THEORY (14 hours)

1. Computer crystallochemical analysis: an overview
2. Applied computer crystallochemical analysis: software, databases, expert systems
3. Periodic Structures and Crystal Chemistry... aka the Topological Approach to Crystal Chemistry
4. Graph, Nets & Tilings (Quotient Graphs & Natural Tilings)
5. Topological Analysis of Entanglement : interpenetration, polycatenation, self-catenation
6. DFT computing as the tool for modern theoretical materials science.
7. Introduction to VASP and CRYSTAL.


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 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
1.8. Topological identification and taxonomy of nets in the on-line SCTMS services

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
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 (ToposPro & 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 (2 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. Searching for topological relations between nets and working with net relation graph
5.4. Applications of net relations to reconstructive phase transitions

Module 6. Toward expert systems in crystal design (2 hours)

6.1. Searching for topological relations with the TTD, TTO, TTR, TTL, TTM, and TTN collections
6.2. Estimating probabilities of occurrence of topological motifs depending on the chemical composition of reactants

Module 7. Combined topological and DFT methods (12 hours)

7.1. VASP (geometrical optimization, mechanical properties, electronic properties, surface properties)
7.2. ToposPro+VASP (applications for crystal design and prediction of physical properties)

Module 8. Work with the 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.

The school will begin with a theoretical introduction, within that 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 dedicated to practical work with computer programs ToposPro, Systre, and 3dt with a special attention to ToposPro. All participants will get the ToposPro Practical Manual with 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.

The second part includes a brief introduction into the Density Functional Theory and its application combined with the topological methods to design new materials. To perform all computations we use the most popular program DFT package VASP. The trial structures for the DFT modeling will be generated with ToposPro and Systre, while the optimization and calculation of physical properties will be performed with VASP.

Basic literature

1. V.A. Blatov, D.M. Proserpio (2015) ToposPro Practical Manual 1.1.2.
2. V.A. Blatov, A.P. Shevchenko, D.M. Proserpio (2014) Cryst. Growth Des., 14, 3576-3586.
3. L. Ohrstrom, K. Larsson (2005) Molecule-Based Materials: The Structural Network Approach, Elsevier, Amsterdam.
4. 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.
5. S. R. Batten, S. M. Neville, D. R. Turner (2009) Coordination Polymers: Design, Analysis and Application, Royal Society of Chemistry, Cambridge.
6. O. Delgado-Friedrichs, M. D. Foster, M. O’Keeffe, D. M. Proserpio, M. M. J. Treacy, O. M. Yaghi (2005) J. Solid State Chem., 178, 2533-2554.
7. V.A. Blatov, D.M. Proserpio (2011) Chapter 1 in: "Modern Methods of Crystal Structure Prediction", Ed. A.R. Oganov, Weinheim: Wiley-VCH.
8. V.A. Blatov (2011) Struct. Bond., 138, 31-66.
9. M. O'Keeffe, O. M. Yaghi (2012) Chem. Rev., 112, 675-702.
10. M. Li, D. Li, M. O'Keeffe, O. M. Yaghi (2014) Chem. Rev., 114, 1343-1370.
11. V.A. Blatov, T.G. Mitina (2013) Cryst. Growth & Des., 13, 1655-1664.
12. L. Carlucci, G. Ciani, D.M. Proserpio, T.G. Mitina, V.A. Blatov (2014) Chem. Rev., 114, 7557-7580.
13. A.A. Pankova, T.G. Akhmetshina, V.A. Blatov, D.M. Proserpio (2015) Inorg. Chem., 54, 6616–6630.