Electronic structure packages: Two implementations of the projector augmented wave (PAW) formalism

The projector augmented wave (PAW) formalism developed by Blöchl [Phys. Rev. B 50 (1994) 17953] is an accurate and efficient pseudopotential-like scheme for electronic structure calculations within density functional theory and is now implemented in several electronic structure codes. Some of these codes use an implementation of the formalism developed by Kresse et al. [Phys. Rev. B 59 (1999) 1758] which differs slightly from the original Blöchl formalism and which can lead to different electronic structure results. In this paper, we analyze and illustrate the difference between the Blöchl and Kresse PAW formulations.