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Cite This: Cryst. Growth Des. XXXX, XXX, XXX−XXX

Topological Databases: Why Do We Need Them for Design of Coordination Polymers? Published as part of the Crystal Growth and Design Israel Goldberg Memorial virtual special issue Eugeny V. Alexandrov,†,‡ Alexander P. Shevchenko,†,‡ and Vladislav A. Blatov*,†,‡,#

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†

Samara Center for Theoretical Material Science (SCTMS), Samara State Technical University, Molodogvardeyskaya Street 244, 443100 Samara, Russian Federation ‡ Samara Center for Theoretical Material Science (SCTMS), Samara University, Ac. Pavlov Street 34, 443011 Samara, Russian Federation # Samara Scientific Center of the Russian Academy of Sciences, Studencheskiy Lane, 32a, 443001 Samara, Russian Federation S Supporting Information *

ABSTRACT: We describe a set of databases that bear information on geometrical and topological properties of 1 281 254 metal coordination centers and 204 828 ligands in 593 879 crystal structures of coordination compounds from the Cambridge Structural Database. These databases contain a number of structural descriptors, which are calculated according to rigorous algorithms and can be used to derive correlations of “chemical composition − structure − property” in an automated mode then forming a knowledge database. Many examples of such correlations and possible applications of the databases for investigation and design of coordination compounds are considered. symbol,27−29 Hopf ring net,30,31 net topological indices32 and tilings.33 These were formalized, digitalized, and computed for thousands of crystal structures from crystallographic databases such as the Cambridge Structural Database (CSD),34 Inorganic Crystal Structure Database (ICSD),35 or Pearson’s Crystal Database.36 As a result, the first topological databases appeared that gathered the values of the topological descriptors.21,37 The next step is the creation of knowledge databases that would keep correlations between the descriptors for future use in artificial intelligence systems to assist a human expert in elaborating design strategies.7,29 The knowledgebased approach has already been applied for prediction of properties and bioactivity of particular classes of ligands and for the search for correlations between coordination mode of ligands and overall topology in two-periodic coordination networks.7,38 Obviously, this trend promises a significant improvement of the crystal design approach, but requires an essential development and extension. The topological descriptors and databases hold a key position in this trend thus deserving a special attention. In this study, we present a series of topological databases, which, together with the corresponding software, provide new possibilities for the design of coordination compounds, both molecular and polymeric, and can serve as a background for

1. INTRODUCTION The concept of crystal design came to crystal chemistry recently but immediately led to rapid development of structural chemistry of different classes of substances with extended architectures such as coordination polymers of different periodicities (chain one-dimensional, layered twodimensional, or framework three-dimensional). 1−9 This concept gained its theoretical basis from “reticular” chemistry, which is in turn based on the topological (graph) approach.10 Thus, topological properties of crystal structures became important and resulted in successful synthesis of large families of isoreticular metal−organic frameworks (MOFs).11,12 It is the topological methods that enabled one to reveal many correlations of “chemical composition − structure − property”, which were then used in crystal design.9,13−15 The main route of reticular chemistry in obtaining new coordination polymers includes utilizing structural units with predetermined topology and geometry (secondary building units, SBUs) for decoration of a particular topological motif (periodic net). 16−18 Importantly, this approach can be readily algorithmized and implemented into computer tools for analysis of crystal structures, their topological classification, and design of new crystalline compounds.19−22 However, complicated compounds consisting of SBUs with a high degree of freedom and extended connection possibilities are still a challenge for crystal design.23−25 This promoted inventing new structural descriptors and models that could reliably discriminate different topological motifs at both local and overall level, such as coordination figure,26 ligand coordination type © XXXX American Chemical Society

Received: November 18, 2018 Revised: January 30, 2019 Published: April 2, 2019 A

DOI: 10.1021/acs.cgd.8b01721 Cryst. Growth Des. XXXX, XXX, XXX−XXX

Crystal Growth & Design

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generation of underlying nets and the identification of their topologies were formalized within rigorous algorithms.9 Depending on the choice of structural groups, different representations can be considered for the same crystal structure, and each representation is characterized by its own underlying net. The topologies of these representations are obviously interrelated.9,37 The choice of the structural groups depends on the type of the structure and the task in hand; for coordination polymers, the methods of the structure decomposition into building units were recommended by an IUPAC task group.44 Entanglement Parameters. Existence of entanglement of different types (interpenetration, inclined and parallel polycatenation, polythreading) as well as the interpenetration parameters (degree, class, Hopf, and extended ring net) can be determined by ToposPro in an automated mode.30,45,46 The general procedure for computation of the topological descriptors includes the following steps:

components of artificial intelligence systems in coordination and crystal chemistry.

