Ghost states for separable, norm-conserving, Iab initioP pseudopotentials

Some years ago Kleinman and Bylander [Phys. Rev. Lett. 48, 1425 (1982)] proposed a fully nonlocal form of norm-conserving pseudopotentials. Its application reduces—if compared to other ab initio pseudopotentials—the computational effort to calculate potential matrix elements. However, if the procedure is not applied cautiously, it can destroy important chemical properties of the atoms. In this paper we identify the origin of this problem, and we give a theorem which tells if a ‘‘ghost’’ state occurs below the zero-node state of the atom. We also show how the difficulties can be avoided, i.e., how reliable, fully nonlocal, norm-conserving pseudopotentials can be obtained.