Pseudopotentials Plane Waves?Projector Augmented Waves: A Primer

We review the basic concepts underlying the use of plane wave basis sets for the implementation of Density Functional Theory, including pseudopotentials (norm-conserving or ultra-soft pseudopotentials), or their refinement, the projector-augmented wave method. Explicit plane wave expressions for the Hamiltonian and electronic energy based on norm-conserving pseudopotentials are presented.