The fundamental idea of a “pseudopotential” is the replacement of one problem with another. The primary application in electronic structure is to replace the strong Coulomb potential of the nucleus and the effects of the tightly bound core electrons by an effective ionic potential acting on the valence electrons. A pseudopotential can be generated in an atomic calculation and then used to compute properties of valence electrons in molecules or solids, since the core states remain almost unchanged. Furthermore, the fact that pseudopotentials are not unique allows the freedom to choose forms that simplify the calculations and the interpretation of the resulting electronic structure. The advent of “ab initio norm-conserving” and “ultrasoft” pseudopotentials has led to accurate calculations that are the basis for much of the current research and development of new methods in electronic structure, as described in the following chapters.

Many of the ideas originated in the orthogonalized plane wave (OPW) approach that casts the eigenvalue problem in terms of a smooth part of the valence functions plus core (or core-like) functions. The OPW method has been brought into the modern framework of total energy functionals by the projector augmented wave (PAW) approach that uses pseudopotential operators but keeps the full core wavefunctions.