DYNAMICAL MATRICES, BORN EFFECTIVE CHARGES, DIELECTRIC PERMITTIVITY TENSORS, AND INTERATOMIC FORCE-CONSTANTS FROM DENSITY-FUNCTIONAL PERTURBATION-THEORY

Starting from the knowledge of first-order changes of wave functions a nd density with respect to small atomic displacements or infinitesimal homogeneous electric fields within the density-functional theory, we write the expressions for the diagonal or mixed second-order derivativ es of the total energy with respect to these perturbations: dynamical matrices for different wave vectors, Born effective-charge tensors and electronic dielectric permittivity tensors. Interatomic force constan ts and the phonon-band structure are then obtained by computing the Fo urier transform of dynamical matrices on a regular mesh of wave vector s, with an eventual, separate treatment of the long-range dipole-dipol e interaction. The same ingredients also allow one to compute the low- frequency response of the crystal to homogeneous electric fields.