2. TOPOLOGICAL DESCRIPTORS AND METHODS FOR THEIR ESTIMATION Below we list the descriptors, which are included in the databases under consideration, as well as the methods of estimation of these descriptors, a detailed explanation of which was given elsewhere.37 The ToposPro program package was used for computing all the descriptors and creating the topological databases.19 Atom Size and Shape. Voronoi polyhedron is used to represent an atom in the crystal field and to estimate the atomic parameters, such as volume, radius, and second moment of inertia (measure of atom sphericity).39 Coordination number of an atom is estimated by a smart Domains algorithm,40 which uses atomic radii, interatomic distances, and parameters of the Voronoi polyhedron of the atom as the criteria for existence and type of bonding. Coordination figure of an atom or a structural group. The shape of the atomic environment, which is described as a coordination polyhedron for complexing atoms or, more generally, as a coordination figure of a node of the underlying net (see below), can be estimated by several independent algorithms.26 The same algorithms can be used for finite structural groups of any complexity if these have been simplified by squeezing into their centers of mass. Coordination mode or local connectivity of a structural group. The symbol, which characterizes the local connectivity of a structural group, was first proposed for ligands and then extended to molecules.27,41 This symbol includes the number of active centers of the group designated by a letter (1 − M, 2 − B, 3 − T, 4 − K, etc.) and the numbers mbtk... of other groups coordinated by one, two, three, four... active centers (Figure 1).

(i) Atom descriptors are computed as parameters of Voronoi polyhedra of the atoms. (ii) The structure connectivity is determined with the Domains algorithm. (iii) Structural groups (molecules or ligands) are separated according to topological clustering criteria.9 Geometrical parameters (size and shape) of the groups are estimated similar to the atomic parameters; molecular Voronoi polyhedra are used for this purpose.39 Local topological parameters of the groups are determined as their coordination modes. (iv) The underlying net is constructed from the centers of mass of the structural groups in accordance with their connectivity. The topological pattern or motif of the whole structure is determined as the topological type of the underlying net by comparison of its topological indices with those for the reference topological types. (v) Entanglement phenomena are analyzed as threading or catenation between different underlying nets (if any) or a single motif within the same structure, and the entanglement parameters are computed for each type of entanglement.

3. TOPOLOGICAL COLLECTIONS The ToposPro topological databases that are considered in this study were built by computation of the topological descriptors listed in the previous part for all coordination compounds from the CSD; the databases are regularly updated following the CSD updates. All the databases are accessible through the ToposPro software; some of them are also available online (see below). The databases that accumulate the properties of crystal structures at the same level of organization are united in collections. For the coordination compounds we consider atomic, ligand, overall (network), and entanglement (network array) levels of structural organization; there are five collections of databases, which are described below. The Topological Types of Atoms (TTA) collection stores the information about geometrical and coordination properties of 1 281 254 metal atoms from 593 879 structures computed within the Voronoi model. In total, 35 parameters of atomic Voronoi polyhedra can be considered when looking for structural correlations, in particular, coordination number, bond lengths, area of the atom surface, radius, volume and second moment of inertia of the atom.39 The information about composition, topology, and coordination properties of 204 828 ligands is stored in the Topological Types of Ligands (TTL) collection. The ligand topology is represented by molecular graph, and the ligand coordination is described by the ligand active centers indicated in the graph and in the symbol of local connectivity.

Figure 1. Frequently observed coordination modes of oxalate and trimesate ligands. The metal atoms are shown as blue balls. Local topology of a coordination group or a network is encoded by a coordination (or crystallochemical)27 formula, which is composed of the local connectivity symbols for all ligands in stoichiometric ratios with the complexing (metal) atoms A. For example, coordination formula AB22M12 denotes a complex, where metal atom A coordinates four bridging B2 (so the ratio A/B2 is 2:4 = 1:2) and two terminal M1 ligands. Obviously, quite different ligands can provide the same coordination formula if they have the same local connectivity. Overall topology of an underlying net. Underlying net represents the method of connection of structural groups and is comprised by their centers of mass. A number of topological indices were proposed to determine the net topology,32 which is denoted in accordance with several nomenclatures that are used in the topological databases. Below we use the RCSR database three-letter (bold) symbols,21 the NDn41 and s-d-G-n42 symbols from the ToposPro topological collections and the sqcN symbols from the EPINET database.43 The B



