Distortions in Octahedrally Coordinated d<sup>0</sup> Transition Metal Oxides:  A Continuous Symmetry Measures Approach

More than 750 d<sup>0</sup> transition metal oxide octahedra have been examined in order to better understand the out-of-center distortion occurring with these cations. A continuous symmetry measures approach was used to quantify the magnitude and direction of the distortion. Using this approach we were able to divide the d<sup>0</sup> transition metals into three categories:  strong (Mo<sup>6+</sup> and V<sup>5+</sup>), moderate (W<sup>6+</sup>, Ti<sup>4+</sup>, Nb<sup>5+</sup>, and Ta<sup>5+</sup>), and weak (Zr<sup>4+</sup> and Hf<sup>4+</sup>) distorters. We also examined and discussed the directional preference of the distortion for each cation.