Density functional perturbation theory within the projector augmented wave method

Density functional perturbation theory (DFPT) with ultrasoft pseudopotentials (US-PPs) is extended to the projector augmented wave (PAW) method. I show that minor modifications of the existing DFPT codes for US-PPs are sufficient for dealing with PAW. A few applications to small molecules (CO, H2O) and to ferro-magnetic Fe in the body-centered cubic structure validate the theory.