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The TOPOS Topological Database (TTD) is the largest collection of topological types (193 654 in the current version) for the hypothetical and real nets that have been observed or can be realized in crystal structures. The TTD collection contains topological indices for the reference nets and is used for automatic assignment of a crystal structure to a topological type. The Topological Types Observed (TTO) collection is a result of searching underlying nets of crystal structures from crystallographic databases for topological types; it contains 1 927 215 references to these structures including codes of the CSD and ICSD. If the structure admits different representations, then all of them are deposited to the TTO collection. Combining the TTD and TTO resources, one can find the occurrence of a particular topological type in crystal structures. Now the TTD and TTO collections are also available online at https://topcryst.com. The Topological Types Relations (TTR) collection contains a list of the relations observed between the topological types. These relations are found with the TTD and TTO collections in the crystal structures that admit different representations, i.e., have several records in the TTO collection, due to a multivariant choice of structural groups. These databases provide broad opportunities for investigation of different structural aspects of crystalline coordination compounds. Obviously, a combination of these tools provides the best results; some examples are given below.

Figure 2. Distribution over 1 281 254 metal atoms in coordination compounds. The relative occurrences with respect to the total number of metal atoms are specified on the vertical axis.

shows that the most popular complexing atoms are Cu and Fe. The analysis of the distribution of coordination numbers highlights the well-known high occurrence of even coordination numbers 4 or 6, while the most widespread odd coordination number is 5. This distribution is dictated by the abundance of d-complexing atoms, such as Fe, Cu, Ni, Mn, Co, or Al, for which coordination numbers 4−6 are characteristic, while less popular lanthanides have bigger coordination numbers 7−9. However, such correlations already include two parameters. The TTL collection provides the distribution of coordination compounds on the ligand composition (Figure 3), where the most frequent ligands are very simple. Note that water is the most common solvent in the synthesis of coordination compounds, carbonyl is of great interest in catalysis, organic synthesis, and metal purification, cyclopentadienyl is the most popular ligand in π-complexes, and chloride and bromide anions are usual anions in the inorganic salts used in the synthesis of coordination compounds. The first organic ligand in the Werner complexes is triphenylphosphine, which is widely used in organic and organometallic synthesis. 2,2′Bipyridine is the most widespread chelating agent, especially in molecular coordination compounds. The most abundant coordination modes of ligands are terminal M1 (monodentate) and B01 (bidentate chelate) (Figure 4). A more detailed study requires consideration of multiparameter correlations. The TTO collection contains data on periodicity of the coordination groups, and the corresponding distribution shows that molecular (0D) groups are the most widespread, while the occurrences of polymeric chain (1D), layer (2D), or framework (3D) groups are close to each other (Figure 5). In total, the coordination polymers comprise more than 15% of all coordination compounds. The next level of the structure organization, entanglement of coordination networks, can also be analyzed with the TTO collection (Figure 6). In particular, the major part of threeperiodic complexes is comprised by a single framework (21 780), while the interpenetrating structures are less common (4149). The most widespread Z in interpenetrated structures is 2 (2543), and the number of structures sharply decreases with increasing Z. Current records are 25-fold dia, 27-fold and 54-fold srs arrays.47−49 The distribution over the topological types from the TTD collection shows a well-known regularity: only a few of these are abundant, and they possess a high topological symmetry (Table 1).7−9,46 4.2. Two-Parameter Correlations. There are many twoparameter correlations, which are important for crystal design. The correlations of “atom type − atom parameter” provide a

4. CORRELATIONS OF DESCRIPTORS Strictly speaking, any combination of the descriptors stored in the topological databases can be considered to find structural correlations. In some cases, such combination is trivial; for example, the tetrahedral coordination figure of a network node (atom or structural group) provides coordination number four in all cases (but not vice versa). In other cases, the combination can seem unreasonable; however, any pair of parameters can correlate indirectly thanks to correlations with other parameters. For example, volume of the atom seems to not influence the overall topology of the coordination polymer; however, it correlates with oxidation degree and coordination number of the atom, which in turn correlate with the network connectivity. Moreover, trivial or unreasonable combinations look so only for a human, while any computer system needs learning, and thus any correlation (trivial, significant, or insignificant) enriches the knowledge database of the system. This means that the procedure of creation of the knowledge database can be automated by a successive analysis of all possible correlations of the descriptors from the topological databases. The depth of such analysis is however limited by the size and diversity of the initial experimental or modeling data. That is why we consider here in detail only one- and twoparameter correlations; we only touch upon more complex correlations. 4.1. One-Parameter Correlations. The simplest way to use the topological databases concerns the analysis of oneparameter dependences, i.e., distributions of the descriptors. However, in many cases such distributions are uninformative if the chemical composition is not considered as an additional parameter. This means that the most significant one-parameter correlations concern the chemical composition itself. In particular, the TTA collection enables one to obtain important information on occurrence, geometrical, and coordination properties of complexing atoms. Thus, Figure 2 C



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Figure 3. Occurrences (N) of the most abundant ligands in the coordination compounds. Percentage of the total number of occurrences (1 211 359) of all different ligands is given above each bar; the 20 ligands comprise 35.69% of the total sample. Oxo-, hydroxo-, and aqua-ligands are united as they cannot always be distinguished in the structures; the same concerns S, HS, and H2S. Cp = C5H5, Ph = C6H5, methyl = CH3, acetate = CH3COO−, 2,2′-bipy = 2,2′-bipyridine, thf = tetrahydrofuran, phen = 1,10-phenanhroline, py = pyridine (see Table S1 for more details).

