T atoms or complicated stacking disorders. Meanwhile, with the aid of modern computer hardware and software, computer modeling is becoming more important in zeolite structure determination and prediction. Millions of hypothetical zeolite structures have been predicted through computer modeling. Structure databases, which have been built for both existing and hypothetical zeolite structures, serve not only as a complement to conventional structure determination methods but also as a pool providing promising synthetic candidates. The increase in both IZA structures and hypothetical ones has stimulated many new methods for the description and evaluation of zeolite structures, providing new insights into the feasibility of zeolite frameworks. In this Review, we will focus our attention on the most striking discoveries about zeolite structures since the publication of the sixth edition of Atlas of Zeolite Framework Types in 2007. After this brief introduction in section 1, section 2 outlines the recent progress in zeolite framework descriptions; section 3 presents several newly discovered zeolite frameworks with interesting structural features; in section 4, the recent progress in zeolite structure determination is described; new methods and databases for zeolite structure prediction are reviewed in section 5; section 6 addresses the feasibility of zeolite structures; and the last section includes the concluding remarks and brief outlooks. In this Review, we only focus on highly crystalline zeolitic frameworks that are built exclusively from TO4 tetrahedra. The physical and chemical properties of zeolites, as well as the host−guest interactions between zeolite frameworks and extra-framework species, are beyond the topics of this Review.

1. INTRODUCTION Zeolites are an important class of inorganic crystalline materials that have been widely used in the fields of petroleum refining, petrochemical industry, and fine chemical industry, as catalysts, adsorbents, and ion-exchangers.1−30 The frameworks of zeolites possess orderly distributed micropores with diameters typically less than 2 nm. In comparison with those of other microporous materials, a zeolite framework is built exclusively from TO4 tetrahedra (T denotes tetrahedrally coordinated Si, Al, or P, etc.). Each TO4 tetrahedron is connected with four neighbors by sharing their vertex O atoms, forming the three-dimensional four-connected zeolite framework. Although all zeolites are constructed from TO4 tetrahedra, the different ways in which they can be connected lead to the rich variety of zeolite structures. Because of the wide applications of zeolites, the pursuit of novel zeolites with desired framework structures has never stopped. By the time the sixth edition of Atlas of Zeolite Framework Types was published in 2007,31 the Structure Commission of the International Zeolite Association (IZA-SC) had approved 176 distinct zeolite framework types, each of which was assigned a three-letter code. These framework types are often called the IZA structures. Thanks to the development of synthetic strategies, the number of IZA structures has reached 218 to date (Figure 1).32 Besides, there are many zeolite frameworks that have not been approved by IZA-SC yet. Many of these newly discovered zeolites possess interesting structural features, such as extra-large pores, low framework density, extremely complex framework topology, and intrinsically chiral frameworks, etc. Some of these structural features have never been observed before, such as 15-, 16-, 28-, and 30ring pore-openings. Besides the development of synthetic strategies, the progress in structure determination techniques is another important factor that has led to the rapid growth in the number of zeolite framework types during the past few years. In particular, new structure determination methods for powder X-ray diffraction, for electron microscopy, and for the combination of the two

2. STRUCTURE DESCRIPTION Zeolites have very complex three-dimensionally extended framework structures. The TO4 tetrahedra are connected in different ways to form complex framework topologies, and the pores inside the frameworks can be of any shape. Describing the structure of a zeolite framework has always been a challenging task. Toward this end, many structural descriptors have been devised during the past decades. Meanwhile, the efficient calculation of complex structural features is also an important challenge in this field. Since the publication of the sixth edition of Atlas of Zeolite Framework Types in 2007,31 many efforts have been made to develop new structure 7269


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than 6-ring. Channels may intersect to form two- or threedimensional channel systems. 2.1.8. Effective Channel Width. The effective width of a channel can be defined as the free diameter of the smallest aperture along the direction of a channel. The free diameter is calculated as the O···O distance with the diameter of O subtracted. For instance, the effective width of the 12-ring channel in faujasite is 7.4 Å, assuming the diameter of O to be 2.7 Å. 2.1.9. Building Unit. A zeolite framework can be deconstructed in different ways into different types of building units. Table 1 lists several types of building units that have been used often. Because some of these building units lack strict definition, framework deconstruction can be quite arbitrary. In practice, people tend to focus on the simplest or the most representative building units that reflect the topological characteristic of the given zeolite framework. Among these building units, the secondary building unit (SBU) and the composite building unit (CBU) are the most frequently encountered. More detailed information about these building units and the complete lists of SBUs and CBUs can be found in refs 31−33, 35, 36. 2.1.10. The Largest Included Sphere and the Largest Free Sphere. The largest included sphere is the largest sphere that can be fitted inside a zeolite framework without distorting or overlapping with any framework atom. The largest free sphere is the largest sphere that can move freely through the periodic zeolite framework. The diameters of these two types of spheres are often denoted by Di and Df, respectively. The ratio of Df/Di may indicate the smoothness of channel walls within a zeolite framework.37 2.1.11. Available, Occupiable, and Accessible Pores. The available pore in a zeolite framework is the void space that consists of no framework atom. The occupiable pore is the void space that can be reached by the center of a specific guest molecule. If the occupiable pore has an opening wide enough for the guest molecule to visit from outside, it is also an accessible pore. Apparently the available pore is only related to the nature of the host framework, whereas the occupiable and the accessible pores are related to both the host framework and the guest molecule. In practice, a rigid sphere with a diameter of 2.8 Å is often used as the default guest molecule, which corresponds to the kinetic size of a water molecule.38

descriptors and new methods for the calculation of complex porous structures, which will be the main topic of this section. 2.1. Basic Definitions

Before introducing the most recent progress, we will briefly review some basic definitions that are important for zeolite structure descriptions. Some of these definitions are related only to the topological features of a zeolite framework, such as coordination sequences and vertex symbols. Other definitions are more related to the geometric features of a zeolite, such as the framework density and accessible pores. Isotypic materials with different chemical compositions may have the same topological features but different geometrical features. More detailed information about these basic definitions can be found in the Database of Zeolite Structures 32 and IUPAC Recommendations 2001.33 2.1.1. Framework Type Code. The framework type code is a three-capital-letter code assigned by IZA-SC to each distinct zeolite framework type. A type code beginning with a “−” indicates an interrupted framework, whereas the one beginning with a “*” indicates an experimentally observed zeolite that possesses intergrowth or structural disorders. To avoid being confused with other three-letter abbreviations, all of the framework type codes are written in bold throughout this Review. 2.1.2. The Idealized Framework. To get a “standard” geometric model for each framework type, IZA-SC has optimized each IZA structure assuming a silica polymorph with the highest topologically allowed symmetry.34 This optimized structure is the idealized framework for the corresponding zeolite framework type. 2.1.3. Framework Density (FD). The framework density is defined as the number of T atoms per 1000 Å3. Isotypic materials with different chemical compositions may have different FDs. 2.1.4. Coordination Sequences and Vertex Symbols. Each T atom in a zeolite framework corresponds to a coordination sequence and a vertex symbol. The coordination sequence consists of a sequence of integers, where the nth integer represents the number of T atoms involved in the nth neighboring shell surrounding the original T atom. The vertex symbol indicates the size of the smallest ring associated with each of the six angles of a T atom. Zeolite frameworks with different coordination sequences or vertex symbols are topologically different. Detailed information about these two definitions can be found in the Database of Zeolite Structures.32 2.1.5. Ring. There are many conflicting definitions of ring between the mathematics and chemistry communities. For zeolites, a ring is usually referred to as a cycle of T and O atoms that is not the sum of any number of shorter cycles. A ring composed of n T and n O atoms is called an n-ring. 2.1.6. Cage and Cavity. A cage is a polyhedral pore whose faces are all too narrow to be penetrated by guest species larger than a water molecule, whereas a cavity is the pore with at least one face large enough to be penetrated. In practice, a cage has no face larger than 6-ring, whereas a cavity has at least one. A list of the most frequently observed cages and cavities can be found in refs 2 and 35. 2.1.7. Channel. The channel in a zeolite framework is a pore infinitely extended in one dimension and is large enough for guest species to diffuse along its length. Similar to the definition of cavity, the opening of a channel has to be larger

2.2. New Descriptors

2.2.1. Hard Sphere Packing. In 2009, Treacy and Foster devised a procedure to pack idealized hard spheres inside a zeolite framework.38 By simulating the close packing of idealized spheres at various sizes, one can get useful information regarding the pore geometry of a zeolite framework. In this approach, hard spheres are packed under two basic artificial interactions: attraction and repulsion. Spheres are attracted to each other when they are close, which ensures the close packing of spheres; spheres also repel each other strongly if they overlap, ensuring the hardness of the spheres. At the beginning of the packing procedure, a small number of hexagonal close packed spheres are placed into the zeolite framework without overlapping any framework atom. An excess of spheres are supplied outside the unit cell. To force the external spheres to move into the unit cell, an additional attractive potential toward the center of the unit cell is applied. The whole system of spheres is optimized by simulated annealing to minimize the total packing cost. Once the 7270


optimization procedure is finished, the number of spheres inside the unit cell is counted as the maximal number of spheres that can be packed in a zeolite framework. Treacy and Foster calculated the sphere packing in 176 idealized IZA frameworks. Part of their results is listed in Table 2, where NH2O, NHe, NNe, NAr, NKr, and NXe are the maximal Table 2. Maximal Numbers of Spheres That Can Be Packed per 1000 Å3 in Idealized Zeolite Frameworks38 zeolite

NH2O

NHe

NNe

NAr

NKr

NXe

CAN CHA FAU LTA OFF SOD

18.4 21.6 20.8 23.0 23.7 16.2

24.1 29.4 24.7 27.5 25.2 19.5

18.9 21.9 19.0 21.5 19.5 15.5

10.3 10.1 9.6 10.2 9.5 6.5

6.5 8.7 8.1 8.3 7.2 3.8

5.9 6.8 6.3 6.5 3.3 3.1

FBUs are cCBUs that do not share T atoms; selection of FBUs must follow a series of hierarchical rules

numbers of spheres that can be packed, per 1000 Å3, with diameters of 2.80, 2.60, 2.75, 3.40, 3.60, and 3.96 Å, respectively (corresponding to the kinetic diameters of water, helium, neon, argon, krypton, and xenon). From this table, the difference in the porosity of different zeolite frameworks is already shown. However, because it ignores the true nonbonding repulsions as well as other experimental factors, the sphere packing approach cannot be used to predict the real adsorption isotherms. For every zeolite framework, if one calculates the sphere packing for all possible sphere diameters, a plot of the number of packed spheres as a function of sphere diameter (d) will be obtained. For instance, Figures 2 and 3 are such plots for

Figure 2. Log-linear plot showing the number of packed spheres in one unit cell of zeolite LTL as a function of sphere diameter. Reprinted with permission from ref 38. Copyright 2009 Elsevier.

zeolites LTL and MFI, respectively. The general trend for all zeolite frameworks is that the number of packed spheres decreases as the sphere diameter is increased. However, the ways that the packing decreases differ in different zeolites, reflecting their intrinsic porous features. For zeolite LTL, the decrease of packed spheres undergoes several distinct regimes (Figure 2). At low sphere diameter (d < 4.0 Å), the number of packed spheres is proportional to d−3, indicating that the packing is essentially three-dimensional. With the increase of d, the number of packed spheres is proportional to d−2 (4.0 < d < 6.0 Å) and d−1 (6.4 < d < 8.8 Å), respectively. At high sphere diameter (8.8 < d < 10.0 Å), LTL cannot hold multiple spheres in the same cavity any more. Thus, the numbers of packed spheres at this regime can only be constants like 1.0, 0.67, and 0.5, etc. At d > 10.0 Å, no spheres can be packed inside because

constituting composite building unit (cCBU) fundamental building unit (FBU)

composite building unit (CBU)

PerBUs are zero-, one-, or two-dimensional building units constructed from a finite or infinite number of BBUs; the definition of PerBU has been developed to systematically describe disordered zeolite frameworks, which are structurally related and can be considered as a family; each member of the family can be generated by applying simple symmetry operations, such as translations and/or rotations, to the corresponding PerBU; therefore, PerBU is not an abstract object as other building units; neighboring PerBUs do not share T atoms CBU is the combination of a finite or infinite number of BBUs, which usually reflects the characteristic of a zeolite framework; CBUs may share T atoms with their neighbors, and they may not be able to build the entire zeolite framework; the most frequently encountered CBUs are rings, chains, and polyhedral cages/cavities; IZA-SC has assigned a three-lowercase-letter designation to each of these CBU; to avoid being confused with other three-letter codes, the designations of all of the CBUs are written in italic throughout this Review cCBUs are the smallest CBUs that can build the entire zeolite framework; cCBUs are defined such that the number of different cCBUs in a zeolite framework is the lowest (usually one or two); neighboring cCBUs may share T atoms

an SBU is constructed from a small number of BBUs; in general, a zeolite framework is built of one type of SBU only; neighboring SBUs do not share T atoms

definition name

Review

basic building unit or primary building unit (BBU) secondary building unit (SBU) periodic building unit (PerBU)

Table 1. Definitions of Various Building Units

BBU is the TO4 tetrahedron in a zeolite framework; other building units are all constructed from BBUs

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and one 6-ring (42·6), O3 with one 4-ring and two 6-rings (4· 62), and O4 with one 4-ring, one 6-ring, and one 12-ring (4·6· 12). By showing the different environments around O atoms, ring indices can be used to locate catalytically active Brønsted sites in a zeolite framework. For instance, zeolite IWW contains a porous system made by interconnecting 8-, 10-, and 12-ring channels. IWW consists of 34 different O sites, the ring indices of which are shown in Table 3. O sites located in 12-ring Table 3. Ring Indices of O Sites in Zeolite IWW39

Figure 3. Log-linear plot showing the number of packed spheres in one unit cell of zeolite MFI as a function of sphere diameter. Reprinted with permission from ref 38. Copyright 2009 Elsevier.

it exceeds the diameter of the largest included sphere. As compared to that in LTL, the sphere packing in zeolite MFI is simpler, because the channel walls in MFI are smoother (Figure 3). Therefore, analyzing the sphere packing as a function of sphere diameter has provided a new way to illustrate the pore geometry in a zeolite framework. 2.2.2. Ring Index. In 2009, Sastre and Corma suggested using a new descriptor, the ring index, to describe the rings present in a zeolite structure.39 The ring index of an atom is defined as the list showing the sizes and numbers of rings that pass through that atom. According to its definition, ring index is valid for both T and O atoms. For instance, in zeolite FAU, there are one unique T and four unique O atoms (Figure 4). The ring index of the only T atom is 43·62·12, indicating that it is involved in three 4-rings, two 6-rings, and one 12-ring. Each O site in FAU is associated with three rings. O1 is associated with two 4-rings and one 12-ring (42·12), O2 with two 4-rings

atom

ring index

atom

ring index

atom

ring index

O1 O2 O3 O4 O5 O6 O7 O8 O9 O10 O11 O12

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

O13 O14 O15 O16 O17 O18 O19 O20 O21 O22 O23 O24

4·62·126 4·52 53·6·123 4·64 52·63·123 4·62·82 52·63·8 53·6·8 52·82·10 52·62·10·12 54 52·10·127

O25 O26 O27 O28 O29 O30 O31 O32 O33 O34

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

channels amount to 12%, and those located in 10-ring channels are relatively rare, implying that molecules diffusing preferentially through 12-ring channels will undergo major reactivity than those diffusing through 10-ring channels. Besides for analyzing the O sites in zeolite frameworks, ring indices may have other applications. Using ring indices, the numbers of rings of various sizes and the average ring size in a zeolite framework can be calculated, which cannot be deduced from vertex symbols in general cases.39 2.2.3. Natural Building Unit. As we have already shown, a zeolite framework can be decomposed in many ways, in which the building units can be SBUs, CBUs, and PerBUs, etc. However, choosing the building units for a zeolite framework, as well as the way they assemble, is quite arbitrary. Therefore, we need a general procedure to remove the ambiguity in zeolite framework decomposition. The concept of natural tiling can be one of the solutions. According to the theory of tiling, a threedimensional net can be decomposed into a number of facesharing, edge-sharing, and vertex-sharing three-dimensional polyhedral tiles. The way all of the tiles assemble together is the tiling of the net. According to O’Keeffe’s definition,40 a tiling is natural when it obeys the following rules: (a) its symmetry coincides with the symmetry of the net; (b) the faces of the tiles are strong rings that are not the sum of smaller rings; (c) all strong rings that are not the tile faces intersect each other; and (d) if more than one tiling obey rules a−c, the different tiles of all of the tilings are united to larger tiles to obtain a unique tiling. This algorithm can be used to construct the natural tiling for a net of any complexity, which has been implemented in computer programs such as TOPOS.41 In 2010, Blatov and co-workers showed that a zeolite framework could be unambiguously decomposed in only one way following the concept of natural tiling.42 In this approach, the zeolite framework corresponds to a three-dimensional net, and the tiles composing the natural tiling of the zeolite net are the natural building units (NBUs). Blatov and co-workers constructed the natural tilings for 194 IZA structures and found

Figure 4. Perspective views of ring indices associated with the unique atoms in zeolite FAU. Top left, T1 showing rings 43·62·12; top-right, O1 showing 42·12 rings; bottom-left, O2 showing 42·6 rings; bottommiddle, O3 showing 4·62 rings; bottom-right, O4 showing 4·6·12 rings. Reprinted with permission from ref 39. Copyright 2009 American Chemical Society. 7272


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between different zeolite frameworks can be analyzed by comparing their NBUs and natural tilings. Because of these advantages, IZA-SC has employed the concept of natural tiling to describe zeolite frameworks in its official database since 2008.32 2.2.4. T-Ring Graph. In 2010, Haranczyk and co-workers developed a special abstract two-dimensional graph, that is, the T-ring graph, to depict important topological and geometrical features of zeolite frameworks.43 A T-ring graph is composed of nodes and edges. Each node is a colored circle representing a specific building unit (such as an NBU) of a zeolite framework; the diameter of each node is proportional to the diameter of the largest included sphere (di) for the corresponding building unit. Figure 7 shows the nodes describing the NBUs of zeolite LTA.

308 topologically distinct NBUs. Each of these NBUs was assigned a unique name. Figure 5 shows the natural tiling of

Figure 5. Natural tiling of zeolite −CLO. Different NBUs are in different colors. Reprinted with permission from ref 42. Copyright 2010 American Chemical Society.

zeolite −CLO. Although most of the IZA frameworks (80%) are built with no more than five types of NBUs, there exist some frameworks that consist of over 10 types of topologically different NBUs. The occurrence of the 308 distinct NBUs among the 194 IZA frameworks is quite different. Fourteen NBUs occur at least in 10 IZA frameworks (Figure 6), whereas 213 NBUs occur only once.

Figure 7. Representations of the NBUs of zeolite LTA in a T-ring graph. (a) The three NBUs in LTA. (b) The T-ring nodes representing the NBUs of LTA; a color key denoting the sizes of rings is also shown. Reprinted with permission from ref 43. Copyright 2010 American Chemical Society.

The colors in each node correspond to the sizes of the rings composing the building unit; the width of each color is proportional to the corresponding ring composition in the building unit. Between the neighboring nodes in a T-ring graph, there are edges representing the pathways between neighboring building units (Figure 8). The edge is drawn as a black line with a width

Figure 6. Most frequently encountered NBUs and their occurrence among 194 IZA structures. Reprinted with permission from ref 42. Copyright 2010 American Chemical Society.

Decomposing zeolite frameworks into NBUs has several important advantages over other decomposition methods. First, the choice of NBU is unambiguous, and the decomposition procedure can be done easily by computer programs. Second, all of the minimal cages and cavities are represented by NBUs, and all of the windows of the pores in zeolite frameworks are represented by the faces of NBUs. Third, the resemblance

Figure 8. T-ring graph representing zeolite LTA. Cages A, B, and C correspond to the [412.68.86], [46.68], and [46] NBUs, respectively. Reprinted with permission from ref 43. Copyright 2010 American Chemical Society. 7273


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2.2.5. Packing Unit. In 2012, Blatov and co-workers proposed a new framework decomposition method for aluminophosphate zeolites.44 In general, the framework of an aluminophosphate zeolite can be decomposed into packing units (PUs), which are separate essential rings or NBUs confined by essential rings. The choice of PUs follows two rules: (1) the PUs should not share T-atoms; and (2) the framework should be completely constructed from the chosen PUs. According to these rules, PUs are actually the bigger and more unambiguously defined SBUs. The positions of PUs, including the connectivity between them, can be described by a packing net, where every vertex coincides with a PU center and edges describe the connectivity between PUs (Figure 10).

proportional to the diameter of the largest free sphere (df) that may diffuse along the corresponding pathway. A dashed edge indicates that the corresponding pathway is too narrow for guest species (usually water molecules) to diffuse. The length and shape of the edge are not important. The T-ring graphs can be used for the quick analysis and categorization of the pores in zeolite frameworks. Figure 9

Figure 10. (a) The packing units of zeolite AST and (b) its packing net. Reprinted with permission from ref 44. Copyright 2012 American Chemical Society.

