Topology of 2-Periodic Coordination Networks - American Chemical

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Topology of 2-periodic coordination networks: towards expert systems in crystal design Tatiana G. Mitina, and Vladislav A. Blatov Cryst. Growth Des., Just Accepted Manuscript • DOI: 10.1021/cg301873m • Publication Date (Web): 26 Feb 2013 Downloaded from http://pubs.acs.org on February 28, 2013

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Crystal Growth & Design

Topology of 2-periodic coordination networks: towards expert systems in crystal design Tatiana G. Mitina, Vladislav A. Blatov* Samara State University, Ac. Pavlov St. 1, Samara 443011, Russia. [email protected]

*

Vladislav A. Blatov, Samara State University, Ac. Pavlov St. 1, 443011 Samara, Russia. Phone: +7-

8463345445, Fax: +7-8463345417, [email protected]

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ABSTRACT: We have performed comprehensive topological analysis of 2-periodic coordination networks in 10371 metal-organic compounds. Both local and overall topologies of complex groups were determined, classified, and stored in the electronic databases. Two plane nets, square lattice (sql) and honeycomb (hcb), were found to compose 2/3 of all the coordination networks. There were found strong correlations between local topological characteristics (coordination numbers of atoms or complex groups, coordination figures, formalized coordination modes of ligands and coordination formula) and the overall topology that in many cases allowed us to predict possible topological motifs from the data on chemical composition with high probability. The possibility to develop an expert system that could envisage local and overall topology of periodic coordination networks is discussed and an example is given of how such system can work.

KEYWORDS: coordination networks, topology, prediction, knowledge database, expert system


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Introduction Extended metal-organic structures have been attracting great interest in the past 15 years as fascinating architectures as well as perspective catalysts, gas containers, and NLO materials.1-5 Since the useful properties of these compounds strongly depend on the structure of polymeric coordination groups, enormous attempts were undertaken to develop methods of structural description and prediction. Among these methods, the topological approaches play the leading role as they deal with connectivity of structural groups (coordination network). At present, more and more authors include the description of the coordination network to characterize novel coordination polymers and metal-organic frameworks. This progress was achieved thanks to the development of advanced software and electronic databases,6-9 which allow one to perform complete topological analysis of any complex structure in an automatic mode. These tools were extensively used to make a comprehensive analysis and classification of 3-periodic coordination networks.10-12 The results obtained compose a good deal of information that can be used in predicting architectures of new coordination networks.13 Surprisingly, although 3-periodic coordination networks (frameworks) were thoroughly studied, any detailed topological systematics of 2-periodic ones (layers) has not been performed yet. At the same time, theoretical investigations of 2-periodic nets have long history. Eleven uninodal plane nets (with one kind of node), aka Kepler-Shubnikov nets,14 were discovered in the 17th century. Since all edges and nodes in Kepler-Shubnikov nets are equivalent, these nets can be related to packings of equal spheres (or circles) on the plane; the centers of the spheres coincide with the net nodes. Many other plane nets were collected by Grünbaum and Shephard.15 As early as 1978, Koch and Fischer16 enumerated 64 additional 2-periodic sphere packings that correspond to double-layer nets (see some examples below, Figs. 3, 5). Such nets should be considered as 3-dimensional 2-periodic because they cannot be embedded into the plane without crossing edges. Thus the terms “N-periodic” and “Ndimensional” should be thoroughly separated when applying to networks.17 Many 2-periodic plane nets, not only uninodal, to be significant for crystal chemistry were considered by O’Keeffe and Hyde,18,19


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however, abundance of these nets in crystals was not analyzed in detail. 2-periodic nets are also widely used to describe intermetallic compounds. On the other hand, 2-periodic coordination networks are likely the best objects to develop the methods for predicting crystal topology as they are much simpler than 3-periodic ones while possessing rather rich topological diversity. Automation of the prediction process requires creating a computer expert system, which could suggest possible coordination networks for a given set of complexing atoms and ligands. Such expert systems, being familiar in macromolecular crystallography,20 are still unknown in crystal design. In this paper, we will show a possibility to develop an expert system that could envisage local and overall topology of periodic coordination networks, so we have chosen 2periodic coordination networks also from this point of view. Experimental Section Methods of generating coordination network topologies from crystal data Resting upon the crystallographic data, one can generate the crystal structure topology as a network whose nodes and edges correspond to atoms and interatomic bonds.21 In coordination compounds, the topology of such network is supported by valence (coordination) interactions between metal (complexing) atoms and organic or inorganic molecular ligands. The resulting coordination network has a unique topology, which can be repeated only in series of isostructural compounds with different complexing atoms or interstitial molecular species. To find more relations between coordination networks, we should use methods of crystal structure simplification.12,22 With these methods, the initial network is represented as an underlying net whose nodes correspond to centroids of structural groups. The method of selecting structural groups determines the method of simplification as well as the resulting representation of the crystal structure as an underlying net. We will use two kinds of representation: standard one, where structural groups correspond to metal atoms and ligands (this is the most typical method of decomposition of complex groups in coordination chemistry) and cluster one, where polynuclear complex groups are treated as nodes of the underlying net. In many cases, both representations make sense manifesting different ACS Paragon Plus Environment

