Application of graph theory to detect disconnected structures in a crystallographic database: copper oxide perovskites as a case study

Every crystal structure can be described as a graph with atoms as vertices and bonds as edges. Although such a graph loses the space arrangement of atoms and symmetry elements, it can mathematically represent the connectivity between atoms. This topological approach was used to develop a new method for detecting disconnected structures, in which individual atoms or structural fragments are located too far from each other, forming impossibly large gaps. Approximately 2300 perovskite-related crystal structures have been extracted from the Inorganic Crystal Structure Database (in 1999) and the maximum disconnecting distances, and the relations between them and the ionic radii of elements, have been analysed. Several disconnected structures, which are erroneous by our definition, have been revealed. Conventional tests for crystallographic data checking did not detect those entries.