Predicting New Zeolites: A Combination of ... - ACS Publications

Article Cite This: Chem. Mater. 2018, 30, 2829−2837

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Predicting New Zeolites: A Combination of Thermodynamic and Kinetic Factors Ekaterina D. Kuznetsova,†,‡ Olga A. Blatova,† and Vladislav A. Blatov*,†,‡ †

Samara Center for Theoretical Materials Science (SCTMS), Samara University, Ac. Pavlov St. 1, Samara 443011, Russia Samara Center for Theoretical Materials Science (SCTMS), Samara State Technical University, Molodogvardeyskaya St. 244, Samara 443100, Russia

‡

S Supporting Information *

ABSTRACT: Zeolites are a special class of inorganic compounds which potentially possess an infinite variety of different structures that are energetically very close to each other. Although the databases of hypothetical zeolite frameworks, which are thermodynamically close to the ground state, contain hundreds of thousands of entries, the number of experimentally obtained frameworks (currently 235) is essentially smaller. We discuss kinetic factors, which should be taken into account along with the thermodynamic ones to explain such great inconsistency and predict more thoroughly new robust zeolite frameworks. In addition to the thermodynamic factors, which determine energetically favorable structures, we consider structural parameters that provide the easiest ways of the structure assemblage. Exploring the existing zeolites, we derive geometrical and topological criteria that should be obeyed when the framework is being formed in the reaction gel. Resting upon these criteria, we extract from the databases of hypothetical zeolite frameworks those frameworks which are the most prospective for synthesis. We discuss also the problem of the purposeful sampling of proper organic structure directing agents and propose a list of them for a target synthesis of the selected hypothetical frameworks.

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INTRODUCTION

Zeolites compose a very important class of compounds which have been widely used, especially as adsorbents and catalysts.1 Although their frameworks have rather simple chemical composition of the ideal formula TO2, where T is a tetrahedrally coordinated atom, different ways of connection of the tetrahedra can provide millions of topologically different structures, many of which are energetically favorable. These hypothetical structures are stored in the databases2,3 and very likely promise a lot of new advanced materials. However, just a few of these frameworks can be synthesized, and only 235 have been obtained up to now.4 Various criteria were proposed to select the frameworks to be prospective for synthesis,5−8 but most of such frameworks remain hypothetical.9 Moreover, if the framework does not fit the criteria, this does not mean that it cannot be synthesized. So, the existing criteria are neither sufficient nor necessary but just claim some framework properties to be favorable for synthesis. Obviously, this is not enough for a rational design of new zeolites, and the problem of search for new both favorable and unfavorable framework properties remains crucial. Remarkably, all mentioned criteria concern thermodynamic stability of the framework. Recently,10 we proposed a new method for selection of promising hypothetical zeolite frameworks which, in contrast to all known “thermodynamic” criteria, deals with kinetic factors of fastest and easiest assembling of the framework from a set of building units. In this paper, we develop this predictive scheme and provide a list of hypothetical frameworks, which can be considered as promising candidates for the zeolite synthesis. © 2018 American Chemical Society

EXPERIMENTAL SECTION

Tile Packing Model. According to the model,10 zeolite framework is formed as a result of polycondensation of building units which are stabilized by template cations or molecules presenting in the reaction gel. During polycondensation, the primary units T+4(OH)4 or [T+3(OH)4]− combine together, eliminate water molecules, and form secondary building units, which can be chain-like, ring-shaped, or polyhedral. Only most stable oligomeric particles remain in the reaction media under the equilibrium conditions. Cations of alkali and alkaline earth metals as well as organic molecules act as templates for the secondary building units. Cations tend to surround themselves with oxygen atoms of the TO4 groups, and as a result, polyhedral building units are formed. The secondary building units condense further to form the whole zeolite framework. Thus, the zeolite framework can be divided into building units that must fit the following conditions: (i) they have no common T atoms, (ii) they form the whole framework, and (iii) they should be associated with templates. A strict algorithm of decomposition of the zeolite framework into the building units that satisfy these criteria was proposed,10 where the building units represent natural tiles, i.e. smallest cages of the framework.11 The centers of the natural tiles compose an underlying net, which shows the method of their assembling (Figure 1). Because the tiles have no common T atoms, such model was called tile packing.10 It was suggested that those frameworks are favorable for synthesis, which (i) fit the tile packing model and (ii) have the local connectivity of the tiles similar to that in the known zeolites (minerals or synthetic structures). This provided an important additional criterion for screening the hypothetical zeolite frameworks: they should satisfy these two tile packing conditions. This criterion Received: March 1, 2018 Revised: April 4, 2018 Published: April 4, 2018 2829