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views of the same structure. For example, 2-periodic coordination network in [(µ2-azido-N,N)(µ2azido-N,N')(N,N-diethylethylenediamine)Cd] (QIKYOY)

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can be treated as a honeycomb (hcb)

underlying net of Cd centers in the standard representation or as a square (sql) underlying net of centroids of Cd2(N3)2 dimers (Fig. 1). Both kinds of simplification are realized as computer procedures in the program package TOPOS,9 which we have used in this study to perform all steps of topological analysis. Figure 1. Standard and cluster representations of coordination network in [(µ2-azido-N,N)(µ2-azidoN,N')(N,N-diethylethylenediamine)Cd] (QIKYOY). Simplification methods facilitate the classification of coordination networks and elucidate relations between them. Importantly, these methods can be easily algorithmized and, hence, provide humanindependent analysis of large samples of crystal data. Coordination compounds of quite different chemical composition can be reduced to underlying nets of the same topology and grouped in the same isoreticular series,24 which is the main taxon of topological classification. Description of local and overall topology of coordination network To describe coordination modes of ligands and local topology of complex groups we use the notation proposed by Serezhkin et al.25 Each ligand L is designated by letters M, B, T, K, P, G, H, O, N depending on the number (1–9) of donor atoms which are connected to metal atoms (A). The total number of metal atoms coordinated by the ligand (ν) is given as upper index in the form of the string mbtkpghon where each integer m, b, t, … is equal to the number of metal atoms coordinated by one, two, three, … donor atoms; ν = m + b + t + … The coordination mode of the ligand by the symbol Lmbtkpghon, where L is represented by one of the letters mentioned above; all right terminal integers mbtkpghon are omitted. For example, M1, B01, and T001 designate mono-, bi-, and tridentate ligands, which are coordinated to the same metal atom with all their donor atoms. This notation is compact and more informative than the IUPAC notation based on µ and η symbols (Fig. 2). Then the local topology of the complex group is written as coordination formula AnL1mL2k… where L1, L2, … designate ACS Paragon Plus Environment

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coordination modes of ligands. For example, 5-carboxybenzene-1,3-dicarboxylato ligand in [(µ2-5carboxybenzene-1,3-dicarboxylato)(µ2-piperazine)Co(H2O)] (COHHAJ)26 coordinates one Co atom via one donor atom (η1 mode) and one Co atom via two donor atoms (chelate η2 mode), so L=T (three donor atoms are used in total), m=1, b=1, hence the symbol for coordination mode is T11 (Fig. 2). Another µ2 bridge ligand, piperazine, has coordination mode B2 because it uses two donor atoms for coordination (L=B) and connects to two Co atoms via one donor atom each, hence m=2. At last, terminal water molecule has coordination mode M1 since it possesses only one donor atom (L=M) and coordinates only one Co atom (m=1). The stoichiometric coefficients n, m, k, … can be computed using the coordination balance equations. For example, if coordination group contains only one ligand with coordination mode L the coordination balance equation for formula AnLm looks like n/m=ν/CN where CN is coordination number of A. Figure 2. Coordination modes of ligands and coordination formula (local topology) of coordination network in [(µ2-5-carboxybenzene-1,3-dicarboxylato)(µ2-piperazine)Co(H2O)] (COHHAJ). Overall topology of any periodic net can be determined using sets of topological indices with Systre6 or TOPOS9 programs. To designate the overall topology of coordination network we use three different notations. Most of 2-periodic nets mentioned below have three-letter symbols of the Reticular Chemistry Structure Resource (RCSR) notation.7 We have also found some 2-periodic but 3dimensional uninodal sphere packings that are not deposited in RCSR; for them we use Fischer and Koch’s symbols like 44Ia or KIa.16 At last, for the topologies that are not listed in RCSR or by Fischer and Koch, we apply the TOPOS NDn nomenclature,12 where N is a sequence of degrees (coordination numbers) of all non-equivalent nodes of the net, D is the periodicity symbol (D = M, C, L, or T for 0-, 1-, 2-, or 3-periodic nets), n enumerates non-isomorphic nets with a given ND sequence. In Fig. 3, most abundant underlying nets of coordination networks are given together with their symbols. TOPOS characterizes both local and overall topologies in an automated mode using the notations described above. A set of topological indices (invariants) is used to identify numerically the overall ACS Paragon Plus Environment

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topology.27 Now TOPOS TTD collection9 contains indices for more than 70000 reference topologies of underlying nets that are used in the classification procedure. Figure 3. Most abundant underlying nets of coordination networks. 2-periodic coordination networks in the Cambridge Structural Database We took initial crystallographic data on coordination networks from CSD (release 5.33, November 2011).28 To extract all 2-periodic complex groups the following algorithm was realized in TOPOS: (i) Determining all interatomic bonds using the method of intersecting sectors.29 This method allows one to determine valence bonds in compounds of different nature. All bonds with participation of alkali or alkaline-earth metal (Na, K, Rb, Cs, Ca, Sr, Ba) as well as all metal-metal bonds were ignored. As a result, the networks supported by only coordination bonds metal-ligand were considered. (ii) Determining periodicity of the networks. Starting from any atom A of the network, TOPOS finds all equivalent neighboring atoms in the network that are related to A by independent translations. The number of such translations (0, 1, 2, or 3) determines the network periodicity. In what follows, we have considered only 2-periodic networks. (iii) Determining coordination modes of ligands, coordination numbers of metal atoms and coordination formulae, i.e. local topology of the network. At this stage we have created a new type of TOPOS topological collections, TTL (Topological Types of Ligands) collection, of coordination modes and occurrence of 4087 ligands. The TTL collection was used to find relations between coordination modes of ligands, local and overall topology of coordination networks. (iv) Simplifying all networks with all metal atoms and ligands treated as nodes, i.e. building standard representation. We have also checked if polynuclear complex groups could be separated in each network and, hence, if a cluster representation could be proposed. Both representations were tabulated in such cases. (v) Determining overall topologies with the TOPOS TTD collection and grouping all structures in isoreticular series.


