Methods of crystallochemical analysis of supramolecular complexes by means of Voronoi–Dirichlet polyhedra: a study of cucurbituril host–guest compounds

Crystallochemical analysis methods based on the Voronoi–Dirichlet partition of crystal space are extended to supramolecular complexes of any complexity. The sizes and shapes of receptor cavities and substrate molecules are shown to be successfully estimated as volumes and the second moments of inertia of the corresponding molecular Voronoi–Dirichlet polyhedra. To predict which organic substrates can occupy the receptor cavity a mini-expert system known as MOLVOL was created, comprising a database on completely determined crystal structures of almost 60 000 organic molecular compounds. Using the developed methods, volumes and shapes are assessed for cucurbit[n]uril receptors (n = 5–10) and their cavities. A number of organic and inorganic molecules are found which can optimally fit the cavities inside the cucurbit[5]uril and cucurbit[6]uril molecules.