DOI: 10.1021/acs.chemmater.8b00905 Chem. Mater. 2018, 30, 2829−2837

Article

Chemistry of Materials

Figure 1. Decomposition of the zeolite framework ERI to natural tiles: initial framework, its natural tiling, packing of t-can tiles, and the corresponding underlying net. essentially extends already known criteria of thermodynamic stability because it touches the kinetic aspects of the framework formation. To predict the framework viability, one should consider a combination of thermodynamic and kinetic factors. The tile packing approach was implemented into the program package ToposPro,12 which was used in our work to perform all topological analyses of real and hypothetical zeolite frameworks. The three-letter symbols13 and the ToposPro NDk-n nomenclature14 are used to designate the topologies of the underlying nets; the topological types of tiles are assigned with the t-xxx symbols.15 Objects. To determine the ways of connection of natural tiles in already known zeolites we analyzed all 235 zeolite frameworks from the Database of Zeolite Structures.4 The data on hypothetical zeolite frameworks were taken from the databases2,3 containing 274 611 and 331 167 zeolite frameworks, respectively; further, we call these databases DB_A and DB_B. For all the frameworks, the tile packing models were constructed, and those frameworks were further considered that are formed by tiles of the same type (Table 1). Such monotile models are the simplest, and the corresponding zeolites are expected to be obtained most easily because only one type of template is required in this case to stabilize the building units. The

local connectivity of the packing tiles was studied, and the underlying nets, which nodes coincide with the centers of the building units, were constructed to characterize the overall topology of the frameworks. Selection Criteria. The results obtained are arranged below with respect to the type of the packing tile. For each framework, we explored the following topological descriptors, which can influence the assembling rate: (i) Size of the tile treated in a topological sense as the number of T atoms which compose the tile. The tile should be neither too small to include the template nor too large to be assembled and stable in the reaction gel. The high limit was experimentally estimated to about 20 T atoms.16 Because the estimation was approximate, we assume that the packing tiles can be a bit larger (up to 25 atoms).

Table 1. Topological Parameters of the Monotile Zeolite Frameworks packing tile t-afo t-ato t-can

