Coordination polymers and Metal-Organic Frameworks (MOF) are important for chemistry and materials science. A finite representation of these infinite molecules is needed for their understanding and analysis. The theory behind how we can represent infinite molecules was first introduced in [1] through the use of quotient graph, which capture translationally equivalent bonds and atoms. However, it is rarely used in crystallographic software. There are no tools that provide standard output that can be used on large databases, and the available software is proprietary. One tool is cif_molecule [2], which is part of cod-tools, is open source and provides output as a CIF [3] file, and can work with a large number of files. However, there was a limitation on how polymers are detected, and the correct detection and stoichiometry of reconstructed molecules cannot be guaranteed. This work focuses on extending existing software cif_molecule by introducing quotient graph. By using quotient graphs, we can always correctly detect infinite molecules, and determine their properties.
The algorithm in cif_molecule was modified to use the quotient graph to determine "edge" of a polymer. This allowed us to distinguish polymers correctly, preserve their stoichiometric ratios, determine correct dimensionality, and calculate polymer multiplicity. Output of the cif_molecule was extended with TOPOCIF data names that represent quotient graph, this allows use of quotient graph by other programs, and addition of topol_net data items allows us to distinguish different nets in the crystal. Programs were developed to convert quotient graph in CIF to other formats: cif2qg converts to graphviz format, and to cgd format for Systre [4] input, cif_polymer_multiplicity to calculate polymer multiplicity (number of self-penetrated molecules in the crystal). The calculations were done on the COD [5]. A repository for calculations was created at svn://databases.crystallography.lt/quotient-graphs. The repository contains rules defined as Makefiles, and calculations are easily reproducible. A website to search and display the results of the calculations was created in the repository svn://databases.crystallography.lt/cif-explorer , available at http://databases.crystallography.lt:8080/.
All 511329 structures from COD revision 291294 were processed. The calculations show that 22.7% of structures are polymers. The result of Systre [4] identified 56 unique R͡CSR [6] symbols. The most common are hcb, dia and kgm symbols. Multiplicity calculations show that among self-penetrated structures in COD, 2 and 3 multiplicity is the most common. Structures with a higher multiplicity of 27, 25, 18 and 13 were found.
With quotient graph we can guarantee finite representation of infinite molecules.