MaThCryst forthcoming activities

Summer School, June 2023, Nancy (France)

Eleventh basic and second advanced training course on symmetry and group theory, July 2023, Tsukuba (Japan)

MaThCryst recent activities

Tenth training course on symmetry and group theory, August 2022, Tsukuba (Japan)

2022 Spring Festival Crystallographic School and Workshop on Crystal-field Applications February 2022, Berijing (China)

Crystallography Online: Workshop on the use and applications of the structural and magnetic tools of the Bilbao Crystallographic Server January 2022, Leioa (Spain)

Mathematics and Computer Science for Materials Innovation, September 2021, online

Ninth training course on symmetry and group theory, September 2021, Tsukuba (Japan)

2021 SIAM Conference on Mathematical Aspects of Materials Science, May 2021, Bilbao (Spain)

AMS Sectional Meeting, November 2019, Gainesville, FL (USA)

ECM32 Satellite, August 2019, Wien (Austria)

Eighth training course on symmetry and group theory, July 2019, Tsukuba (Japan)

Second Shanghai International Crystallographic School, July 2019, Shanghai (China)

Summer School, June 2019, Nancy (France)

Sixth MaThCryst School in Latin America, November 2018, Bogotà (Colombia)


International Scientific School "Combined topological and DFT methods for prediction of new materials"

Samara, Russia, 14 - 20 September 2015

Introduction and motivation

In the previous school we dwelled on the topological approach to description and prediction of structure and properties of new crystalline substances and materials. This field of science has been rapidly developed in the past 15 years. The program package, where the corresponding methods, algorithms, and software are implemented most comprehensively is ToposPro; other programs like Gavrog Systre and 3dt Gavrog Systre and 3dt are intended for more special tasks. The topological databases (TOPOS TTD, TTO, TTR, TTM, TTL, and TTN collections, RCSR and EPINET databases) include more than 100000 topological types of nets 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 is 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 on the one hand 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 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 (DFT), 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.

Contents and objectives

The main goal of this tutorial was 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. An important difference of this school compared to previous ones is that it consists of two interrelating parts. The first part contained the full introduction to the topological methods while the second part was devoted to how they can be combined with the DFT methods. There was large time dedicated to hands-on session on the use of the novel and still not so widespread computer methods/software/databases so the student at the end of the course should be able to analyse any kind of extended structure through the eye of the topology and describe it in term of nets, entanglements, catenation etc. A special attention has been paid to the analysis of various classes of crystalline materials, in particular, MOFs, supramolecular crystals, zeolites, fast-ion conductors. All participants had an ability to analyze their own crystal structures with the help of tutors that were available also in the evening time. A special session has been devoted to summarize the results of such personal/free works.

The tutorial started with a theoretical introduction where the background of the topological methods was briefly, but rigorously, considered. No special mathematical skills were required, but the participants had to be aware of crystal chemistry and crystallography basics. The main abilities, problems, and perspectives of topological analysis of crystalline networks have been outlined.

The main part of the tutorial was devoted to practical works with the computer programs ToposPro, Systre, and 3dt with a special attention to ToposPro. All participants have got the ToposPro Practical Manual that contains the detailed description of all practical works.

The second part included a brief introduction into the Density Functional Theory and its application combined with the topological methods to design new materials. Two popular program DFT packages, VASP and CRYSTAL, have been used to solve some practical tasks, where the trial structures are generated with ToposPro and Systre, while the optimization and calculation of physical properties are performed with VASP and CRYSTAL.

As a result, the participants have gained the following knowledge:

  1. A general view of modern topological and DFT methods in crystal chemistry and materials science, the corresponding algorithms, software, databases, and expert systems.
  2. A skill of application of these tools to various classes of crystal structures and crystalline materials.
  3. A vision of how to apply the software and databases to investigate the participant's own specific field of science.


Program and details

See the official school website.

The Organizers of the school have observed the basic policy of non-discrimination and affirmed the right and freedom of scientists to associate in international scientific activity without regard to such factors as citizenship, religion, creed, political stance, ethnic origin, race, colour, language, age or sex, in accordance with the Statutes of the International Council for Science. At this school no barriers existed which would have prevented the participation of bona fide scientists.