A DFT study on the correlation between topology and Bader charges: Part V, on the correlation between interatomic distances and Bader charges in the structures of TinOm compounds - A comment on the “charge and size concept” in crystal chemistry

The analysis of structures in crystal chemistry is mainly based on geometric parameters such as distances, coordination numbers and connectivity of polyhedral constituents. We thereby venture to define sizes and even charges of ions based on a large data set of distances, and we compile them in tables of radii. In turn we allocate charges by comparison of such “sizes”. Quantum chemical approaches offer a direct path to such an analysis by presenting electron densities, force constants, energies etc. In this paper we present the results of DFT calculations combined with a Bader analysis of the electron densities, and we compare the results of charge allocation by both approaches in the series of Ti-O compounds where already the geometric description seems to drum home the information. We point out that a comparison of distances alone can be misleading in the attempt to localize different charges of ions. The pattern of distances and seeming sizes is severely influenced by the topology of catenation of coordination polyhedra.