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The program package for multipurpose geometrical and topological analysis of crystal structures

Home page ToposPRO Modules


- constructs Voronoi-Dirichlet polyhedra (VDPs) of atoms in crystal structures taking into account both all basis atoms and an arbitrary subset of atomic sublattices given by the user;
- images VDPs, the corresponding Delaunay stars, coordination polyhedra and Schlegel projections;
- calculates all the main geometric characteristics of VDPs;
- determines the topological characteristics of VDPs and automatically forms the library of topological types of VDPs;
- allows one to calculate VDPs of atoms in a group of crystal structures from a database and forms summary tables for the following statistical analysis.

In the Dirichlet program a very fast "gift wrapping" algorithm of VDP calculation by means of construction of a convex hull for a set of atoms has been realized for the first time. This algorithm allows one to calculate hundreds of thousand VDPs with a reasonable outlay of machine time.

ADS(Automatic Description of Structure)

- analyses the crystal structure topology;
- calculates the number, composition and dimensionality of all structural groups in crystal structure and their orientation along the crystallographic directions (for chain or layer groups);
- determines the topology of structural groups and the coordination types of ligands;
- calculates molecular coordination numbers for the molecules of any complexity and analyzes the topology of their mutual arrangement;
- determines the way of combination of coordination polyhedra or molecules;
- calculates the composition of the far coordination spheres of complexing atoms or molecules.

The program ADS uses an adjacent matrix of crystal structure calculated by the AutoCN program and realizes the representation of a crystal structure as a finite "contracted" graph. This method allows one to analyze the topology of a crystal structure as a whole.


- constructs stick, sphere-and-stick and polyhedral images of crystal structures and provides the convenient service for rotation, scaling and editing an image;
- calculates the geometrical characteristics of crystal structure (interatomic distances, bond and torsion angles, RMS planes, etc.);
- constructs VDPs and coordination polyhedra immediately on an image of a crystal structure;
- differs valent and non-valent (specific or van der Waals) interatomic contacts and allows one to analyze visually the packing of polymeric or molecular structural units.

DiAn (Distances and Angles)

calculates interatomic distances and bond angles for a set of atoms.


calculates automatically the positions of hydrogen atoms, which have not been localized in crystal-structural experiment.


Calculates an adjacent matrix of crystal structure, including atomic coordination numbers. The AutoCN program uses VDPs and a number of special algorithms to build an adjacent matrix.


- automatically tests crystal structures on isotypism (topological similarity) and determines the degree of their similarity. You can find the relations between crystal structures, which would seem to be absolutely different !
- provides topological analysis of atomic sublattices and detects close packings at any degree of their distortion;
- automatically classifies crystal structures according to structure type concept.
The IsoTest program uses the adjacent matrices, the method of "contracted" graph, the method of coordination sequences and the analytical algorithms of the ADS program.


realizes a number of standard statistical methods for processing the results of a calculation of VDP characteristics, which have been done by the programs ADS and Dirichlet.