Out-of-Center Distortions around Octahedrally Coordinated d0 Transition Metals

The bond valence approach is used to model the characteristic out-of-center electronic distortions around d0 transition metal cations in octahedral coordination. The distortions are influenced not only by the electronic structure of the cation but also by the structure of the bond network, by lattice incommensurations, and by cation-cation repulsion. These latter effects often determine whether a distortion will occur and, if so, in what direction. Once the direction of an expected out-of-center distortion is known, its magnitude can be modeled using modified bond valence network equations, where certain bonds are weighted to take into account the intrinsic inequality of the bonds in such a distorted coordination. The arguments are illustrated by examples.