Ab-initio calculation of phonon dispersion curves : accelerating q-point convergence

I present a scheme for describing the long-range interatomic force constants, which is more accurate than the procedure which is commonly used within plane-wave based density-functional perturbation-theory calculations. The scheme is based on the inclusion of a q -point grid which is denser in a restricted region around the center of the Brillouin zone than in the remaining parts, although the scheme is applicable to other regions. I have tested the validity of the procedure in the case of high-pressure body-centered tetragonal and simple hexagonal phases of bulk silicon.