Figure 4. Distribution of 204 828 ligands over most widespread coordination modes. Percentage of the total number of crystallographically different ligands (1 336 269) is given above each bar; the 20 coordination modes comprise 88.45% of the total sample (see Table S2 and Figure S1 for more details).

Figure 5. Distribution of 478 322 coordination groups over periodicity. The numbers of structures with a particular periodicity are given over the bars.

Figure 6. Distribution of 25 929 3D coordination networks over degree of interpenetration (Z). The numbers of structures with a particular Z are given over the bars.

lot of information about properties of a particular atom. For example, for Cu atom the TTA collection gives typical coordination numbers 3, 4, 6, and the O and N donor atoms are the most common in the coordination environment. The distribution of interatomic contacts Cu-Nm determined by the Domains algorithm, where Nm is nonmetal, reveals three main groups of valence contacts in ranges 1.8−2.2 Å, 2.2−2.3 Å, and 2.3−2.6 Å, which reflect the Jahn−Teller distortion, and weak

interactions at distances larger than 2.6 Å (Figure 7). A more detailed exploration requires more complex correlations, for example, with accounting for Cu oxidation state and the type of surrounding atoms. Other important correlations, which concern correspondences of local coordination and overall network topology, can be revealed with a combined analysis of the TTA, TTD, TTL, and TTO collections. The correlation “ligand composition − ligand coordination” enables one to determine the most typical D



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formation of coordination networks. We consider some examples of such analysis in the next sections. 4.3. Multiparameter Correlations. Strictly speaking, any multiparameter correlation can make sense and should be considered. At the same time, if the number of descriptors exceeds 10−12 it is hardly possible to enumerate all correlations; moreover, the size of the sample in many cases does not enable one to establish reliable multiparameter correlations. Thus, a human should still participate in the smart selection of the most important combinations of descriptors to be analyzed. Below we consider an example of such analysis for the aluminum coordination compounds with bridging organic ligands. The first step of any analysis is a rational construction of a sample. For this purpose, we use a stepwise filtering of the data from the TTA and TTL collections (Scheme 1). The set of structures containing only Al as a central atom consists of 5879 entries, but after excluding inorganic complexes, i.e., coordination groups containing no organic ligands, as well as disordered motifs, the sample shrinks to 1619 entries. The resulting sample is still big enough for exploration of several important multiparameter correlations. Metal Atom Type − Coordination Number − Coordination Figure − Environment Composition − Network Periodicity/Interatomic Distance. These two five-parameter correlations are typical when we analyze the local environment of complexing atoms and its influence on the overall network topology. For example, in 1619 Al-containing coordination compounds (complexing atom, CA = Al) the most frequent coordination numbers of Al atoms are 4, 5, or 6; they occur in 72.0% of the total sample (Table 4). All other occurrences wi in Table 4 are calculated with respect to a partial sample obtained for a particular value of the parameter at a previous level of the correlation; the robustness of the correlation (R) at the ith level can be estimated as the product R = Πj ≤ i(wj). For example, the most robust is the correlation (CN = 4) − (coordination figure = tetrahedron) − (environment composition = C2N2) − (network periodicity = 0D) with R = 0.480 × 0.992 × 0.222 × 1.000 = 0.106 that is equal to the probability for an Al-organometallic compound to be molecular with a tetrahedral C2N2 environment of the Al atom. Table 4 shows that the most typical coordination figures (polyhedra) are tetrahedron (T-4), trigonal bipyramid (TBPY-5), and octahedron (OC-6), and the most abundant environments are C2N2, C2NO2, or O6, respectively. An important conclusion for crystal design is that a three-periodic coordination network can be most probably obtained for the O6-octahedral coordination of Al, while if one wants to obtain a molecular complex, he/she should provide a tetrahedral or trigonal− bipyramidal Al coordination. Considering interatomic distance as an alternative fifth descriptor one can for instance conclude that the octahedral oxygen environment of Al is essentially flexible as the Al−O distances range within 1.75−2.1 Å (Figure 8). Metal Atom Type − Ligand Composition − Coordination Formula − Overall Topology − Entanglement. This fiveparameter combination concerns correlations between local and overall topologies of the coordination polymer and can answer the following questions to be important for crystal design: (i) What are the typical ligands for a particular complexing atom? (ii) What are the typical methods of their coordination to the complexing atom? (iii) What is the expected dimensionality/periodicity of the resulting complex