t-hpr

t-kaa t-lau t-lio t-opr t-toc

underlying net

coordination figure

number of bonds

CN

BPH OFF ERI OFF LTL MOZ LIO AEI CHA FAU KFI SAV GME TSC AFT

bnn hex hex

trigonal bipyramid hexagonal bipyramid hexagonal bipyramid

9 30 18

5 8 8

bnn tfs hcp pcu pcu crs pcu pcu asc flu-e sta

trigonal bipyramid octahedron cuboctahedron octahedron

18 18 18 12

5 6 12 6

trigonal prism

12

6

octahedron + trigonal prism

12

6

AFX EMT SFW LTL LAU FAR MER TSC FAU EMT LTA

nia lon-e stb kag pcu hcp bcu reo dia lon pcu

octahedron octahedron cuboctahedron cube

20 16 42 16

6 6 12 8

tetrahedron

24

4

octahedron

36

6

zeolite

Figure 2. Packing of tiles in the zeolite GME: (left) the local environment of a packing t-hpr tile, which has 12 bonds with its neighborhood and CN = 6; (right) the coordination figure of the tile (trigonal prism) in the underlying net of the acs topology. (ii) Local environment of the tile that is the shape of the configuration formed by a given tile and its neighboring tiles in the packing (Figure 2). One can expect that such configurations are being formed in the reaction gel at the precrystallization stage. Obviously, only those of them which promote the subsequent assembling of the whole framework “survive” and remain “frozen” in the crystal. To determine a particular configuration in the framework, we used a unique possibility of ToposPro to search for a finite fragment of any complexity in an infinite structure.17 (iii) Number of bonds between the tile and its neighborhood. This number shows how strongly the tile connects to its neighbors (Figure 2). Obviously, this number cannot be too small, otherwise the configuration will be unstable because of low connectivity, but it should not be too large to provide the configuration with a sufficient flexibility for embedding into the framework. (iv) Coordination number (CN) of the tile. This is the number of the neighboring tiles in the local environment (Figure 2). It essentially predetermines the coordination figure of the tile. (v) Coordination figure of the tile. This is the geometrical solid that is formed by the centers of the neighboring tiles (Figure 2). It is known18 that coordination figure strongly correlates with the topology of the underlying net. 2830


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Chemistry of Materials (vi) Topological type of the underlying net. The underlying net characterizes the method of assembling of the packing tiles, i.e., the entire architecture of the framework (Figure 1). It is hardly possible to determine a priori what types or values of the descriptors are the most favorable to provide the easiest and fastest assembling of the framework. That is why at the first stage of our study we analyzed the topological descriptors of already known zeolite frameworks and used their values as filters for screening the databases2,3 for the hypothetical frameworks to be prospective for synthesis. Because the hypothetical frameworks were already selected in the databases2,3 as energetically favorable, we have in fact applied two main criteria to predict which frameworks are synthesizable: (i) the energy of the framework of the SiO2 composition should be close to the energy of the quartz structure19 and (ii) topological properties (i−vi) of the packing model of the framework should be similar to at least one of already known zeolite frameworks. While the former criterion accounts for thermodynamic stability of the framework, the latter one is in charge of the optimal assembling, i.e. the kinetic factors, which rule the crystal formation.

Figure 4. Methods of connection and coordination figures of the t-can tiles in the zeolites: (a) ERI, OFF, (b) LTL, (c) LIO, and (d) MOZ.

The zeolites OFF, LTL, and MOZ can be constructed from other tiles (t-ato, t-kaa, and t-kaa + t-ato, respectively, Figure 5).

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RESULTS AND DISCUSSION Existing Zeolite Frameworks. The known zeolite monotile frameworks are formed from nine types of tiles, which have the topological parameters collected in Table 1. Below we analyze in more detail those frameworks that are constructed from tiles t-hpr, t-can, t-ato or t-lio as the corresponding architectures exist in hypothetical zeolites. Packings of t-can Tiles. The local environment of any t-can tile contains the same tiles coordinated in an equatorial plane being parallel to the planar hexagonal faces of the origin tile. All the tiles are connected to each other through the edges separating the square faces in the manner shown in Figure 3.

Figure 5. Tiles t-kaa (a) and t-ato (b); the MOZ zeolite framework constructed as packing of t-kaa and t-ato tiles (c).

However, these tiles should not be considered as building units due to their flatness, which prevents location of templates inside the tiles. These are typical “gluing” tiles,15 i.e., the tiles that fill the space between the packing tiles. Packings of t-hpr Tiles. The frameworks formed from the thpr tiles have already been analyzed10 for all zeolites known at that time (AEI, AFT, AFX, CHA, EMT, FAU, GME, KFI, SAV, and TSC). In all cases, the t-hpr were found connected to six other tiles (Table 1) by pairs of vertices of the hexagonal faces in a trigonal-prismatic or octahedral fashion. Since that time, one more zeolite of this group (SFW) was obtained, which also fitted the packing model. Two inequivalent t-hpr prisms have both octahedral and trigonalprismatic coordination figures (Figure 6) like in the zeolite AFX.21 These topological features reflect the polytypic nature of SFW and AFX, which belong to the ABC-6 family.22 Nonetheless, the global topologies are different in these zeolites because underlying nets are not the same (Table 1). Packings of t-lio Tiles. Only the FAR framework can be constructed from t-lio tiles. However, these tiles are too large (they consist of 42 T atoms) to consider them as building units. An alternative way of assembling from t-toc (24 T atoms) and tcan (18 T atoms) tiles seems much more preferable (Table 1, Figure 7). Hypothetical Zeolite Frameworks. The topological parameters, which characterize the structure of existing zeolites, can now be used to select the hypothetical zeolite frameworks with similar geometrical−topological properties (Table 2). One can expect that these zeolites can be available for synthesis because not only is the energy of their frameworks low enough, but also their assembling mimics the ways that nature has already chosen. Below, we consider these groups of hypothetical zeolite frameworks in more detail depending on the type of the packing tile.

