A DFT study on the correlation between topology and Bader charges: Part III, the development of charge, “size” and coordination in alkali and alkaline earth titanates(IV)

The notion of a “size” of the ions plays an important role in crystal chemistry. In this paper we demonstrate how “size” varies with the combination of elements and also with varying stoichiometric composition of a compound taking the A-Ti-O series (A = Li, Na, K, Mg, Ca, Sr, Ba) as an example. We analyse the correlation between the topology of a structure, i.e. the coordination geometry and the distances observed, and the charges of the atoms as derived from a Bader analysis of the electron distribution which has been calculated in DFT relaxations of the structures. We demonstrate how charge relations of the atoms in specific stoichiometric relations are strictly fixed within small ranges which are constraint by electronegativity differences of the constituting atoms and how atomic charges are “delicately” balanced by minute movements of the atoms and changes in coordination. The balance of charges proves to be a decisive structure determining parameter.