Non-Muffin-Tin Augmented-Plane-Wave Method for Diamond and Zinc-Blende Lattices

Abstract

The augmented-plane-wave method is adapted to the diamond and zinc-blende lattices by including both "nonflat" and "nonspherical" corrections to the usual "muffin-tin" potential. The former are treated exactly while the latter are treated perturbatively. The method is tested for silicon where "nonflat" corrections are as large as 3.4 eV with "nonspherical" corrections less than 0.4 eV. Plane wave convergence is superior to the orthogonalized-plane-wave method. The atomic-sphere radius was varied from $2.15a_0 \mathrm{to} 1.35a_0$ with energy changes of less than 0.03 eV. Nonflat matrix elements are easily computed by use of a spherical-harmonic expansion of the potential due to point charges. Multipole-lattice-sum coefficients are given for the fcc, diamond, and zinc-blende lattices.