Lattice dynamics of the potential-induced breathing model: Phonon dispersion in the alkaline-earth oxides

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Abstract
We find the dynamical matrix for the potential-induced breathing (PIB) model for ionic solids, and calculate with no adjustable parameters the phonon-dispersion relations for the alkaline-earth oxides in the B1 structure. Our approach is similar to that of Gordon and Kim, in which the crystalline charge densities are estimated by overlapping atomic charge densities, which are then converted to energy by electron-gas approximations. It goes beyond the original Gordon-Kim model by allowing for spherical breathing of the atoms in response to the long-range potential, and beyond later refinements of the modified-electron-gas models by explicitly including the effects of PIB on the self-energy and the overlap interactions. This allows us to treat general deformations and lattice dynamics including the many-body PIB effects. PIB couples the long- and short-range forces in a way that is not present in any other lattice-dynamical model, since the spherical charge relaxation is coupled to the long-range electrostatic potential. PIB gives better agreement for the splitting of the longitudinal- and transverse-optic mode frequencies than is found with rigid-ion models, as well as much improved acoustic branches. PIB is a nonempirical model; no experimental data are used other than the values of fundamental constants such as Planck’s constant and the atomic masses.