A. P. Shevchenko

TOPOS3.2: a new version of the program package for multipurpose crystal-chemical analysis

The principal features of the package are as follows. (i) Management of crystal structure information with DBMS (database management system) which has gateways to the CSD and ICSD databases. (ii) Comprehensive analysis of geometrical and topological properties of crystal structures (employing the programs Dirichlet, AutoCN, ADS, DiAn, IsoCryst and IsoTest). (iii) Special facilities for statistical analysis of large sets of crystal structures (the program StatPack). In addition to the programs contained in the previous version (Blatov et al., 1999), version 3.2 includes the following two programs. (a) IsoTest, which provides an automatic search for the topological similarity (isotypism) in large groups of stoichiometrically and structurally different compounds, on three levels: the whole topological and geometrical similarity (crystal-chemical isotypism; Lima-deFaria et al., 1990); only the whole or partial topological similarity of crystal structures (topological isotypism; Blatov, 2000); topological similarity of separate atomic subnets and packings. (b) HSite, which searches for hydrogen positions in crystal structures of organic, organometallic and inorganic compounds. Besides traditional methods of geometrical and statistical analysis, and graphical representation of crystal structures (the programs DiAn, IsoCryst and StatPack), there are two novel concepts used in TOPOS algorithms: the concept of an atomic domain represented as a Voronoi±Dirichlet polyhedron (the program Dirichlet; Blatov et al., 1995) and the concept of a periodic net described as a contracted graph (the programs ADS, AutoCN and IsoTest; Blatov, 2000). The program IsoTest automatically enumerates all variants of topological representation of crystal structures and ®nds similar ones through a given list of compounds by comparing coordination sequences (Brunner & Laves, 1971) of corresponding atomic subnets (Blatov, 2000). The program HSite uses characteristics of Voronoi±Dirichlet polyhedra to predict the optimal positions of hydrogen atoms and orientation of atomic groups.

Crystal space analysis by means of Voronoi–Dirichlet polyhedra

The method of analysis of crystal space topology by means of Voronoi-Dirichlet tessellation is described. The possibilities of using Voronoi-Dirichlet polyhedra in the investigation of local and global geometrical/topological properties of the crystal lattice in structures of simple and complex substances are discussed. Examples of the application of the proposed method in crystal-chemical analysis are given.

New knowledge and tools for crystal design: local coordination versus overall network topology and much more

The problem of predicting crystal structures is discussed in the context of artificial intelligence systems. The steps of creation of an expert system are considered as applied to crystal design, where the crucial step is the invention of new structure descriptors. A number of such descriptors proposed quite recently are listed; most of them characterize local coordination or overall topology of the structure network. An important part of the expert system is the knowledge database that contains correlations between the descriptors; it is used by a computer analyzer, the inference machine, to make a conclusion about the possibility of obtaining a particular structural motif. All the steps for developing the expert system are illustrated with the analysis of 811 cyanide complexes and examples of the structure prediction are given.

Methods of crystallochemical analysis of supramolecular complexes by means of Voronoi-Dirichlet polyhedra: a study of cucurbituril host-guest compounds.

Crystallochemical analysis methods based on the Voronoi-Dirichlet partition of crystal space are extended to supramolecular complexes of any complexity. The sizes and shapes of receptor cavities and substrate molecules are shown to be successfully estimated as volumes and the second moments of inertia of the corresponding molecular Voronoi-Dirichlet polyhedra. To predict which organic substrates can occupy the receptor cavity a mini-expert system known as MOLVOL was created, comprising a database on completely determined crystal structures of almost 60000 organic molecular compounds. Using the developed methods, volumes and shapes are assessed for cucurbit[n]uril receptors (n = 5-10) and their cavities. A number of organic and inorganic molecules are found which can optimally fit the cavities inside the cucurbit[5]uril and cucurbit[6]uril molecules.

