Wannier Orbital Overlap Population (WOOP), Wannier Orbital Position   Population (WOPP) and the Origin of Anomalous Dynamical Charges
  Most d^0 transition metal (TM) oxides exhibit anomalously large Born dynamical charges associated with off-centering or motion of atoms along the TM-O chains. To understand their chemical origin, we introduce "Wannier Orbital Overlap Population" (WOOP) and "Wannier ond Orbital Position Population" (WOPP) based on the Wannier function based description of electronic structure obtained within first-principles density functional theory. We apply these concepts in a precise analysis of anomalous dynamical charges in PbTiO_3, BaTiO_3 and BaZrO_3 in the cubic perovskite structure. Determining contributions of different atomic orbitals to the dynamical charge and their break-up into local polarizability, charge transfer and covalency, we find that p orbitals of oxygen perpendicular to the -TM-O- chain contribute most prominently to the anomalous charge, by facilitating a transfer of tiny electronic charge through one unit cell from one TM atom to the next. Our results explain why the corner-shared linkage of TMO_6 octahedra, as in the perovskite structure, is ideal for large dynamical charges and hence for ferroelectricity. 
Joydeep Bhattacharjee, Umesh V Waghmare