Table 1. Absolute (N) and Relative (w) Occurrences of the Most Abundant Topological Types of Three-Periodic Underlying Net in Coordination Polymers topology

N

w

topology

N

w

dia pcu pts sra srs xah cds ths mog bpq ins

1617 774 516 378 365 341 317 314 238 224 193

0.062 0.030 0.020 0.015 0.014 0.013 0.012 0.012 0.009 0.009 0.007

bnn fet dmc 3,5T1 nia 4,8T24 acs tcs sqc493 Other 7027 Total

181 173 170 161 152 152 151 148 135 19242 25942

0.007 0.007 0.007 0.006 0.006 0.006 0.006 0.006 0.005 0.742

Figure 7. Distribution of 1 503 102 Cu-(nonmetal) distances for 114 821 Cu atoms in 66 463 coordination compounds.

coordination modes of ligands, and that is an important step in the design of coordination compounds. Some ligands have only one preferable coordination mode, while other ligands can be coordinated in several different ways with similar probabilities that should be taken into account in the design. For example, the oxalate ligand prefers the tetradentate bridging coordination mode (K02), while the trimesate ligand displays three different coordination modes (G6, T3, or K4) with close probabilities (Table 2, Figure 1). The correlation “ligand coordination − overall topology” opens a route to the design of particular motifs of coordination polymers. If the ligand coordination is described by coordination formula, the correlation is quite strong in many cases (Table 3). One-parameter distributions and two-parameter correlations can be combined to reveal more complicated regularities in the Table 2. Absolute (N) and Relative (w) Occurrences of Coordination Polymers with the Most Abundant Coordination Modes (CM) of Oxalate and Trimesate Ligandsa C2O42‑

C9H3O63‑

CM

N

w

CM

N

w

K02 B01 K22 T11 K12 other 36 total

2819 1441 243 103 101 302 5009

0.563 0.288 0.049 0.021 0.020 0.060

G6 T3 K4 B2 G03 other 50 total

220 193 124 66 64 493 1160

0.190 0.166 0.107 0.057 0.055 0.425

a

See also Figure 1. E



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Table 3. Ten Most Abundant Coordination Formulae (CF) and the Corresponding Most Typical Overall Topologies (OT) in Three-Periodic Coordination Polymers CF 2

AB

2

AB23

AK4

A2K42B2

OT dia cds qzd dmp sod other 49 pcu acs jsm other 18 pts sra dia crb other 64 xah sqc493 4,5T4 other 23

N 378 48 38 32 31 171 260 78 26 76 97 49 23 20 129 102 35 17 53

w

CF 21 2

0.542 0.069 0.054 0.046 0.044 0.245 0.591 0.177 0.059 0.173 0.305 0.154 0.072 0.063 0.406 0.493 0.169 0.082 0.256

AK B

A2T32B2

AB22M12

AK02B2 AT32

AK4M2

OT

N

w

fet 3,5T1 other 28 dmc 3,4T1 ins other 35 dia mab cds other 11 dia other 15 rtl ant other 13 bpq other 21

51 37 72 33 22 19 83 49 38 29 40 107 37 64 37 27 79 37

0.319 0.231 0.450 0.210 0.140 0.121 0.529 0.314 0.244 0.186 0.256 0.743 0.257 0.500 0.289 0.211 0.681 0.319