Blatov and co-workers investigated 61 aluminophosphate zeolite frameworks and found that 18 of them could be built from one type of PUs. Among the 308 types of NBUs42 found in IZA structures, only 26 could serve as PUs. Figure 11 shows some of these NBUs. Among ring-like PUs, 4- and 6-rings are of special importance; they appear in the packing models of 41 (67.2%) and 32 (52.5%) aluminophosphate zeolite frameworks, respectively. In particular, 40 frameworks can be built entirely from 4- or 6-rings.

Figure 9. Categorization of zeolites according to the T-ring representations. (a) The cavity-type structures, (b) the channel-type structures, (c) the inaccessible cage-type structures, and (d) the color key denoting the sizes of rings. Reprinted with permission from ref 43. Copyright 2010 American Chemical Society.

shows several representative T-ring graphs. All zeolites presented in Figure 9a have accessible pathways (shown as solid black lines) wide enough for guest species to diffuse. In addition, these accessible pathways are narrower than the largest cavities they connect. Therefore, they can be quickly categorized as cavity-type zeolites. In contrast, all three zeolites presented in Figure 9b are channel-type structures, in which the widths of the connecting pathways are about the same size as the largest cavities. Figure 9c shows the T-ring graphs for cagetype structures, which are inaccessible to guest species as indicated by the absence of solid edge. It is worth noting that each T-ring graph corresponds to a specific guest molecule. Therefore, one may produce several T-ring graphs for the same zeolite framework when different guest molecules are considered. By comparing the T-ring graphs corresponding to different probes, one can easily generate preliminary conclusions about the selectivity of mixtures of guest species corresponding to a specific zeolite framework.

Figure 11. Most frequently encountered NBUs in the packing unit models of aluminophosphate zeolites. Reprinted with permission from ref 44. Copyright 2012 American Chemical Society. 7274


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a more reliable evaluation of the complexity of zeolite frameworks. In 2013, Krivovichev applied this method to 201 IZA frameworks.47 According to his result, IMF, *SFV, *STO, − SVR, and TUN have the highest IG values (>6), which agrees well with one’s intuitive feeling because they all possess large numbers (>20) of distinct T atoms. Other complexitymeasuring parameters, such as IG,total (the total information content) and IG,norm (the normalized information content), can also be derived from IG.47 These quantitative parameters can be used not only for evaluating the complexity of zeolite structures, but also for investigating the evolution of zeolite structures during crystallization and transformation.47 2.2.7. Voronoi Hologram. In 2012, Haranczyk and coworkers devised a new geometric descriptor, the Voronoi hologram, to depict the accessible void space in a zeolite framework.48 Before dipping into the Voronoi hologram, we should start with the definition of Voronoi decomposition. For a zeolite framework m, the Voronoi decomposition is to divide the space surrounding the framework atoms into polyhedral cells such that each face of the polyhedral cells is a plane equidistant from the neighboring two atoms. The Voronoi network w, built of the nodes and edges of these polyhedral cells, maps the void space in a zeolite framework (Figure 12). Notice that the Voronoi network is the dual of the Delaunay triangulation.37 When a specific probe diameter (for instance, 3.25 Å for CH4 molecule) is defined, the guest-accessible regions in zeolite frameworks can be determined, which correspond to v, a periodic subgraph of w (Figure 12).

The natural tiling approach and the packing unit model both utilize NBUs as the essential building units. These two framework decomposition methods are both useful for the comparison of different structures. On the other hand, these two methods have obvious differences. First, the NBUs in a natural tiling share T atoms, whereas the PUs in the packing unit model do not. Second, NBUs in a natural tiling cannot be essential rings, whereas PUs can be. Third, each zeolite framework unambiguously corresponds to a unique natural tiling, whereas a zeolite framework may correspond to several packing models. Recently, Blatov and co-workers extended this PU study to 201 IZA frameworks and found that the existence of a valid packing model might be an essential feature of feasible zeolite structures (see section 6.4). 2.2.6. Information-Based Topological Complexity. Although the term complex has been widely used in the description of zeolite structures, its strict definition has rarely been mentioned. In practice, the number of crystallographically distinct T atoms has often been used as a measure of the framework complexity. Because it neglects both the site symmetry of T atoms and the contribution of bridging O atoms, the number of distinct T atoms cannot precisely reflect the total degree of freedom of a zeolite structure. In 2012, Krivovichev proposed a quantitative informationbased approach to evaluate the topological complexity of zeolite frameworks.46 Within this approach, the content in the reduced unit cell of a zeolite structure is considered as a message with atoms as symbols. The more information this message contains, the more complex this zeolite structure is. According to Shannon’s information theory, the entropy of information encoded in this message (i.e., the complexity of a zeolite structure), IG, can be calculated according to the following formula: IG = − ∑ [(mi /v) log 2(mi /v)] i = 1, k

(1)

where k is the number of topologically distinct atoms (including both T and O atoms), mi is the multiplicity of the ith distinct atom in the reduced unit cell, and v is the total number of atoms in the reduced unit cell. According to this definition, it is easy to deduce that the minimal information content is zero when all of the atoms are equivalent and the maximal information content is log2 v if all of the atoms are nonequivalent. For instance, the idealized frameworks of SOD and NPO both have 6 T and 12 O atoms in their reduced unit cells (v = 18). SOD has one topologically distinct T atom and one distinct O atom, the multiplicities of which are 6 and 12, respectively. Therefore, for SOD: IG = − {6/18 × [log 2(6/18)] + 12/18 × [log 2(12/18)]} = 0.918

NPO has one distinct T and two distinct O atoms, the multiplicities of which are all 6. Therefore, for NPO: Figure 12. Top left: The idealized framework of FAU, m (atoms in blue), and its three-dimensional Voronoi network w (orange). Top right: Within w, the CH4-accessible Voronoi subgraph v is highlighted (purple). Bottom left: Only v is shown, illustrating the pore topology encoded as Voronoi nodes and edges. Bottom right: A visualization of the pore landscape corresponding to the CH4-accessible network, with the Si and O atoms in the structure in tan and red, respectively. Reprinted with permission from ref 48. Copyright 2012 American Chemical Society.

IG = −3 × {6/18 × [log 2(6/18)]} = 1.585

By comparing the IG values for these two structures, one can directly draw a conclusion that NPO is more complex than SOD. Notice that the numbers of distinct T atoms and cell contents in these two structures are both the same. As compared to other empirical methods, inclusion of site symmetry information and contribution of O atoms leads to 7275


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Notice that the Voronoi hologram is an abstraction or simplification of v. Information such as interconnectivity of edges and their positions is lost in the Voronoi hologram. However, with this simplified representation, the porous systems in two zeolites can be compared more easily. Haranczyk and co-workers have defined a series of similarity coefficients to compare the Voronoi holograms of two different zeolites,48 one of which is defined as follows:

The Voronoi hologram is a three-dimensional histogram that encodes the frequency of occurrence of edges in v. Its three axes are l (the length of each edge), ra, and rb (the distances from the two Voronoi nodes connected by each edge to the surface of the nearest framework atom; ra ≥ rb), respectively. The Voronoi hologram is further divided into many small cubic bins; each edge in v belongs to exactly one of the small bins in this three-dimensional hologram. The frequency of occurrence of edges in each bin is denoted by a distinct color. Figure 13 shows two examples of Voronoi holograms for zeolites FAU and TUN.

MTUbin = 0.5 × [c /(a + b − c) + (n + c − a − b) /(n − c)]

(2)

where a and b are the numbers of active bits in arrays A and B that represent two holograms, c is the number of active bits in common, and n is the length of the arrays. It has a range from 0 (maximal dissimilarity) to 1 (identity). With these similarity coefficients defined, the least similar zeolite frameworks can be efficiently selected as representative ones from a large set of structures. Haranczyk and co-workers employed a MaxMin maximum-dissimilarity selection method to select the least similar ones among the 148 IZA frameworks, which have pores accessible to a spherical probe in the size of a CH4 molecule.48 By setting the MTUbin similarity threshold of 0.5, Haranczyk and co-workers obtained a total of 20 least similar structures (Figure 14). These selected structures can be considered as the representatives of all of the 148 CH4-accessible zeolites, because any of the remaining 128 structures should be similar to at least one of the 20 selected ones (MTUbin > 0.5). In addition to studying existing zeolites, Haranczyk and co-

Figure 13. Left: The Voronoi hologram for FAU. Bins are assigned a color on the basis of their frequency of occurrence, ranging in this case from 64 (dark blue) to 256 (red). Right: The Voronoi hologram for TUN. The frequency of occurrence in this case ranges from 4 (dark blue) to 104 (red). Reprinted with permission from ref 48. Copyright 2012 American Chemical Society.

Figure 14. First 20 IZA structures selected by the diversity selection method. Reprinted with permission from ref 48. Copyright 2012 American Chemical Society. 7276


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Figure 15. PSD histograms for (A) AFT and (B) SIV. Both histograms were generated with a 0.5 Å probe radius. Reprinted with permission from ref 52. Copyright 2013 Elsevier.

Figure 16. Illustration of randomly placed and oriented rays in MFI. Rays are displayed according to their lengths: (A) 0−0.3 nm, (B) 0.3−0.6 nm, (C) 0.6−0.9 nm, (D) larger than 1.2 nm, and (E) 0−10 nm. Reprinted with permission from ref 53. Copyright 2013 Elsevier.

workers extended their study to 139 397 CH4-accessible hypothetical zeolite structures and retrieved 174 least similar ones (MTUbin < 0.5).49 Haranczyk’s approach has important significance. Because the quantity of zeolite structures, including the synthesized and hypothetical ones, is becoming larger, the computational cost for evaluating all of the structures is prohibitively high (see section 5). Efficient sampling in such a large data set is highly in demand, which ensures that valuable resources are spent on the most representative structures. On the other hand, the

accessible pores are the most important structural feature for zeolites that may decide their final applications. Diversityselection of zeolite structures on the basis of pore geometry enables the researchers to focus only on a much smaller quantity of high-performance zeolites. 2.2.8. Pore Size Distribution Histogram and Ray-Trace Histogram. The pore size distribution (PSD) histogram indicates the fraction of the void volume that corresponds to certain pore sizes in porous materials. Although the PSD histograms are widely applied to present the results of 7277


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crossing the diameter of the main channels (Figure 16B) and those crossing the channel intersections (Figure 16C), respectively. As that in Voronoi holograms (see section 2.2.7), the information about the locations, shapes, and connectivity of zeolite pores is lost in PSD and ray-trace histograms due to dimensionality reduction. Nonetheless, because of the same reason, the complex porous structures in different zeolites can be directly compared via these two-dimensional histogram representations. For instance, Iglesia and co-workers defined a Euclidean distance, Sd,euc, to measure the similarity between two ray-trace histograms:

adsorption measurements, they have rarely been studied in a theoretical way.50,51 In 2013, Haranczyk and co-workers developed an efficient computer algorithm to generate the ideal PSD histograms for zeolite frameworks.52 According to this algorithm, a specified number of sample points are chosen randomly within a zeolite framework. The largest spherical pore containing each sample point then can be calculated through Voronoi decomposition. A PSD histogram can eventually be generated by counting the number of sample points related to a particular pore diameter. To mimic the real PSD histograms determined in adsorption experiments, the sample points can be assumed to have the radius equivalent to that of the probe molecule. Figure 15 shows the PSD histograms of zeolites AFT and SIV. In 2013, Iglesia and co-workers developed another twodimensional descriptor, the ray-trace histogram, to depict the landscapes of the pores in zeolite frameworks. Although the ray-trace histogram may look like the PSD histogram, they are calculated in completely different ways and have quite different meanings.53 The ray-trace histogram assumes the accessible void space in a zeolite framework is filled with a large number of randomly placed straight “rays”. Each ray intersects the surface of the pores at two points, the distance between which is the length of each ray. Figure 16 shows the pores in zeolite MFI filled by rays of different lengths. A ray-trace histogram can then be generated by grouping the length and the number of rays in a series of bins. Figure 17 shows the ray-trace

Sd,euc = [ ∑ (P1, i − P2, i)2 ]1/2 i = 1, n

where P1,i and P2,i are the probability densities of rays in bin i for histograms 1 and 2, and n is the number of bins in each histogram. Following this definition, Iglesia and co-workers calculated the similarities between MFI and all other individual IZA zeolites. The most and least similar zeolites to MFI are TER (Sd,euc = 0.129) and VSV (Sd,euc = 0.439), respectively. Using this similarity metric, candidate catalytic solids that are capable of stabilizing specific transition states can be easily selected. For instance, MOR is an important catalyst for the carbonylation of dimethyl ether to methyl acetate owing to its 8-ring side pockets. To find an alternate carbonylation catalyst, Iglesia and co-workers performed a similarity search for raytrace histograms with features similar to those in MOR in the region between 0.12 and 0.46 nm, which correspond to the shape and size of the 8-ring side pockets in MOR.53 As a result, they found that AFS, AFY, SFO, and EON had the 8-ring side pockets most similar to those in MOR. Considering the fact that AFS, AFY, and SFO were not available as aluminosilicates yet, Iglesia and co-workers predicted that EON should be a promising alternate carbonylation catalyst or an even better one than MOR, because the 8-ring side pockets in EON were connected with 12-ring channels, which might allow faster diffusion of guest species. The PSD histogram and the ray-trace histogram are complementary to each other.52 The PSD histogram is highly sensitive to small changes in pore diameter, whereas the raytrace histogram is more sensitive to the subtle deviations in pore texture. These two-dimensional histograms enable us to assess a large number of zeolite structures in an automated and high-throughput manner without the necessity to visualize each one of them. 2.3. New Methods for the Calculation of Pores

2.3.1. The Grid-Based Approaches. In 2010, Sholl and co-workers introduced a grid-based approach to identify the diameters of the largest included sphere and the largest free sphere in a zeolite framework.54 This approach begins by dividing the unit cell of a zeolite framework into equally spaced discrete grid points. At each grid point, the distance from the grid point to the nearest framework atom can be calculated and recorded. The radius of the largest included sphere is simply the largest distance recorded among all of the grid points. To further calculate the diameter of the largest free sphere, the connectivity of pores within the zeolite framework must be determined. To do this, Sholl and co-workers adopted an efficient multiple-labeling algorithm.55 This algorithm begins by identifying all grid points at which a spherical probe of a given size could be located without overlapping any framework atom.

Figure 17. Ray-trace histogram of MFI (blue; solid line), the average one for IZA zeolites (orange; dashed line), and the average one for hypothetical zeolites accessible to a spherical probe of 0.325 nm in diameter (green; dotted line). Reprinted with permission from ref 53. Copyright 2013 Elsevier.

histogram of MFI, as well as the average ones calculated from 194 IZA structures and 139 396 hypothetical ones, respectively. The number, locations, and shapes of peaks in a ray-trace histogram are specific to each zeolite structure. For instance, the two highest peaks in the ray-trace histogram of MFI are located at 0.40 and 0.82 nm, which correspond to the rays 7278


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Figure 18. Graphical representation of the zeolite FER viewed along the [001] (left) and the [100] directions (right). The framework atoms are colored red (O) and beige (Si). The largest cage present in the structure is represented as a yellow sphere with a diameter of 6.250 Å. The green points represent the coordinates that are accessible to the largest free sphere. Reprinted with permission from ref 54. Copyright 2010 American Chemical Society.

the grid-based approach could be highly improved by parallelizing the main calculation routines.60 For complex zeolite structures such as LTN, the computation time speedup was over 23 times on a 24-core CPU, and a further speedup over 7 times was achieved by utilizing the Fermi GPU.60 2.3.2. ZEOMICS. ZEOMICS is a web tool developed by Floudas and co-workers for automatically characterizing the accessible cavities and channels in a given zeolite framework.61 Important quantities such as pore size distribution, accessible volume, surface area, and the diameters of the largest included sphere and the largest free sphere can be easily calculated using this tool. Different from other approaches, ZEOMICS simplifies the cavities and channels in a zeolite framework as simple overlapping spheres and cylinders, respectively (Figure 19). ZEOMICS starts with identifying the candidate portals within a zeolite framework, which are regular ring-like openings that guest molecules can pass through. Next, ZEOMICS finds

If two neighboring grid points are both feasible locations for a probe, then the probe can move continuously between the two grid points. If a set of feasible grid points connects the opposite sides of the unit cell of a zeolite framework, it forms a spanning cluster in which a probe can move freely. The largest free sphere that is capable of traversing the unit cell of a zeolite corresponds to the smallest spanning cluster. Sholl and co-workers calculated the diameters of the largest included sphere and the largest free sphere for 165 IZA frameworks54 and >250 000 hypothetical ones56,57 using the grid spacing of 0.1 Å. Most of their results were in good agreement with Foster and co-workers’ work based on the Delaunay triangulation.37 Moreover, the grid-based approach has shown two major advantages over other approaches. The first one is its capability to detect the largest accessible porous regions. For instance, zeolite FER possesses cages that are large enough to hold a spherical probe with the diameter of 6.25 Å (Figure 18). However, these cages are inaccessible from the main channels along the [001] direction, because their face openings are too small. The grid-based approach automatically detects this situation. According to Sholl and co-workers’ results, the largest accessible cavity in FER should have the diameter of 5.54 Å, 0.7 Å smaller than the global largest included sphere. The second advantage of the grid-based approach is its capability to model complex systems. Haranczyk and Sethian showed that the movement of a nonspherical molecule along the zeolite channel could be calculated through a high-dimensional grid-based approach.58,59 To model a real traversing molecule, the molecular worm, which was the assembly of solid blocks connected by flexible links, was used to replace the hard spherical probe that was often used in other approaches. On the other hand, the grid-based approaches have an obvious disadvantage. The precision of every grid-based approach is highly dependent on grid spacing. To reach high precision, it is necessary to use small grid spacing, which may lead to a large number of grid points to calculate. This can be computationally expensive for complex zeolite structures. In 2012, Haranczyk and co-workers showed that the efficiency of

Figure 19. Pores in zeolite MFI represented by overlapping cylinders and spheres. Reproduced with permission from ref 61. Copyright 2011 PCCP Owner Societies. 7279


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ray-tracing histogram (see section 2.2.8) can also be generated by Zeo++. As compared to grid-based approaches (see section 2.3.1), Zeo++ requires much less computation resources and therefore runs much faster. However, Zeo++ assumes that the traversing guest molecules are all hard spheres, which may not be accurate when nonspherical or flexible guest molecules are considered. Therefore, Zeo++ is better suited for high-throughput early stage analysis of a large set of zeolitic materials.

the largest void cylinder linking each pair of portals. A cylinder large enough for the passing of guest molecules indicates the presence of a channel. Spheres representing the cages and cavities are identified afterward through three-dimensional Delaunay triangulation. The junctions where a guest molecule can change its travel direction within a zeolite framework are located by intersecting the cylinders and spheres that have been found. This leads to the construction of a connectivity graph describing how channels and cavities connect to one another. The connectivity graph can be pruned to remove all channels and cages that are not accessible by guest molecules of a given size. The accessible porous volume and surface are calculated as those of the union of all cylinders and spheres within a unit cell using the pruned connectivity graph. Using ZEOMICS, Floudas and co-workers characterized the accessible pores in 194 IZA structures with respect to different guest molecules.61 On the basis of these results, a continuoustime Markov chain model was developed to estimate the distribution of guest molecules within a zeolite framework. With the aid of ZEOMICS, Floudas and co-workers carried out studies in the prediction of shape-selective separations62 and cost-effective CO2 capture63 in existing zeolites. Besides IZA structures, ZEOMICS also works well in principle for other microporous materials, including hypothetical zeolites and MOFs. 2.3.3. Zeo++. Zeo++ is an open-source software package developed by Haranczyk and co-workers for the analysis of the void space inside crystalline porous materials.64 Zeo++ is based on Voronoi decomposition, capable of calculating many geometric parameters describing the pores in zeolites. First, Zeo++ can be used to calculate various pore diameters in zeolite frameworks, such as the diameters of largest included sphere, the largest free sphere, and the largest accessible included sphere. As shown in section 2.2.7, the void space in a zeolite framework can be represented by a Voronoi network. The distance from each Voronoi node to each of its neighboring framework atom is calculated. The diameter of the largest included sphere is simply the largest distance obtained during this procedure. To calculate the largest free sphere that can travel between two Voronoi nodes, the path in the Voronoi network that leads through the nodes and edges with the largest distances to framework atoms needs to be found. This can be realized through the “lowest-cost path” algorithm.65 Second, Zeo++ is capable of calculating the accessible surface area and the accessible volume inside a zeolite framework. To determine the accessibility of the void space for a given guest molecule, each Voronoi node has to be classified as accessible or inaccessible. An accessible node in a Voronoi network is connected, directly or indirectly, to its periodic image in another unit cell. Furthermore, a node connected to an accessible channel or cavity must also be part of the channel or cavity. Once the accessibility is determined, the accessible surface area and the accessible volume can be calculated through the Monte Carlo sampling approach. Meanwhile, the dimensionality of the channel system can also be determined by recording whether a Voronoi node is connected to its copy in more than one direction. Third, Zeo++ can be used to generate multidimensional data to depict the pore landscapes of zeolite frameworks. For instance, the Voronoi holograms shown in section 2.2.7 were all generated using Zeo++. Moreover, the PSD histogram and the

