Voronoi-dirichlet polyhedra in crystal chemistry: theory and applications

• Published in: Crystallography reviews Vol. 10; no. 4; pp. 249 - 318
• Main Author: Blatov, Vladislav A.
• Format: Journal Article
• Language: English
• Published: Taylor & Francis Group 01.10.2004
• Subjects: Analysis of voids and cavities; Atomic domain; Crystallochemical analysis; Supramolecular complexes; Voronoi-Dirichlet polyhedron
• ISSN: 0889-311X; 1476-3508
• DOI: 10.1080/08893110412331323170

This review is devoted to the new three-dimensional geometrical methods of crystallochemical analysis based on the Voronoi-Dirichlet partition of crystal space. It is emphasized that the model of an atom in the crystal field as its Voronoi-Dirichlet polyhedron seems to be in many cases of interest in crystal chemistry, and satisfactorily reflects the form of an atomic domain. Moreover, the Voronoi-Dirichlet approach becomes not only a particular and very limited method of crystallochemical analysis, but also a universal model of crystal structure representation on the level of its geometrical description. E-mail: blatov@ssu.samara.ru The scope of the review is restricted to only crystallochemical applications of the Voronoi-Dirichlet partition. In the first part, the physical meaning of the basic parameters of atomic Voronoi-Dirichlet polyhedron is considered; some crystallochemical regularities are discussed following the Voronoi-Dirichlet model of an atom. The correctness and restrictions of the model are reviewed in detail; the main attention is drawn to its relations with the quantum-mechanical representation of an atom according to Bader's approach. The subject of the second part is the method of describing polyatomic structural units with the molecular Voronoi-Dirichlet polyhedra. It is shown that this model of molecular crystals developed in the last few years, substantially extends the scope of the Voronoi-Dirichlet method in crystal chemistry for the first time to supramolecular complexes. One of the prospective new directions in this area is the analysis of cavities in a wide range of molecular and polymeric cavitandes. The third and final part concerns the problems of computer implementations of the Voronoi-Dirichlet method in crystal chemistry. The main algorithms of constructing Voronoi-Dirichlet polyhedra are considered; the capabilities of the modern program package TOPOS are discussed where all the modern methods of the Voronoi-Dirichlet crystallochemical analysis are realized as a unit.