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All these stages are completely automated in TOPOS that allowed us to scan the whole the Cambridge Structural Database (CSD) and study all 2-periodic coordination networks. Results and Discussion Overall topology of 2-periodic coordination networks Altogether, we have found and analyzed 10371 2-periodic coordination networks; the classification of local and overall topologies of their underlying nets is given in the Supporting Information, Tables S1-S7. We have considered only networks without entanglements; the classification of interweaved 2periodic motifs is the matter of a future work. The underlying nets in standard representation were obtained for all networks; in 3288 structures, polynuclear complex groups were separated and cluster representations were additionally generated, moreover, in 137 of them clusters can be selected in two different ways (Table S6). We have stored all the information about occurrence of the underlying nets in the TOPOS TTO collection.30 First, we will consider the overall topologies of those 7083 coordination networks that admit only one (standard) type of underlying net. If you ask a crystal chemist who works with 2-periodic coordination polymers, what topological motif is most preferable for them, you will likely get an answer: “Tetragonal (square) or hexagonal (honeycomb) plane net”. Statistical analysis confirms this statement: although we have found 746 topologically different underlying nets, sql and hcb motifs occur in 2/3 of all 2-periodic networks (Fig. 4 left, Table S2). Moreover, sql is an absolute champion as it is realized more than in 50% cases. Thus the distribution of topological types of underlying nets in 2-periodic coordination polymers is much sharper than in 3-periodic ones where the leading topology (primitive cubic lattice, pcu) was found in less than 10% cases.12 The following topological features provide high abundance of particular 2periodic topologies (underlying nets, Table S2): (i) The net should have high topological symmetry, i.e. high crystallographic symmetry (high order of the symmetry group) in the most symmetrical embedding, and high site symmetry of the nodes positions. Indeed, plane groups of the leading nets, sql and hcb, are p4mm and p6mm, the most symmetrical, and their nodes occupy positions of high symmetry. This feature was first mentioned for ACS Paragon Plus Environment

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most abundant 3-periodic nets.11 Note that some low-symmetrical 2-periodic nets, in particular, 3,4L83 and 3,4L13, with plane groups c2mm and p2mm, can also be rather frequent. Figure 4. Distributions of overall topologies of 2-periodic underlying nets in coordination networks. (ii) The number of topologically different structure groups should be 1 or 2. Indeed, all leading nets are uninodal or binodal (the most abundant 3-nodal net, 3,3,4L4, occurs only in 22 structures). This feature follows from the first one. (iii) The net should be two-dimensional, i.e. embeddable into plane: the first six nets in the list have this feature. Nonetheless, these first three features are not enough to warrant high abundance of two-periodic topology. Thus out of 11 plane uninodal Kepler-Shubnikov nets only sql, hcb, hxl, fes, and kgm are rather frequent, while tts, cem, hca, htb occur much rarer (Fig. 5). High-symmetrical fsz (p6) and fxt (p6mm) (Fig. 5) have never been realized, but their nodes occupy general positions with the lowest symmetry. At the same time, even in frequent hcb, fes, and kgm the most symmetrical positions are vacant, that formally contradicts the symmetry criterion. Figure 5. Rare of never realized Kepler-Shubnikov nets. (iv) The net should include mainly 3-, 4-, or 6-rings; nets with small number of different rings are preferable. This is a consequence of features (i) and (iii). Indeed, nets with high topological symmetry have small number of different rings, while planarity of the net restricts the maximum size of its rings: plane can be covered by 3-, 4-, 5-, or 6-rings (the corresponding nets are hxl, sql, kgd, hcb are among the most abundant ones) or their combinations;15 the plane nets with larger rings must contain small rings as well, in particular, as in fes. The nets with 5-rings are rare; these nets are also absent among the Kepler-Shubnikov nets. (v) Coordination of a node should not exceed six; the most abundant net with larger coordination, 3,4,8L2, occurs with frequency 0.1%.


