Topological relations between crystal structures: a route to predicting inorganic materials

We review topological approaches to the analysis of crystal structures of intermetallic compounds and to searching for structural relations between them as the relations between their underlying atomic nets. We introduce the concept of skeletal net to find the simplest system of interatomic contacts in intermetallic compounds, which supports the three-periodic crystal architecture. Using the observed approaches, we have revealed topological relations between crystal structures of binary MeX compounds (Me = Re, Ti or Rh; X = B, C, N, or Si) and found a key role of the body-centered cubic net in their topological hierarchy. We have explored the configuration space of the corresponding crystalline systems by generating all possible ‘subnet-supernet’ topological transformations, optimized the resulting topological motifs with DFT methods and found a new phase of RhB to be stable above 22 GPa. We discuss the role of topological representations in the prediction of new crystalline chemical substances.