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

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. 15a₀ to 1. 35a₀ 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.