entangled arrays that is an important feature for the MOF design and a challenge to the crystal architects. These two examples reflect the most widespread methods of analysis of the structures of coordination polymers; however, any other combination can make sense. For example, the reverse correlation entanglement − overall topology − coordination formula − ligand composition − metal atom enables one to find possible structural units (atoms and ligands) for a particular type of entanglement, local and overall topology of the complex group (Table S4). In general, the problems of crystal design that can be solved with this correlation can be stated by reversing the five questions formulated above for the direct correlation. For example, question (v) can be reversed as “What overall topology of coordination network can provide a particular type of entanglement?” Thus, two types of nets, 2,4L1 and 2,6L1, represent almost all cases of 2-fold interpenetrating 2D coordination polymers with the Hopf ring net of the 8,10L1 topology. The 2,4L1 and 2,6L1 nets contain 2-loops, i.e., 4rings formed by two pairs of 2- and higher (4- and 6-) coordinated nodes. Analysis of ligand coordination shows that the strongest 50% correlation is observed for the 2,6L1-type networks and the coordination formula A2K42B2. This correlation rules the structure of [Zn2(μ4-4,4′-sdba)2(μ2-4,4′bpy)]·2H2O (4,4′-sdba = 4,4’-sulfonyldibenzoato; 4,4′-bpy = 4,4′-bipyridine),51 where the structural units are paddle-wheel dimeric complexes of five-coordinated Zn atoms connected through angular dicarboxylate anions (4,4′-sdba2‑) and straight N2-donor ligands (4,4′-bpy) coordinated in tetradentate (K4) and bidentate (B2) modes, respectively. Thus a strong correlation entanglement (8,10L1) − overall topology (2,6L1) − coordination formula (A2K42B2) − ligand composition (dicarboxylate) − metal atom (paddle-wheel dimer) enables us to choose optimal components for the synthesis of the required entangled array (Figure 9). Such correlation can also be used for the solution of an opposite task of how to avoid any entanglement that is important in manufacturing of porous frameworks (MOFs).

Scheme 1. Multistep Filtering of the Data on Undisordered Al-Organic Complexes with Bridging Organic Ligands from the TTA and TTL collections

group? (iv) What is the anticipated overall connectivity of building units in the coordination network? (v) Should we expect any entanglement in the network? For example, there is a variety of 210 functional groups in Al-organic compounds, and the most widespread ligands have functional groups CH3, CO, C2N, CO2, O (H2O, OH) coordinated to Al (Table S3). In most cases, only one coordination mode is typical for a particular ligand, and hence, one coordination formula is preferable for a given combination of ligands. Thus, the ligands that contain CO2 and O groups are mostly tetradentate (K4) and monodentate bridging (M2), respectively, resulting in the coordination formula AK4M2. This local topology corresponds to a series of compounds [Al(RBDC)(OH)] (H2RBDC = benzendicarboxilic acid and its substituted analogues). These compounds can have two-periodic 4,6L26 or three-periodic bpq or gis-e-4,6-I41/amd network topologies, of which the bpq topology is the most probable and unsurprisingly attracted a great interest as a basic architecture for breathing MOFs.50 A surprise is that the Al-organic coordination polymers form no F



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Table 4. Absolute (Ni) and Relative (wi) Occurrences of N0 = 1619 Al-Containing Coordination Compounds at the Most Abundant Values of the Descriptors: Coordination Number (CN), Coordination Figure (CFig), Environment Composition (EC) and Network Periodicity (NP)a CN

N1

w1 = N1/N0

N2

w2 = N2/N1

EC

N3

w3 = N3/N2

NP

N4

w4 = N4/N3

R

4

777

0.480

T-4

771

0.992

5

238

0.147

TBPY-5

159

0.668

6

150

0.093

OC-6

143

0.953

C2N2 C2O2 C2NO C3N CN3 O4 C3O CO3 HN3 N2Cl2 C2NO2 C2O3 O6

171 106 72 37 32 30 20 19 18 17 41 22 113

0.222 0.137 0.093 0.048 0.042 0.039 0.026 0.025 0.023 0.022 0.258 0.138 0.790

17

0.119

0D 0D 0D 0D 0D 0D 0D 0D 0D 0D 0D 0D 3D 0D 0D

171 105 72 37 32 30 20 19 18 17 40 22 78 19 17

1.000 0.991 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.976 1.000 0.690 0.168 1.000

0.106 0.065 0.044 0.023 0.020 0.019 0.012 0.012 0.011 0.011 0.025 0.014 0.048 0.012 0.011

CFig

N2O4

Only the correlations with wi > 0.01 and R = w1·w2·w3·w4 > 0.01 are given.

a

Figure 8. Distribution of 1704 Al-O distances in 161 octahedral Al complexes.

Figure 9. Entanglement of coordination networks [Zn2(μ4-4,4′sdba)2(μ2-4,4′-bpy)] (4,4′-sdba = 4,4′-sulfonyldibenzoato; 4,4′-bpy = 4,4′-bipyridine; CSD reference code SULKEQ) in a 2-fold interpenetrating array: (top left) the Hopf ring net that characterizes the topology of the entanglement; (top right) the Hopf ring net merged with the two underlying nets (bottom left), which correspond to the interpenetrating coordination networks.