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Any of these features is not sufficient to predict high or low abundance of the underlying net, but their combination does it with high probability. In turn, these features are strongly predetermined by the local topology of structural groups, in particular, by their coordination and shortest rings. Let us consider uninodal nets as an example. If all nodes are 3-coordinated the set of abundant nets is restricted to hcb, fes or KIa; all other nets have probability 0.2% or less. In turn, these three nets are distinguishable by ring size: 4-rings occur only in fes, while 6-rings are realized only in hcb. If a uninodal net is 4-coordinated, it will be sql with high probability, however, kgm, 63Ia, 63Id, 4L1 or 4L4 topologies are also expected (Fig. 6). The sets of rings are quite different for sql (4-rings) and kgm (3- and 6-rings); the last four nets are similar to each other; all of them are 3-dimensional and contain both 4- and 6-rings. To distinguish them, some additional criteria are required, but importantly all of them have rather small and similar abundance. Figure 6. Other important topologies of 2-periodic coordination networks. 5-coordinated net will have 44Ia topology with highest probability, and it is the net that is based on 4rings only. If 6-rings occur as well, 63IIa topology is realized. If there are 3-rings in addition to 6-rings, one can expect plane nets cem or tts that are quite similar both topologically (Fig. 5) and by occurrence. At last, 6-coordinated net will be likely hxl, but if 4-rings exist, 44IIb topology will be realized. Distribution of overall topologies of underlying nets in cluster representation essentially differs from standard one by much stronger expressed role of sql topology (Fig. 4 right); this difference is caused by relations between representations that will be analyzed in detail below. Local topology of coordination centers and ligands Further discrimination of the nets can be performed if one takes into account geometry of coordination figures. Recall that coordination figure of a node is a solid formed by adjacent nodes in the underlying net. Thanks to a simplification procedure, coordination figure can differ from the full coordination of an atom or structural group but is always derived from such coordination (Fig. 7). Both 10 ACS Paragon Plus Environment

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metal atoms and ligands can be nodes of the underlying net and as a result, the coordination features of metal atoms and ligands influence the geometry of coordination figures and, finally, the overall topology of the underlying net. Thus triangular coordination figures usually result in plane hcb or fes nets while T shape coordination figure leads to 3-dimensional sphere packing topology KIa (Fig. 7). The T shape can be caused either by asymmetric coordination of metal center or by special positions of donor atoms in three-coordinated ligand. The difference between hcb and fes consists mainly in asymmetric form of 3-coordinated ligands in fes that facilitates formation of different 4- and 8-rings in contrast with hcb. Despite different geometrical forms, the coordination modes of ligands can be the same as for pyridine-3,5-dicarboxylato and 1H-imidazole-4,5-dicarboxylato (Fig. 7). Figure 7. Triangular coordination figures in hcb, fes and KIa underlying nets existing in the coordination networks of [(µ3-pyridine-3,5-dicarboxylato)Cd(H2O)2] (AQOJOF),31 [(µ3-1H-imidazole4,5-dicarboxylato)Cd(H2O)] (YELYIY)32 and [(µ3-pyridine-2,6-dicarboxylato)Zn],33 respectively. Pyridine-3,5-dicarboxylato with regular triangular coordination figure, 1H-imidazole-4,5-dicarboxylato with distorted triangular coordination figure and pyridine-2,6-dicarboxylato ligand with a T-shaped coordination figure have coordination modes P12, P12 and P201, respectively. Centroids of ligands are shown as black balls. To obtain 4-coordinated kgm instead of sql, one has to provide formation of 3-rings that can be achieved by utilizing chelate bridge ligands in addition to simple bridge (M2 or B2) ligands (Fig. 8, cf. Fig. 2). Figure 8. The kgm underlying net in the coordination network of [(µ4-squarato)(µ2-O)2(UO2)2(H2O)2] (RABFIL)34 with coordination modes K4 and M2 for squarato and oxo ligands, respectively. Realization of 5-coordinated nets also often requires special ligands. For example, a geometrically regular

coordination

network

with

the

44Ia

topology

occurred

in

[(µ5-4-oxypyran-2,6-

dicarboxylato)Ho(H2O)] (VUNDAK)35 thanks to 4-oxypyran-2,6-dicarboxylato ligand that coordinates to five metal centers with a square-pyramidal coordination figure (Fig. 9). Some other ligands that ACS Paragon Plus Environment

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provide the 44Ia topology are also given in Fig. 9. Although they have different coordination modes, all of them coordinate five metal atoms (ν=5). All 31 structures with the 6-coordinated hxl topology possess the following common features: (i) metal atom has a 6-fold (octahedral) coordination and is transformed into a 6-coordinated node of the underlying net; (ii) there are no terminal ligands, hence the 6-coordinated metal centers retain their coordination in the underlying net; (iii) all ligands are bidentate and prolonged to be transformed into long edges of the underlying net and to provide the coordination network with topologically dense hxl underlying net of appropriate (not too high) geometrical density (Fig. 10). Figure 9. The 44Ia underlying net in the coordination network of [(µ5-4-oxypyran-2,6dicarboxylato)Ho(H2O)] (VUNDAK). Other examples of coordination figures of ligands in the 44Ia underlying (DEJTOC);36

nets:

L=

2-(N,N-dimethylene(hydrogenphosphonato)-(phosphonato)ammonio)acetate

bis(4-iodobenzenesulfonyl)amido

(MIWHUW);37

2-cyano-2-isonitrosoacetamido

(XUSDIZ).38 Figure 10. The hxl underlying net in the coordination network of [(µ2-1,4-bis(1,2,3-triazol-1yl)butane)3Fe](ClO4)2 (QARSIM).39 The coordination formula is AB23. The underlying nets with mixed coordination are not so frequent because in many cases the ligands are either terminal (M1) or bridge µ2 with the most typical coordination B2. Hence, after simplification they are either removed or transformed to the edges of the underlying net and the net is formed by only metal centers. In cluster representation, there is usually one type of cluster group and the resulting underlying net is again uninodal. There are preferable topologies for each combination of degrees of nodes (Tables S2 and S5): 3,4L13 and 3,4L83 for 3,4-coordinated nets (Fig. 3); gek1 and 3,5L2 for 3,5coordinated nets (Fig 6); kgd for 3,6-coordinated nets (Fig. 3); other combinations are less frequent. The data on coordination modes of all ligands as well as their stoichiometric relations in the network are contained in coordination formula that is one more important topological descriptor of high selectivity. In Table 1 the most abundant coordination formulae are given; the full list of local ACS Paragon Plus Environment

