Electrons in matter can be broadly categorised into two types - core electrons, which are strongly localised in the closed inner atomic shells, and valence electrons, which exist outside the core. Unfortunately, a plane-wave basis set is generally not suitable for describing electron wavefunctions since a prohibitively large number would be required to accurately describe the oscillations in the core regions which maintain orthogonality between valence and core electrons. As a result, all-electron plane-wave calculations demand a huge computational expense that is simply not practical. However, by realising that the electronic structure of the core-electrons remains largely unchanged in different chemical environments, and is also of minimal interest generally, the problems relating to the core-electrons can be overcome by use of the pseudopotential approximation [25,26,27]
The pseudopotential approximation replaces the strong ionic potential in the core region, by a weaker pseudopotential . The corresponding set of pseudo-wavefunctions and the all-electron wavefunctions are identical outside a chosen cutoff radius and so exhibit the same scattering properties, but does not possess the nodal structure that cause the oscillations inside , which means they can now be described with a reasonable number of plane-waves. A schematic illustration of the pseudopotential concept is shown in Fig. 1.1.