Introduction

For the norm-conserving pseudopotentials introduced in Section 3.1.5 and discussed in detail in Section 4.2, the all-electron wave function gets replaced inside some core radius by a soft, nodeless, pseudo wave function. The crucial restriction, however, is that the pseudo wave function must have the same norm as the all-electron wave function within the chosen core radius; note that the pseudo and all-electron wave functions are identical outside the core radius. As shown previously, good transferability requires a core radius around the outermost maximum of the all-electron wave function, because only then are the charge distribution and moments of the all-electron wave function well reproduced by the pseudo wave functions. Therefore, for elements with strongly localized orbitals (like first row, 3d, and rare earth elements), the resulting pseudopotentials require large plane wave basis sets. To avoid large basis sets, compromises are often made by increasing the core radius significantly beyond the outermost maximum of the all-electron wave function. However, this does not usually lead to a satisfactory solution because the transferability is always adversely affected when the core radius is increased, and for any new chemical environment, additional tests are required to establish the reliability of such soft norm-conserving pseudopotentials. Similarly, compromises concerning the plane wave cutoff are easily made in these cases at the expense, however, of sacrificing accuracy and reliability.

An elegant solution to this problem was proposed by Vanderbilt [1548]. In his method, the norm-conservation constraint is relaxed and to make up for the resulting charge deficit, localized atom-centered augmentation charges are introduced.