Application of time-dependent density-functional theory to the dielectric function of various nonmetallic crystals

Abstract

The dielectric function of a range of nonmetallic crystals of various lattice types is studied by means of a real-space and full-potential time-dependent density-functional method within the adiabatic local-density approximation. Results for the dielectric constant ${\ensuremath{\epsilon}}_{\ensuremath{\infty}}$ (at optical frequencies) are given for crystals in the sodium chloride, the fluoride, the wurtzite, the diamond, and the zinc-blende lattice structure. The frequency-dependent dielectric function $\ensuremath{\epsilon}(\ensuremath{\omega})$ for the crystals in the diamond and zinc-blende lattice structure are also presented. We compare our calculated results with experimental data and other theoretical investigations. Our results for the dielectric constants ${\ensuremath{\epsilon}}_{\ensuremath{\infty}}$ and the dielectric functions $\ensuremath{\epsilon}(\ensuremath{\omega})$ are in good agreement with the experimental values. The accuracy of the results is comparable to the one which is commonly found for time-dependent density-functional theory calculations on molecular systems. On average we find a deviation of 4--5 % from experiment for the group IV and III-V compounds in the wurtzite, zinc-blende and diamond lattice structure, 8--9 % for the II-VI and I-VII compounds in the zinc-blende and sodium chloride lattice structure, and up to 14% deviation for the fluoride lattice structure. The spectral features of the dielectric functions $\ensuremath{\epsilon}(\ensuremath{\omega})$ appear in the calculations at somewhat too low energies compared to experiment.