5. FROM DESCRIPTORS TO KNOWLEDGE DATABASES An important step toward artificial intelligence systems in materials science includes development of knowledge databases, which should accumulate all significant correlations between descriptors of the properties of the material. As the number of the correlations can be very large, the search for them should be formalized and adjusted to the computer processing. This means that if the number of correlations is not huge, they should be enumerated in an automated way, and the results should be stored in a rigorous format to be readable by artificial intelligence systems. This format, which still needs to be developed, should accept the logical statements like IF (CA = Al) AND (NP = 3) AND (LC = carboxylate AND hydroxo) AND (CF = AK4M2) THEN OT = bpq WITH P = 0.65 which determines the probability P of realization of the 4,6-coordinated bpq overall topology (OT) (Figure 10 right) if the complexing atom (CA) is Al; the periodicity of the coordination polymer (NP) is equal to 3; there can be two kinds of ligands (carboxylate and hydroxo), and the local topology corresponds to the coordination formula AK4M2; i.e.,

the carboxylate ligand must be tetradentate (K4; at least dicarboxilate-anion), while the hydroxo group must be bridging (M2). Importantly, the knowledge database cannot and should not provide an exact (unique) conclusion; instead, it lists all possible events with the corresponding probabilities. The full list of these events can be represented as a decision tree, or a so-called FP-Tree − frequency pattern tree (Scheme 2; Table S5). At each level of the tree, the occurrence of a particular descriptor value is presented, and a combination of descriptors at different levels of the tree designates a particular correlation. To obtain the probability for realization of a combination of descriptors, their occurrences should be multiplied. For example, the realization of the bpq underlying topology can be determined at different levels of restriction, which correspond to different tree levels (Table 5). G



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Figure 10. Coordination network (left) and the corresponding underlying net of the bpq overall topology in the crystal structure of MIL-53 [Al(OH)(bdc)]·0.7H2bdc (H2bdc = 1,4-benzendicarboxylic acid) (CSD reference code SABVOH01).52

Scheme 2. Frequency Pattern Tree for Al-Organic Compounds and the Descriptors: Network Periodicity → Ligand Composition → Coordination Formula → Overall Topologya

a

The ligand composition is restricted by functional groups connected to the Al atom.

If the number of descriptors (N) is not too large, the knowledge database can accumulate all N! possible correlations. For example, to explore the correlations between local and overall topology of a coordination polymer with a fixed metal atom (Al in our examples) one should consider only three properties: ligand composition (LC), coordination formula (CF), and underlying net topology (OT). Each combination of these descriptors takes sense and enables one to answer an important question about the polymer structure (Table 6).

Table 5. Probabilities of Realization of the bpq Underlying Topology (OT = bpq) in Coordination Polymers at Different Levels of Restriction level

restriction criteria (RC)

PRC(OT)

0 1 2 3

no CA = Al (CA = Al) AND (NP = 3) (CA = Al) AND (NP = 3) AND (LC = carboxylate AND hydroxo) (CA = Al) AND (Period = 3) AND (LC = carboxylate AND hydroxo) AND (CF = AK4M2)

0.0010 0.0167 0.2872 0.4407

4

0.6500

6. DESIGN OF COORDINATION POLYMERS WITH KNOWLEDGE DATABASES Thus, the topological collections provide the researcher with two main features: (i) a general overview of the structural chemistry of the chosen class of coordination compounds within the direct correlation “from structural units to topological properties”, and (ii) with an appropriate selection

As a result, one can see how the descriptors influence the underlying topology, which of these are significant and hence should be accounted in the design. For example, according to Table 5 descriptors CA, NP, LC, and CF are significant, because fixing them results in a dramatic increase of the probability of realization of the desired underlying topology. H



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Table 6. Possible Correlations between Ligand Composition (LC), Coordination Formula (CF), and Overall Underlying Net Topology (OT) for a Coordination Polymer with a Fixed Complexing Metal Atom combination

meaning

LC-CF-OT

What overall topology corresponds to specified ligands with specified coordination modes What ligands correspond to a specified overall topology built with specified coordination modes of the ligands What overall topology corresponds to a specified coordination mode of specified ligands What coordination mode of specified ligands correspond to a specified overall topology What coordination mode corresponds to specified ligands in underlying nets with a specified overall topology What ligands can be coordinated with a certain mode resulting in a specified overall topology

