Wannier interpolation scheme for phonon-induced potentials:: Application to bulk MgB2, W, and the (1x1) H-covered W(110) surface

We present an efficient scheme for calculating phonon-induced potentials with high precision. The method exploits the idea of Wannier functions applied to the change of the electron potentials, allowing for an accurate evaluation of coupling constants for arbitrary wave vectors. In order to demonstrate the capability of the method, we include three examples: bulk MgB2, bcc tungsten, and the hydrogen covered 1x1 W(110) surface. For these cases we calculate the momentum resolved (k dependent) Eliashberg function for a selected set of k points and the electron-phonon mass enhancement parameter lambda(k).