2.4. Future Development

Describing a zeolite structure is not simply showing how it looks. A good structure descriptor should be able to be used for quantitative estimation of the physical and chemical properties of a zeolite framework. For instance, the accessible NBUs may be associated to the gas-separation ability of a zeolite framework;66 the Gaussian and mean curvatures of the zeolite pores are correlated to the adsorption sites and heats.67 On the other hand, rational synthesis of a specific zeolite structure requires clear understanding of the relationship between zeolite structures and zeolite syntheses.68−73 Recently, various computer data mining techniques have been used to partly solve this problem.74−88 In these studies, different zeolite structures have been simply represented by framework type codes, featured rings, or combinations of simple crystallographic parameters. Because of these simplifications, the instructive information obtained in these studies was only valid for a small number of specific structures. In general, the ideal descriptor for zeolite structures should have the following features: (1) it should be easy to calculate and to interpret; (2) it should carry the key topological and geometric information for each specific zeolite structure; (3) the similarity between different zeolite structures can be quantitatively measured using this descriptor; and (4) the structural feature described by this descriptor should have one-to-one correspondence to each specific structure. Descriptors with all of these features can be used both for quantitative property estimation and for analyzing the complex relationship between structures and syntheses. However, devising such descriptors is extremely difficult; it will be a long-term target in the studies of zeolite structures and deserves more efforts toward this end. It is worth noting that most structure description methods mentioned in this Review assume the zeolite frameworks to be rigid and static. For instance, the dimension of a zeolite ring is usually calculated by measuring the distances between the nearest and the farthest oxygen-pairs in that ring. Such calculations assume all of the framework atoms stay static at their average or ideal positions determined from X-ray data. In fact, zeolite frameworks are flexible; the framework atoms oscillate around their average positions all the time, especially at a high temperature. This dynamic effect may significantly change the geometrical features of zeolites, as well as their physical and chemical properties. For instance, theoretical calculations and experimental measurement have shown that the temperature-dependent effective pore sizes of zeolites are usually larger than the nominal pore sizes calculated using the static models.89−97 Because of this dynamic effect, zeolites are often able to adsorb and/or produce guest molecules with kinetic diameters larger than their static pore sizes. Besides temperature, the entrance and diffusion of guest species may also change the geometrical features of zeolite frameworks through host−guest nonbonding interactions.94−96,98−104 Although they are so important for the evaluation of zeolite 7280


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structures, the framework flexibility and dynamics have been neglected in nearly all of the current structure description methods. This is mainly because the calculation of these effects usually requires ab initio or classical molecular dynamics simulations over enough long time, which can be quite computationally expensive. New descriptors and new methods for the quick calculation of framework dynamics are both highly desired in the future.

3. NEW STRUCTURES Although zeolitic materials were already known as early as the 18th century, it is in the recent three decades that the large majority of zeolite structures were discovered. One of the most important reasons for this rapid progress is the further understanding of zeolite formation mechanisms as well as the development of synthetic strateties.12,23,71−73,105−116 For instance, Corma and co-workers synthesized a series of new zeolite structures by using designed organic structure-directing agents (OSDAs), such as novel quaternary ammonium cations, proton sponges, phosphonium cations, and superbasic phosphazenes, etc.;73 Lewis and co-workers developed a charge density mismatch (CDM) strategy, through which a series of new zeolitic materials have been prepared.117−121 Because of these recently developed synthetic strategies, the number of zeolite framework types has been growing rapidly in the past few years. Since the publication of the sixth edition of Atlas of Zeolite Framework Types in 2007,31 about 50 new zeolite framework types have been reported. Many of these new zeolite frameworks possess previously unseen or record-breaking structural features, leading to new understanding of the intrinsic nature of zeolite structures. 3.1. Structures with Unprecedented Pore-Openings

The pore-openings in zeolite frameworks are one of the most important factors that affect the physical and chemical properties of zeolitic materials. By 2007, pore-openings of many different sizes had been discovered, including 7-, 8-, 9-, 10-, 11-, 12-, 14-, 18-, and 20-rings. Different sizes of poreopenings have different shape-selective applications. Therefore, zeolite structures with unprecedented pore-openings have always been highly desired. Extra-large pore-openings, especially those larger than 14-rings, are of special interest, because they allow the entrance of large guest molecules that are inaccessible to regular zeolite structures. By 2007, there were only three zeolite structures possessing pore-openings larger than 14-ring: ETR (18-ring), VFI (18-ring), and −CLO (20-ring). To date, many new zeolite structures with unprecedented pore-openings have been synthesized. Fascinatingly, some of these structures possess pore-openings in the range of mesopores. 3.1.1. JU-64 (JSR). Gallogermanate zeolite JU-64 (| (Ni(C3H10N2)3)36Ni4.7|[Ga81.4Ge206.6O576]) was solvothermally synthesized by using [Ni(C3H10N2)3]2+ cations as the structuredirecting agent.122 JU-64 has a trigonal unit cell (R3; a = 30.012 Å, c = 37.301 Å). The framework of JU-64 can be described as the combination of three types of CBUs, including 6-rings, lov units, and d6r cages. The 6-rings and d6r cages are connected with each other alternately via the lov units, forming a layered structure (Figure 20a). Linking of these layers via lov units results in the three-dimensional structure of JU-64 (Figure 20b). The framework of JU-64 features a three-dimensional intersecting 11-ring channel system. The 11-ring channels

Figure 20. (a) The single layer of 6-rings and d6r cages connected via lov (spiro-5) units, and (b) the three-dimensional framework of JU-64. Yellow sticks show the three-dimensional interconnecting 11-ring channel system. Reprinted with permission from ref 122. Copyright 2013 Wiley-VCH.

running along three orthogonal directions have the free diameters of ca. 5.2 × 7.0 Å2. Such a highly porous system leads to a framework density of 9.9 T/1000 Å3, which is the lowest among all known oxide zeolites to date. [Ni(C3H10N2)3]2+ cations reside in the 11-ring channels; they could not be removed by calcination because of their strong electrostatic interactions with the host framework. JU-64 is the first four-connected zeolitic structure possessing three-dimensionally intersecting 11-ring channels. The other zeolite possessing 11-ring channels is NU-86, where 11-ring channels intersect with 10- and 12-ring channels.123,124 The idealized framework topology of JU-64, named JSR by IZA-SC, has the cubic symmetry of Pa3. 3.1.2. ITQ-40 (−IRY). Germanosilicate zeolite ITQ-40 ([Ge 32.4 Si 43.6 O 150 (OH) 4 ]) could be prepared by using dimethyldiphenylphosphonium (Me2Ph2POH) or diethyldiphenylphosphonium (Et2Ph2POH) as the structure-directing agent.125 ITQ-40 has a hexagonal unit cell (P63/mmc; a = 16.469 Å, c = 32.192 Å). The basic building unit of ITQ-40 is the [64·53·43·3] cage, in which one of the T atoms is only threeconnected to its neighbors. The [64·53·43·3] cages connect to one another horizontally via d4r cages and vertically via d3r cages (Figure 21). ITQ-40 is the first zeolite framework 7281


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Figure 22. 16-ring channels in ITQ-51. Oxygen atoms are omitted for clarity.

idealized framework topology of ITQ-51 (framework IFO with symmetry Pmmn) was theoretically predicted by Deem and co-workers before ITQ-51 was synthesized.57 3.1.4. ITQ-44 (IRR). Germanosilicate zeolite ITQ-44 ([Ge17.7Si34.3O104]) was synthesized by using (2′-(R),6′-(S))2′,6′-dimethylspiro[isoindole-2,1′-piperidin-1′-ium] as the structure-directing agent.127 ITQ-44 has a hexagonal unit cell (P6/mmm; a = 19.536 Å, c = 14.450 Å). The framework structure of ITQ-44 is closely related to that of ITQ-33, another germanosilicate zeolite (IZA framework type code: ITT).128 ITQ-33 is built up from the [32·43·69] cage with two additional T atoms inside (Figure 23a). The [32·43·69] cages

Figure 21. Frameworks of ITQ-40 showing (a) the 16-ring pores and (b) the 15-ring pores. Oxygen atoms are omitted for clarity.

possessing d3r cages. The T−O−T angles in d3r cages are all smaller than 130°. Similar to those in d4r cages, the T−O−T angles in d3r cages can be relaxed by germanium atoms, which have larger ionic radii than silicon, allowing for more acute T− O−T angles. The framework of ITQ-40 features a very large threedimensional channel system (Figure 21). It possesses near circular 15-ring channels running along the [001] direction (9.9 Å in diameter), which further connect to a two-dimensional channel system formed by 16-ring channels running along the ⟨100⟩ directions (9.4 × 10.4 Å2). ITQ-40 is the first zeolite structure possessing 15-ring channels and also the first possessing 16-ring channels. The interconnecting extra-large porous system in ITQ-40 leads to a framework density of 10.1 T/1000 Å3, which is one of the lowest among all known zeolite structures. 75% of the organic structure-directing agent residing in ITQ-40 could be removed without structural degradation by in situ calcination at 450 °C. The idealized framework topology of ITQ-40 was named −ITV by IZA-SC recently. 3.1.3. ITQ-51 (IFO). Silicoaluminophosphate zeolite ITQ-51 ([Si2.6Al14.7P14.7O64]) was synthesized by using 1,8-bis(dimethylamino)naphthalene as the structure-directing agent.126 ITQ-51 has a monoclinic unit cell (P21/n; a = 23.345 Å, b = 16.513 Å, c = 4.9814 Å, β = 92.620°). The framework of ITQ-50 is built from parallel lau chains and helical 4-ring chains, which connect to one another by sharing the common T atoms. ITQ-51 features one-dimensional 16-ring channels along the [001] direction with free diameters of 9.9 × 7.7 Å2 (Figure 22). The framework density of ITQ-51 is 16.7 T/1000 Å3. ITQ-51 is the first aluminophosphate-based zeolite possessing 16-ring channels. More importantly, ITQ-51 is stable after the organic structure-directing agent is removed by calcination in air at 550 °C, being one of the very few examples of hydrothermally stable molecular sieves containing extra-large pores. The

Figure 23. Framework structures of ITQ-33 and ITQ-44. (a) The primary building unit in these two structures. (b) The building units connect to one another via d4r cages. The bold arrow indicates the connection. (c) The 18-ring channels viewed along the [001] direction. (d) The formation of the 10-ring channels in ITQ-33: 3rings are fused. (e) The formation of d3r and 12-ring channels in ITQ44: 3-rings are not fused. Oxygen atoms have been omitted for clarity. Reprinted with permission from ref 127. Copyright 2010 Wiley-VCH.

connect to one another horizontally via d4r cages, forming extra-large 18-ring channels along the [001] direction; meanwhile, the [32·43·69] cages connect to one another vertically by fusing adjacent 3-rings, forming interconnecting 10-ring channels running along the ⟨100⟩ directions (Figure 23b−d). In comparison, in ITQ-44, the 3-rings vertically connecting adjacent [32·43·69] cages are not fused; they form the d3r cages instead (Figure 23e). As a consequence, the 18ring channels (12.2 Å) along the [001] direction in ITQ-33 are retained in ITQ-44 (12.5 Å); the interconnecting 10-ring 7282


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channels (4.3 × 6.1 Å2) along the ⟨100⟩ directions in ITQ-33 are expanded to 12-ring channels (8.2 × 6.0 Å2) in ITQ-44, due to the existence of d3r cages. ITQ-44 is the first zeolite possessing a three-dimensional channel system formed by interconnecting 18- and 12-ring channels. The framework density of ITQ-44 is 10.9 T/1000 Å3. The organic structuredirecting agent residing in ITQ-44 could be removed by calcination at 550 °C under a N2/O2 flow. The idealized framework topology of ITQ-44, named IRR by IZA-SC, has the same symmetry as ITQ-44. The topology of IRR had been predicted by Foster and Treacy129 in theory before ITQ-44 was synthesized. 3.1.5. ITQ-43. ITQ-43 ([Ge0.31Si0.69O2]) is a germanosilicate zeolite synthesized by using (2′R,6′S)-2′,6′-dimethylspiro[isoindoline-2,1′-piperidin]-1′-ium hydroxide as the organic structure-directing agent.130 ITQ-43 has an orthorhombic unit cell (Cmmm; a = 26.090 Å, b = 41.866 Å, c = 12.836 Å). The framework of ITQ-43 is constructed from d4r cages, mel cages, and 6-rings (Figure 24a). Two distorted d4r cages (with

Figure 25. Framework of ITQ-43 viewed along (a) [100], (b) [010], and (c) [001] directions. Oxygen atoms are omitted for clarity.

structure-directing agent.131 ITQ-37 crystallizes in a cubic unit cell (P4132 or P4332; a = 26.513 Å). The CBUs for ITQ-37 are lau cages and d4r cages with one or two terminal hydroxyl groups (Figure 26a). Three lau and four d4r cages form a tertiary building unit; the tertiary building units connect to one another and eventually form the three-dimensional framework of ITQ-37 (Figure 26b). The connectivity of the tertiary building units follows a three-coordinated gyroidal srs net.132 The framework of ITQ-37 possesses a very open threedimensional channel system. The channel-openings are asymmetric and enclosed by 30 T atoms (4.3 × 19.3 Å2), which are the largest among all known zeolites to date. The extra-large 30-ring channel system leads to an extremely low framework density (10.3 T/1000 Å3). Unlike other extra-largepore zeolites, ITQ-37 is quite thermally stable after the removal of the organic structure-directing agent. Corma and co-workers showed that a pelletized sample of ITQ-37 calcined at 540 °C could remain stable for 2 weeks at room temperature in a moisture-free environment. The idealized framework topology of ITQ-37, named −ITV by IZA-SC, has the same symmetry as ITQ-37, indicating its intrinsic chirality (see section 3.3).

Figure 24. (a) The primary building blocks in ITQ-43. (b) The composite building unit formed by the primary building blocks. (c) The sheet structure viewed along the [001] direction. Oxygen atoms are omitted for clarity.

terminal hydroxyl groups), one mel cage, and a pair of fused 6rings form the CBU of ITQ-43 (Figure 24b), which connects to its neighbors along the [010] direction, forming two-dimensional sheet structures (Figure 24c). These sheets are connected to one another via d4r cages along the [001] direction and form the complete framework of ITQ-43 (Figure 25a,b). ITQ-43 features one-dimensional cloverleaf-like 28-ring channels running along the [001] direction (Figure 25c). The 28-ring channel-openings have the dimensions of 21.9 × 19.6 Å2 in their longest axes, which are in the range of mesopores. These mesoporous 28-ring channels are further connected to a two-dimensional channel system formed by 12-ring channels along the [100] direction (6.8 × 6.1 Å2) and the ⟨110⟩ directions (7.8 × 5.7 Å2) (Figure 25). The resulting threedimensional channel system leads to a framework density of 11.4 T/1000 Å3. ITQ-43 is the first hierarchical crystalline zeolitic structure consisting of both micropores and mesopores that are intrinsic to the framework. The organic structuredirecting agent within these pores could be removed by in situ calcination at 700 °C under a continuous flow of dry air. 3.1.6. ITQ-37 (−ITV). ITQ-37 (|(C22N2H40)10.5(H2O)x| [Ge80Si112O400H32F20]) is a germanosilicate zeolite synthesized by using a bulky diquaternary ammonium molecule as the

3.2. Structures with Unprecedented Complexity

Although the information-based topological complexity reflects the complexity of a zeolite framework more accurately (see section 2.2.6), the number of topologically distinct T atoms has actually been the most widely used complexity measure because of its simplicity. By the time the sixth edition of Atlas of Zeolite Framework Types was published in 2007,31 the most complex 7283


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Figure 26. Framework and corresponding net of ITQ-37. (a) A slice (15.3 Å thick) viewed down the [111] direction. Only the T−T connections and the terminal hydroxyl groups are shown. All d4r cages have the same orientation. (b) The 30-ring built from 10 tertiary building units. One of them is highlighted (lau cage in orange and d4r cage in green). The centers of the tertiary building units fall on the nodes of the srs net (in orange). Reprinted with permission from ref 131. Copyright 2009 Nature Publishing Group.

Figure 27. Framework structure of SSZ-74. (a) A portion of the structure showing the T vacancy and the interaction between O3 and O33 of the framework with N13 and N5 of the structure-directing agent. (b) Projections of the framework structure down the [010], [110], and [001] directions showing the arrangement of the vacancies and of the 10-ring pore-openings. Bridging oxygen atoms are omitted for clarity. Reprinted with permission from ref 135. Copyright 2008 Nature Publishing Group.

zeolite frameworks (TUN133 and IMF134) possessed 24 distinct T atoms. In this section, we will show several recently reported structures with unprecedented complexity, which are difficult to solve and to describe. These complex structures may contain distinct T atoms more than 24, consist of many topologically distinct building units, or possess defects and stacking disorders.

3.2.1. SSZ-74 (−SVR). High-silica zeolite SSZ-74 (| (C16H34N2)4|[Si92□4O184(OH)8]; □ stands for a vacancy site) was synthesized by using 1,6-bis(N-methylpyrrolidinium)-hexane as the structure-directing agent. In 2008, McCusker and co-workers solved its structure by combining powder X-ray diffraction and electron microscopy data within the charge-flipping algorithm (see section 4.1.2).135 SSZ-74 has a monoclinic unit cell (Cc; a = 20.4756 Å, b = 13.3839 Å, c = 7284


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20.0859 Å, β = 102.1°). SSZ-74 features a three-dimensional channel system, in which 10-ring channels running along the [010], [110], and [001] directions are interconnected with one another (Figure 27). SSZ-74 is a complex zeolite structure because it contains 24 crystallographically distinct T atom sites. In addition, one of the 24 T sites has zero occupancy. In other words, SSZ-74 contains ordered T vacancies. Each vacancy is tetrahedrally surrounded by four framework oxygen atoms, which has never been observed before. Assuming the charge-balance argument, two of the four O atoms near the T vacancy are siloxy oxygens, which are close to N atoms of the doubly charged structure-directing agents; the remaining two O atoms should be silanol oxygens (Figure 27). Because of these vacancies, the framework of SSZ74 is not stable upon calcination. The idealized framework topology of SSZ-74, named −SVR by IZA-SC, has the same symmetry as SSZ-74. 3.2.2. SSZ-31 (*STO). High-silica zeolite SSZ-31 is an extreme example of highly complex and faulted structures.136,137 SSZ-31 was first synthesized in 1991 by using N,N,N-trimethyltricyclo[5.2.1.02,6]decaneammonium as the structure-directing agent. It took over 10 years until its final structure was elucidated with the aid of adsorption measurement, TEM, high-resolution X-ray diffraction, and modelbuilding techniques. The basic building units of SSZ-31 are tubular 12-ring pores with diameters of 8.6 × 5.7 Å2, which are constructed from rolled-up honeycomb-like sheets of fused 6rings (Figure 28a). These tubular pores are arranged into

The stacking disorder is not the only factor that makes SSZ31 so complex. Actually, some of the individual end structures of SSZ-31 are very complex, too. For instance, its polymorph I has the symmetry of P2/m and contains 28 topologically distinct T atoms. To build the framework structure of polymorph I, it requires 9 topologically distinct and 40 crystallographically distinct NBUs (see section 2.2.3). SSZ-31 was named *STO by IZA-SC, and its polymorph I was selected as its type material (Figure 28b). 3.2.3. ITQ-39. Pure silicate and aluminosilicate zeolites ITQ-39 were synthesized by using dicationic piperidine derivatives as the structure-directing agents.138 In 2012, Zou and co-workers solved its structure with the aid of rotation electron diffraction tomography (see section 4.2.2).139 ITQ-39 is constructed from the intergrowth of three different polymorphs (designated A, B, and C), which are all built from the same building layer (Figure 29a) but stacked differently along c*. In polymorph A, the neighboring building layers are shifted alternately by +1/3b and then −1/3b; in polymorph B, the neighboring layers are shifted by −1/3b; in polymorph C, the neighboring layers are stacked with no shift (Figure 29b). All three polymorphs give the same projection along b, showing the unique pairwise 12-ring channels (Figure 29c). The 12-ring channels are interconnected by three zigzagged 10-ring channels along the a, c, and a + c axes. Just like that in SSZ-31 (see section 3.2.2), the stacking disorder does not block these channels. The three polymorphs of ITQ-39 have the symmetries of P2/c, P1̅, and P2/m, respectively. The structure of each individual polymorph is very complex; they contain 28, 28, and 16 topologically distinct Si atoms, respectively. Two of the silicon atoms in polymorphs A and B and one in polymorph C are three-connected, each of which has an occupancy of 0.5. 3.2.4. SSZ-57 (*SFV). High-silica zeolite SSZ-57 was synthesized in hydroxide media by using the bulky N-butylN-cyclohexylpyrrolidinium cation as the structure-directing agent. In 2011, McCusker and co-workers solved this structure by applying the advanced crystallographic techniques to highquality single-crystal X-ray diffraction data collected for a microcrystal.140 The idealized model of SSZ-57 has a complex modulated structure (space group: P4m ̅ 2; a = 20.091 Å, c = 110.056 Å). It can be described as a disturbed ZSM-11 structure (MEL), where one of the 16 10-ring channels is replaced by a 12-ring channel (Figure 30). Because of the tetragonal symmetry, there are two mutually perpendicular 12ring channels per unit cell; at each 12-ring interruption, the ZSM-11 structure is rotated by 90° around the c axis. The idealized framework model of SSZ-57 was named *SFV by IZA-SC. The number of crystallographically distinct T atoms in *SFV has reached 99, which is an overwhelmingly large number in comparison with 28, the second largest number known so far (see SSZ-31 and ITQ-39). To build the idealized model of *SFV, it requires 15 topologically distinct and 113 crystallographically distinct NBUs. However, *SFV is only the idealized framework model of SSZ-57, which cannot explain all of the peaks in the electron density map.140 In fact, the 12-rings and the 8-rings are disordered in the structure of SSZ-57. A detailed description of the disorder in this structure can be found in ref 140.

