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, ${\text{H}}_2\text{O}$) and to ferromagnetic Fe in the body-centered cubic structure validate the theory.

Figure 1

(Color online) Calculated PAW phonon dispersions (solid lines) for ferromagnetic bcc-Fe compared to inelastic neutron scattering data at $T=295\text{K}$ (diamonds) (Ref. 35). Dispersions calculated with the US-PP of Ref. 37 at the theoretical lattice constant $\left(a_0=5.40\text{a}\text{.u}\text{.}\right)$ (dotted line) and at the lattice constant expanded to account for thermal effects $\left(a_0=5.42\text{a}\text{.u}\text{.}\right)$ (dot-dashed line) are also shown.