Topology of Intermetallic Structures: From Statistics to Rational Design

More than 38 000 substances made only of metal atoms are collected in modern structural databases; we may call them intermetallic compounds. They have important industrial applications, and yet they are terra incognita for most of our undergraduate students. Their structural complexity and synthesis are not easily adaptable to first years laboratories, keeping them away from the standard curricula. They have been described over the years following alternative and complementary views such as coordination polyhedra, atomic layers, and polyatomic clusters. All of these descriptions, albeit relying on grounded principles, have been applied on a subjective basis and never implemented as a strict computational algorithm. Sometimes, the authors generated multiple views of the same structure reported with beautifully drawn figures and/or photos of hand-crafted models in seminal works of the precomputer age. With the use of our multipurpose crystallochemical program package ToposPro, we explored the structural chemistry of intermetallics with objective and reproducible topological methods that allow us to reconcile different structure descriptions. After computing the connectivity patterns between the metal atoms on the basis of Voronoi partitioning of the crystal space, we were able to group the 38 000 intermetallic compounds into 3700 sets of crystal structures with the same topology of atomic net. We have described the different views used in the literature and shown that 12-vertex polyhedra are the most frequent (33%) and that almost half of them are icosahedron-like (46%), followed by cuboctahedron (25%) and, unexpectedly, by bicapped pentagonal prism (13%). Looking for layers, we have found that the hexagonal lattice, which corresponds to the closest packing of spheres on a plane, exists in more than 11 000 crystal structures, confirming the close-packed nature of intermetallics. We have also applied the nanocluster approach, which goes beyond the first coordination sphere and looks for structural units as multishell clusters that assemble the whole structure. This approach shows that 41% of intermetallics can be assembled with a single nanocluster and that 22.4% of these are packed according to the face-centered cubic motif of the closest packing of spheres in three-dimensional space. We have shown that our approach can easily adopt any other building model and hence could become a platform for a universal predictive scheme. Within this scheme, all of the structural descriptors can be related to experimental data and theoretical modeling results and then can be used to synthesize new intermetallic compounds and to foresee novel materials.

Multilevel topological analysis in application to design of coordination networks

Topological methods of analysis of coordination networks have become an integral part of design of coordination polymers, MOFs, and zeolites. It helps to chemists to understand the novelty of findings, to reveal relations between different structures, to propose new design concepts, and to communicate effectively with each other. However, this is not the limit of the methods. Description of coordination environment of structural units (metal atoms, ligands, SBUs), network topology (topological type), and topology of entanglement (entanglement pattern) intrinsically leads to finding relations between the topological parameters. Further, the correlations can be grouped (systematized) in a hierarchical manner to produce a knowledge database for design and prediction of new materials (their structure and properties) [1, 2]. Thus, new structural characteristics, the so-called descriptors, have to be invented for prediction of particular structural features. For example, we have proposed to use topological type of Hopf ring net for analysis of topology entanglements in coordination networks. Now we put forward Extended ring net (ERN), which incorporates information about topology of entangled nets and topology of entanglements. ERN is able to distinguish patterns of entanglements up to isomorphism and polymorphism, that allowed us to describe new type of isomerism of coordination polymers, entanglement isomerism. MOF structures are usually considered as a result of assembly of secondary building units in an isoreticular manner. Usually SBU is considered as a topologically dense 0D polynuclear complex group, which coordination figure is predetermined by orientation of points of extension (functional groups of ligands connected by linkers). However, many practically important MOFs contain infinite SBUs; e.g. rod-shaped 1D {AlOH(CO2)2} groups are connected by benzene linkers in parallel fashion into framework MIL-53. We have produced a comprehensive systematics of infinite SBUs and ways for their connection with new algorithms of rod-MOFs description as 2D net of rods connections. Selection of correct structural groups is also important for design of self-catenated networks. We proposed a universal algorithm for selection of all reasonable subnets and determining the structure driving ones. To describe the geometry and topology of voids and channels in porous structures we combined topological methods and Voronoi partitioning. The improved Voronoi partitioning provides much more characteristics of porous structures, e.g. periodicity, topology and crystallographic orientation of channels, minimal cages of framework, open sights of metal atoms etc. These descriptors give us an opportunity to define metal-organic nanotube as a 1-periodic tiling of face-shared 3D tiles. To enhance the usability of the results of topological analysis we collected values of descriptors into a knowledge database [2]. The database was applied in finding relations between topological parameters for heterometallic coordination polymers based on {Cu(Me2mal)2} SBU (H2Me2mal = dimethylmalonic acid) [3]. The authors thank the Russian government (grant No. 14.B25.31.0005), Russian Science Foundation (grant No. 16-1310158), and Russian Ministry of Science for finantinal support. E.V.A. is gratefull to Russian Foundation for Basic Research (grant No. 16-37-00147). [1] Alexandrov, E.V. et al. (2015) Chem. Rev. 115, 12286-12319. rn[2] Alexandrov, E.V. et al. (2015) CrystEngComm., 17, 2913-2924. rn[3] Gogoleva, N. V. et al. (2016) Eur. J. Inorg. Chem., doi: 10.1002/ejic.201601047.