Figure 28. (a) The tubular 12-ring pore in SSZ-31. (b) The polymorph I viewed along the pore axis.

different types of layers depending on whether the shift between adjacent pores in the layer is zero or one-half of the repeat distance along the pore. Different 12-ring layers may be stacked in different ways to form various three-dimensional framework structures. According to van Koningsveld and Lobo’s result, SSZ-31 might be the intergrowths of 10 end structures (polymorphs A−J), each of which is constructed from a unique stacking of 12-ring layers.137 The local porous structures are the same in all of these end structures; therefore, the stacking disorder in SSZ-31 does not block the 12-ring pores in it.

3.3. Structures with Intrinsically Chiral Frameworks

Chiral zeolitic materials are highly desired because of their potential applications in enantioselective catalysis and separa7285


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Figure 29. Three-dimensional electron potential map and atomic structure model of the stacking disorder in ITQ-39. (a) Three-dimensional electron potential map of the building layer of ITQ-39. The refined structure model of ITQ-39 is superimposed, and only the Si−Si connections are shown. (b) Atomic structure model of the three polymorphs viewed along a. The building layers (highlighted) are stacked along c*. (c) Projection along b showing the unique pairwise 12-ring channels. Reprinted with permission from ref 139. Copyright 2012 Nature Publishing Group.

Figure 30. Framework structure of SSZ-57 viewed along the [010] direction. Bridging O atoms have been omitted for clarity. The arrow indicates the 12-ring channel along the [100] direction.

tion. In general, a zeolitic structure is “chiral” if it does not possess any improper rotational symmetry element. The chirality of a zeolite may come from its underlying framework topology, the distribution of framework heteroatoms, or the arrangement of extra-framework species.141 A zeolite framework is intrinsically chiral if the maximum symmetry of its underlying topology is chiral.142 Intrinsically chiral zeolite frameworks are quite rare. When the sixth edition of Atlas of Zeolite Framework Types was published in 2007, there were only four intrinsically chiral zeolite framework types, including *BEA, CZP, GOO, and OSO. To date, more intrinsically chiral zeolites have been discovered. For instance, ITQ-37 (−ITV) shown in section 3.1.6 is an intrinsically chiral zeolite. In this section, we will show a few more examples of intrinsically chiral structures. It is worth mentioning that most chiral zeolites, including intrinsically chiral ones, can only be prepared as racemic mixtures. 3.3.1. SU-32 (STW). silicogermanate zeolite SU-32 (| (H 3 NCH(CH 3 ) 2 F) 6 |[Ge 31.68 Si 28.32 O 120 ]) was synthesized

under hydrothermal conditions by using diisopropylamine as the structure-directing agent.143 SU-32 has the chiral symmetry of P6122 or P6522. Its framework structure is composed of the d4r cages and the [46·58·82·102] cavities. The [46·58·82·102] cavities connect to their neighbors by sharing the common 10rings to form helical channels running along the c axis (Figure 31a). All of the helical channels have the same handedness (Figure 31b). The helical channels are interconnected with 8ring channels running along the [100], [010], and [110] directions at different heights (Figure 31b). The free diameters of the 10- and 8-ring channel-openings are 5.5 × 5.0 and 4.7 × 3.0 Å2, respectively. The organic structure-directing agent residing in these channels could be removed by calcination at 400 °C. The framework density of SU-32 is 15.3 T/1000 Å3. The idealized framework topology of SU-32 has the same chiral symmetry as SU-32, which was named STW by IZA-SC. In 2012, a pure silica polymorph of STW, HPM-1, was synthesized by using 2-ethyl-1,3,4-trimethylimidazolium cations as the structure-directing agent.144 This is the first pure silica 7286


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arrangement around the 10-ring channel. Protonated diethylamine molecules reside in the 10-ring channels; removal of them by calcination results in the collapse of the host framework. The idealized framework topology of CJ-40, named JRY by IZA-SC, has the chiral symmetry of I212121. It is worth mentioning that the bulk products of CJ-40 obtained from synthesis were not racemic even though no chiral starting materials were added into the reacting mixtures. 3.3.3. Linde J (LTJ). Aluminosilicate zeolite Linde J (| (NH4)8(H2O)4|[Al8Si8O32]) was first synthesized in the early 1960s. Although the framework model of Linde J had already been built in the 1990s, it is until recently that the structure of the as-synthesized Linde J was determined.146 The assynthesized Linde J has the chiral symmetry of P212121. The primary building units of Linde J are parallel two-dimensional 4·82-nets, which are further linked to their neighbors to form the complete three-dimensional framework of Linde J (Figure 33). The AlO4 and SiO4 tetrahedra are connected alternately. Figure 31. Helical channels in SU-32. (a) The right-handed helical channels in SU-32 (space group: P6122). One of the [46·58·82·102] cavities is marked in yellow. Only the T−T connections are shown. (b) Tiling representation showing the channel system in SU-32. All of the helical channels have the same handedness. Reprinted with permission from ref 143. Copyright 2008 Nature Publishing Group.

chiral zeolite with helical pores. It is worth mentioning that STW is closely related to SOF. Both frameworks are constructed by the same chiral layer.143 The relation between these two frameworks is analogous to that between the polymorphs A and B of zeolite beta. 3.3.2. CJ-40 (JRY). Cobalt aluminophosphate zeolite CJ-40 (|(C4NH12)2|[Co2Al10P12O48]) was synthesized by using diethylamine as the structure-directing agent under solvothermal conditions.145 CJ-40 has the chiral symmetry of P212121. The framework of CJ-40 possesses one-dimensional 10-ring channels running along the [010] direction (Figure 32a). The free diameters of the 10-ring channels are 4.4 × 2.2 Å2. The 10ring channels are enclosed by double-helical ribbons of the same handedness made of the fused 6-rings along the 21 screw axis (Figure 32b). Unlike those in other heteroatom-containing aluminophosphate zeolites, the cobalt atoms in CJ-40 selectively occupy one of the three Al sites, forming a helical

Figure 33. Linde J viewed along the [010] direction showing Sitetrahedra (yellow) and Al-tetrahedra (red). Extra-framework species are also shown. Reprinted with permission from ref 146. Copyright 2011 Elsevier.

The zigzag 8-ring channels along the [010] direction interconnect with the 8-ring channels along the [100] direction, forming a two-dimensional 8-ring channel system. The

Figure 32. Framework structure of CJ-40. (a) View along the [010] direction. (b) The 10-ring channel enclosed by double-helical ribbons made of fused 6-rings. Reprinted with permission from ref 145. Copyright 2009 Wiley-VCH. 7287


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has C1 symmetry (C1-3Rs) and the other C3 symmetry (C33Rs). Each C3-3R is surrounded by three C1-3Rs, whereas each C1-3R is surrounded by two C1-3Rs and one C3-3R. Adjacent 3-rings connect to each other to form a lov (spiro-5) unit, and the lov units are connected to one another to construct the complete framework of CJ-63. The idealized framework topology of CJ-63 was named JST by IZA-SC. It was found afterward that JST was also realizable as aluminogermanates, but the Al/Ge ratio in them could not exceed 1/2 due to the restriction of Loewenstein’s rule.149 3.4.2. PKU-9 (PUN). Aluminogermanate zeolite PKU-9 (| (C5H14N)8|[Al8Ge28O72]) was synthesized under hydrothermal conditions by using trimethylethylammonium hydroxide as the structure-directing agent.150 PKU-9 has an orthorhombic unit cell (Pbcn; a = 15.578 Å, b = 9.1704 Å, c = 19.993 Å). PKU-9 possesses a two-dimensional channel system formed by the 10ring channels running along the [001], [110], and [110̅ ] directions. The 10-ring channel system is further connected with the 8-ring channels along the [001] direction, forming a three-dimensional channel system. Trimethylethylammonium cations are located in the 10-ring channels; they could not be removed by calcination because of their strong nonbonding interactions with the host framework. The framework of PKU-9 can be decomposed into undulating CGS layers (Figure 35a), which can be further decomposed into zigzag 4-ring ladders (Figure 35b). The zigzag ladders connect to one another through 4-rings to form the CGS layers; adjacent CGS layers connect to one another through additional T atoms, forming the lov units and the complete framework of PKU-9. The idealized framework topology of PKU-9, named PUN by IZA-SC, has the same symmetry as PKU-9. PUN contains five crystallographically distinct T atoms, three of which are involved in 3-rings. 3.4.3. Oxonitridophosphate-2 (NPT). As compared to oxygen, nitrogen atoms can be either two- or three-coordinated to tetrahedral centers, and therefore are more suitable for small T−X−T angles. Replacing oxygen by nitrogen can not only stabilize the 3-rings but also produce adjustable charges in zeolite frameworks. Therefore, nitride zeolites may possess a larger diversity of 3-ringed structures than conventional oxide zeolites. The first successful example of nitride zeolites with a large quantity of 3-rings is oxonitridophosphate-1,151 whose framework topology was named NPO by IZA-SC in 2004. NPO is constructed exclusively from 3-rings, possessing onedimensional 12-ring channels. In 2011, the second nitride zeolite, oxonitridophosphate-2 (| Ba152Cl100.32|[P288O84.32N491.68]), was reported.152 Oxonitridophosphate-2 has a cubic unit cell (Fm3c̅ ; a = 26.854 Å). The basic building units in oxonitridophosphate-2 are cornersharing P(O/N)4 tetrahedra (Figure 36). Oxonitridophosphate-2 features a new type of cavities, that is, the [38·46·812] cavities. These new cavities connect to one another via 4-rings, yielding 8-ring channels along the ⟨100⟩ directions with free diameters of 2.9 × 2.9 Å2 (assuming the diameter of N to be 2.94 Å). Oxonitridophosphate-2 possesses a large quantity of 3rings; all of the T atoms in this structure are involved in 3-rings. Oxonitridophosphate-2 has a surprising thermal stability up to at least 1100 °C, a temperature where most 3-ringed zeolites are already decomposed. The idealized framework topology of oxonitridophosphate-2, named NPT by IZA-SC, has the symmetry of Pm3̅m. The unit cell of NPT is 1/8 the size of the original oxonitridophosphate-2.

idealized framework topology of Linde J, named LTJ by IZASC, has the chiral symmetry of P41212. 3.4. Structures with 3-Rings

Since the prediction made by Brunner and Meier that zeolites consisting of lots of small rings might possess very low FD,147 many efforts have been made to synthesize 3-ringed zeolites because of their potentially high porosity. However, 3-rings are not favored in conventional silicate or aluminophosphate zeolites. By the time the sixth edition of Atlas of Zeolite Framework Types was published in 2007,31 there were only 13 zeolite structures possessing 3-rings. This is because 3-rings require very small T−O−T angles that are energetically unfavorable for SiO4 and AlO4 tetrahedra. To date, it has been widely accepted that the strains in 3-rings can be effectively released by nonconventional T elements, such as Be, Ge, and transition metals. Following this idea, many new zeolites with 3-rings have been synthesized during the past few years. For instance, as we have shown above, ITQ-40 and ITQ44 (IRR) both possess d3r cages (double-3-rings); LSJ-10 (JOZ) possesses lov units (corner-sharing 3-ring pairs). In this section, we will show a few more examples of 3-ring-dominant structures. 3.4.1. CJ-63 (JST). Gallogermanate zeolite CJ-63 (|Ni(en)3| [Ga2Ge4O12], en = ethylenediamine) was synthesized by using [Ni(en)3]2+ cations as the structure-directing agent under solvothermal conditions.148 CJ-63 has a cubic unit cell (Pa3;̅ a = 16.572 Å). The framework of CJ-63 possesses interconnecting 10-ring channels running along the [100], [010], and [001] directions (Figure 34a). This large three-dimensional channel

Figure 34. (a) The framework of CJ-63 viewed along the [100] direction, (b) the [34·6·103] cavity, and (c) the [38·106] cavity. The gray spheres show the pores in cages. All oxygen atoms are omitted for clarity. Reprinted with permission from ref 148. Copyright 2011 Wiley-VCH.

system leads to a low framework density of 10.5 T/1000 Å3. The channel-openings have free diameters of 6.7 × 5.6 Å2. The framework of CJ-63 features two types of unique cavities, the [34·6·103] cavities (Figure 34b) and the [38·106] cavities (Figure 34c). The [34·6·103] cavity is chiral, which holds the [Ni(C3H10N2)3]2+ cations of the same handedness. Because of their strong nonbonding interactions with the host framework, these [Ni(C3H10N2)3]2+ cations could not be removed by calcination in air. The framework of CJ-63 is constructed exclusively from 3rings (all of the T atoms in CJ-63 are involved in 3-rings). There are two types of unique 3-rings in CJ-63, one of which 7288


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Figure 35. (a) The framework of PKU-9 viewed along the [010] direction. The lov (spiro-5) unit is emphasized by an ellipse; the tetrahedra in the CGS layers are shown in red and blue. (b) The CGS layer, with two zigzag 4-ring ladders shaded in green and cyan, respectively. Reprinted with permission from ref 150. Copyright 2009 American Chemical Society.

Figure 36. Framework of oxonitridophosphate-2. Top: Drawing with P−N bonding. Bottom: Representation with only P−P linking. Reprinted with permission from ref 152. Copyright 2011 American Chemical Society.

3.4.4. Be-10 (BOZ). Beryllium arsenate zeolite Be-10 (| (C2H5NH2,H2O)x|[Be66.7As25.3O80.5(OH)103.5] was synthesized under hydrothermal conditions by using ethylamine as the structure-directing agent.153 80% of the extra-framework species, including ethylamine and water molecules, could be removed from the host framework by calcination below 250 °C. Be-10 has the monoclinic symmetry of P21/m, whereas its idealized framework topology, named BOZ by IZA-SC, has the orthorhombic symmetry of Cmcm. The structure of BOZ features two unique cavity types: the [310·85·102] cavities and the [36·41·62·84] cavities (Figure 37a,b). These cavities connect to one another, forming thick layers in the ac plane; neighboring thick layers are connected via lov units, forming the complete framework of BOZ. BOZ possesses a complex two-dimensional channel system constructed by 10-ring channels running along the [001], [100], [101], and [101̅] directions, and 8-ring channels along the [001] and [100] directions (Figure 37c,d). BOZ possesses a large quantity of 3rings; all of the eight crystallographically distinct T atoms in BOZ are involved in 3-rings. Along with Be-10, Be-11 and Be-12 were also synthesized under similar conditions.153 The framework structures of Be-11 and Be-12 are similar to that of Be-10. They both possess twodimensional channel systems formed by interconnecting 10-

Figure 37. Framework structure of BOZ. The (a) [310·85·102] and (b) [36·41·62·84] cavities. (c) The structure viewed down the [100] direction and (d) along the [001] direction. The T(O/OH)4 tetrahedra are shaded blue, and oxygen atoms are shown as red spheres. One position of each of the two cavities is outlined with pale yellow shading in each view, as an ellipse and a circle, respectively. Reprinted with permission from ref 153. Copyright 2012 Nature Publishing Group.

and 8-ring channels. There are a large quantity of 3-rings in these two structures, too. 3.5. Future Development

Because of their high adsorption capability and special shapeselectivity for bulky molecules, many efforts have been made to synthesize large-pore zeolites. Before 2007, the largest poreopening was 20-ring (−CLO). To date, both 28- (in ITQ-43) and 30-rings (in −ITV) have been discovered. However, it is worth noting that all of these record-holding rings can only be 7289


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Table 4. Structure Determination Methods for the 50 Newly Reported Zeolite Structures Since 2007 type material 153

Be-10 beta polymorph B168 CJ-40145 CJ-62171 CJ-63148 CJ-69172 COK-14157 ERS-18173 IM-16174 IM-20176 IPC-4177 ITQ-26178 ITQ-33128 ITQ-34179 ITQ-37131 ITQ-38181 ITQ-39139 ITQ-40125 ITQ-43130 ITQ-44127 ITQ-49185 ITQ-50186 ITQ-51126 ITQ-52187 JU-64122 Levyne B188 Linde J146 LSJ-10189 LZ-135190 MCM-70191 oxonitridophosphate-2152 PKU-9150 SSZ-31136,137 SSZ-52193 SSZ-56194 SSZ-57140 SSZ-65195 SSZ-74135 SSZ-77196,197 SSZ-82199 STA-15200 SU-15143 SU-32143 SU-78201 UCSB-7202 UCSB-9203 UCSB-15202 ZnAPO-57121 ZnAPO-59121 ZSM-48205

IZA code BOZ JRY JSW JST JSN OKO EEI UOS UWY PCR IWS ITT ITR −ITV ITG −IRY IRR

IFO JSR LTJ JOZ LTF MVY NPT PUN *STO SFW SFS *SFV SSF −SVR SVV SEW SAF SOF STW BSV SBN BOF AFV AVL *MRE

data typea

determination programb

SXRD ED+HRTEM SXRD SXRD SXRD SXRD PXRD PXRD PXRD PXRD PXRD PXRD+ED PXRD PXRD PXRD+ED ED+HRTEM ED (3D)+HRTEM PXRD ED (3D) PXRD PXRD PXRD ED (3D) PXRD SXRD SXRD PXRD SXRD PXRD PXRD PXRD+ED+HRTEM SXRD PXRD+HRTEM PXRD+HRTEM PXRD SXRD PXRD PXRD+HRTEM PXRD PXRD PXRD SXRD SXRD SXRD+ED+HRTEM SXRD SXRD SXRD PXRD PXRD PXRD+ED+HRTEM

SHELX CRISP169+eMap170 SHELX SHELX SHELX SHELX model-building FOCUS/EXPO EXPO175 EXPO model-building FOCUS FOCUS FOCUS Superflip180 model-building CRISP+eMap PowderSolve182 SIR183 FOCUS184 FOCUS FOCUS SHELX FOCUS SHELX SHELX SHELX SHELX Superflip FOCUS/Superflip TOPAS192 SHELX model-building model-building FOCUS Superflip FOCUS Superflip ZEFSAII198/Superflip Superflip model-building SHELX SHELX model-building SHELX SHELX SHELX204 model-building SHELX model-building

a

SXRD = single-crystal X-ray diffraction; PXRD = powder X-ray diffraction; ED = electron diffraction; HRTEM = high-resolution transmission electron microscopy. bOnly the key programs that have rendered the initial structure models are shown.

found in interrupted frameworks. Among fully four-connected frameworks, the largest pore-opening is still 18-ring (in ETR, IRR, ITT, and VFI). Because these frameworks are generally more stable than interrupted ones, more efforts should be made to realize uninterrupted zeolites with ring-openings larger than 18-ring. Meanwhile, 13- and 17-rings are the last two missing members in the family of pore-openings less than 18-ring.

