Real-space-partitioned separable pseudopotential

It is known that the conventional separable pseudopotential proposed by Kleinman and Bylander [Phys. Rev. Lett. 48, 1425 (1982)] does not work for some atoms, if the d component of the pseudopotential is chosen to be, in order to save computational time, the local part of the pseudopotential. We thus propose another separable pseudopotential: First, the nonlocal pseudopotential for which the above-mentioned approximation does not work well is partitioned into two parts in the real space and, second, a separable potential is then constructed for each partitioned potential. We apply this partitioned-potential method to Ga and Ge pseudopotentials and find that the partitioned-potential method provides accurate results and is not time consuming.