Computation of phonon spectra from density-functional perturbation theory in the projector augmented-wave approach

The density-functional perturbation theory expressions have been derived within the projector augmented-wave formalism (PAW) and compared to those found in the ultrasoft pseudopotential framework~[1]. They have been recently implemented in the \textsc{abinit} package~[2] in the case of perturbations of the atomic-displacement type. We summarize the key points of this implementation: The variational and non-variational forms of the 2nd-order total energy changes are detailed. The resolution of the variational principle by a generalized Sternheimer equation is explained (the 1st-order wave-function change is found with a band-by-band conjugate gradient algorithm). We focus on some difficulties: metallic electronic occupations, response to incommensurate perturbations of periodic systems {\ldots} Results on pure compounds are presented; a comparison with results from pseudopotentials approach is performed in order to highlight the effect of the PAW methodology and its accuracy. [1] Audouze, Jollet, Torrent and Gonze. Phys. Rev. B \textbf{73}, 235101 (2006); \textbf{78}, 035105 (2008) [2] \textit{http://www.abinit.org}.