  We present an ab-initio density-functional-theory approach for calculating
electron-phonon interactions within the projector augmented-wave method. The
required electron-phonon matrix elements are defined as the second derivative
of the one-electron energies in the PAW method. As the PAW method leads to a
generalized eigenvalue problem, the resulting electron-phonon matrix elements
lack some symmetries that are usually present for simple eigenvalue problems
and all-electron formulations. We discuss the relation between our definition
of the electron-phonon matrix element and other formulations. To allow for
efficient evaluation of physical properties, we introduce a
Wannier-interpolation scheme, again adapted to generalized eigenvalue problems.
To explore the method's numerical characteristics, the temperature-dependent
band-gap renormalization of diamond is calculated and compared with previous
publications. Furthermore, we apply the method to selected binary compounds and
show that the obtained zero-point renormalizations agree well with other values
found in literature and experiments.
