MaThCryst forthcoming activities

Third Shanghai International Crystallographic School, June 2024, Shanghai (China)

Twelth basic training course on symmetry and group theory, July 2024, Tsukuba (Japan)

Seventh MaThCryst School in Latin America, August 2024, Lima; (Peru)

MaThCryst recent activities

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

Summer School, June 2023, Nancy (France)

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 in Materials Science 2017

Beijing, 13-15 October 2017

Introduction and motivation

At this school we consider qualitative and semi-quantitative geometrical and topological approaches in crystal chemistry for comprehensive crystal structure description and rapid data mining.

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 intended for more special tasks. The topological databases (TOPOS TTD, TTO, TTR, TTM, TTL, TTN, TTA, TTS 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 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, 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 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. We will give the full introduction to the topological methods and will briefly consider their combination with the DFT methods. 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 will be able to analyze 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, intermetallics. 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. The final 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 ToposPro. All participants will get the ToposPro Practical Manual that contains the detailed description of all practical works. New on-line services, which provide access to topological knowledge databases, will be considered for the first time.


Prof. Vladislav A. Blatov
Samara Center for Theoretical Materials Science (SCTMS), Samara University, Russia
Northwestern Polytechnical University, Xi'an, People's Republic of China


Dr. Eugeny V. Alexandrov
Samara Center for Theoretical Materials Science (SCTMS), Samara University, Russia


1st day
900-915 Welcome and Introduction
915-1045 V.A. Blatov, Lecture "Computer crystallochemical analysis: an introduction"
1045-1100 Coffee break
1100-1230 V.A.Blatov, E.V. Alexandrov, Exercises "Introduction to ToposPro"
1230-1400 Lunch
1400-1530 V.A.Blatov, E.V. Alexandrov, Exercises "Visualization of 0D, 1D, 2D and 3D structures"
1530-1545 Coffee break
1545-1715 V.A. Blatov, Lecture "Methods, software, databases, and expert systems for crystallochemical analysis"
1715-1800 Q&A

2nd day
900-1030 V.A. Blatov, E.V. Alexandrov, Exercises "Methods of simplification of crystal structures"
1030-1045 Coffee break
1045-1215 V.A. Blatov, E.V. Alexandrov, Exercises "Topological identification of nets. Working with the TTD collection and SCTMS Online Services"
1215-1400 Lunch
1400-1530 V.A. Blatov, E.V. Alexandrov, Exercises "Analysis of molecular crystals and metal-organic frameworks with topological methods"
1530-1545 Coffee break
1545-1715 V.A. Blatov, E.V. Alexandrov, Exercises "Computing natural tilings and their parameters with ToposPro. Analysis of zeolites and fast-ion conductors"
1715-1800 Q&A

3rd day
900-945 V.A. Blatov, E.V. Alexandrov, Exercises "Nanocluster representation of intermetallic compounds"
945-1030 V.A. Blatov, E.V. Alexandrov, Exercises "Combining topological and DFT methods"
1030-1045 Coffee break
1045-1215 V.A. Blatov, E.V. Alexandrov, Exercises "Data mining and knowledge databases in crystal chemistry and materials science"
1215-1230 Summary and Conclusions

Address and Date

Address:Building B8-3, TsingHua University Technology Incubator, The Emerging Industries Demonstrative Region,Gu'an County, Langfang City, Hebei Province, China (Beijing South 50KM) Dates:October 13-15,2017

Local website

Furhter details are available at the local website.

Report and photo gallery

A report of the school, with a photo gallery, is available at the Samara Center for Theoretical Material Science webiste.

The Organizers of the school Topological Methods in Materials Science 2017 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.