Theoretically speaking, both of these two extra-large oddnumbered rings should be energetically realizable.49 The lack of experimental exploration is unlikely to be the true reason for their missing. In fact, small and medium odd-numbered rings (3-, 5-, 7-, and 9-rings) are not rarely observed; 3- and 5-rings are even abundant in germanate and silicate zeolites, respectively. In comparison, 11-rings occur only in NU-86 7290


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and JSR; 15-rings occur only in −IRY. The reason large oddnumbered rings are so rarely observed deserves more theoretical and experimental explorations. In practice, the pores in most as-synthesized zeolites are blocked by extra-framework structure-directing agents, which have to be removed to make the pores accessible. Among the 50 recently reported zeolitic materials, 40% are conventional pure silicate or aluminosilicate zeolites, another 40% are germanate or germanosilicate zeolites, and the rest are mainly heterometal-containing aluminophosphate zeolites. Conventional silicate and aluminosilicate zeolites usually have good thermal stability. The organic structure-directing agent occluded in the pores of conventional zeolites can be removed easily by calcination in air without framework degradation. In germanate and germanosilicate zeolites, the Ge−O bonds can be quickly hydrolyzed by ambient water. To remove the extraframework species in their pores, germanium-containing zeolites usually need to be calcined and kept in a moisturefree environment. The extra-framework species in heterometalcontaining aluminophosphate zeolites are even more difficult to remove, because they usually have strong nonbonding interactions with the host framework. Removing the extraframework species in these zeolites usually causes the host frameworks to collapse. To make all of these nonconventional zeolites practically usable, efforts have to be made to enhance their thermal or hydrothermal stability. A promising approach toward this end is to substitute silicon or aluminum for germanium or heterometals in zeolite frameworks through postsynthesis treatment. Through this approach, unstable structures that were realized before by nonconventional framework elements can now be prepared as hydrothermally stable high-silica materials.154−160 Alternatively, milder treatments other than calcination, such as UV radiation, acid extraction, and chemical oxidation by H2O2 or O3, are promising approaches for the removal of extra-framework species in nonconventional zeolites.112 Although more zeolites with chiral structures have been reported, most of them could only be prepared as racemic mixtures of opposite handedness. To date, the only zeolite showing enantiomeric excess in its bulk product is CJ-40 (JRY). Unfortunately, the structure-directing agent in CJ-40 cannot be completely removed. Concerning their applications in chiral separation and catalysis, new methods for producing chiral structures with accessible pores and more importantly for inducing enantiomeric excess are highly desired. The number of zeolite structures containing 3-rings has grown rapidly during the past few years. Because most zeolite structures with extremely low FD are constructed by 3-rings, any approach that releases the stress in 3-rings may facilitate the formation of low-FD structures. Currently, the most effective way to stabilize 3-rings is to induce unconventional T elements such as Ge and Be. Meanwhile, one should not overlook the success in the preparation of nitride and sulfide zeolitic frameworks, in which the linking O atoms are replaced by N and S. Because they are more suitable for small T−X−T angles than O atoms, N and S have great potential in 3-ring stabilization. The discovery of nitride and sulfide zeolites has opened a new possibility to produce low-FD zeolites, especially those with highly distorted structures with respect to oxide zeolites.

4. STRUCTURE DETERMINATION The number of zeolite framework types has been growing rapidly during the past few years. A very important reason for such rapid growth is the recent development of new structure determination techniques. Table 4 lists the structure determination methods for 42 new IZA structures since 2007 and 8 recently reported four-connected structures. These new structures have been determined by methods based on X-ray crystallography, electron crystallography, model-building, or the combination of them. Besides these methods, there are some other approaches developed recently for zeolite structure determination. Although they have not been used to solve “new” structures yet, blind tests have shown that these recent approaches may have great potential in the future as important supplements to conventional methods. However, structure determination involves many complicated physical and mathematical theories. In this section, we will focus only on the most representative ideas recently developed in this field. Readers who are interested in theoretical and technical details are referred to refs 161−167. 4.1. X-ray Crystallography

Like all other solid-state crystalline materials, most zeolite structures are determined using X-ray diffraction (XRD) techniques. The electron density at point (x, y, z) in the unit cell, ρxyz, can be calculated through Fourier transform, when the amplitude (|Fhkl|) and the phase (ϕhkl) of each reflection hkl are known: ρxyz =

∑ |Fhkl| cos(2π(hx + ky + lz) − ϕhkl)/V

(3)

The electron density peaks in the unit cell correspond to the locations of atoms. If the measured sample is a single crystal of suitable size and quality, the amplitude of each reflection (|Fhkl|) can be measured reliably because the square of |Fhkl| is proportional to the corresponding intensity of X-ray diffraction. Although the phase information is lost in X-ray diffraction data, it can be retrieved by many mathematical approaches, among which the direct methods are the most successful.206 For zeolites available as single crystals, structure determination through direct methods is now a routine procedure and could be accomplished within an hour. Modern computer software, such as SHELX,204 implements direct methods as a black box, enabling the determination of 1/3 of the new zeolite structures listed in Table 4. The remaining zeolitic materials listed in Table 4 cannot be prepared as single crystals; they are only available as polycrystalline powders. As compared to three-dimensional single-crystal XRD data, powder XRD (PXRD) data are only one-dimensional in reciprocal space. Dimension-reduction in PXRD data causes the notorious reflection-overlapping problem, which leads to severe ambiguity in unit cell determination and space group assignment. Moreover, the intensities of reflections with similar d-spacings cannot be reliably extracted.161,163,207,208 To reduce the reflection overlaps, synchrotron radiation should be used as the X-ray source. In addition, sophisticated peak partitioning methods are also helpful for better intensity extraction.209−211 However, theoretically speaking, all of these approaches cannot completely solve the reflection-overlapping problem. As a result, conventional methods that highly rely on the accuracy of reflection intensities often fail for PXRD data. As shown in Table 4, over one-half of the newly reported zeolite structures 7291


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Figure 38. Flow diagram for FOCUS. Reproduced from ref 164 with permission from The Royal Society of Chemistry.

determination of TNU-9 (framework type code TUN, with 24 distinct T atoms).133 TNU-9 is one of the most complex zeolite structures, which could be determined when a number of phases were prescribed for FOCUS. Alternately, the structure envelope, which is a periodic surface in real space separating the regions of atoms from those of pores, can be generated from the Fourier transform of several strong and lowindex reflections.214 The framework atoms should all lie on the positive side of the envelope. If FOCUS restricts the search of framework atoms only on the positive side of the structure envelope, its efficiency could be improved by 2 orders of magnitude.215 4.1.2. Charge-Flipping. As compared to FOCUS that is specifically designed for zeolite structure determination, the charge-flipping (CF) algorithm is a more general structure determination method. In 2004, Oszlányi and Sütő introduced the original CF algorithm for single-crystal X-ray diffraction data.216,217 After several years’ development, CF has now become one of the most widely applied structure determination methods.216,218−223 The original CF algorithm is not very complicated. It starts in almost the same way as FOCUS does (Figure 39). At the beginning, random phases are assigned to a set of reflection amplitudes (|Fhkl|), which are extracted from the measured

were determined using PXRD data, most of which were not able to be solved through conventional direct methods. The inefficiency of conventional methods inspires the development of new structure determination methods for zeolites. 4.1.1. FOCUS. FOCUS is a zeolite-specific structure determination program that uses zeolite framework information (in real space) to compensate for the ambiguities in PXRD data (in reciprocal space).184 Its flow diagram is shown in Figure 38. FOCUS reads the reflection amplitudes extracted from PXRD data, and then assigns a random starting phase for each of them. An electron density map is generated through Fourier transform (eq 3) using the measured amplitudes and randomly assigned phases. FOCUS conducts an exhaustive search for a three-dimensional zeolitic framework in this electron density map either according to peak heights or according to the largest framework fragment that can be found. The resulting framework is used to calculate a set of new phases, which are applied to the measured amplitudes again to generate a new electron density map through Fourier transform. This Fourier recycling procedure continues until the phases converge or the required number of cycles is achieved. In general, the framework found most frequently should be the correct structure solution. Since its invention in 1997, FOCUS has been employed to determine about 30 zeolite framework types.212 Among the new zeolite structures reported recently, 1/5 were determined through FOCUS (Table 4). Because FOCUS works in both reciprocal and real spaces, various types of information can be added as additional inputs to improve its efficiency. For instance, a limited number of prescribed phases derived from other approaches can be used to generate the initial electron density map instead of generating a random one. Tests on ITQ-22 (framework type code IWW, with 16 distinct T atoms) showed that by imposing the phases of just 31 of the 992 strongest reflections as additional inputs, the efficiency of FOCUS could be improved by over 10 times.213 Another example is the structure

Figure 39. A simple outline of the charge-flipping algorithm. 7292


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diffraction intensities. An electron density map (ρxyz) is generated using the measured amplitudes and the randomly assigned phases through Fourier transform (eq 3). The signs of all electron densities below a user-defined threshold δ (a small positive number) then are reversed (flipped) to produce a disturbed electron density map (gxyz). By doing this, all physically meaningless negative electron densities are made positive. From this disturbed map, a new set of reflection amplitudes (|Ghkl|) and phases (ϕhkl) are calculated. The new phases are combined with the measured amplitudes (|Fhkl|), generating a new electron density map through Fourier transform. This cycling is repeated until the calculated amplitudes (|Ghkl|) match the measured ones (|Fhkl|) or until the required number of cycles is achieved. To accommodate PXRD data, McCusker and co-workers developed the pCF algorithm,224 which is now implemented in the program Superflip.180 As compared to the original CF algorithm, the pCF algorithm contains an addition procedure to modify the electron density map through histogram matching. This approach is based on the fact that the electron density histograms in similar materials should be similar. In zeolite structure determination, the calculated electron density map (ρxyz) can be modified so that its histogram could match that of a known zeolite structure. From this modified map (hxyz), a new set of reflection amplitudes (|Hhkl|) is calculated, which can be used to improve the partitioning of reflection intensities (Figure 39). One of the most important advantages of the CF algorithm is that it does not require any a priori knowledge of the space group. All calculations can be performed in P1, and the space group can be determined from the final electron density map generated in P1.225 For instance, to determine the structure of MCM-70, McCusker and co-workers extracted the intensities from a PXRD pattern assuming its space group to be Pmnm.191 After 100 pCF runs in P1, the space group Pmn21 was found 83 times, whereas Pmnm was not found at all. Furthermore, 8 of the 10 best electron density maps showed Pmn21 symmetry. All of these results indicated that Pmn21 was the correct space group, which was confirmed by a different study from another research group.226 The CF algorithm works in both reciprocal and real spaces; therefore, additional information from either space can be used to improve its efficiency. Moreover, the CF algorithm runs very fast, usually requiring only seconds to minutes for each run. All of these important features enable the success of CF in the determination of many complex zeolite structures. As shown in Table 4, six new zeolite structures have been determined by CF, including SSZ-74, one of the most complex zeolite structures. The framework of SSZ-74 contains 24 distinct T sites. Over 80% of the reflections in its PXRD pattern were overlapped.135 To determine its structure, a structure envelope showing the pores in its structure was constructed with the aid of HRTEM techniques (Figure 40). The structure envelope was imposed in real space in the pCF algorithm to eliminate any electron density in the pores. After a series of pCF runs, the best electron density maps generated with reasonable porous structures were averaged. The averaged electron density map was used to calculate a new set of phases, which were input as the starting phases in the final 100 pCF runs. During each run, up to 25% of the starting phases were randomly varied. The 10 best electron density maps from the final 100 pCF runs were averaged again, and the framework structure of SSZ-74 was finally interpreted in this averaged map.135

Figure 40. Structure envelope showing the pores in SSZ-74. Reprinted with permission from ref 135. Copyright 2008 Nature Publishing Group.

Like FOCUS, the CF algorithm may also benefit from the inclusion of a limited number of prescribed phases. In most cases, these phases can only be obtained from electron microscopy techniques. In 2011, McCusker and co-workers developed the 2D-XPD approach to retrieve important phase information from two-dimensional subsets of X-ray powder diffraction data.227 In general, the 2D-XPD approach starts with the intensity extraction from PXRD data. The two-dimensional subsets of reflections corresponding to several main crystallographic projections then are selected from the full list of the extracted reflection intensities. A number of CF runs are performed on each two-dimensional data set. The best electron density maps generated for each projection are averaged, from which the phases of the contributing reflections can be calculated through Fourier transform. These calculated phases are imposed as the starting phases for the final pCF runs using the complete three-dimensional PXRD data. With the inclusion of these prescribed two-dimensional PXRD starting phases, the structure solution may become much more reasonable than that obtained with random starting phases. Through this 2DXPD approach, many complex zeolite structures that were solved before by combining PXRD and electron microscopy (such as TNU-9, IM-5, and SSZ-74) can now be determined using PXRD data alone.199,227 4.2. Electron Crystallography

Electron crystallography is probably the most important complement to PXRD in zeolite structure determination.164,166 Because electrons interact with matter much more strongly than X-rays, an electron microscope can examine very tiny crystals individually. Therefore, the reflection-overlapping problem does not exist in electron crystallography. Furthermore, the phase information lost in XRD is retained in electron microscopy, which is the key for successful structure determination. However, the electron diffraction intensities are strongly affected by dynamical/multiple scattering. Besides, operating an electron microscope requires considerable expertise. Because of these difficulties, electron crystallography was not as widely used as X-ray crystallography in structure determination for quite a long time.228 During the past few years, significant progress has been made in zeolite structure determination using electron crystallography techniques.164,166,229−232 As shown in Table 4, many new zeolite structures were determined with the aid of electron microscopy; some of them were even determined solely by electron crystallographic techniques. 7293


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determined in a similar way.201 In 2008, Yu and co-workers developed a computer method (Framework Generation in Density Maps, FGDM) to automatically generate the threedimensional structure model according to one or more twodimensional HRTEM images.234 FGDM is a Monte Carlo global optimization program that builds up feasible zeolite structure models according to not only framework connectivity and bonding geometry, but also the agreement between the generated structure model and the HRTEM images. For example, to generate the framework structure of IM-5, its twodimensional HRTEM image was expanded over the whole unit cell to form a three-dimensional potential map (Figure 42a,b).

4.2.1. High-Resolution Transmission Electron Microscopy. High-resolution transmission electron microscopy (HRTEM) is a powerful technique for the characterization of zeolitic materials.233 In particular, aberration-corrected microscopes are able to deliver real space information with atomic resolution. With the aid of HRTEM, many complex zeolite structures that were inaccessible before by other methods have been solved successfully. In general, HRTEM can provide important structural information in the following respects. 4.2.1.1. Information of Space Group and Unit Cell Dimensions. Because of the reflection-overlapping problem and the fact that many space groups may share the same reflection conditions, the space group and the cell parameters of a zeolite structure usually cannot be determined unambiguously through PXRD. As a comparison, HRTEM is capable to give reliable symmetry information. For instance, the space group of oxonitridophosphate-2 (framework type code: NPT) could not be determined by high-resolution synchrotron PXRD. The reflection conditions only indicated that its space group could be one of the face-centered cubic space groups. To remove the ambiguity, high-resolution scanning transmission electron microscopy (STEM) images were recorded in highangle annular dark field (HAADF) along the [100] and [110] directions (Figure 41).152 By comparing their plane groups (p4mm and p2mm) with the symmetry of special projections, it was found that the only possible space group for oxonitridophosphate-2 was Fm3c̅ .152

Figure 42. Generation of the IM-5 framework using the FGDM approach. (a) The HRTEM image of IM-5 along the [100] direction. (b) The potential map generated from the image shown in (a). (c) T atoms placed randomly in the potential map at the beginning of the simulation. (d) T atoms rearranged in the potential map during the simulation. (e) Agreement between the generated structure model and HRTEM image along the [100] direction. (f) Plot of the cost values of the generated structure models. Model 1 has the lowest cost value, corresponding to the correct structure solution. Reprinted with permission from ref 234. Copyright 2008 Wiley-VCH.

Figure 41. STEM-HAADF images (left) indicating the positions of heavy atoms (right) in oxonitridophosphate-2. Top: Image along [100] with plane group p4mm. Bottom: Image along [110] with plane group p2mm. Reprinted with permission from ref 152. Copyright 2011 American Chemical Society.

FGDM randomly generated T atoms in the unit cell (Figure 42c), and adjusted their positions step by step to fit the potential map with the restraints on bonding geometry (Figure 42d). The framework model generated by FGDM should have reasonable bonding geometry and a good match for the original HRTEM image (Figure 42e). As compared to XRD that gives the average information of the whole crystal, HRTEM delivers the local information, making itself an ideal tool for analyzing the stacking disorders in zeolite structures. Stacking disorders are often found in zeolites, which originate from different connections of similar building units. Figure 43 shows the stacking disorder of 10-ring channels in zeolite ITQ-39, which is one of the most complex intergrown zeolites. If the stacking disorders in a zeolite framework are clearly shown in HRTEM images, its structure model could be built according to related known structures. Otherwise the determination of such structures could be quite difficult. Readers who are interested

4.2.1.2. Projection of Atoms in Real Space. If the samples are thin enough and not very beam-sensitive, it is possible to obtain an HRTEM image showing directly the two-dimensional projection of framework atoms. With this two-dimensional information, it is possible to build the three-dimensional structure model according to a priori structural or chemical knowledge. For instance, to determine the structure of zeolite ITQ-38, an HRTEM image along the [010] direction was taken.181 This image clearly showed that the structure of ITQ38 contained the same layers as those found in ITQ-22. In addition, the b parameter of ITQ-38 was similar to that of ITQ22, so the structure model of ITQ-38 could be deduced from the structure of ITQ-22. The structure of zeolite SU-78 was 7294


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supplied to real-space algorithms to facilitate the search of framework atoms. For instance, the computer program FraGen has a function to encourage the framework atoms generated on the negative side of the structure envelope to move toward the positive side (see section 4.3.2).236 As a result, the structures generated by FraGen are biased toward having the desired pores consistent with the HRTEM images. Tests on zeolite SSZ-51 showed that when a structure envelope generated from three unique reflections was given, FraGen found the best structure solution several times faster than running without it. Besides FraGen, dual-space approaches, such as FOCUS and pCF, can also benefit from the inclusion of structure envelopes. Such examples have already been shown in section 4.1. Instead of reconstructing a three-dimensional potential map in real space, the phase information derived from HRTEM images can also be used directly in reciprocal space. In this case, it is not necessary to have HRTEM images from all of the main directions, and the derived phases are not necessarily 100% correct. In general, the phases derived from HRTEM images are supplied to a structure solution program as a starting phase set. They are usually fixed at the beginning and allowed to correct themselves afterward during the structure determination procedure. According to eq 3, while correcting the incorrect phases step by step, the structure models obtained from Fourier transform will be closer to the real structure solution. As a matter of fact, many complex zeolite structures were solved in this way. For instance, the structure of TNU-9 was solved by FOCUS using synchrotron PXRD intensities and 258 prescribed phases derived from three high-quality HRTEM images.133 4.2.2. Electron Diffraction. Although HRTEM images are extremely useful in zeolite structure determination, they are not easy to obtain, especially when the sample is beam sensitive. In comparison, electron diffraction (ED) requires a lower electron dose on samples. Unfortunately, because ED data are generally incomplete and their intensities are not reliable due to the dynamical scattering effects, they are not very well suited for zeolite structure determination.237−239 To minimize the dynamical effects, selected area electron diffraction (SAED) and precession electron diffraction (PED) techniques are often employed. Although the intensities of SAED and PED are still not ideal, they are significantly improved over conventional ED intensities.228,240−243 During the past few years, new methods for both ED data collection and ED structure determination have been developed, leading to the structure solution of several new zeolite frameworks. 4.2.2.1. Progress in Data-Collection Methods. Because electrons interact with matters much more strongly than X-rays, polycrystalline materials can be measured as individual tiny crystallites by ED just like single crystals measured by XRD. However, obtaining SXRD-like three-dimensional ED data has been quite difficult; it usually cannot be done in an automated way and therefore demands considerable expertise and patience from the microscope operator. Traditionally, the crystal sample needs to be manually tilted around a selected crystallographic axis. ED patterns are recorded at various crystallographic zones, each of which covers a very limited part of the reciprocal space. After all of the ED patterns are collected, they are further merged into a three-dimensional data set. In 2007, Kolb and coworkers developed the automated diffraction tomography (ADT) technique for the collection of three-dimensional ED data.244 Under the control of computer programs, the crystal sample is tilted with 1° steps around the goniometer axis; two-

