A transferable representation of the induced multipoles in ionic crystals

Electronic structure calculations of the induced dipole and quadrupole moments on a fluoride ion at low symmetry sites in a model crystalline environments are described. The results are used to characterize the short range contributions to the induced multipoles on the F^? ion that arise from overlap between the wavefunctions of the ions. These are represented by general functions of the positions of the surrounding ions, suitable for use in a computationally tractable simulation model. The present calculations are designed to test the transferability to other classes of materials of this representation which, to date, largely has been deduced from calculations on distorted alkali halide crystals. First, the induced multipoles in mixed crystals of the alkali halides are considered, in order to check that they are predicted reliably by combining the representations deduced for the corresponding pure materials. Second, polarization effects in the alkaline earth fluorides MgF₂, and CaF₂, in a locally distorted fluorite crystal structure are examined. It is found that the material-specific parameters in the representation are related through simple functions of the ionic radii. This relationship holds between MgF₂, and CaF₂, in the fluorite structure, but also extends to the alkali fluorides previously studied. In order to illustrate the significance of polarization effects, the polarization model for CaF₂ is combined with an ab initio pair potential for the repulsion and dispersion interactions and used in a molecular dynamics simulation. Inclusion of the polarization term improves greatly the calculated phonon frequencies in the crystal.