Born charge differences ofTiO2polytypes: Multipole expansion of Wannier charge densities

The bonding Wannier functions (WF’s) associated with the O $2s/2p$ valence states of ${\mathrm{TiO}}_2$ have been calculated for both the rutile and the anatase forms. They are similar in the two polymorphs, and correspond to three distorted O ${\mathrm{sp}}^2$-like hybrids in the plane of the ${\mathrm{Ti}}_3$ coordination triangle, and one p-like orbital perpendicular to this plane. For both structures, the WF’s show that the ${\mathrm{OTi}}_3$ triangular complex is the relevant structural unit for understanding ${\mathrm{TiO}}_2$ electronic properties. WF’s differences between the two phases are quantitatively measured with a multipole expansion of the static charge density of the fourfold WF complex. These differences reflect the opposite distortion from equilateral shape that the isosceles ${\mathrm{Ti}}_3$ triangle has in the two structures, and correlate quantitatively with the opposite anisotropy of the dynamical Born charge tensors calculated for the two polytypes.