Microscopic Theory of Dielectric Screening and Lattice Dynamics in the Wannier Representation. I. Theory

The microscopic quantum-mechanical expressions for the dielectric screening matrix and for the electronic contribution to lattice dynamics are derived in terms of generalized Wannier functions. The Wannier representation makes practical an inversion of the dielectric matrix within the random-phase approximation and thus allows for an explicit calculation of local field effects in the dielectric response. This result leads, with the help of the dynamical matrix of an electron-nucleus system, to a multipole model of lattice dynamics. The formalism can be applied to conducting as well as to nonconducting crystals, and in this way provides a possibility to examine the relationship between the various methods and models used to describe lattice vibrations in all these solids.