Symmetrized Relativistic Augmented-Plane-Wave Method: Gray Tin and the Warped Muffin-Tin Potential

A symmetrized form of the relativistic augmented-plane wave (RAPW) method is described. This symmetrized relativistic APW technique (SRAPW) uses the double-space-group projection operators to greatly reduce the size of the Hamiltonian matrix that must be dealt with on symmetry points and lines. This enables one to obtain better convergence than can be obtained with the unsymmetrized RAPW technique and identifies the symmetry properties of the states found. The technique has also been generalized to include the effects of a nonconstant potential outside the muffin-tin spheres. The SRAPW method is then applied to gray tin to test a number of potential approximations, including non-self-consistency and the treatment of exchange as well as the various features of the muffin-tin approximation to the model potential. The results show that, of the terms left out of the muffin-tin approximation to the model potential, the additional warping of the potential outside the muffin-tin spheres has the most significant effect.