Calculated effects of charge fluctuations on the phonon dispersion of YBa2Cu3O6 and YBa2Cu3O7. I. The model

In this paper we present a microscopic model that allows us to study the effects of charge fluctuations on the phonon dispersion of the high-temperature superconductor YBa₂Cu₃O₇ and its insulating counterpart, YBa₂Cu₃O₆. An ab-initio rigid-ion model with pair potentials calculated by the Gordon-Kim method from the free-ion charge densities is used as a reference system. Starting from this reference system, charge fluctuations at the copper- and oxygen ions are introduced into the model. The charge fluctuations are treated as adiabatic degrees of freedom in a non-phenomenological way. The parameters entering the model are estimated consistently with the reference system from first principles rather than refering to the experimentally determined phonon dispersion. In addition to the metallic behavior (appropriate to YBa₂Cu₃O₇) obtained in this way, insulating behavior (appropriate to YBa₂Cu₃O₆) is simulated by requiring the polarizability function to fulfill a corresponding long. wavelength sum rule. Screened site-potential changes are defined that (besides the charge fluctuations) constitute a qualitative measure of the electron-phonon-interaction potential. Furthermore we investigate the long-wavelength limiting behavior of the most important quantities occurring in our formalism. We derive formulae that allow us to calculate the contribution of the charge fluctuations to the macroscopic dielectric constant and the transverse effective charges in the insulating phase.