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topologies is contained in Table S3. It can be seen that the local topology is very specific for overall topologies: only a few possible underlying topologies correspond to each coordination formula and for any coordination formula there is strongly preferred overall topology. In some cases the local topology unambiguously predetermine the underlying net (AT112 → sql and AT11B2M1 → sql, cf. Fig. 2). On the other hand, some underlying nets are realized with the only coordination formula. For example, all hxlbased coordination networks have the same coordination formula AB23. Using Table S1 one can easily check these points and find other similar relations by applying the Excel data filters. Exceptions from this scheme can appear due to some special features to be individual for a particular structure, for example, novel or rarely used ligands or their combinations, unusual experiment conditions, additional molecular complex groups or solvate molecules. Let us consider an exception for 3-coordinated underlying nets. Besides hcb, fes or KIa, there is only one more 3-coordinated uninodal net in the structures considered, self-catenated 3L1, that is locally similar to hcb, but contains 10-rings instead of 6-rings and hence is 3-dimensional (Figs. 6, 11). It occurs only in [(µ3-tris(4carboxyphenyl)(methyl)phosphine)2Zn2(DMFA)(H2O)]⋅DMFA⋅2H2O (HOWVAR).40 In this case, some geometrical constraints, probably solvate molecules that were not allocated in the X-ray experiment, prevent closure of 6-ring and force formation of 10-rings. One more reason could be a special twisted form of the ligand (Fig. 11), which can also allow the formation of large rings. Relations between different representations of the same coordination network As was mentioned above, the same coordination network can be represented in different ways depending on what structural groups are considered as nodes of the underlying net. 3288 2-periodic networks, where polynuclear coordination groups can be separated, show a clear relation between standard and cluster representations. The distributions of the underlying topologies for these two kinds of representation are quite different and differ from the distribution for 7083 networks considered in the previous part (Fig. 4). These differences can be explained if one considers methods of mutual transformation of the nets; the most typical transformations observed are hcb(2)→sql and fes(2)→sql (Table 2 and Table S8). Hereafter the A(n)→B notation means that net A transforms into net B after 13 ACS Paragon Plus Environment


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replacing n-meric complexes of nodes in A by nodes in B. Thus both hcb and fes can be transformed to sql after a proper choice of dimers (see Fig. 1 with an example of the hcb(2)→sql transformation), so high occurrence of the sql topology (Fig. 4) is caused by its key role in the network transformations. Any A(n)→B transformation can be reversed as B→A(n) that means splitting nodes in B into groups of n nodes in A. In particular, this is a way to transform sql topology into hcb or fes: the coordination centers in sql should be replaced with dimeric groups (Fig. 1). We emphasize that oligomers A(n) can be topologically separated if chains/rings are essentially shorter inside A(n) than outside. The list of net relations can help in search for possible transformation paths between a particular pair of nets as was discussed in detail for 3-periodic nets.27,30 For example, hcb can be transformed to fes via intermediate formation of dimers and sql underlying net: hcb(2) → sql → fes(2). This information can be useful for modeling reactions of formation of coordination polymers. Such relations form one more TOPOS topological database, TTR (Topological Types Relations) collection. Figure

11.

The

coordination

network

and

underlying

net

of

[(µ3-tris(4-

carboxyphenyl)(methyl)phosphine)2Zn2(DMFA)(H2O)]⋅DMFA⋅2H2O (HOWVAR) and the coordination mode of tris(4-carboxyphenyl)(methyl)phosphine. One 10-ring of the 3L1 underlying net is selected both in the network and in the underlying net. Towards expert systems in crystal design The results obtained show close relations between chemical composition of complex groups, local topology of coordination centers and ligands, and overall topology of coordination networks. Although such relations are not strict in most cases and assume several possible outcomes at particular initial conditions, statistical analysis allows us to predict the most probable coordination network. Thus a heuristic algorithm can be invented that could help the chemist to answer questions like “What topology of coordination group can be assembled from a given set of reactants?” With such algorithm, expert systems for searching for possible paths of design of coordination networks could be created. The following steps are seen on this way: ACS Paragon Plus Environment