Figure 43. HRTEM image of ITQ-39 along the [100] direction. The 10-ring channel stacking is traced by a line. The different ways of stacking lead to three polymorphs. Reprinted with permission from ref 139. Copyright 2012 Nature Publishing Group.

in how to elucidate the stacking disorders in zeolite structures are referred to a recent review article wrote by Willhammar and Zou.167 4.2.1.3. Reciprocal-Space Phase Information. One of the most important advantages of HRTEM over XRD is its capability to yield not only reflection amplitudes but also reflection phases. In most cases, the HRTEM images need to be aberration-corrected and symmetry-averaged. Fourier transform of these modified images would generate the desired phase information by computer programs such as CRISP.169 The reciprocal-space phase information derived from HRTEM images can be applied in different ways. When a large number of phases are available and the majority of them are correct, a three-dimensional potential map can be generated through Fourier transform, from which the framework atoms could be directly located. For instance, to determine the structure of IM5, high-quality HRTEM images along the [100], [010], and [001] directions were taken.235 From these images, the amplitudes and phases of 144 independent reflections were deduced. A three-dimensional potential map was calculated using these reflections, directly showing the positions of all of the 24 distinct Si atoms in IM-5. The structures of the polymorph B of zeolite beta and ITQ-39B were determined in a similar way. For beta B, the positions of all of its nine distinct Si atoms were determined from a three-dimensional potential map reconstructed from 39 independent reflections;168 for ITQ39B, its 28 distinct Si atoms were located in a potential map reconstructed from the 53 strongest reflections.139 Despite all of these successful examples, high-quality HRTEM images are quite difficult to get. In most moderate-quality HRTEM images, only the phases of a small number of low-index reflections are available. The potential map generated from such few reflections cannot be used to interpret the positions of framework atoms directly. Instead, the structure envelope describing the porous system of a zeolite framework can be derived from this map.214 Such a structure envelope can be 7295


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better estimated, therefore facilitating the final structure solution. For instance, 412 of the 3042 reflections in the PXRD pattern of ZSM-5 were weak reflections according to the corresponding PED patterns along four projections.259 If these weak reflections were eliminated, Rmap, the agreement factor measuring the difference between the generated electron density map and the reference map calculated from the true structure, would decrease from over 55% to less than 25%. ED data can also be used to retrieve phases, which can combine with PXRD data to solve complex zeolite structures. Using the same PED patterns for ZSM-5, 100 pCF runs were performed on each of the four ED data sets.259 For each projection, the five maps with the best Superflip R-values were averaged. Fourier transform was applied to the averaged maps to calculate the phases of the corresponding reflections. Combining 594 phases retrieved from PED patterns with 3042 PXRD intensities led to a significant decrease of Rmap to 18%. The combination of weak-reflection-elimination and phase-retrieval approaches may further lead to the solution of zeolite structures of high complexity.259

dimensional PED patterns are recorded during this automated tilting. The crystal sample does not need to be oriented during the whole data collection, therefore producing less dynamical intensities. Using the three-dimensional ED data obtained by this ADT technique, the structure of zeolite ITQ-43 was successively determined through direct methods.183 Later studies by Kolb and co-workers have shown that this ADT technique can be further improved for obtaining high-quality three-dimensional ED data for zeolite structure determination.165,245−248 In 2010, Hovmöller and co-workers developed another way to collect three-dimensional ED data automatically, that is, the rotation electron diffraction (RED) technique.249−251 As compared to ADT, the RED technique combines both the rough mechanical rotation of goniometer and the fine rotation of electron beam. At each angle of crystal tilting, a series of SAED patterns is collected at every step of beam rotation. The crystal sample is kept stationary during beam rotation. When the limit of beam rotation is reached, the crystal is tilted by a given angle, and another series of ED patterns is collected. This procedure is repeated until the limit of the goniometer rotation is reached. By combining goniometer tilt with beam tilt, this RED method can obtain a finer reciprocal-space sampling than the ADT method. With the three-dimensional ED data collected by RED method, the structure of ITQ-51 was solved by direct methods.126 4.2.2.2. Progress in Structure Determination Methods. Recent progress in ED data collection cannot completely resolve the inherent problems for ED (such as dynamical scattering, low completeness). Conventional direct methods are usually not suitable for ED data in the determination of complex zeolite structures. Several new methods accounting for imperfect ED data have been developed recently. For instance, the maximum entropy method based on Bayesian statistics has been widely used for structure determination using singlecrystal and powder XRD data.252 Recent studies have shown that this method is also suitable for zeolite structure determination using ED data.178,242,243,253−256 The maximum entropy method has now been implemented in computer software such as MICE.257 FOCUS is another method that can solve complex zeolite structures using ED data. As shown in section 4.1.1, FOCUS uses zeolite-specific chemical information to compensate, at least in part, for the ambiguity of the reflection intensities in PXRD. Recently, McCusker and coworkers showed that FOCUS could also compensate for the incompleteness and dynamical scattering problems in ED data.258 To accommodate ED data, the FOCUS program was modified by adding analytical scattering factors for ED. Using the modified FOCUS program with three-dimensional ED data collected by ADT or RED method, McCusker and co-workers successfully solved five zeolite structures of different complexity. 4.2.2.3. Combining ED with PXRD. ED and PXRD techniques are remarkably complementary to each other. During the past few years, several methods for combining them have been developed to solve structures that were inaccessible by either method alone. For instance, the ED data can be used to identify weak reflections to improve PXRD intensity extraction.259 Because the scattering factors for X-rays and electrons show the same general trend, reflections that are weak in the ED pattern should also be weak in the corresponding XRD pattern. Thus, by eliminating the reflections with weak ED intensities during PXRD intensity extraction, the intensities of the remaining reflections should be

4.3. Computer-Aided Model-Building

The model-building methods are the most intuitive and straightforward approaches for zeolite structure determination. As compared to conventional reciprocal-space methods, the model-building methods aim to find the arrangement of framework atoms directly in real space. During a modelbuilding procedure, individual atoms are moved together to form a series of feasible zeolite frameworks under the restraints of framework connectivity, bonding geometry, framework density, and/or the agreement with experimental observations. The correct structure solution, which has the most feasible framework structure or the best agreement with experimental observations, is expected to be among the models that have been built. Because of the inclusion of a priori direct-space information, the model-building methods usually do not depend on the quality of experimental measurement as much as reciprocal-space methods do. As shown in Table 4, about 1/ 5 of the new zeolite structures have been determined by modelbuilding methods. The correct models of these new structures have been built manually with reference to HRTEM images or highly related already-known structures. Nonetheless, computer modeling techniques can significantly improve the efficiency of model-building, enabling the structure solution of very complex structures.161−163,260−262 In this section, we only focus on the two model-building computer programs that are especially effective for zeolite structure determination. 4.3.1. ZEFSA II. ZEFSA II198 is a free computer program developed by Deem and co-workers on the basis of their previous research.263,264 It aims to generate the most feasible zeolite structures in real space under a set of restraints on framework density, bonding geometry, and PXRD intensities. ZEFSA II is based on configuration-biased Monte Carlo simulation method. The space group, cell parameters, and the number of unique T atoms are necessary inputs for ZEFSA II. At the beginning of each simulation cycle, unique T atoms are randomly generated within the unit cell. Equivalent atoms are generated automatically by symmetry operations. Next, ZEFSA II adjusts the locations of T atoms by minimizing a cost function reflecting the deviation of current structural model from the expected one. A typical cost function used by ZEFSA II can be defined as the summation of several cost terms: 7296


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function through parallel tempering. A typical cost function used by FraGen is defined as:

H = α TTHTT + αTTTHTTT + α TTT H TTT + αucHuc + αNBHNB + αMHM + αDHD + αXRDHXRD...

(4)

E = wCNECN + wT − TE T − T + wT − T − TE T − T − T + w3R E3R

where each H represents a type of cost contribution and each α is the corresponding weight. The first three cost terms reflect the deviations of T−T distances, T−T−T angles, and average T−T−T angles in current structural model from those in ideal zeolites; the Huc and HNB terms account for the fourconnectedness of current structural model, which are defined to be positive whenever a T atom has more or fewer than four close neighbors, respectively; the HM term favors merging of T atoms at special positions; HD reflects the disagreement between the actual and the expected numbers of T atoms; HXRD accounts for the difference between the simulated XRD intensities and the measured ones. To minimize this cost function, the simulated annealing or parallel tempering global optimization algorithm is performed.265 At the end of each simulation cycle, the cost function is minimized; T atoms are moved together to form a feasible zeolite structural model. ZEFSA II has shown high efficiency in zeolite structure determination. Many zeolite structures, including ECR-9, UiO6, UiO-7, ECR-34, ERS-7, MCM-47, and SSZ-55, were determined by ZEFSA II and its predecessor, that is, ZEFSA. The latest zeolite structure that was determined by ZEFSA II is SSZ-77.196 4.3.2. FraGen. FraGen (Framework Generator) is a computer program for real-space structure determination of extended inorganic frameworks.236 It was developed by Yu and co-workers in 2012 on the basis of their previous computer program FGDM (see section 4.2.1).234 Figure 44 shows the flowchart for FraGen. At the beginning of each simulation cycle, FraGen checks whether the site symmetry of each unique T atom has been defined by the user; if not, FraGen will assign the site symmetry for each atom according to various forms of constraints. FraGen then adjusts the location of each atom by minimizing a cost

+ wXRDE XRD + wdensEdens

(5)

where E’s are different cost terms and w’s are their corresponding weights. The first three terms describe the restraints on coordination numbers, T−T distances, and T−T− T distances. E3R adds penalty for the occurrence of 3-rings that are not favored in conventional zeolites. EXRD describes the mismatch between the calculated XRD intensities from the generated model and the experimental XRD intensities. Edens is a unique cost term in FraGen, which measures the match between the generated structural model and one or more userdefined electron density maps. The density map carries the pore information of a zeolite structure, which can be obtained from HRTEM images234 or the Fourier transform of a few lowindex reflections.214 Atoms in high-density regions have no contribution to the total cost, while those in low-density regions contribute a lot. Under this restraint, atoms are encouraged to move toward high-density regions, therefore forming a framework model with desired porous structure. After the required number of Monte Carlo steps is achieved, FraGen will record the best structural model that has been generated and start a new cycle from the beginning. The most important difference between FraGen and many other model-building programs is the way the site symmetry (and the multiplicity) of each atom is handled. In many other programs, the site symmetry of an atom is decided by its location and should be frequently updated. When an atom is moved close to a special position (such as an inversion center, a rotation axis, or a mirror plane), it will be merged with its own images, and the total number of atoms in the unit cell will be reduced. However, this atom-merging procedure may cause fluctuations in the total cost and unwanted bias toward the occurrence of certain site symmetry. In FraGen, the site symmetry of every atom is fixed within each simulation cycle, therefore avoiding the problems arising in atom-merging. Meanwhile, in FraGen, the number of unique atoms does not have to be correct; FraGen is able to automatically remove excessive atoms according to the constraints on cell contents. Moreover, because the site symmetry for each atom is fixed in FraGen, a complicated model-building task can be divided into a set of parallel and less complicated ones with different combinations of site symmetries. Therefore, FraGen may readily benefit from the powerful distributed computing techniques. Tests have shown that FraGen is highly effective for the generation of zeolitic framework structures.236 For simple zeolite structures, given only the correct cell parameters and the space group, FraGen is able to find the correct structure solution within a few seconds on a regular desktop PC. The efficiency of FraGen can be further improved by including a few experimental observations. Tests on zeolite SSZ-51 (containing four distinct Al and four distinct P atoms) showed that including the XRD intensities of only three low-index reflections could reduce the average time consumption from 3.6 to 1.8 min. If the phases of the three low-index reflections were also provided, a structure envelope (Figure 45) could be generated, and the time consumption of FraGen would be further reduced to 1.1 min.

Figure 44. Flowchart for FraGen. 7297


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advantage of NMR or PDF technique is their less dependence on long-range crystallinity, making them more suitable than conventional XRD methods when highly crystalline samples are not available. However, the application of these methods in zeolite structure determination has just begun. Convenient methods for data collection, data interpretation, and structure determination are highly desired. Although they have not been used as widely as other experimental approaches, various computer-aided techniques should have a promising future in zeolite structure determination. With a priori structural information provided, the realspace model-building methods have the least reliance on the quantity and quality of measured data; those key factors that determine whether the structure can be solved in reciprocal space have little influence on real-space model-building methods. Because of this reason, the structures of less crystalline materials might be accessible only with the aid of model-building techniques. Meanwhile, various computer artificial intelligence techniques, such as data mining, pattern recognition, or machine learning, etc., have shown enormous potential in crystal structure determination.79,80,82,83,246,297−310 With more new zeolite structures discovered, these computer methods can be used to derive important structural information from known structures, which can further be used to aid the determination of unknown ones in the future.84 More importantly, there seems to be no theoretical upper limit for the development of computational power. The updating speed of computer hardware has almost surpassed that of all other experimental instruments. It can be anticipated that the computer-aided techniques will play a more important role in zeolite structure determination in the future. In theory, given enough computational power and time, any structure can be solved by model-building in the absence of experimental data. This might be the real ab initio structure determination; someone may prefer to call it structure prediction.

Figure 45. Generating the framework of zeolite SSZ-51 using a structure envelope derived from the intensities and the phases of reflections 110, 200, and 002. Al and P atoms are denoted by yellow and pink spheres, respectively. The outer surface of the structure envelope is denoted by blue and the inner surface by white. O atoms are omitted for clarity.


As compared to other inorganic materials, zeolites are more difficult for structure-determination because they are usually difficult to prepare as large single crystals. Thanks to the significant advances in X-ray and electron crystallography, many new zeolite structures, which are only available as crystalline powders, have been determined recently. Some of these structures are so complex that they had been inaccessible for quite a few years. For PXRD, although the reflectionoverlapping problem cannot be completely solved, a wide variety of approaches have been developed recently and made the determination of zeolite structures of moderate complexity an almost routine procedure. Electron crystallography has experienced a rapid development during the past few years. However, it is still far from being a convenient technique as today’s X-ray crystallography. Major challenges remain in automated three-dimensional data collection, automated data processing, and software development for routine structure determination.229 Therefore, combining the advantages of both electron crystallography and PXRD seems to be the best way for zeolite structure determination so far. There are many other characterization methods for zeolite structures, such as solid-state NMR, X-ray absorption spectroscopy (XAS), electron spin resonance (ESR), Mössbauer spectroscopy, and pair distribution function (PDF) analysis, etc. Most of these characterization methods are only sensitive to local structural environment, and therefore are not suitable for the purpose of structure determination. However, solid-state NMR is worthy of particular attention.266−280 Recent studies have shown that it is possible to determine the structures of organic crystals using solid-state NMR data, which is known as NMR crystallography.281−283 For zeolites and related openframework compounds, NMR crystallography has also shown some promising applications. As a matter of fact, provided that the cell parameters and the space group are given, solid-state NMR data are able not only to determine but also to refine the framework structures of zeolites.270,284−289 A very recent report even showed the possibility of zeolite structure determination by NMR crystallography without knowing its space group.290 PDF analysis of PXRD data is another emerging opportunity for zeolite structure determination.291−296 The most essential

5. STRUCTURE PREDICTION In a narrow sense, a priori structure prediction is theoretical generation of nonexistent structures, which are later confirmed by the synthesis of real corresponding compounds.311 Without synthesis, a theoretically generated structure is only a possible candidate structure, not a predicted structure. In a broader sense, structure prediction is theoretical generation of any previously unknown structure. If the corresponding compound has already existed, structure prediction will be equivalent to structure determination, which is also known as a posteriori structure prediction. In the field of zeolites, true examples of a priori prediction are very rare. Therefore, in this section, we will discuss zeolite structure prediction (ZSP) in the broad sense. All theoretically generated zeolite structures are considered as predicted structures. ZSP has many useful applications. ZSP may assist researchers in identifying newly synthesized materials through PXRD fingerprint and providing the starting models for structure refinement.311,312 More importantly, ZSP may predict novel zeolite structures with interesting microporous characteristics, thus providing a huge pool of potential candidates for future function-oriented synthesis. To date, various ZSP approaches have produced millions of hypothetical candidate zeolites, which are collected in several databases. The progress in ZSP and the development of hypothetical zeolite structure databases will help us find alternate zeolites for known applications and synthesize new ones with completely new functions. 7298


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Figure 46. Thirteen binodal hypothetical structures (225_2_1 to 225_2_13) generated by SCIBS. Reprinted with permission from ref 353. Copyright 2004 Elsevier.

5.1. A Short History

trinodal four-connected networks according to the mathematical tiling theory.355,356 In general, these approaches require only a few topological and geometric constraints, which guarantees the generation of a large number of four-connected networks. The other direction of ZSP is to generate hypothetical zeolites with desired structural features, which will be highly important for function-oriented synthesis. For instance, Mellot-Draznieks and co-workers generated many hypothetical zeolite frameworks by automated assembly of desired secondary building units (AASBU);357−361 Yu and coworkers introduced predefined forbidden zones into computer simulation and generated a series of hypothetical zeolites with desired porosity;362−365 Woodley and co-workers combined evolutionary algorithms with predefined exclusion zones to generate a series of porous structures.366−369 Because of these efficient approaches, in the past decade there has been an explosive increase of hypothetical zeolite structures. In the following sections, we will focus on the latest ZSP approaches that have produced lots of hypothetical structures during the past few years.

The prediction of hypothetical zeolite frameworks goes back to the late 1960s.313 By varying the connections of known structure-building units, a considerable number of hypothetical zeolite topologies have been predicted.314−326 Notably, Smith and co-workers systematically predicted a series of zeolitic structures by linking known two-dimensional nets,327−342 among which a hypothetical structure with 18-ring poreopenings was realized later as zeolite VFI. Most of these pioneer studies were performed by hand. With the development of computer techniques, new algorithms, especially various global optimization algorithms, have been designed for more efficient ZSP, yielding millions of hypothetical zeolite structures.198,260,263−265,343−345 Currently, the studies in ZSP have two major directions. One direction is to generate hypothetical zeolite frameworks as many as possible, or to enumerate all possible three-dimensional four-connected networks under certain constraints. For instance, O’Keeffe and coworkers generated many hypothetical zeolite structures by moving one crystallographically unique T atom in small increments throughout the asymmetric units of orthorhombic, tetragonal, trigonal, hexagonal, and cubic unit cells;346−351 Treacy and co-workers expanded this research to more unique T atoms and to all space groups, and refined the derived structures through simulated annealing;129,352−354 DelgadoFriedrichs and co-workers enumerated uninodal, binodal, and

5.2. Recent Progress in ZSP

5.2.1. SCIBS and the Atlas of Prospective Zeolite Structures. The SCIBS (Symmetry Constrained Intersite Bonding Search) method was developed by Treacy and coworkers,352,353 aiming to enumerate all possible four-connected networks within each space group given the number of unique 7299


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experimental XRD intensities. As a matter of fact, ZEFSA II can work without any experimental input. In this case, ZEFSA II serves as a ZSP program. Using ZEFSA II, Deem and coworkers have examined all of the 230 space groups and successfully generated over 2.6 million unique hypothetical zeolite frameworks.49,376,377 For each space group, they have examined unit cells with edges from 3 to 30 Å in steps of 3 Å. The FD has been varied from 10 to 20 T/1000 Å3 in steps of 2 T/1000 Å3, covering the whole FD range of typical zeolites. To avoid expensive computations, the total number of unique T atoms has been limited to no more than eight. Duplicated topologies have been identified and removed by calculating the coordination sequences. All of the generated structures have been optimized by using the GULP program371−373 with SLC374,375 and BKS378 potentials, which have been modified to enforce the Pauli exclusion principle and to eliminate the negative energy divergence. As a result, over 2.3 million and over 2.0 million unique structures have been obtained by using the SLC and the BKS potentials, respectively. When combined, there have been over 2.6 million unique four-connected structures generated. Figure 47 shows some of these hypothetical structures.