Figure 3. Method of connection of the t-can tiles located in the equatorial plane of the origin tile in the zeolites: (a) ERI, LIO, OFF (ERI plane), (b) LTL (LTL plane), and (c) MOZ.

The first method of connecting, which we call ERI plane, occurs in 12 known zeolites (AFG, CAN, ERI, FAR, FRA, GIU, LIO, LOS, MAR, OFF, SAT, and TOL), but the framework is formed exclusively by the t-can tiles only in the 5 zeolites mentioned above. In the ERI plane, each t-can tile is adjacent to six other tiles (Figure 3a). The tiles located in the parallel planes above and below are connected to the origin tile through its planar hexagonal face. Each face is adjacent to a similar face of another tile in zeolites ERI, LTL, MOZ, and OFF (Figure 4); thus, the tiles form infinite columns described by Smith.20 The t-can tiles in LTL are connected to three other tiles in the plane, which we call LTL plane. In LIO, each planar hexagonal face of t-can forms bonds with three such faces (Figure 4c). As a result, the coordination figure of each t-can tile is hexagonal bipyramid in zeolites ERI and OFF, trigonal bipyramid in zeolite LTL, cuboctahedron in zeolite LIO, and distorted tetragonal bipyramid in zeolite MOZ (Figure 4). 2831


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type of tile connection differs from real zeolites (Figure 8). Only 17 of these frameworks have rather regular t-can tiles with

Figure 8. Coordination figures of t-can tiles in hypothetical zeolite frameworks (a) 225_3_18 and (b) 223_3_2214398 (database DB_A); the tiles are distorted, and their local environment is dissimilar to existing zeolites.

Figure 6. Methods of connection and coordination figures (trigonal prism on the left and octahedron on the right) of the t-hpr tiles in the zeolite SFW. Hereafter the red lines in the coordination figures show bonds between the tiles, and the black lines show edges of the polyhedron.

CN = 8 or 12, which occur in existing zeolites. The t-can tiles in these 17 frameworks have 3 types of coordination figures (Figure 9) which reflect the polytypic character of this series. Indeed, the frameworks can be considered as packings of hexagonal layers of t-can tiles (ERI planes) differently shifted with respect to each other (Figure 10). As a result, most of the 17 frameworks are characterized by the underlying nets with the topology of a hexagonal packing (hex, hcp, tck, tcd, and their derivatives, Table 3). The coordination figure with CN = 10 has not been found in the existing zeolite frameworks but seems reasonable as a mixture of the figures with CN = 8 and 12. Because the ERI plane seems an important infinite building block, we additionally selected 20 geometrically robust hypothetical zeolite frameworks which are constructed from ERI planes, but the local connectivity of their packing tiles differs from that of existing zeolites. At the same time, the underlying topologies of both 20 and 17 frameworks are similar (Table 3). Note that the frameworks with the same motif of the binding of packing tiles differ by the cages that are formed by the tiles (Figure 11). We call these cages stuffing tiles as they fill in the space between the packing tiles. Thus, we distinguish 17 + 20 = 37 hypothetical zeolite frameworks where the ERI plane building block plays an important structure-forming role. Six of the frameworks are

Figure 7. Zeolite FAR built from (a) t-lio tiles and (b) t-toc and t-can tiles.

