**LABORATORY OF CRYSTAL CHEMISTRY AND CRYSTAL DESIGN**

**Staff:**

** Head of the Laboratory** — Prof. Vladislav A. Blatov

**— Candidate of Chemistry Aleksandr P. Shevchenko**

*Senior Researcher***— Candidate of Chemistry Inna V. Medrish**

*Researcher***— Candidate of Chemistry Evgeny V. Alexandrov**

*Researcher***— Natalia A. Kabanova**

*Junior Researcher***— Arina A. Pankova**

*Junior Researcher***— Andrey A. Golov**

*Junior Researcher***— Nikita S. Zakharov**

*Junior Researcher***— Pavel N. Zolotarev**

*Junior Researcher***— Tatiana G. Ahmetshina**

*Laboratory Assistant***— Andrey V. Goltsev**

*Laboratory Assistant***— Elizaveta A. Timofeeva**

*Laboratory Assistant***— Denis E. Yablokov**

*Senior Software Engineer*

## Geometrical and topological methods in crystal chemistry and materials science

#### The main directions:

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

**The innovative nature of the activity:** software, databases and services in all the above areas have no analogues in the world.

#### Experience and existing developments

We work in the field of materials science more than 15 years, and during the last 10 years we have been actively engaged in the development of new methods of supramolecular chemistry and crystal engineering. We developed unique methods of crystal analysis to study the structure and properties of crystalline materials of any composition that are realized into the TOPOS software package (V. A. Blatov & A. P. Shevchenko).

The main system algorithms of TOPOS which will form the basis of creating of new software in the Center are summarized below.

- Algorithm for representing infinite periodic atomic net as a finite factor graph, details of which can be saved in an electronic form. TOPOS uses a unique format for presentation of adjacency matrix of the quotient graph which presents the adjacency matrix of the structure of any chemical compound in a compact form. The quotient graph is presented to contain all information about the topology of the atomic net; this information can be used to find the correlations between chemical composition and physical properties of the substance.
- The algorithm for searching finite subgraphs in infinite periodic graphs. This algorithm has no analogues in the world – all well-known search algorithms operate with finite graphs. Infinite periodic graph is represented as a finite graph on account of factorization procedure. As a result, in particular, it is possible to search nanoclusters and molecular objects in the structure of crystals.
- The algorithm for determining the topological type of atomic net by comparing the set of topological indices of its graph with topological indices of the standard nets. TOPOS uses a wide range of indices (coordination sequence of atoms, point and vertex symbols) in contrast to the well-known programs of calculation of topological indices. As a result, the topology of atomic net is unambiguously characterized by the set of indices, which can be saved in an electronic form.
- The algorithm for representing atoms and molecules in the form of the Voronoi-Dirichlet polyhedra. In contrast to other programs, the construction of Voronoi domains in TOPOS implemented the efficient algorithm «gift wrapping», which allows you to count millions of Voronoi-Dirichlet polyhedra within a reasonable time and therefore can be used in the processing of large databases. As a result, in TOPOS, every atom and molecule is matched to its geometric image (Voronoi-Dirichlet polyhedron) whose characteristics can be compared with the physical properties of atoms and molecules.
- Algorithm for constructing a tiling (partitions) of infinite periodic atomic net on finite domains (tiles) which characterize the porous structure of the material, this is important in predicting the ionic conductivity and ion-exchange properties of solids. TOPOS is the unique program that allows building a tiling for any atomic net. This algorithm is based on the analysis of co-called “strong” rings of atomic net (i.e the rings which are not the sum of the 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.
- Heuristic search algorithms of correlations between chemical composition of the compound, crystal structure and physical properties such as volatility, ionic conductivity, ion-exchange capacity, magnetic susceptibility. These algorithms were validated theoretically but their software implementation is not yet completed. Their main feature is to consider the topology as the most important characteristics of the crystal structure correlating with its physical properties. The establishment of such correlations is possible thanks to the electronic representation the topology of the crystal structure as a factor graph into TOPOS. All of these heuristic algorithms do not have analogues in the world.

The automated TOPOS system is provided by permanently updating databases which contains the information about almost all up-to-date structurally studied chemical compounds. Currently, the collection of **TTD**, **TTO** and **TTR** database includes the information about more than 75000 types of topological crystalline structures and their occurrence in chemical compounds.