On the microscopic theory of electronic contributions to lattice dynamics of anharmonic crystals

A formalism is set up to study the electronic contribution to the phonon dynamics in an arbitrary crystal, conducting or insulating, without assuming small ionic oscillations. Therefore, in contrast to a harmonic Born-Oppenheimer approximation, such an approach allows for renormalization effects due to phonon-phonon interaction over the complete temperature range of the solid phase. The “weak coupling” approximation between nuclei and electrons is shown to be sufficient in order to obtain the dynamical matrix microscopically in terms of the complete inverse dielectric function of the electrons.