Packings of t-can Tiles. In 96 hypothetical zeolite frameworks, which can be constructed as packings of t-can tiles, the coordination numbers of the tiles range from 4 to 12. In 58 frameworks, the tiles are strongly distorted and/or their

Table 2. Numbers of Hypothetical Zeolite Frameworks with Topological Parameters Similar to Those of Existing Zeolite Frameworks frameworks contain the tile

a

frameworks are formed by the tiles

local coordination is similar to an existing zeolitea

frameworks with distorted tiles

packing tile

DB_A

DB_B

DB_A

DB_B

DB_A

DB_B

DB_A

DB_B

t-afo t-ato t-can t-hpr t-lau t-lio t-opr t-toc

138 17 670 8050 62 738 19 866 118 45 116 10 170

264 5754 1546 37 386 5183 17 6062 1340

11 39 72 433 117 6 445 57

68 5 24 228 8 0 17 22

0 2 9 8 0 0 0 0

0 2 8 2 0 0 0 0

9 12 32 17 15 2 84 39

0 0 2 8 1 0 0 18

The frameworks do not contain distorted tiles. 2832


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Table 3. Topological Types of Underlying Nets of the Hypothetical Zeolites Similar to Those of Existing Zeolites and Consist of Regular t-can Tiles Underlying net hex

codes of the 17 frameworks similar to existing zeolites

codes of the 20 frameworks constructed from ERI planes

194_5_3920386 PCOD8327034

194_3_1140 PCOD8330642 166_3_6806 PCOD8321510 194_5_3713587 PCOD8322800 194_5_3713592 194_5_3722034

fcu hcp

194_5_3722027

tck

194_5_3713591

tck-8,10-P63/ mmca

194_5_3713580 194_5_3713581 194_5_3722022 194_5_3722023 194_5_3920382

tck-10,12P63/mmca tca

Figure 9. Coordination figures of t-can tiles in hypothetical zeolites from database DB_A: (a) cuboctahedron in 194_5_3713591, (b) hexagonal pyramid in 194_5_3722022, and (c) ten-vertex polyhedron in 194_5_3920380.

tcd

166_3_8899

10,12T2856

PCOD8327146

unusual topologyb

PCOD8327034 PCOD8327036 PCOD8327040 PCOD8327041 PCOD8327068 PCOD8327072

194_5_3920375 194_5_3920376 194_5_3920380 194_3_858 194_3_867 PCOD8330680 PCOD8330668 166_3_8899 166_3_8908 PCOD8327143 PCOD8327180 PCOD8327183

a

The topology is derived from the 6-layered close packing tck. bThe topology is not contained in any known topological collection.

frameworks have also nodes with an atypical connection of tiles compared to that of existing zeolites (Figure 12 bottom). Moreover, the size of framework-determining tiles range from 2633 to 4459 Å3 in these frameworks, significantly exceeding the maximum size of tiles (815 Å3) in the existing zeolite (LTL) with the LTL plane building blocks. Such big tiles are difficult to stabilize as they require too large of templates; hence, these zeolites can hardly be obtained. Packings of t-hpr Tiles. Out of the 78 frameworks of hypothetical zeolites constructed from t-hpr tiles, we selected 10 frameworks where the t-hpr tiles are geometrically robust and their local environment is similar to existing zeolites (Table 4). As in real zeolites, all underlying nets in this group have nodes with only two different coordination figures: trigonal prism and octahedron. Only the framework 227_3_593 has a bit different type of tiles connection; however, this type was observed in the zeolite TSC (Figure 13). Many underlying nets belong to the series of the acs polytypes (Table 4) that reflects the polytypic character of these frameworks. Packings of Other Tiles. Other packing models of real zeolite frameworks contain either too large tiles, which consist of far more than 20 T atoms and can hardly be stable in the reaction gel, or too small tiles, which cannot include any template. As a rule, in such cases, there is an alternative packing

Figure 10. Underlying net and local environments of t-can tiles in the hypothetical framework 8327036 (CN = 8, 10, and 12).

