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In terms of the Voronoi-Dirichlet partition of the crystal space, definitions are given for such concepts as ;void', ;channel' and ;migration path' for inorganic structures with three-dimensional networks of chemical bonds. A number of criteria are proposed for selecting significant voids and migration channels for alkali cations Li+-Cs+ based on the average characteristics of the Voronoi-Dirichlet polyhedra for alkali metals in oxygen-containing compounds. A general algorithm to analyze the voids in crystal structures has been developed and implemented in the computer package TOPOS. This approach was used to predict the positions of Li+ and Na+ cations and to analyze their possible migration paths in the solid superionic materials Li3M2P3O12 (M=Sc, Fe; LIPHOS) and Na1+xZr2SixP3-xO12 (NASICON), whose framework structures consist of connected M octahedra and T tetrahedra. Using this approach we determine the most probable places for charge carriers (coordinates of alkali cations) and the dimensionality of their conducting sublattice with high accuracy. The theoretically calculated coordinates of the alkali cations in MT frameworks are found to correlate to within 0.33 A with experimental data for various phases of NASICON and LIPHOS. The proposed method of computer analysis is universal and suitable for investigating fast-ion conductors with other conducting components.

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We present the results of a comprehensive geometrical and topological analysis of 3D coordination networks in 33,790 coordination polymers. We have found relations between topological descriptors and free space of...

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We compared the topologies of protein and small molecule crystals, which have many common features – both are molecular crystals with intermolecular interactions much weaker than intramolecular interactions. They also have different features – a considerably large fraction of the volume of protein crystals is occupied by liquid water while no room is available to other molecules in small molecule crystals. We analyzed the overall and local topology and performed multilevel topological analyses (with the software package ToposPro) of carefully selected high quality sets of protein and small molecule crystal structures. Given the suboptimal packing of protein crystals, which is due the special shape and size of proteins, it would be reasonable to expect that the topology of protein crystals is different from the topology of small molecule crystals. Surprisingly, we discovered that these two types of crystalline compounds have strikingly similar topologies. This might suggest that molecular crystal formations share symmetry rules independent of molecular dimension.

Topological exploration of crystal structures demonstrates the presence of known zeolites, inorganics, and MOFs in a database of predicted materials.

Zeolites are a special class of inorganic compounds which potentially possess an infinite variety of different structures that are energetically very close to each other. Although the databases of hypothetical zeolite frameworks, which are thermodynamically close to the ground state, contain hundreds of thousands of entries, the number of experimentally obtained frameworks (currently 235) is essentially smaller. We discuss kinetic factors, which should be taken into account along with the thermodynamic ones to explain such great inconsistency and predict more thoroughly new robust zeolite frameworks. In addition to the thermodynamic factors, which determine energetically favorable structures, we consider structural parameters that provide the easiest ways of the structure assemblage. Exploring the existing zeolites, we derive geometrical and topological criteria that should be obeyed when the framework is being formed in the reaction gel. Resting upon these criteria, we extract from the databases of hypothetical zeolite frameworks those frameworks which are the most prospective for synthesis. We discuss also the problem of the purposeful sampling of proper organic structure directing agents and propose a list of them for a target synthesis of the selected hypothetical frameworks.