We invite researchers, graduate, master’s and postgraduate students interested in crystallography, materials science and modern topological and DFT methods to participate in the School.

The participants will gain the following knowledge:
  • a general view of modern topological and DFT methods in crystal chemistry and materials science, the corresponding algorithms, software, databases, and expert systems;
  • a skill in application of these tools to various classes of crystal structures and crystalline materials;
  • a vision of how to apply the software and databases to investigate the participant’s own specific field of science;
  • ideas of how to use together the topological and DFT methods to design new materials and predict their physical properties.
Introduction and motivation

The present school develops the topic of combined application of topological and Density Functional Theory (DFT) methods for prediction structure and properties of crystalline substances and materials. In the previous (September 2015) school we have introduced the idea of how to apply qualitative and semi-quantitative geometrical and topological approaches in crystal chemistry for rapid and effective data mining, and to use the results in the subsequent precise DFT modelling.

The topological methods have been dramatically developed in the past 15 years and proved their effectiveness for systematization and rationalization of huge amounts of crystal data. The program package, where the geometrical and topological approaches, algorithms, and software are implemented most comprehensively is ToposPro (; other programs like Gavrog Systre and 3dt ( are meant for more special tasks. The topological databases (TOPOS TTD, TTO, TTR, TTM, TTL, and TTN collections, RCSR and EPINET databases) include more than 100,000 topological types of underlying topologies that can occur in extended crystalline architectures as well as in molecular crystals. Many of these resources are available for free and become more and more popular; now the description of the overall topology of new structures becomes ordinal in such journals as CrystEngComm or Crystal Growth & Design. The search for relations between local topology of coordination groups, coordination abilities of metal atoms and ligands, and the overall topology of the whole network becomes one of the important tasks in the structure investigations.

These relations could be important to create the first expert systems in crystal design; the knowledge database of such systems could rest upon the topological databases, while the inference machine could use the relations to provide an expert conclusion about the possibility of appearance of a particular topological motif. Thus, the topological approaches are crucial for taxonomy of the experimental information and for developing predictive tools.

At the same time, the topological methods, being able to work with large samples of crystallographic data, provide only qualitative or semi-quantitative prediction. To make it precise we need to merge the topological methods with the quantitative methods of mathematical modelling. Recent progress in theoretical materials science is especially caused by development of Density Functional Theory, which is a basis of quantum mechanical calculations of various crystal properties. The present state of theoretical calculations in quantum chemistry and solid state physics can be considered as an ab initio approach. It means that we can describe already known crystalline structures, predict new crystalline materials and perform calculations of their physical properties without any empirical parameters. An important part of this ab initio approach is the high-performance numerical calculations on supercomputers or cluster systems.

Content and objectives

The main goal of the tutorial is to give an introduction to this whole new area that we call Topological Crystal Chemistry and to show how the topological methods and tools can be used together with the DFT methods for creating expert systems in materials science. Like the last (September 2015) our school the present one consists of two interrelating parts. The first part will give a full introduction to the topological methods while the second part will be dedciated to how they can be combined with the DFT methods. Compared to the first school on this topic we will consider new features of ToposPro and relating on-line services as well as new interfaces between ToposPro and DFT packages. A large part of the school program will be dedicated to hands-on session on the use of the novel and still not so widespread computer methods/software/databases, so the participants at the end of the course will be able to analyze any kind of extended structure through topology and describe it in terms of nets, entanglements, catenation etc. A special attention will be paid to the analysis of various classes of crystalline materials, in particular, MOFs, supramolecular crystals, zeolites, fast-ion conductors. All participants will have possibilities to analyze their own crystal structures assisted by our tutors who will be available also in the evening time. The final session will be aimed at summarizing the results of such individual/free work.