Laboratory of Crystal Chemistry and Crystal Design 

Geometrical and topological methods in crystal chemistry and materials science.

The main scientific areas:

  • development of unique software for novel materials modeling and intellectual analysis of experimental data;
  • creation of next generation electronic databases for heuristic prediction of physical properties of solids;
  • development of the first expert systems in materials science for efficient retrieval of materials with predetermined properties;
  • online consultations on the application of theoretical methods in materials science;
  • organization of scientific schools and seminars on theoretical materials science.

  • Our experience and developments

    We’ve been working in the field of materials science for more than 25 years, and over the past 15 years we’ve been actively engaged in development of novel methods of supramolecular chemistry and crystal engineering. We have developed unique methods of crystal analysis which enable to study structures and properties of crystalline materials of any composition. We successfully implemented these methods in the ToposPro software package (Vladislav A. Blatov & Aleksandr P. Shevchenko).

    The main algorithms of ToposPro, the basis for the new software being developed in SCTMS, are summarized below.
      1. The algorithm for representing an infinite periodic atomic net as a finite factor graph, details of which can be saved in an electronic form. ToposPro uses a unique format for presentation of adjacency matrix of a quotient graph. The format enables to present the adjacency matrix of any chemical compound structure in compact form. The quotient graph presented in such format contains all information about the atomic net topology; the information can be used to find correlations between chemical composition and physical properties of the substance.

      2. The search algorithm for a finite subgraph in an infinite periodic graph. The present algorithm has no analogues in the world; all known search algorithms apply finite graphs. In our algorithm an infinite periodic graph is presented as a finite graph by means of factorization procedure. As a result, it’s possible to search for nanoclusters and molecular objects in crystal structures.

      3. The algorithm for determining topological type of an atomic net by comparing a set of topological indices of its graph with topological indices of the standard nets. ToposPro uses a wide range of indices (coordination sequence of atoms, point and vertex symbols) as compared to the well-known programs of calculation of topological indices. As a result, the atomic net topology is unambiguously characterized by the set of indices, which can be saved in an electronic form.

      4. The algorithm for representing atoms and molecules in the form of the Voronoi-Dirichlet polyhedra. Unlike other programs of Voronoi domains construction, ToposPro contains the efficient algorithm of «gift wrapping», which allows users to count millions of Voronoi-Dirichlet polyhedra within a reasonable time, and therefore can be used in processing of large databases. As a result, every atom and molecule in ToposPro is matched to its geometric image (Voronoi-Dirichlet polyhedron) which characteristics can be compared to the physical properties of atoms and molecules.

      5. Algorithm for constructing a tiling (partitions) of an infinite periodic atomic net from finite domains (tiles) which characterize porous structure of a material; this is important for predicting ionic conductivity and ion-exchange properties of solids. ToposPro is the unique program that allows building a tiling for any atomic net. The present algorithm is based on the analysis of co-called “strong” rings of an atomic net (i.e the rings which are not the sum of smaller size rings). Tiles are bodies limited by the set of non-overlapping «strong» rings; each tile corresponds to a cavity in the atomic net.

      6. Heuristic search algorithms of correlations between chemical composition of a compound, its crystal structure and physical properties such as volatility, ionic conductivity, ion-exchange capacity, magnetic susceptibility. These algorithms have been validated theoretically but their software implementation hasn’t completed yet. Their main feature is to consider the topology as the most important characteristic of a crystal structure correlating with its physical properties. The establishment of such correlations is possible by means of electronic representation of a crystal structure topology as a factor graph in ToposPro. All of these heuristic algorithms do not have analogues in the world.
    The automated ToposPro system is provided with ever-growing databases which contain the information about almost all chemical compounds structurally studied by now. Currently, the collection of TTD, TTO, TTS and TTR databases include the information about more than 104000 types of topological crystalline structures and their occurrence in chemical compounds. More recently developed TTL, TTM and TTN databases contain information about molecular fragments (ligands, molecules, nanoclusters) of crystalline structures of various chemical nature. Services of remote access to topological information of above mentioned databases are currently being developed.