T atoms. This approach consists of the following major procedures: (1) Crystallographically unique T atoms are put in the fundamental region (the asymmetric unit) of a given space group. T atoms may be put inside the fundamental region (the general Wyckoff sites) or on the surfaces, edges, or vertices of the fundamental region (the special Wyckoff sites). The symmetry operations of the given space group generate the images of the unique T atoms and fill the entire unit cell. (2) N unique T atoms are distributed systematically over all Wyckoff sites. For each distribution of T atoms, all permutations of the interatomic bonding configurations are examined, and only those consistent with tetrahedral coordination are retained. (3) The unit cell dimensions are adjusted by simulated annealing to obtain reasonable T−T distances and T−T−T angles. T atoms and cell dimensions then are annealed together to achieve ideal bonding geometries. At the last step, oxygen atoms are added between bonded T atoms, and the whole unit cell is annealed using a modified BGB cost function devised by Boisen and co-workers. 343 The last step is the most computationally expensive step. To avoid wasting valuable resources at the last step on infeasible graphs (which are unfortunately the majority of the four-connected graphs generated), a geometric structure optimizer, SiGH (Silica General Handler), has been devised to rapidly establish whether the TO4 tetrahedra in a framework structure could exist as minimally deformed regular tetrahedra.370 Any structure failing to pass the SiGH optimizer is deemed as an infeasible graph and is not necessary to be further annealed in the last step. Using the SCIBS approach, Treacy and co-workers have generated millions of hypothetical four-connected zeolite frameworks with ≤7 unique T atoms, which are now collected in an online database, that is, the Atlas of Prospective Zeolite Structures.129 This database currently contains two subsets, that is, the bronze and the silver structures. The bronze database currently contains over 5.3 million hypothetical structures with low BGB costs. At least 2.1 million structures in the bronze database have been confirmed to be unique by calculating the coordination sequences and vertex symbols. All of the hypothetical zeolite structures have been reoptimized using the GULP code371−373 with the SLC atomic potentials devised by Sanders and co-workers.374,375 Structures with low SLC costs are saved in the silver database. Currently, the silver database contains over 1.2 million hypothetical zeolite structures. Figure 46 shows some hypothetical structures in this database. The Atlas of Prospective Zeolite Structures has an online query page, where hypothetical structures can be searched according to various structural properties, such as space group, the number of unique T atoms, FD, TD10, framework energy, cell parameters, the diameters of the largest included sphere and the largest free sphere, and coordination sequences, etc. The query page also provides a filter to remove all structures with 3-rings from the retrieved list. By default, the retrieved structures are ordered by framework energy. Nonetheless, users have the options to order the query results by FD, TD10, and the diameters of the largest included sphere and largest free sphere. 5.2.2. ZEFSA II and the Database of Hypothetical Structures. As shown in section 4.3.1, ZEFSA II is able to generate feasible zeolitic structural models according to

Figure 47. Examples of some predicted SLC structures. Reproduced with permission from ref 49. Copyright 2011 PCCP Owner Societies.

Among these hypothetical structures, Deem and co-workers found over 330 000 low-energy structures in the SLC database and over 590 000 in the BKS database.49 In addition, Deem and co-workers have studied the distributions of ring size, framework energy, framework density, relative XRD intensity, and dielectric constants in all of these low-energy structures. The results were similar to those of known zeolites. The hypothetical structures generated by ZEFSA II have been collected in Deem’s Database of Hypothetical Structures, which is freely accessible from the Internet.57 Crystal system, space group, the number of unique T atoms, FD, cell volume, 7300


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framework energy, and cell parameters are all searchable in this database. Low-energy structures in this database have also been deposited in the Predicted Crystallography Open Database (PCOD, see section 5.2.3).311,379 5.2.3. GRINSP and the Predicted Crystallography Open Database. GRINSP (Geometrically Restrained INorganic Structure Prediction) was developed by Le Bail, aiming for the generation of all possible framework structures constructed exclusively from corner-sharing polyhedra.345 In general, GRINSP consists of two stages to generate a hypothetical zeolite framework in a given space group. The first stage is to generate the initial structural models through Monte Carlo tests. First, a single initial T atom is placed randomly in a unit cell with randomly selected dimensions. The next T atom is randomly placed close to the previous T atom, and the distance between them is restricted by the predefined interatomic distances. At this stage, T atoms are not moved; they are retained or discarded depending on whether the tetrahedral coordination is satisfied or not. The unit cell is progressively filled to satisfy the geometric restraints. As can be seen, the number of T atoms is determined “on the fly” in GRINSP, which is different from many other ZSP approaches that require it to be predetermined.263,264,352,353,357 The second stage is to refine the initial models into feasible zeolite structures. First, the bridging O atoms are added at the midpoints between the T−T first neighbors. GRINSP adjusts the atomic coordinates and the cell dimensions according to the following cost function:

Figure 48. Two hypothetical zeolite frameworks generated by GRINSP. (a) PCOD1030081; (b) PCOD4409546.

most of them cannot ensure the generation of zeolite frameworks with desired porosity. Actually, many predicted four-connected structures, especially those with the lowest energies, do not have any accessible pores. In 1992, Deem and Newsam proposed an idea to place movable cylinders or spheres in the unit cell to facilitate the formation of porous structures.264 In 2003, Yu and co-workers developed the concept of forbidden zones, which represents regularly shaped pores within zeolite frameworks.362 Atoms in the unit cell are forbidden to occur in predefined forbidden zones, thus forcing the generation of structures with desired porosity. Following this idea, Yu and co-workers successfully generated a series of hypothetical zeolite structures with predefined one-dimensional channels, interconnecting channels, and chiral channels.363,364 On the basis of these studies, in 2012, Yu and co-workers developed a real-space model-building program, that is, FraGen (see section 4.3.2).236 A key feature of FraGen is its ability to generate framework structures according to one or more userdefined density maps. Notice that the information of desired pores can be carried by these density maps. To describe a simple porous system constructed by one-dimensional straight channels or perfect spherical pores, an artificial density map can be built, in which the density value of each pixel is its distance to the nearest center of the desired channel or pore. A more complex porous system can be described in a density map generated from the Fourier transform of a few low-index reflections calculated from known structures. With such density maps implemented, FraGen is an ideal tool for the generation of structures with desired pores. To date, Yu and co-workers have generated hundreds of hypothetical zeolite frameworks with interesting porous structures using FraGen. All of these frameworks have been further optimized by the GULP program371−373 with the SLC potentials.374,375 These structures have been collected in the Hypothetical Zeolite Database, which is freely accessible from the Internet.365 In addition, Yu and co-workers have calculated many structural features for each predicted structure, including space group, cell parameters, cell volume, FD, numbers of unique/total T atoms, TD10, coordination sequences, loop

R = {∑ [wTO(DTO − d TO)]2 +

∑ [wOO(DOO − dOO)]2 + ∑ [wTT(DTT − d TT)]2 }/[∑ (wTODTO)2 + ∑ (wOODOO)2 + ∑ (wTTDTT)2 )]1/2 (6)

where D’s and d’s are the expected and the observed interatomic distances in the structure model, respectively, and w’s values are their corresponding weights. The total cost is progressively reduced when GRINSP refines the coordinates of T and O atoms as well as the cell dimensions through a Monte Carlo approach. A promising zeolite structure resembling the known ones will be obtained at the end of the simulation when the total cost reaches its minimum. Because the original space group may not be conserved after addition of bridging O atoms, the real symmetry of every generated structure has to be rechecked.380,381 Using GRINSP, Le Bail has generated over 10 000 unique hypothetical zeolite frameworks as well as nearly 50 000 isotypic phases. Figure 48 shows two hypothetical zeolite structures generated by GRINSP. All structures generated by GRINSP are gathered in the Predicted Crystallography Open Database (PCOD), which is freely accessible from Internet.379 Users can search structures according to PCOD entry number, space group, cell volume, and cell parameters. The R factor, FD, and the coordination sequences are stored in the CIF file of each structure, but unfortunately not searchable. As mentioned in section 5.2.2, this database also contains nearly one million low-energy hypothetical zeolite frameworks generated by ZEFSA II. PXRD patterns for all PCOD structures are gathered in its satellite database, that is, the Predicted Powder Diffraction Database (P2D2), where newly synthesized zeolites may be identified by comparing the PXRD fingerprints. 5.2.4. FraGen and the Hypothetical Zeolite Database. Although many efficient ZSP approaches have been proposed, 7301


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Figure 49. Obtained speed-up on the complete algorithm depending on the population size and number of iterations of the local search algorithm. Reproduced with permission from ref 387. Copyright 2011 PCCP Owner Societies.

zeolite frameworks with a high number of unique T atoms. Baumes and co-workers tested this strategy by generating zeolite frameworks in three different unit cells. The number of T atoms in each unit cell was assumed to be 96 ± 8, corresponding to 6−14 unique T atoms. The whole procedure took a total of 1 week. Nearly 400 structures were found, from which 88% showed proper framework energetics comparable to known zeolites.

configurations, largest ring size, vertex symbols, accessible volumes, type of cavity, channel dimensionality, channelopenings along different directions, the positions of the first three peaks in the simulated PXRD pattern, and the calculated framework energy. All of these features are searchable in this database. Different from many other databases that collect as many structures as possible, the Hypothetical Zeolite Database only collects promising or realizable structures with reasonable bonding geometries, accessible pores, and framework energetics. 5.2.5. ZSP Using GPGPU Programming. General Purpose Computation on Graphic Processing Units (GPGPU) is the means of using a graphic processing unit (GPU) to perform the computations that are traditionally handled by the central processing unit (CPU). Because of their design, GPUs are effective for tasks that need to process multiple independent data sets in the same way. According to this concept, tasks are split and run simultaneously on multiple processors; all processors execute the same instruction at the same time but using different data. During the past few years, GPGPU techniques have shown their power in solving chemical problems such as molecular modeling and quantum chemistry computations. The evolutionary algorithm (EA) is a global optimization algorithm widely used in structure determination and prediction of crystal structures.366−369,382−386 In theory, EA evaluates all of the individual crystal structures using an identical fitness function, which can be efficiently handled by GPGPU techniques. In 2011, Baumes and co-workers showed a boosting theoretical zeolite framework generation using the combination of EA and GPGPU programming.387 In this approach, the EA engine is run on the host CPU, which performs the evolutionary operations and passes the entire population to GPU for parallel evaluation. The results are sent back to CPU for the creation of the next generation. The fitness of each individual candidate structure is calculated according to the deviations of T−T distances, T−T−T angles, and connectivity from their ideal values (3.07 Å, 109.5°, and 4, respectively). The efficiency of EA running on both CPU and GPU could be 100 times higher than that running on the CPU (Figure 49). Such a speed-up enables the generation of complex


In general, a posteriori ZSP aims to determine the structures of newly synthesized zeolite samples, whereas a priori ZSP is intended for finding feasible candidate zeolites with desired structural features for function-oriented target-synthesis. Although significant progress has been made along these two directions, there are still many challenging problems that need to be solved. 5.3.1. Maddox’s “Continuing Scandal”. In 1988, Maddox made a provocative statement that “one of the continuing scandals in the physical sciences is that it remains impossible to predict the structure of even the simplest crystalline solids from a knowledge of their composition”.388 Although some progress has been made for materials such as MOFs,361,389 Maddox’s statement is still true for most crystalline materials, including zeolites. The number of theoretically possible structures grows exponentially with the number of unique T atoms. So far, the number of hypothetical zeolite structures with ≤8 unique T atoms has reached several million.57,129 When the number of unique T atoms increases, the number of theoretically possible structures will be overwhelmingly large for current computation power. To date, the number of unique T atoms in known zeolites has reached 99 (in *SFV). If no revolutionary ZSP algorithm or computation device is invented, Maddox’s scandal will still continue for a long time in the field of zeolites. The good news is that some researchers are trying to implement ZSP with high performance computing techniques. GPU programing and distributed computation have shown their advantages in scientific computations, which might be the future of ZSP for extremely complex structures. 5.3.2. Hypothetical Zeolite Databases. The establishment of several databases for hypothetical zeolite structures 7302


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wasting our valuable time and resources on poor structures that are unlikely to be synthesized at all. However, evaluating the feasibility of zeolite structures is unfortunately not easy, because we are still not sure what on earth makes a zeolite framework realizable. In 1982, Gramlich-Meier and Meier found that, although a very large number of four-connected three-dimensional nets could be generated on purely topological grounds, the number of permissible zeolite framework types should be very limited.390 That means a realizable zeolite framework should have some unique structural features quite different from those of other four-connected nets. Yet what are these features? Why are they so important? There might be no simple answers to these questions.390 Many researchers have tried to associate the feasibility of zeolites with the framework energy (or enthalpy of formation). They found, experimentally or computationally, that the framework energy might be negatively linearly related to the framework density (or the average population of the fourth shell of CSQ).391−402 Only a small fraction of fourconnected three-dimensional nets obey this linear relationship, and those violating this correlation are usually deemed to be infeasible or unrealizable structures.56,364,377,403−408 Alternately, other researchers have tried to associate the feasibility of a zeolite framework with its geometric or topological features. For instance, Gramlich-Meier and Meier found that the T−O distances, O−T−O angles, T−O−T angles, and O−T−O−T− O twisting angles in feasible zeolite frameworks should vary within very narrow ranges;390 Akporiaye and Price discovered the positive correlation between framework density and the fourth shell of CSQ in high silica zeolites;391 Brunner and Meier found the dependence of framework density on the average size of the smallest rings in known zeolites;147 Stixruge and Bukowinski discovered the close associations among the population of T-clusters, the characteristic ring size, and framework density;409 Brunner found that the feasibility of a silica zeolite frameworks might be related to the types of loop configurations;410 Khosrovani and Sleight found the difference in framework flexibility of some cubic zeolite structures;411 Bromley and co-workers developed a methodology to predict framework energies according to the distribution of faces and cages in zeolite structures;412,413 O’Keeffe considered the fourconnected nets related to edge-transitive sphere packing to be the realizable structures of special interest.414 Inspired by these studies, researchers have made important progress recently toward the understanding of the feasibility of zeolite structures.

might be the most important progress in ZSP during the past few years. To date, there are millions of hypothetical zeolite structures stored in these databases, aiming to help users identify their newly synthesized structures or find synthetic targets with certain structural features by search-and-match procedures. However, to reach these aims, several problems have to be solved. The most obvious problem is that these databases are far from complete. Current databases only collect zeolites with small numbers of unique T atoms; most of the newly synthesized zeolites cannot find their counterparts in current databases. This problem cannot be completely solved as long as Maddox’s scandal continues. Another problem of current ZSP databases is the lack of efficient search tools. To identify a newly synthesized zeolite in ZSP databases, one of the most important properties users may want to search would be the PXRD pattern. Unfortunately, most of the current ZSP databases do not have this function. In fact, even if a highly efficient search-and-match tool is available, it will still be difficult to use in practice. Nearly all predicted structures in current ZSP databases are stored as silica polymorphs. However, their synthesized counterparts are usually made of nonsiliceous elements. As a result, the measured PXRD pattern may look different from the calculated ones based on silica polymorphs even if they represent the same framework type. To address this problem, Le Bail has used GRINS, a satellite program of GRINSP, to generate isostructural counterparts of various compositions for structures generated as silica polymorphs.345 Currently, Le Bail’s PCOD contains hypothetical zeolites consisting of Al, P, and Si. However, these three elements are far from enough for practical applications. 5.3.3. Function-Oriented ZSP. To generate candidate zeolites with desired structural features is crucial for functionoriented target-synthesis. The key structural feature of zeolites is their porosity. Current approaches could efficiently control the generation of zeolitic frameworks with predefined pores. The remaining problem is how to define the pores for ZSP. To design structures with new functions and applications, we have to learn how to design a new porous system. Just like the frameworks of zeolites, the pores in zeolites are also very complicated. The sizes, shapes, directions, and connectivity of pores all affect the functions of zeolites. Designing such a complicated porous system requires more extensive studies in the relationship between functions and structures.

6. FEASIBILITY OF ZEOLITE STRUCTURES Although millions of hypothetical four-connected frameworks have been predicted, the number of zeolites that have been found either in nature or by synthesis is quite limited. Apparently not every theoretically possible four-connected framework is truly realizable. Evaluating the feasibility of predicted structures is crucial to the refinement of ZSP algorithms. If infeasible structures can be avoided from being generated in the first place, the efficiency of ZSP will be highly improved. Eliminating infeasible structures is also very important to our current ZSP databases that have stored millions of predicted structures. Searching a specific PXRD pattern or framework topology among such a large number of structures can be very time-consuming. If we can trim these databases by removing all of the infeasible or unrealizable structures, these complex search tasks will be much quicker and easier. More importantly, if we are able to rank all predicted structures according to their feasibility, we can focus our synthetic efforts on the most promising candidates, avoiding

6.1. The Feasibility of Low-FD Zeolites without 3-Rings

In 1989, Brunner and Meier performed a topological analysis on over 70 dense and porous zeolite structures known at that time. They noticed that when these structures were grouped together according to the average size of the smallest rings, the minimum FD (calculated as pure silica polymorphs) for each of the groups decreased with the size of the smallest rings.147 To date, there have been over 200 distinct zeolite framework types discovered, none of which violates Brunner and Meier’s empirical observation.31 According to this observation, only frameworks constructed by 3-rings could have FD less than 12.0 T/1000 Å3. Consequently, to synthesize low-FD zeolite frameworks, elements known to be able to stabilize 3-rings (such as Be and Ge) are often added into the reaction mixtures. Following this idea, many low-FD zeolites with 3-rings have been successfully synthesized (see section 3.4). 7303


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Table 5. Smallest Rings (SR), FDs, Pore Sizes (PS), Average Si−O−Si Angles (AA), Total Tetrahedral Distortions (TTD), Pore Diameters (PD), and the Relative Lattice Enthalpies for Some of the Hypothetical Zeolite Frameworks Optimized as Siliceous Structures415 framework

SR

FD

PS

AA (deg)

TTD (Å)

FAU ZM30 ZM36 ZM42 194_5_4713570 194_3_189 191_4_9370 194_4_6238

4 4 4 4 4+ 4 4 4

13.5 10.8 8.8 8.5 8.3 9.0 8.1 7.3

12 30 36 42 42 36 42 48

143.3 144.5 146.7 143.9 148.8 148.7 148.9 149.0

0.036 0.049 0.026 0.047 0.035 0.026 0.025 0.024

PD (Å2)

ΔEquartz (kJ/mol SiO2)

× × × × × × × ×

19 24 24 26 19 20 20 20

9.8 21.1 24.8 30.1 30.5 24.9 29.5 34.0

9.9 23.8 28.3 34.6 33.1 28.9 33.8 39.3

Figure 50. Views parallel and perpendicular to the channel direction of a hypothetical structure, 194_5_4713570, showing the pore circumscribed by 42 Si atoms and the pore-wall consisting of only 6-rings, respectively (Si atoms in yellow and O atoms in red). Reprinted with permission from ref 415. Copyright 2008 American Chemical Society.

works can also be made of elements other than the conventional elements, such as Ge, Be, and transition metals. As a matter of fact, most of the recently reported zeolites contain unconventional framework elements. The bonding natures of different types of framework elements are usually quite different, and so are their energy landscapes. A zeolite structure feasible for conventional framework elements might be infeasible for unconventional elements, and vice versa. For instance, many zeolites that are energetically not favored as silicates have been successfully realized as germanates.148,420 Therefore, the feasibility of a zeolite structure is highly associated with its framework composition, which should be studied case by case.359,393,399−401,421−425 During the past few years, a great number of Ge-containing zeolites have been reported (see section 3). Some of these structures are realized as pure germania, whereas the others can only be obtained as silicogermanates. It would be of much interest to be able to predict whether a theoretical structure is feasible as a silicate, a germanate, or a silicogermanate zeolite. In 2010, Sastre and Corma conducted a computational study aiming toward this end.426 At the beginning, they performed ab initio calculations on three 4-ring cluster models, including H8Ge4O4, H8Si4O4, and H8Ge2Si2O4. Figure 51 shows how the energies change with T−O−T angles in these clusters. As expected, the minimum energies appear at 157.7° for Si−O−Si, 137.8° for Ge−O−Si, and 133.3° for Ge−O−Ge angles. Figure 51 also shows that a Si−O−Si angle smaller than 140° or a Ge−O−Ge angle larger than 145° will induce an energetic penalty larger than 2 kJ/mol. Therefore, the relative number of unfavorable angles in a zeolite structure should reflect its structural infeasibility.

