Charge densities and quasi-ions in lattice dynamics

In the preceding paper we have proposed a decomposition of the total charge density of a crystal into contributions which can be uniquely assigned to the individual ions or sublattices. This decomposition leads naturally to a definition of ``quasi-ions'' and a description of the chemical bonds in terms of partial charge densities of the respective ions. In the present work the partial charge distributions are used for achieving a decomposition of the displacement-induced charge-density variations into two parts: one which rigidly follows the motion of the ions and another one that distorts during the motion. The relevant quantities are expressed in terms of linear-response theory and their influence on the phonon dispersion and the force constants is discussed. The decomposition of the phonon-induced charge-density variations is performed quantitatively for Si and it is shown that the distortion part is small. The results lead to a new class of models for lattice dynamics based on the partial charge densities.