First-principles norm-conserving pseudopotential with explicit incorporation of semicore states

We develop a pseudopotential generation scheme which provides, in a systematic way, first-principles, transferable, norm-conserving pseudopotentials which include, in addition to standard valence electrons, semicore electrons. The scheme improves the quality of the pseudopotential for some transition metal polyatomic systems where the semicore states can play an active role in the chemical bonding of those systems. The method is employed to generate pseudopotentials for Ti and Cu, taken as limiting examples of $3d$ transition metals, which are then used to study the structural properties of both homonuclear dimers and the bulk solid of these elements. The results obtained put in evidence the excellent agreement obtained in all cases between the pseudopotential results and benchmark all-electron calculations for the same systems.