OT-CF-LC CF-LC-OT OT-LC-CF LC-OT-CF CF-OT-LC

of the components for the synthesis within the reverse correlation. If some parameters, for example, local topology, are unimportant in a particular analysis, the corresponding descriptors (ligand coordination or coordination formula) can be excluded from the correlation that widens the list of structural units. On the contrary, if one needs more rigorous prediction, some specific descriptors should be added to the correlation. Let us design a framework of the bpq topology. The TTO collection contains 225 examples of MOFs with the bpq topology, out of which 14 structures represent well-known framework MIL-53(Al) (Figure 10 left) with different guest molecules, while others are isoreticular to MIL-53(Al) and are formed by 49 types of μ4-ligands, 32 types of μ2-ligands, and 30 types of metal atoms (Table S6). To find the best components for the synthesis, we need first to find the correlations of the OT-LC type, where OT = bpq. These correlations show that the dicarboxylate anion (DC) + hydroxide (OH) pair of ligands forms 92.6% of all Al coordination polymers of the bpq topology; i.e., this set of ligands seems most promising for the design. At the same time, the opposite correlation LC-OT, where LC = DC,OH and OT = bpq, is still realized with a high probability of 65.8%, but is more ambiguous. This means that dicarboxylic and hydroxide anions can result in other underlying topologies except bpq in 34.2% of cases. To decrease the ambiguity of the prediction, we need to add more descriptors in the correlation LC-OT. Including the coordination mode of ligand does not improve the correlation, since the same local topology AK4M2 occurs in the networks with seven different underlying topologies (bpq, 4,4,6,6T1, 4,6,6T37, 4,6,6T50, 4,6,6T84, gis-e-4,6-I41/amd, and sqc3754). An important additional descriptor could be the geometrical arrangement of carboxylic groups in the dicarboxylic ligand (Figure 11). Including this descriptor significantly improves the correlation; for example, planar linear (PL) arrangement gives the correlation DC(PL),OH-bpq with P = 92.6%. Isomerism (polymorphism) was found only for 4,4′-ethene1,2-diyldibenzoate-anion (edb2‑): [Al(edb)(OH)] exhibits bpq (XERJOV01) and 4,4,6,6T1 (XERJOV) underlying topologies.53,54 The TTL collection contains seven anion ligands with a possible K4 coordination mode that obeys this condition: terephthalate, 2-aminoterephthalate, cyclohexane1,4-dicarboxylate, naphthalene-2,6-dicarboxylate, dihydrogen pyromellitate, 4,4′-ethene-1,2-diyldibenzoate, and fumarate. In general, the 36 carboxylate ligands found in isoreticular frameworks with other metals (Table S6) can also be

Figure 11. Different arrangements of carboxylic groups in dicarboxylic ligands of coordination mode K4. The metal atoms are shown as blue balls.

recommended for the synthesis of Al-MOFs with the bpq underlying topology.

7. CONCLUSIONS The databases presented above do not cover the whole information required for the design of coordination compounds; they just show a route of further development of artificial intelligence in this field. In the near future, we will input the geometrical and topological data on more complicated SBUs (polynuclear complex groups, clusters, molecular building blocks, rod units, etc.) and the methods of their connection to the databases. Using this information, the researcher will be able to extend knowledge database with the correlations between the SBUs characteristics and the overall network topology. Further development of the artificial intelligence tools can include a network constructor, which will use the information from the knowledge database for assembling coordination networks with predetermined underlying topology from an appropriate set of SBUs. Such construction procedure will take into account all topological and geometrical constraints stored in the knowledge database. The resulting model will be ready for the DFT optimization that will provide the final recommendation for the synthetic chemists. We emphasize that the main reason of using the topological tools is not in extracting unusual facts or building schemes (though it can also be done in some cases) but in robust and comprehensive prediction of possible ways of crystal design resting upon all known experimental and modeling data. A combination of the topological approach and the evolutionary methods of crystal structure prediction can provide a real breakthrough in modeling new extended crystal architectures.55

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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.cgd.8b01721. I



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Article

Tables S1 and S2 contain occurrences of the first 20 most abundant ligands and most abundant coordination modes in coordination compounds; the coordination modes are illustrated in Figure S1. Table S3 contains the occurrences of Al-organic compounds at the most abundant values of the descriptors. Table S4 contains the occurrences for sets of descriptors of 2-fold interpenetrating 2D coordination polymers with Hopf ring net of the 8,10L1 topology in the most important correlations. Table S5 contains frequency pattern tree in the format of table for Al-organic compounds (PDF) Table S6 contains the list of metal−organic frameworks with the bpq underlying topology (XLSX)

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AUTHOR INFORMATION

Corresponding Author

*Phone: +7-8463356798. Fax: +7-8462784400. E-mail: [email protected] ORCID

Eugeny V. Alexandrov: 0000-0001-9229-8892 Alexander P. Shevchenko: 0000-0002-2298-6507 Vladislav A. Blatov: 0000-0002-4048-7218 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Russian Foundation for Basic Research (Grant Nos. 18-07-00183, 18-29-04010) for financial support. E.V.A. is grateful to Russian Ministry of Education and Science (Grant No. 1.6101.2017/9.10). We thank Prof. Davide M. Proserpio and Andrey V. Goltsev for their contribution to the topological collections.

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