Density-functional perturbation theory with ultrasoft pseudopotentials

Density-functional perturbation theory for lattice dynamics is presented in a general framework which includes Vanderbilt's ultrasoft pseudopotentials, nonlinear exchange and correlation core corrections, the local spin-density approximation, and spin-polarized generalized gradient corrections. The dynamical matrices of metallic and of insulating solids are calculated at arbitrary wave vectors. The method is applied to the Cu(001) surface and to the nitrobenzene molecule