Reformulation of generalized separable pseudopotentials

The possibility of constructing transferable and separable pseudopotentials for use in conventional electronic-structure calculations is examined and a scheme to derive fully separable (nonlocal) pseudopotentials from isolated atoms is described. The transferability of these potentials can be improved systematically by increasing the number of reference energies in the construction, as proposed previously by Bl\"ochl Phys. Rev. B 41, 5414 (1990). However, in the current scheme, the logarithmic derivatives of the pseudo-wave-functions at these reference energies are matched directly to the all-electron results as closely as possible, while keeping the nonlocal operator Hermitian. An example is shown for the sodium atom.