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)

Topological methods in crystal chemistry and materials science

The IUCr Commission on Mathematical and Theoretical Crystallography (MaThCryst), co-organises a school on Topological methods in crystal chemistry and materials science on September 9, 2013 to September 13, 2013 at CECAM-HQ-EPFL, Lausanne, Switzerland.



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, and TTR 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 2200, with almost 700 citations in the scientific literature. Now the description of 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.

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 five 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), and 2012 (UIMP, Santander, Spain) that collected in total about 190 students and researchers from about 20 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. The summer school in Nancy ( was the most populous and the final questionnaire showed that many participants were eager to visit such schools in the future. Thus organizing the next school in 2013 in Switzerland would be a natural development of this education process.


THEORY (10 hours)

1. Computer crystallochemical analysis: an overview
2. Periodic Structures and Crystal Chemistry... aka the Topological Approach to
Crystal Chemistry
3. Graph, Nets & Tilings (Quotient Graphs & Natural Tilings)
4. Topological Analysis of Entanglement : interpenetration, polycatenation, self-catenation
5. Applied computer crystallochemical analysis


Module 1. Standard topological analysis and classification of nets in MOFs
(Metal-Organic Frameworks), organic and inorganic crystals (6 hours)

1.1. Creating a database from CIF, SHELX or Systre formats
1.2. Computing adjacency matrix (complete set of interatomic bonds) for chemical compounds with different chemical bonding (valence, H bonding, specific interactions, intermetallic compounds)
1.3. Visualizing 0D, 1D, 2D and 3D structures
1.4. Standard simplified representations of MOFs or hydrogen-bonded organic crystals
1.5. Computing topological indices (coordination sequences, point, Schlafli and vertex symbols)
1.6. Topological identification of nets. Working with TTD collection and Systre
1.7. Taxonomy of nets. Working with TTO and TTR collections

Module 2. Special topological methods of searching for building units in crystal
structures (4 hours)

2.1. Special methods of simplification. Edge nets and ring nets. Analysis of synthons. Skeleton representation
2.2. Standard cluster representation of MOFs
2.3. Nanocluster representation of intermetallic compounds

Module 3. Analysis of entanglements in MOFs and molecular crystals (4 hours)

3.1. Visualization, topological analysis and classification of interpenetrating MOFs
3.2. Detection and description of other types of entanglement in MOFs: polycatenation, self-catenation and polythreading. Classification of entanglements with Hopf ring nets

Module 4. Analysis of microporous materials and fast-ion conductors with natural tilings (4 hours)

4.1. Computing natural tilings and their parameters. Visualizing tiles and tilings (TOPOS & 3dt). Simple and isohedral tilings. Constructing dual nets
4.2. Analysis of zeolites and other microporous materials, constructing migration paths in fast-ion conductors

Module 5. Crystal design and topological relations between crystal structures (4 hours)

5.1. Group-subgroup relations in periodic nets. Subnets and supernets
5.2. Maximum-symmetry embedding of the periodic net, working with the Systre program
5.3. Mappings between space-group symmetry and topology of the periodic net
5.4. Searching for topological relations between nets and working with net relation graph
5.5. Applications of net relations to crystal design, reconstructive phase transitions, taxonomy of crystal structures

Module 6. Analysis of results of free works with the individual tasks based on the participants' own structures (4 hours)

Participants are invited to bring their own data/structures to be analysed as well as personal computers to install the software.

=== Website of the school ===


  1. V.A. Blatov, D.M. Proserpio (2012) TOPOS Practical Manual.
  2. L. Ohrstrom, K. Larsson (2005) Molecule-Based Materials: The Structural Network Approach, Elsevier, Amsterdam.
  3. L. Carlucci, G. Ciani, D. M. Proserpio (2007) Chapter 1.3 in Making Crystals by Design: Methods, Techniques and Applications, ed. D. Braga and F. Grepioni, Wiley-VCH, Weinheim.
  4. S. R. Batten, S. M. Neville, D. R. Turner (2009) Coordination Polymers: Design, Analysis and Application, Royal Society of Chemistry, Cambridge.
  5. O. Delgado-Friedrichs, M. D. Foster, M. O'Keeffe, D. M. Proserpio, M. M. J. Treacy, O. M. Yaghi, J. Solid State Chem., 2005, 178, 2533-2554.
  6. V.A. Blatov, D.M. Proserpio (2011) Chapter 1 in: "Modern Methods of Crystal Structure Prediction", Ed. A.R. Oganov, Weinheim: Wiley-VCH.
  7. V.A. Blatov (2011) Struct. Bond., 2011, 138, 31-66.
  8. M. O'Keeffe, O. M. Yaghi, (2012) Chem. Rev., 112, 675-702.

The Organizers of the school will observe 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 conference no barriers will exist which would prevent the participation of bona fide scientists.