In 2008, Zwijnenburg and Bell found that there might exist some structures violating Brunner and Meier’s observation.415 Zwijnenburg and Bell selected several hypothetical zeolite frameworks with extra-large pores and optimized their framework geometries as pure silica polymorphs. For each hypothetical structure, the FD, the average Si−O−Si angle,416 the total tetrahedral distortion,417 the pore diameters, the relative lattice enthalpies, and the relative entropies as compared to quartz were calculated.373,375,395,418,419 Some results are listed in Table 5. It can be seen that these hypothetical structures have enthalpies as low as those of existing zeolites (such as FAU). These structures have extralarge pores; their FD values are well below the minimum values predicted by Brunner and Meier for frameworks without 3rings. Figure 50 shows one of these hypothetical structures. In addition, Table 5 shows that the calculated tetrahedral distortion values and the average Si−O−Si angles for all of these hypothetical structures are similar to those in typical highsilica zeolites. All of these results imply that these low-FD and extra-large-pore structures are theoretically realizable despite the absence of 3-ring. However, so far there has been no such structure realized in experiment yet. 6.2. The Feasibility of Zeolites with Unconventional Framework Elements

Si, Al, P, and O are the conventional framework elements that occur most frequently in existing zeolites. Zeolites constructed by these elements are referred to as the conventional zeolites. By evaluating the relationship between framework energy and framework density, the feasibility of conventional zeolite structures has been extensively studied.391−402 Zeolite frame7304


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of these optimized topologies show dramatic differences between their SiO2 and SiS2 polymorphs (Table 7). Among Table 7. Total Energies Relative to Quartz, Total Tetrahedral Distortions, and Average Si−X−Si Angles for the Optimized SiO2 and SiS2 Materials429 E (kJ/mol SiX2) quartz diamond SOD CHA RWY

Sastre and Corma selected 16 zeolite framework types and optimized them as pure silica and germania structures using a force field developed from the ab initio calculations. According to the results listed in Table 6, AST, BEC, ITH, and SOF Table 6. Numbers of Unfavorable T−O−T Angles (%) in Zeolites with SiO2 and GeO2 Compositions426 zeolite

SiO2

GeO2

zeolite

SiO2

GeO2

0 40 0 10 33 0 4 0

0 0 0 17 0 9 0 6

ITH IWR IWW LTA SOF STW UOZ UTL

0 0 0 0 0 10 40 24

0 4 5 10 0 0 0 8

⟨Si−X−Si⟩ (deg)

SiS2

SiO2

SiS2

SiO2

SiS2

0 2 7 9 46

0 −33 −31 1 −37

0.022 0.034 0.023 0.030 0.071

0.19 0.17 0.11 0.31 0.15

141 141 144 147 123

119 112 111 116 105

SiO2 materials, quartz has the lowest framework energy and RWY the highest. However, as SiS2 materials, quartz becomes an infeasible structure and RWY the most feasible one. The total tetrahedral distortion values (i.e., the root-mean-square distances between the bridging atoms in the optimized and the ideal tetrahedral structures) also show significant difference between SiO2 and SiS2 polymorphs. The total tetrahedral distortion values for SiS2 polymorphs are 1 order of magnitude higher than that for SiO2, indicating the fact that chalcogenide zeolites prefer to have distorted frameworks. Meanwhile, the Si−X−Si angles in SiS2 polymorphs are much smaller than those in SiO2 polymorphs. The smaller is the average Si−S−Si angle is, the more stable a SiS2 zeolitic framework would be. In 2008, Zwijnenburg and co-workers extended their study to halide zeolites, including BeF2 and BeCl2.430 Through DFT computations, Zwijnenburg and co-workers discovered that many properties of BeF2 matched those of SiO2, and BeCl2 matched SiS2. These properties included the energy landscapes, the bonding geometries, and the effective charges. The energies of some BeX2 compounds were predicted to be comparable to those of the experimentally observed ones. However, there has been no halide zeolitic material reported yet, which requires more extensive experimental explorations to verify their true feasibility.

Figure 51. Plot of energetic stability with respect to Si−O−Si, Ge− O−Si, and Ge−O−Ge angles obtained from 4-ring cluster models. Reprinted with permission from ref 426. Copyright 2010 American Chemical Society.

AST ASV BEC ITQ-21 ITT ITR IHW ISV

TTD (Å)

SiO2

should be feasible as both pure silica and pure germania, due to the absence of unfavorable angels in both forms. ITQ-21 and UTL are not feasible at both pure end compositions and may only be realizable as silicogermates. ITR, ISV, and LTA are not feasible as pure germania, whereas ASV, ITT, and UOZ are not feasible as pure silica. All of these theoretical results agree well with experimental discoveries. In 2014, Treacy and co-workers studied the energy dependence of T−O−T angles in silica and germania crystalline systems.427 Their results based on periodic models are generally similar to those obtained by Sastre and Corma using the cluster models. Knowing the difference between Si−O−Si and Ge−O−Ge ranges, Treacy and coworkers found 994 low-energy hypothetical frameworks might be realizable as pure silica and 48 as pure germania in the Atlas of Prospective Zeolite Structures.129 The discovery of chalcogenide zeolites has opened a new way to realize four-connected frameworks that are not feasible as oxides, such as those containing supertetrahedral units.428 In 2007, Zwijnenburg and co-workers conducted a theoretical study to evaluate the feasibility of four-connected chalcogenide frameworks.429 The framework topologies they studied included quartz, diamond, SOD, CHA, and RWY. The SiO2 and SiS2 polymorphs of these topologies were fully optimized through periodic DFT computations. The framework energies

6.3. The Flexibility of Zeolite Frameworks

As compared to the rigid TO4 tetrahedra, the T−O−T linkages in zeolite frameworks are much more flexible. Because of this reason, many zeolite frameworks can be expanded or compressed without distorting their TO4 tetrahedra.411,431−439 The flexibility of zeolite frameworks could be understood by the concept of rigid-unit modes (RUMs), which are the vibrational modes propagating in the whole framework structure with no distortion of tetrahedra. According to this concept, the tetrahedra could rotate or translate as rigid units. Because RUMs are directly related to the bending of flexible T−O−T linkages, they usually have low frequencies and are very useful for the understanding of phase transition and thermal behavior of many four-connected framework structures.417,439−448 When a flexible zeolite framework deforms, its framework density is also varied. The variation range of FD in which TO4 tetrahedra can retain their ideal shape is called the flexibility window.449 Figure 52 shows the frameworks of zeolite FAU at the highest, the medium, and the lowest FDs, respectively, which were calculated using the GASP program assuming pure silica polymorphs.417 The simulated Si−O lengths, O−Si−O angles, and Si−O−Si angles at different FDs are shown in 7305


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Figure 52. Frameworks of pure silica FAU at different FDs viewed down the [110] direction. The upper half of each framework shows the rigid SiO4 tetrahedral units, with small spheres representing the corner-sharing oxygen anions. The lower halves show the oxygen anions drawn with their van der Waals radius of 1.35 Å. (a) At high FD (16.3 T/1000 Å3). (b) In the middle of the flexibility window (FD = 14.8 T/1000 Å3). (c) At low FD (density 13 T/1000 Å3). Reprinted with permission from ref 449. Copyright 2006 Nature Publishing Group.

Figure 53. The shaded range of FD defines the flexibility window, in which the Si−O lengths and O−Si−O angles retain their ideal values. Outside the flexibility window, the tetrahedra start to deform. Further studies have shown that this flexibility is a prevalent structural feature for existing zeolite frameworks. Treacy and co-workers found that most of the existing zeolite frameworks were flexible when modeled as pure silica polymorphs.450−452 To measure the flexibility of a zeolite framework, Treacy and co-workers defined the flexibility index, FO, as the ratio of the maximum to the minimum FDs within the flexibility window. Zeolites BCT and BIK, with FO’s close to 2.0, are the most flexible zeolite frameworks. It should be noticed that the calculation of the framework flexibility is highly dependent on framework composition and symmetry. Many inflexible frameworks become flexible once a mixed-tetrahedron composition or a lower-symmetry representation is allowed.414,450,451 Meanwhile, one should not overlook the existence of a small number of inflexible zeolites, such as aluminosilicate GOO and silicate STW. Their feasibility might be the result of the extra stabilization effect coming from the strong host−guest interactions between zeolite frameworks and extra-framework species. Because most existing zeolite frameworks are flexible, it can be used as an important criterion to evaluate the structural feasibility of hypothetical zeolite frameworks. In 2012, Treacy and co-workers calculated the flexibility of 117 570 hypothetical zeolite frameworks with low framework energies. They found only 10% of these structures were flexible.453 In comparison, over 80% of the real zeolite frameworks were found to be flexible through the same approach. Therefore, the framework flexibility is an effective prescreening tool for the selection of feasible candidates from a large number of hypothetical structures.

frameworks are constructed by the packing of essential rings only or the packing of the combinations of NBUs and rings; 30 IZA frameworks are constructed by the packing of NBUs and/ or rings in a low-symmetric form. In total, 163 out of the 201 IZA frameworks can be decomposed into PUs. Some examples are shown in Figure 54. The packing models of these PUs have a few important characteristics: (i) a feasible zeolite framework should fit its packing model; (ii) the number of PUs that are able to form IZA frameworks is very limited; (iii) the number of topologically different PUs in each IZA framework is typically equal to 1 or 2; (iv) typical PUs and packing nets can combine in different ways to generate a variety of IZA frameworks; and (v) most IZA frameworks correspond to more than one packing model. Because most IZA frameworks can be described using these packing models, a theoretical zeolitic structure that can be decomposed into PUs is probably a feasible one like most of the IZA structures. Following this idea, Blatov and co-workers analyzed the building schemes of 1220 hypothetical zeolite frameworks.129 They found that only 237 hypothetical frameworks were constructed by the packing of NBUs, among which 189 were composed of NBUs occurring in existing zeolites. Blatov and co-workers believed that these 189 zeolite frameworks should be the most realizable candidates for future target-synthesis. Notice that this PU model is a purely topological approach, in which the framework stability, bonding geometry, and the effect of structure-directing agents are completely ignored. Although there are a number of existing zeolites violating this model, it is still a useful tool for the preliminary screening of a large number of hypothetical structures. 6.5. Local Interatomic Distances

The correlation between framework density and framework energy, the flexibility window, and the packing unit representation are the common characteristics of most existing zeolites. However, none of them is universally valid to every existing zeolite structure without exception. In 2013, Yu and coworkers discovered that the local interatomic distances (LIDs) in all existing four-connected oxide zeolitic frameworks strictly obeyed a set of criteria without exception, which might represent certain intrinsic structural features capable of discriminating between feasible and infeasible hypothetical structures.420 Yu and co-workers optimized the frameworks of 200 existing four-connected zeolites as pure silica polymorphs. Three types of LIDs were calculated, including DTO (T−O distance), DOO

6.4. The Packing Unit Model

The definition of packing unit (PU) was developed by Blatov and co-workers for the description of the building schemes of aluminophosphate zeolites (see section 2.2.5). According to their previous study, an aluminophosphate zeolite framework can be decomposed into PUs without sharing common T atoms. PUs could be polyhedral NBUs or essential rings; their positions and connectivity can be described by a packing net.44 In 2013, Blatov and co-workers extended this study to 201 IZA frameworks.45 According to their results, 51 IZA frameworks are constructed by the packing of NBUs only; 82 IZA 7306


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(O−T−O distance), and DTT (T−O−T distance). Yu and coworkers found that the average LIDs (designated ⟨DTO⟩, ⟨DOO⟩, and ⟨DTT⟩, respectively) were highly linearly correlated (Figure 55). All of the 200 existing zeolite frameworks strictly obey these linear relationships, which are the first two of the LID criteria. The third and the fourth LID criteria are related to the standard deviations and the ranges (i.e., differences between the maximum and minimum values) of LIDs, respectively. In every existing zeolite, the standard deviations and the ranges of the LIDs are all very small.420 Because the four LID criteria are strictly obeyed by all of the existing zeolite structures, any fourconnected framework satisfying these criteria should be a feasible zeolite structure. If the 200 existing frameworks are divided into conventional zeolites (including silicates, aluminosilicates, and aluminophosphates) and unconventional ones, we may find that the average LIDs in conventional zeolites vary in narrow ranges (⟨DTO⟩, 1.5967−1.6076 Å; ⟨DOO⟩, 2.6070−2.6251 Å; ⟨DTT⟩, 3.0998− 3.0490 Å). In comparison, the average LIDs in unconventional zeolites vary in much wider ranges (⟨DTO⟩, 1.5991−1.6284 Å; ⟨DOO⟩, 2.6111−2.6588 Å; ⟨DTT⟩, 3.0882−2.9435 Å). If the average LIDs of a zeolite framework fall into the regions of conventional zeolites, this framework might be realizable with conventional framework elements; otherwise, it can only be realized with unconventional framework elements. This is the fifth LID criterion. Yu and co-workers applied these LID criteria to evaluate the feasibility of 665 hypothetical zeolite frameworks derived from three different databases (Figure 55).57,129,365 Their results indicated that only 197 hypothetical zeolites were realizable (satisfying LID criteria 1−4) and 93 were realizable as conventional zeolites (satisfying LID criteria 1−5). In comparison with other structure-evaluating methods, the LID approach has two major advantages. The first advantage is its full coverage of all existing four-connected zeolites; all other methods have exceptions that could not be explained. The second advantage of the LID approach is its sensitivity to unreasonable structures; it focuses on the local bonding environment and is therefore more sensitive to local structural distortions and theoretical artifacts than other methods that are based on average structural properties. 6.6. Future Development

Feasibility evaluation is an important complement to ZSP. Current evaluation methods can be divided into two groups: the topology-specific methods and the embedding-specific methods. The topology-specific methods correspond only to the topologies of the underlying nets of zeolite frameworks (such as the packing unit model). These methods usually run

Figure 53. Flexibility window, shown as a shaded region, for pure silica FAU. Outside this window, structural distortions develop rapidly as shown by (a) bond lengths, (b) tetrahedral angles, and (c) bridging angles, for various FDs. The experimental FD of FAU is marked by an asterisk in each panel. Reprinted with permission from ref 449. Copyright 2006 Nature Publishing Group.

Figure 54. Packing of the same PU (sod cage) in EMT, FAU, and LTA. The topologies of the packing nets are given in parentheses. Reprinted with permission from ref 45. Copyright 2013 American Chemical Society. 7307


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Figure 55. Linear relationships between the average LIDs in optimized zeolite frameworks. (a) ⟨DOO⟩ versus ⟨DTO⟩ in existing zeolites; (b) ⟨DTT⟩ versus ⟨DTO⟩ in existing zeolites; (c) ⟨DOO⟩ versus ⟨DTO⟩ in hypothetical zeolites; (d) ⟨DTT⟩ versus ⟨DTO⟩ in hypothetical zeolites. Red circles denote existing conventional zeolites; blue circles denote existing unconventional zeolites; black dots denote hypothetical zeolites. The regression lines derived from existing zeolites are also displayed. The regions occupied by existing zeolites are highlighted in cyan. Reprinted with permission from ref 420. Copyright 2013 Wiley-VCH.

On the other hand, a theoretically feasible zeolite may be too difficult to synthesize because of the restrictions of synthetic conditions. Unfortunately, none of the current feasibility evaluation methods has considered these synthetic issues. This is because how these synthetic factors determine the formation of a zeolite framework is still a mystery. Therefore, to predict whether a zeolitic framework is practically synthesizable requires more comprehensive studies not only in its theoretical feasibility but also in the mechanism of the formation of zeolite frameworks.

very fast, and are therefore more suitable for the prescreening of infeasible structures. If a fast topology-specific method can be implemented in a ZSP approach in the future, infeasible structures will be avoided in the first place or be removed as soon as they are generated. By doing this, the efficiency of ZSP will be significantly improved. In comparison, the embeddingspecific methods correspond to specific embeddings of the underlying nets,454 which are related not only to framework topologies but also to framework elements, compositions, cell parameters, and atomic positions, etc. (such as the flexibility and LID criteria). The embedding-specific methods can be used to predict which elements should be used to realize a specific framework topology, and therefore are very important for rational synthesis of target structures. However, in these approaches, the structure of each embedding has to be fully refined before evaluation, which can be computationally expensive when a large number of structures are evaluated. For this reason, embedding-specific methods can be used to filter out infeasible structures in the last stage of ZSP; it cannot be frequently performed during ZSP to remove infeasible structures instantly. Moreover, if a different embedding of the same framework topology is considered, we have to start over with the whole procedure, including full structure refinement and evaluation. All of these disadvantages limit the practical application of embedding-specific methods, which should be minimized as much as possible in the future. It is worth noting that an infeasible zeolite framework may become feasible under the influence of many important synthetic factors, such as reaction temperature,157,177,188 reaction pressure,186,455 and extra-framework species,144 etc.

7. CONCLUDING REMARKS The past few years have witnessed the rapid development of studies in zeolite structural chemistry. In this Review, we have shown the most recent progress in zeolite structure description, including the inventions of new structure descriptors and new calculation methods for porous structures. Many new zeolite structures have been discovered after the publication of the sixth edition of Atlas of Zeolite Framework Types in 2007. We have devoted our attention especially to the new zeolitic frameworks with unprecedented rings, unprecedented complexity, intrinsically chiral structures, and a large number of 3-rings. Such rapid growth in the number of new zeolite structures is partly due to the recent development in structure determination methods, especially those based on X-ray and electron crystallography. We have noticed that the computer modeling techniques are becoming more important not only as an important complement to conventional structure determination techniques but also as a powerful tool for the prediction of 7308


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Biographies

hypothetical zeolite structures. With the rapid development of both computer hardware and software, the number of hypothetical zeolite structures has been growing explosively. With the aid of various recently developed structure evaluation methods, we are now able to filter out the infeasible structures that are unlikely to be realized and to focus our synthetic efforts on the most promising ones. Despite all of the success, we have noticed that there are many unsolved problems in this area. We believe some studies would be our short-term goals toward the solution of these problems in the future, for example: (A) to develop new structure descriptors suitable for quantitative estimation of the physical and chemical properties of a given zeolite framework; (B) to realize fully four-connected zeolite structures with unprecedented structure features, such as 13-, 17-, and >18ring; (C) to develop convenient methods for the collection and interpretation of electron crystallography and solid-state NMR data; (D) to improve the efficiency of computer modeling for structure determination and prediction; (E) to build versatile structure databases with a variety of efficient search-and-match functions, such as topology match and PXRD peak match; and (F) to develop structure evaluation methods that could predict the feasibility of a zeolite framework under a specific synthetic condition. This is not the end of the story. One should notice that all of the structures we have discussed so far are highly crystalline. During the crystallization of a zeolite structure, nucleation is the most important step, where amorphous structures start to transform into crystalline frameworks under the control of various kinetic factors. Understanding the nucleation state in solution is the key to understand the formation of zeolite structures.111,456−474 Unfortunately, the nucleation process is also the most difficult step to monitor, because the initial nucleation state is so complex for any current in situ or ex situ detection techniques.475−492 Although we have not yet found any convincing way to monitor the formation of zeolite structures directly, several approaches proposed by various groups have definitely shed some light on this problem.105,107,493−500 Meanwhile, computer modeling offers us another opportunity to unravel the nucleation process without actually “seeing” it.501−514 Considering the fact that the computer power has grown so rapidly and continuously, we can safely anticipate that computer modeling will become a powerful tool for the study of zeolite nucleation in the near future. Once all of the problems for both crystalline and nuclei structures are satisfactorily solved, we will be able to unravel the ultimate mysteries of zeolite structures as well as their formation mechanism.

Yi Li was born in Changchun, China, in 1978. After he received his Ph.D. degree from Jilin University in 2006, he joined the State Key Laboratory of Inorganic Synthesis and Preparative Chemistry at Jilin University and worked as a lecturer. In 2009, he was promoted to associate professor. His main research interest is to study the structural chemistry of microporous materials via various computer techniques.

Jihong Yu received her Ph.D. degree from Jilin University in 1995, and worked as a postdoctoral fellow first at the Hong Kong University of Science and Technology and then at Tohoku University (Japan) from 1996−1998. She has been a full Professor in the Chemistry Department, Jilin University, since 1999. She was awarded the Cheung Kong Professorship in 2007. Her main research interest is in the rational design and synthesis of zeolitic functional materials. She serves as the Associate Editor of the Journal of Chemical Science.

ACKNOWLEDGMENTS We thank the State Basic Research Project of China (Grant nos. 2011CB808703; 2014CB931802) and the National Natural Science Foundation of China (Grant nos. 91122029; 21273098; 21320102001). Y.L. thanks the support by Program for New Century Excellent Talents in University (NCET-130246). REFERENCES (1) Auerbach, S. M.; Carrado, K. A.; Dutta, P. K. Handbook of Zeolite Science and Technology; Marcel Dekker, Inc.: New York, 2003. (2) Xu, R.; Pang, W.; Yu, J.; Huo, Q.; Chen, J. Chemistry of Zeolites and Related Porous Materials: Synthesis and Structure; John Wiley & Sons (Asia) Pte Ltd.: Singapore, 2007. (3) Č ejka, J.; Corma, A.; Zones, S. Zeolites and Catalysis: Synthesis, Reactions and Applications; Wiley-VCH Velag GmbH & Co. KGaA: Weinheim, 2010.

AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest. 7309


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