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1. Creating knowledge database from crystallographic data. At this step, geometrical, topological and chemical information should be extracted from the Cambridge Structural Database in an automated mode. Let us consider the Cambridge Structural Database as a database of first level that accumulates information immediately from experimental data. As we saw above, the procedures of simplification and topological identification of geometry and topology of coordination figures and overall net topology as well as determination of ligand coordination mode can be formalized and applied to any size sample of crystal data. With these procedures, we create databases of the second level; starting from initial crystal data, we extract new knowledge on the geometrical and topological properties, which are a subject of crystal design, but is not directly produced by experimental technique. TOPOS TTD, TTO and TTL collections are examples of such second-level databases. The knowledge database includes second-level databases as well as relations between the records in these databases. A set of such relations can be treated as a database of third level (Fig. 12). An example of such database is the TOPOS TTR collection. Another example is a set of relations between coordination of metal atoms, coordination modes of ligands, geometry of coordination figures and overall topology of underlying nets. Such relations can include statements like “hxl topology underlies the coordination networks with coordination formula AB23”, “6-coordinated metal atoms being linked to two terminal ligands result in square coordination figures”, “4- or 6-coordinated metal atoms together with only bridge µ2 ligands of the same type provide sql topology”, etc. The robustness of any statement can be estimated by probability N:

N=

number of structures for which the statement is true total number of structures that obey predicates of the statement

Figure 12. Three levels of databases in the knowledge database of an expert system in crystal design. As was mentioned above, one can extract such relations directly from the Excel tables of the Supporting Information; the N values can also be estimated from these data. Thus the tables like Table S1 can be considered as precursors of the third-level databases. For example, the first statement has N=1 since there are no exceptions, while the second statement will be obeyed only for octahedral 15 ACS Paragon Plus Environment


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coordination and trans-position of the terminal ligands since the remaining four bridge ligands will be forced to form a square coordination figure, which is suitable for the sql topology. This combination is most frequent, so N will be close to unity. The third statement is less strict: it is fulfilled for 255 of the 292 structures that obey the predicates, i.e. have only 4- or 6-coordinated metal atoms and only one kind of ligand, which possesses µ2 coordination mode; N=255/292=0.873. If all the statements are independent, the knowledge database will make a conclusion with some probability that is a product of probabilities of separate statements. The databases of the third level can also be generated automatically in many cases as, for example, TOPOS TTR. Predictive power of topological descriptors or their combinations can be assessed by routine screening of available experimental data and computing N. The combinations with high N will be stored in the knowledge database and then can be translated to statements like given above. 2. Developing the inference machine. The inference machine will start with the information provided by the experimentalist, then will combine the statements of the knowledge database that include this information, and at last will output predictions together with their probabilities. A typical dialog between the expert system (ES) and a human (HU) could be as follows (as one goes, ES outputs some concomitant statements from the knowledge database): ES: “Enter metal atoms.” HU: “Co” ES: “Co will have CN=6 and octahedral coordination with probability 84% (Table 3). Enter ligands.” HU: “Hydroxyacetate (glycolate, Scheme 1) in a single coordination mode. No other ligands.” ES: “Known coordination modes of hydroxyacetate (L) are M1, B2, T11, T02, T21 (Scheme 1). For CoII with CN=6, the composition of the complex is CoL2 that fits coordination formula AT112; other coordination modes result in another Co oxidation state, CN, network topology or composition in accordance with coordination balance equations (Scheme 1). Coordination formula AT112 provides sql topology with probability 100% (Table 1). If CN=4, coordination formula AB22 is realized (Scheme 1) that results in sql underlying topology with probability 96%. Other possible Co coordination numbers ACS Paragon Plus Environment

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(5 or 7, Table 3) do not provide the composition CoL2, so for them N=0. Conclusion: underlying topology of 2-periodic coordination network is sql with probability N = 0.078⋅0.96 + 0.062⋅0.0 + 0.843⋅1.0 + 0.017⋅0.0 = 0.918.” Certainly, this conclusion was made with assumption that the resulting coordination network should be 2-periodic, i.e. the data obtained in this study were only used. In general, the knowledge database has to include the information on coordination networks of any periodicity; thus the comprehensive topological classification of 3-periodic motifs has been already performed.12 The user has also restricted the coordination network with just one type of ligand of the same coordination mode. Removing this restriction leads to a larger number of possible topologies but the conclusion can be obtained according to similar scheme. In any case, this example illustrates what data are required to create the knowledge database and how they can be used to obtain a robust prediction. Scheme 1. Coordination modes of hydroxyacetate in 2-periodic coordination networks, possible fragments of coordination groups, coordination numbers of metal atoms, the corresponding coordination formulae and overall topology. Conclusion and outlook Search for relations between chemical composition and crystal structure features was always a great challenge for crystal chemistry. Now we have tools to reach a real progress in this field. Intensive data mining of past decades provided us with rich information on crystal structures stored in a suitable format in electronic databases. In turn, development of databases invoked new methods for processing this information and, in fact, for generating new knowledge in an automated mode. In this regard, topological approaches have evident advantages as they propose strict criteria and parameters, which can be used in computer processing. The local topology is described by coordination numbers of atoms or complex groups, coordination figures, formalized coordination modes of ligands and coordination formula. The overall topology is unambiguously characterized by topological indices and can be classified with tailored topological databases.


