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)


Topological methods for expert systems in materials science

The IUCr Commission on Mathematical and Theoretical Crystallography (MaThCryst), co-organised a school on Topological methods for expert systems in materials science on 12 to 16 August 2014 at Samara Center for Theoretical Materials Science.

Organisers and lecturers


The explosive growth in inorganic and organic materials chemistry has seen a great upsurge in the synthesis of crystalline materials with extended framework structures (zeolites, coordination polymers/coordination networks, Metal Organic Frameworks (MOFs), supramolecular architectures formed by Hydrogen bonds and/or Halogen bonds etc.). There is a concomitant interest in simulating such materials and in designing new ones. However, it is a truism that before one can embark on systematic design of materials, one must know what the possibilities are. Indeed, in the last two decades there have been many parallel outcomes in the theoretical aspects of description and analysis of periodic structures (nets, tilings, surfaces, etc.), in the elaboration of databases, and in the development of software for analysing and describing topological aspects of both real crystal structures and theoretical extended architectures. With these achievements, materials science and crystal chemistry comes up to a new level of their development that is characterized by deeper integration of mathematical methods, computer algorithms and programs into modelling and interpretation of periodic systems of chemical bonds in crystals.

These methods, algorithms, software, and databases have been extensively developed in the past 15 years. The most general program package is TOPOS (, other programs like Gavrog Systre and 3dt ( are intended for more special tasks. The topological databases (TOPOS TTD, TTO, TTR, and TTL collections, RCSR and EPINET databases) include more than 70000 topological types of nets that can occur in extended crystalline architectures as well as in molecular crystals. All these resources are available for free and become more and more popular. Thus, the current number of TOPOS registered users exceeds 2800, with more than 800 citations in the scientific literature. 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 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 still remain unusual for most of structural chemists and material scientists. In the literature, there are many examples of misuse of the computer tools as well as of wrong analysis and conclusions about crystal structure topology. These problems can be overcome only with a permanent intensive education of young researchers. For this purpose, we have already organized six international schools on the topological methods in crystal chemistry: in 2008 (University of California at Santa Barbara, USA), 2009 (Milano university, Italy), 2010 (University of Nancy, France), 2011 (Max Plank Institute, Stuttgart, Germany), 2012 (UIMP, Santander, Spain), and 2013 (CECAM, Lausanne, Switzerland) that collected in total about 220 students and researchers from about 25 countries. Other schools on TOPOS and related methods were provided by M. O'Keeffe and C. Bonneau in China (Zhuhai college of Jilin University, December 2010), South Korea (Pohang Accelerator Laboratory, January 2011), Sweden (Stockholm University, 2012) totally for 180 students and staff selected nationwide.

Contents and objectives

The main goal of this 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 for creating expert systems in materials science. There will be 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 will be paid to the analysis of various classes of crystalline materials, in particular, MOFs, supramolecular crystals, zeolites, fast-ion conductors, minerals. All participants will have an ability to analyze their own crystal structures with the help of tutors that will be available also in the evening time. A special session will be devoted to summarize the results of such personal/free works.

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

The main part of the tutorial will be devoted to practical works with the computer programs TOPOS, Systre, and 3dt with a special attention to TOPOS. All participants will get the TOPOS Practical Manual that contains the detailed description of all practical works.

As a result, the participants will gain the following knowledge:

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

For details and registration, please refer to the website of the school.

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.