Linear methods for fully relativistic energy-band calculations

Abstract

The linear augmented plane wave (LAPW) method of Takeda and Kubler (1979) and the augmented spherical wave (ASW) method of Williams and others (1979) are extended to the relativistic case. The relativistic LAPW and ASW methods make use of two eigenfunctions of Dirac's equation with a spherically symmetric effective one-particle potential. In the latter method, furthermore, the total angular momentum representation for the spin-orbit coupling is used in the expansion of wavefunctions describing electronic states. In both methods, the augmentation is applied to both large and small components of wavefunctions in bispinor form. By this method of the augmentation, radial derivatives of radial wavefunctions are made continuous at the muffin-tin sphere surface. Formulae are given for self-consistent relativistic LAPW and ASW methods which can be numerically treated just like the nonrelativistic counterparts.