Section 2.2.11.3. The pseudo-potential schemes

In many respects, core electrons are unimportant for determining the stability, structure and low-energy response properties of crystals. It is a well established practice to modify the one-electron part of the Hamiltonian by replacing the bare nuclear attraction with a pseudo-potential (PP) operator, which allows us to restrict our calculation to the valence electrons. The PP operator must reproduce screened nuclear attractions, but must also account for the Pauli exclusion principle, which requires that valence orbitals are orthogonal to core ones. The PPs are not uniquely defined and thus one seeks to satisfy the following characteristics as well as possible:

There are many versions of the PP method (norm-conserving, ultrasoft etc.) and the actual accuracy of a calculation is governed by which is used. For standard applications, PP techniques can be quite successful in solid-state calculations. However, there are cases that require higher accuracy, e.g. when core electrons are involved, as in high-pressure studies or electric field gradient calculations (see Section 2.2.15), where the polarization of the charge density close to the nucleus is crucial for describing the physical effects properly.