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.
Gonze, X., & Finocchi, F. (2004). Pseudopotentials plane waves - Projector augmented waves: A primer. Physica Scripta : an international journal for experimental and theoretical physics, T109, 40-47. https://doi.org/10.1238/Physica.Topical.109a00040 (Original work published 2004)