constructed only from already known tiles, which were found in real zeolites.15 Other frameworks contain only one stuffing tile which does not occur in existing zeolites; thus, if we stabilize this tile by an appropriate template, these frameworks could be obtained. Such unique tiles can be called frameworkdetermining as they reflect the unique topology of the whole framework. One of the 20 frameworks, (194_3_1140) was recently synthesized as the zeolite SWY.21 Polytypic assembling is also observed in the hypothetical zeolite frameworks with the LTL plane building blocks; we found four such frameworks (Figure 12 top). However, these 2833


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Figure 12. Two projections of the trigonal-pyramidal coordination and method of connection of t-can tiles in the hypothetical zeolite framework 191_5_101381 (database DB_A): (top) tiles in an LTL plane and (bottom) tiles with atypical method of connection.

Table 4. Topological Types of Underlying Nets of the 10 Hypothetical Zeolite Frameworks Formed by Undistorted thpr Tiles

Figure 11. Hypothetical frameworks with the tck topology: the stuffing tiles surrounded by packing tiles (left), and coordination figures of packing tiles together with stuffing tiles (right) in the hypothetical frameworks from database DB_A: (a) 194_5_3722034, (b) 194_5_3713592, (c) and 194_5_3713591. The packing and stuffing tiles are shown in blue and brown, respectively.

underlying net

zeolite framework

10-layered acs polytype (chcccchccc) 10-layered acs polytype (chhchchhch) 10-layered acs polytype (chhhcchhhc) 8-layered acs polytype (chccchcc)

194_5_1577966 194_5_1577459 194_5_1577965 PCOD8326505 194_4_47045 PCOD8323843 166_3_6775 166_4_452028 227_3_593 166_5_30850739

5-layered acs polytype (chhcc) stb stc 6,6T740 unusual topologya a

The topology is not contained in any known topological collection.

propose new criteria for selecting hypothetical zeolites to be prospective for synthesis. Size of Packing Tiles. The packing tiles must be rather voluminous to be occupied by template ions and molecules. The so-called “gluing” tiles, like t-kaa or t-ato, cannot serve as structural units even if they form a packing (Figure 15). Because the existence of building units consisting of more than 20 T atoms in the reaction gel has not been proven, essentially larger tiles should also not be considered as building units but can appear as stuffing cages in the packing of smaller tiles. At the same time, large organic molecules can make the stuffing tiles stable, providing new zeolite architectures (see below). The existing zeolite networks, which formally can be represented as packings of large tiles, have an additional tile packing model with smaller building units (Figure 7). Number of Packing Tiles. Because the reaction gel ordinarily contains one or two types of templates, the tile packing should not contain more than two different tiles. At the same time, design of complex packings is possible with a purposeful choice of templates. A database of such templates should be developed with the information on their complementarity to particular packing tiles (see below).

model with the tiles of an appropriate (middle) size. Thus, the zeolite FAR can be constructed from large 42-T-atom t-lio tiles but also from middle-sized t-can and t-toc tiles (Figure 7), which consist of 18 and 24 T atoms, respectively. Although the t-toc tile a bit exceeds the formal 20-atom criterion, we suppose that exceeding by up to 5 atoms is insignificant, and the latter model fits the size condition. In many hypothetical zeolites, the model with the packing tiles of an inappropriate size is single, and such frameworks can hardly be obtained like two frameworks (Figure 14) built with geometrically robust but too large t-lio tiles. The same concerns the models with too small tiles. Thus, the known zeolites OFF and LTL can be assembled from small tato and t-kaa tiles, respectively, but also from middle-sized t-can tiles. At the same time, no hypothetical frameworks of this group (eight nets constructed from t-ato tiles and two nets from t-kaa tiles) can be assembled from middle-sized tiles, but only from their combination with small tiles (Figure 15). This also hinders synthesis of these frameworks. Tiling Criteria of Robustness for Zeolite Frameworks. The analysis of zeolite minerals and synthetic zeolite frameworks within the tile packing model makes it possible to 2834


