Construction of orthonormal local orbitals and application to zinc-blende semiconductors

A $\overrightarrow{\mathrm{k}}$-space procedure for constructing orthonormal local orbitals (OLO's) has been examined in detail, and numerical applications to zinc-blende semiconductors have been carried out. The OLO's constructed from the minimum Gaussian basis are found to be localized, with amplitudes appreciable only within a radius of $2.5a$, where $a$ is the lattice constant. A Hamiltonian that retains only the term values and the first-neighbor interactions in the OLO basis yields a convergence of 0.1 eV for the bond energies but very poor results for the band structures. To achieve a 0.2-eV convergence for the valence bands and the first two conduction bands for all six III-V compounds studied, the interactions up to the fifteenth-neighbor shell have to be included. Comparison of matrix elements for different systems suggests that the Hamiltonian in OLO's for the zinc-blende compounds can be decomposed into a local part which characterizes the bonding of each individual system, and a common long-range part which scales as $\frac{1}{a^2}$. Application of this model and extension of the present work are also discussed.