Linear response in a density-functional mixed-basis approach

We present a generalization of density-functional based linear-response calculations of lattice dynamical properties to the case of general energy-independent basis sets. The formalism accounts for the nonorthogonality and atom-position dependence of the basis functions, and is suited for the application of norm-conserving pseudopotentials. We have implemented this scheme in the framework of a mixed-basis pseudopotential technique, which allows an efficient treatment of localized electrons. The accuracy of the present scheme is demonstrated by calculations of the phonon dispersions of the $4d$ metals Y and Ag.