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connection type of the tiles is also significantly different compared to natural zeolites (Figure 8). Number of Stuffing Tiles. Stuffing tiles, which can be considered as cavities formed by packing tiles, play an important role in the formation of novel zeolite frameworks. It is the stuffing tiles that are often unique for a particular zeolite or rarely occur in other zeolites. At the same time, the number of unique stuffing tiles in the framework should not be too large; real zeolites usually have one or two unique types of stuffing tiles. So, the prospective hypothetical frameworks should bear no more than two new tiles; the other tiles should occur in known zeolites (Table S1). Type of Local Connection of Packing Tiles. The real zeolites demonstrate the most effective ways of tile connection, which provide the easiest and fastest assembling. It is reasonable to expect similar connection in the prospective hypothetical zeolite frameworks. Moreover, in the frameworks with an unusual connection, the packing tiles are often distorted and have unusual CNs, i.e. other criteria are also not satisfied (Figure 16). Note that this criterion implicitly Figure 13. Connection of t-hpr tiles and the corresponding coordination figures in the hypothetical zeolite framework 227_3_593 (database DB_A).

Figure 16. Unusual types of local connection of packing tiles in hypothetical zeolites from database DB_A: (left) the framework 189_4_94574 built from t-hpr tiles; (right) the framework 225_6_26561 built from t-can tiles. The rigid regions are enclosed in red.

reflects the framework flexibility, which was proved as an important thermodynamic (entropy) parameter for feasible zeolites23 as well as some other geometrical criteria such as close O···O contacts.9 In particular, the hypothetical zeolites in Figure 16 contain clearly rigid regions due to the unusual local connection. Coordination Number of Packing Tiles. In real zeolites, the coordination numbers of the tiles in the packing have characteristic values. The robust hypothetical zeolite frameworks should also follow these values. If the coordination numbers are unusual, some other criteria could also be unsatisfied; in particular, the tiles can be geometrically distorted (Figure 17). Coordination Figures of Packing Tiles. Besides coordination numbers, the packing tiles should be arranged in the space following a typical coordination figure. Unusual spatial arrangement leads to distortion of the tiles in many cases (Figure 18). With the criteria described above, we have selected 49 hypothetical frameworks, whose assemblage is similar to real zeolites; these frameworks can be treated as potential objects for synthesis (Table S1). Note that 30 of these frameworks have multidimensional systems of pores with 8-, 10-, or 12-ring windows. Such zeolites could be especially useful for catalytic

Figure 14. Hypothetical frameworks constructed from t-lio tiles: (a) 194_4_85336 and (b) 194_4_80618 (database DB_A).

Figure 15. (a) Natural tiling of the hypothetical framework 191_5_101389 (database DB_A) and the packing models with (b) t-kaa tiles and (c) t-kaa + t-can tiles.

Shape of Packing Tiles. In all existing zeolites, the packing tiles preserve their shape, because they are formed around similar templates, for example, alkali cations, although the tile volume can vary depending on the type of the T atom. Hence, the frameworks composed of geometrically distorted tiles, can hardly be synthesized. Moreover, in such frameworks, the 2835


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approximated by a set of modified secondary Voronoi polyhedra built for the vertices of atomic Voronoi polyhedra belonging to the cage. The modification of the secondary Voronoi polyhedra consists in that their faces are placed not in the midpoints between the vertices and framework atoms but at the distances of van der Waals radii of the framework atoms (Figure 19 left). The shape and size of the OSDAs is estimated

Figure 17. Unusual coordination and geometrical distortion of t-can tiles in the hypothetical framework 194_5_4232119 (database DB_A): (a) a tile with CN = 4 and (b) a tile with CN = 8.

