The predictions of an “extended” ionic interaction model for the phonons and other properties of crystalline MgO are considered. In the extended model, the polarization interactions resulting from the dipoles and quadrupoles induced on the oxide ions by both Coulombic and short-range interactions with other ions are explicitly represented. Furthermore, the shapes of the oxide ions, as perceived through the short-range repulsive interactions with their immediate neighbors, are allowed to respond to their instantaneous coordination environment. Shape deformations of spherical (breathing), dipolar and quadrupolar symmetry are allowed. Each of these many-body effects is independently represented in the simulation model, so that the effect of each term on observed properties can be separately evaluated. It is shown how the polarization and breathing effects may be directly parametrized from ab initio electronic structure calculations. By consideration of the symmetry of the individual phonons at high symmetry points, it can be shown that the remaining effects may contribute only to particular phonons. Consequently, they may be assigned values in an unambiguous manner. The importance of each many-body effect for the different phonon branches is clearly delineated.

Rowley, A. J., J̈emmer, P., Wilson, M., & Madden, P. A. (1998). Evaluation of the many-body contributions to the interionic interactions in MgO. The Journal of Chemical Physics, 108(24), 10209–10219.