Retrieval of isomorphic substructures in crystallographic databases

Local bindings of atoms are often modeled by coordination polyhedra with vertices representing ligands, i.e. atoms with strong bonds to a central atom. Neighbouring polyhedra may be linked by vertices, edges, or faces depending on whether their central atoms share one, two, or more atoms as ligands. Substructures formed by linked polyhedra are of considerable interest for studying crystal structures. We introduce a finite graph representation for infinite polyhedral networks and show how to build an index for a given set of model structures such that the retrieval of isomorphic substructures is supported. A system has been implemented providing this functionality on an interactive graphical Web interface.