Electronic structure methods: Augmented Waves, Pseudopotentials and the   Projector Augmented Wave Method
  The main goal of electronic structure methods is to solve the Schroedinger equation for the electrons in a molecule or solid, to evaluate the resulting total energies, forces, response functions and other quantities of interest. In this paper we describe the basic ideas behind the main electronic structure methods such as the pseudopotential and the augmented wave methods and provide selected pointers to contributions that are relevant for a beginner. We give particular emphasis to the Projector Augmented Wave (PAW) method developed by one of us, an electronic structure method for ab-initio molecular dynamics with full wavefunctions. We feel that it allows best to show the common conceptional basis of the most widespread electronic structure methods in materials science. 
Peter E. Bl\"ochl, Johannes Kaestner and Clemens J. Foerst