Optimized norm-conserving Vanderbilt pseudopotentials

Fully nonlocal two-projector norm-conserving pseudopotentials are shown to be compatible with a systematic approach to the optimization of convergence with the size of the plane-wave basis. A reformulation of the optimization is developed, including the ability to apply it to positive-energy atomic scattering states and to enforce greater continuity in the pseudopotential. The generalization of norm conservation to multiple projectors is reviewed and recast for the present purposes. Comparisons among the results of all-electron and one- and two-projector norm-conserving pseudopotential calculations of lattice constants and bulk moduli are made for a group of solids chosen to represent a variety of types of bonding and a sampling of the periodic table.