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In this paper, we have shown that even existing data and tools are sufficient to make useful conclusions about possible architecture of coordination networks. Although the topological approach does not allow one to establish precise values of geometrical parameters of the crystal structure, like atomic coordinates, it provides rich information on assembling structural groups including recommendations for the choice of appropriate complexing atoms and ligands that is important for crystal design. In general, we still need to generate topological characteristics for 0-periodic (molecular) and 1-periodic (chain) coordination polymers in addition to already investigated 2- and 3periodic ones. Then an exhaustive knowledge database could be formed by machine generation of statements as was shown above. As a result, a full-fledged expert system for predicting methods of connection of coordination groups can be created in the near future. Supporting Information Available: A PDF file with illustrations to Table 1. An Excel file with Tables S1-S8 that contain overall topologies of all studied 2-periodic coordination networks in standard (Table S1) cluster (Table S4) representations, the corresponding distributions of overall topologies (Tables S2 and S5) and coordination formulae (local topologies) for the networks in standard representation (Table S3). Table S6 contains alternative cluster representations for those networks that admit different methods to select clusters. Table S7 lists the networks from Table S4, but in standard representation. In Table S8, all relations between different network representations from Tables S1, S4, S6 and S7 are gathered. This information is available free of charge via the Internet at http://pubs.acs.org.

ACKNOWLEDGMENTS: We are grateful to Prof. D.M. Proserpio for fruitful discussions. V.A.B. thanks the 2011/2012 Fellowship from Cariplo Foundation & Landau Network - Centro Volta (Como Italy).


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REFERENCES (1) Öhrström, L.; Larsson, K. Molecule-Based Materials: The Structural Network Approach, Elsevier, Amsterdam, 2005. (2) Champness, N. Making Crystals by Design: Methods, Techniques and Applications, Ch. 2.4, ed. D. Braga and F. Grepioni, Wiley-VCH, Weinheim, 2007. (3) Batten, S. R.; Neville, S. M.; Turner, D. R. Coordination Polymers: Design, Analysis and Application, Royal Society of Chemistry, Cambridge, 2009. (4) Zhou, H.-C.; Long , J. R.; Yaghi, O. M. Chem. Rev., 2012, 112, 673. (5) Lord, E. A.; Mackay A. L.; Ranganathan, S. New Geometries for New Materials, Cambridge University Press, 2006. (6) Delgado-Friedrichs, O.; O’Keeffe, M. Acta Cryst. 2003, A59, 351; http://www.gavrog.org. (7) O'Keeffe, M.; Peskov, M. A.; Ramsden, S. J.; Yaghi, O. M. Acc. Chem. Res. 2008, 41, 1782; http://rcsr.anu.edu.au/. (8) Ramsden, S. J. Robins, V. Hyde, S. T. Acta Cryst., 2009, A65, 81; http://epinet.anu.edu.au/. (9) Blatov, V.A. Struct. Chem. 2012, 23, 955; http://www.topos.samsu.ru. (10) Blatov, V. A.; Carlucci, L.; Ciani, G.; Proserpio, D. M. CrystEngComm, 2004, 6, 377. (11) Ockwig, N. W.; Delgado-Friedrichs, O.; O'Keeffe, M.; Yaghi, O. M. Acc. Chem. Res., 2005, 38, 176. (12) Alexandrov E.V., Blatov V.A., Kochetkov A.V., Proserpio D.M. CrystEngComm, 2011, 13, 3947.


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(13) Blatov, V. A.; Proserpio, D. M. Modern Methods of Crystal Structure Prediction, Ch. 1, ed. A. R. Oganov, Wiley-VCH, Weinheim, 2011. (14) Smirnova, N. L. Cryst. Rep. 2009, 54, 743. (15) Grünbaum B.; Shephard, G. C. Tilings and Patterns. New York: Freeman, 1987. (16) Koch, E.; Fischer, W. Z. Kristallogr. 1978, 148, 107. (17) Hoffmann, R. Angew. Chem. Int. Ed. 2013, 52, 93. (18) O'Keeffe, M.; Hyde, B.G. Phil. Trans. Royal Soc. London. Ser. A, Math. Phys. Sci. 1980, 295, 553. (19) O'Keeffe, M. Aust. J. Chem. 1992, 45, 1489. (20) Adams, P. D.; Afonine, P. V.; Bunkóczi, G.; Chen, V. B.; Echols, N.; Headd, J. J.; Hung, L.-W.; Jain, S.; Kapral, G. J.; Grosse Kunstleve, R. W.; McCoy, A. J.; Moriarty, N. W.; Oeffner, R. D.; Read, R. J.; Richardson, D. C.; Richardson, J. S.; Terwilliger, T. C.; Zwart, P. H. Methods, 2011, 55, 94. (21) Delgado-Friedrichs, O.; O’Keeffe, M. J. Solid State Chem. 2005, 178, 2480. (22) O’Keeffe, M.; Yaghi, O. M. Chem. Rev. 2012, 112, 675. (23) Mondal, N.; Saha, M.K.; Mitra, S.; Gramlich, V. J. Chem. Soc. Dalton Trans. 2000, 3218. (24) Eddaoudi, M.; Kim, J.; Rosi, N.; Vodak, D.; Wachter, J.; O’Keeffe, M.; Yaghi, O. M. Science, 2002, 295, 469. (25) Serezhkin, V. N.; Vologzhanina, A. V.; Serezhkina, L. B.; Smirnova, E. S.; Grachova, E. V.; Ostrova, P. V.; Antipin, M. Yu. Acta Cryst. 2009, B65, 45. (26) Banerjee, A.; Mahata, P.; Natarajan, S. Eur. J. Inorg. Chem. 2008, 3501. (27) Blatov, V. A. Acta Cryst. 2007, A63, 329. ACS Paragon Plus Environment

