Green’s-function approach to linear response in solids

We present a new scheme to study the linear response of crystals which combines the advantages of the dielectric-matrix and supercell (‘‘direct’’) approaches yet avoids many of their drawbacks. The numerical complexity of the algorithm is of the same order as that of a self-consistent calculation for the unperturbed system. The method is not restricted to local perturbations as the dielectric-matrix one nor to short wavelengths as the direct one. As an application, we calculate the long-wavelength optical phonons in Si and GaAs, both transverse and longitudinal, using norm-conserving pseudopotentials, and without any use of supercells.