First-principles calculations of spin-orbit splittings in solids using nonlocal separable pseudopotentials

We have extended the considerable computational advantages of separable, nonlocal pseudopotentials to the calculation of spin-orbit splittings in solids. We write the total ionic pseudopotential as a sum of scalar relativistic and spin-orbit contributions, where each term can be represented by a fully nonlocal potential of the separable Kleinman-Bylander (KB) form. The scalar term, which reduces to the standard KB expression for the pseudopotential in the limit where one can neglect spin-orbit interactions, is used in the local-density approximation to calculate zeroth-order electronic properties in the usual way, and spin-orbit splittings are calculated to first order using perturbation theory. We have tested our procedure by calculating the spin-orbit splittings at high symmetry points of the zinc-blende III-V semiconductors GaAs, InAs, AlSb, GaSb, and InSb. The calculated splittings in all cases are in excellent agreement with those obtained from other first-principles calculations and with experiment. Since our spin-orbit operator is fully nonlocal in both radial and angular coordinates, a considerable reduction in the labor required to calculate matrix elements has been achieved. This makes our approach ideally suited for use with ab initio molecular-dynamics techniques, which currently have become the methods of choice for exploring the electronic and structural properties of solids. © 1993 The American Physical Society.