Figure 19. (left) The stuffing t-uoz tile in the zeolite UOZ with the Voronoi polyhedron of the cavity (V = 360.93 Å3) and (right) the modified Voronoi polyhedron for the OSDA 1,6-hexanebis(trimethylammonium) (V = 209.15 Å3).

in a similar way as their modified molecular Voronoi polyhedron in a molecular crystal (Figure 19 right). The data for the molecular crystals were taken from the Cambridge Structural Database; parameters for each OSDA were obtained by averaging over at least ten independent molecules. We created a database on molecular Voronoi polyhedra of known OSDAs, existence of which in zeolite cages was experimentally proven (Table S3). The occupation of the cages by the OSDA molecules, which is estimated as the ratio of the molecule and cage volumes VOSDA/Vtile, ranges from 0.47 to 0.94 (Table S3). These values can be used for a rough assessment if a particular molecule fits stuffing tiles in hypothetical zeolites. Out of the 49 prospective hypothetical zeolite frameworks (Table S1), 32 frameworks have unique stuffing tiles, which never occur in real zeolites (Table S2). Using the occupation criterion, we selected OSDAs (Table S4), which geometrically fit these stuffing tiles and can be recommended for the synthesis of the 32 frameworks.

Figure 18. Unusual coordination figures in hypothetical frameworks from database DB_A: (a) the framework 166_3_11536 built from thpr tiles and (b) the framework 225_6_26540 built from t-can tiles.

applications,24 while only 38 zeolites of this type are known so far.4 Almost all of the hypothetical zeolite frameworks, but one (227_3_539), belong to the ABC-6 family, a group of industrially important catalysts constructed from stacking of modular 6-ring layers.25 All the 30 frameworks are composed from t-hpr or t-can tiles, which provide the void space suitable for adsorption, diffusion and reaction of many types of guest species. Tile Packing Model and Organic Structure Directing Agents. As was mentioned above, one of the methods to obtain a new framework consists in stabilizing a stuffing cage (tile), which is characteristic for the framework. For this purpose, a proper organic structure directing agent (OSDA) can be used, which fits the cage size and shape. For example, a new zeolite framework, which was recently synthesized,26 is composed by t-hpr and t-can tiles and contains a unique stuffing tile [49.68.83], which occurs also in six hypothetical zeolites from Table S1. This means that the same OSDA (5λ5azaspiro[4.5]decane) could be used to obtain some of these six frameworks. To select proper OSDAs for other stuffing tiles, we applied the method based on the modified Voronoi polyhedron concept.27 In this method, the cage inside the tile is

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CONCLUSIONS The class of zeolite frameworks is a unique example of topological isomerism of crystal structures: having formally the same composition TO2 the frameworks provide a plethora of topologically different realizations. This fact was known for a long time, and many efforts were undertaken to explain it as well as to predict new zeolite topologies. A paradoxical point was that topological parameters were almost not accounted when treating this topological diversity. At the same time, namely the framework connectivity, also known as topology, 2836


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characterize the method of the structure assemblage, thereby involving kinetic factors into consideration. One can say that the structure geometry reflects thermodynamic (energetic) properties, while the structure topology does kinetic conditions of appearance of a particular framework. The model used and developed in this work suggests a number of new criteria for the purposeful synthesis of new zeolites and selects the synthesizable ones among thousands of thermodynamically favorable candidates. Moreover, these criteria allow us to use the topological approach not only for selection of already proposed frameworks but also for construction of new ones with appropriate building units. Thus, the databases of hypothetical zeolite frameworks can be both squeezed by discarding topologically unrealizable candidates and extended with new topologically favorable ones. Proper structure directing agents can then be found to provide a selective synthesis of these frameworks.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.chemmater.8b00905. Geometrical and topological properties of the hypothetical zeolites and the corresponding organic structure directing agents (PDF)

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AUTHOR INFORMATION

Corresponding Author

*Phone: +7-8463356798; Fax: +7-8463345417; E-mail: [email protected]. ORCID

Vladislav A. Blatov: 0000-0002-4048-7218 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank the Russian Foundation for Basic Research for the support of development of the tile packing model (Grant 17-43-630619). O.A.B. and V.A.B. thank the Russian Science Foundation for support of the search for prospective zeolite frameworks within Grant 16-13-10158.

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REFERENCES

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