Tight-binding theory of the dielectric susceptibilities and transverse charges of insulators

We reformulate, using tight-binding theory, the calculation of the bond polarizability, which leads to the dielectric susceptibility, and of the transverse charge, which gives the local dipole arising from the displacement of a single atom. A major change from earlier treatments is inclusion of empty p and d states on alkali metals and alkaline earths, using existing parameters, or values extrapolated from existing parameters. A second improvement is replacing a second-order expansion in interatomic coupling by more accurate contributions of individual bands based upon the special-point method. A third change is taking this special-point contribution to represent a local cluster of orbitals, which allows calculation of effects locally. The second two approximations are tested using a one-dimensional tight-binding chain which can be treated with, or without, these approximations. These changes bring the resulting predictions, based upon previously tabulated parameters, into reasonable accord with experiment for alkali halides, their divalent counterparts, and for a sample transition-metal compound, SrTiO3. In the course of this we also see how the d bands evolve into free-electron bands to the left of the transition-metal series.