Phonons and related crystal properties from density-functional perturbation theory

This article reviews the current status of lattice-dynamical calculations i n crystals, using density-functional perturbation theory, with emphasis on the plane-wave pseudopotential method. Several specialized topics are treat ed, including the implementation for metals, the calculation of the respons e to macroscopic electric fields and their relevance to long-wavelength vib rations in polar materials, the response to strain deformations, and higher -order responses. The success of this methodology is demonstrated with a nu mber of applications existing in the literature,