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(28) Allen, F. H. Acta Cryst. 2002, B58, 380. (29) Peresypkina, E. V.; Blatov, V. A. Acta Cryst. 2000, B56, 1035. (30) Blatov, V. A.; Proserpio, D. M. Acta Cryst. 2009, A65, 202. (31) Xia, S.-Q.; Hu, S.-M.; Dai, J.-C.; Wu, X.-T.; Zhang, J.-J.; Fu, Z.-Y. Du, W.-X. Inorg. Chem. Commun. 2004, 7, 51. (32) Fang, R.-Q.; Zhang, X.-M. Inorg. Chem. 2006, 45, 4801. (33) Zhang, Z.-Q.; Huang, R.-D.; Xu, Y.-Q.; Hu, C.-W. Chem. J. Chin. Univ. 2008, 29, 1528. (34) Rowland, C.E.; Cahill, C.L. Inorg. Chem. 2010, 49, 6716. (35) Fang, M.; Chang, L.; Liu, X.; Zhao, B.; Zuo, Y.; Chen, Z. Cryst. Growth Des. 2009, 9, 4006. (36) Cunha-Silva, L.; Lima, S.; Ananias, D.; Silva, P.; Mafra, L.; Carlos, L.D.; Pillinger, M.; Valente, A.A.; Paz, F.A.A.; Rocha, J. J. Mater. Chem. 2009, 19, 2618. (37) Wolper, C.; Kandula, M.; Graumann, T.; Hartwig, S.; Blume, E.; Jones, P.G.; Blaschette, A. Z. Anorg. Allg. Chem. 2008, 634, 519. (38) Gerasimchuk, N.; Esaulenko, A.N.; Dalley, N.K.; Moore, C. Dalton Trans. 2010, 39, 749. (39) Bronisz, R. Inorg. Chem. 2005, 44, 4463. (40) Humphrey, S.M.; Allan, P.K..; Oungoulian, S.E.; Ironside, M.S.; Wise, E.R. Dalton Trans. 2009, 2298.


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Table 1. Most abundant local topologies (coordination formulae) with occurrence more than 1% and the corresponding overall topologies in 7083 2-periodic coordination networks in standard representation. Examples of coordination networks are given in Figs. 2, 10 and in the Supporting Information. Coordination formula

Number of Occurrence, structures %

Overall topologies

AB22M12

826

11.66

sql (98.9%); kgm (0.9%); 4L1 (0.1%); 4L2 (0.1%)

AB22

359

5.07

sql (96.1%); kgd (0.8%); kgm (0.8%); 4L1 (0.5%); 4L6 (0.5%); 63Ia (0.3%); 4L9 (0.3%); 4L10 (0.3%); 4,4L37 (0.3%)

AT112

174

2.46

sql (100%)

161

2.27

sql (97.6%); 4L1 (0.6%); 63Ib (0.6%); 3,6L60 (0.6%); 3,6L64 (0.6%)

AM22M12

146

2.06

sql (99.3%); 4,4,4L4 (0.7%)

AB23

129

1.82

sql (72.1%); hxl (21.7%); hcb (6.2%)

AB2M22

92

1.30

sql (92.4%); hcb (7.6%)

AT11B2M1

79

1.12

sql (100%)

A2B23

71

1.00

hcb (93.0%); KIa (4.2%); sql (2.8%)

2

AB 2M

1


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Table 2. Most typical (occurrence more than 0.5%) transformations of 2-periodic nets. Transformation


Transformation


hcb(2) ↔ sql

567

20.41

hcb(2) ↔ hcb

33

1.19

fes(2) ↔ sql

537

19.33

3,4,6L12(3) ↔ hxl

30

1.08

3,5L2(2) ↔ sql

122

4.39

3,4L124(4) ↔ sql

22

0.79

4,4L1(2) ↔ sql

121

4.36

63Ia(2) ↔ kgd

19

0.68

3,4L13(2) ↔ sql

117

4.21

3,4L83(2) ↔ kgd

18

0.65

3,4L83(2) ↔ sql

105

3.78

3,4L36(3) ↔ sql

17

0.61

sql(2) ↔ sql

85

3.06

3,4L125(2) ↔ sql

17

0.61

3,4,5L7(2) ↔ sql

57

2.05

KIa(2) ↔ sql

15

0.54

sql(2) ↔ kgd

44

1.58

3,4L21(2) ↔ sql

14

0.50

3,4L27(2) ↔ sql

42

1.51

KIb(2) ↔ sql

14

0.50

4,5L51(2) ↔ sql

35

1.26

3,5L2(2) ↔ hxl

14

0.50

Table 3. Occurrence of coordination numbers of Co atoms in 1022 2-periodic coordination networks. CN

Number of Occurrence, atoms %

4

113

7.8

5

90

6.2

6

1218

84.3

7

24

1.7


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TABLE OF CONTENTS GRAPHIC We have performed comprehensive topological analysis of 2-periodic coordination networks in 10371 metal-organic compounds. Two plane nets, square lattice (sql) and honeycomb (hcb), were found to compose 2/3 of all the coordination networks. There were found strong correlations between local topological characteristics and the overall topology. The possibility to develop an expert system that could envisage local and overall topology of periodic coordination networks is discussed.


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Topology of 2-Periodic Coordination Networks - American Chemical

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