Time-Dependent (Current) Density Functional Theory for Periodic Systems

In this article we review time-dependent density functional theory for calculating the static and frequency-dependent dielectric function ε(ω) of nonmetallic crystals. We show that a real-space description becomes feasible for solids by using a combination of a lattice-periodic (microscopic) scalar potential with a uniform (macroscopic) electric field for the description of the effective one-electron system. We treat the time-dependent fields as perturbations in a periodic structure calculation. The induced density and microscopic potential can be obtained self-consistently for fixed macroscopic field by using linear response theory in which Coulomb interactions and exchange-correlation effects are included. The dielectric function can then be obtained from the induced current. We obtained ε(ω) for a wide variety of nonmetallic crystals within the adiabatic local density approximation (ALDA) in good agreement with experiment. In particular in the low-frequency range no adjustment of the band gap obtained within the local density approximation (LDA) seems to be necessary. Relativistic effects on the dielectric response have been found to be important for a few semimetals that have inverted bandstructures within the LDA. Exchange-correlation effects beyond the ALDA have been treated by a polarization-dependent functional for the effective electric field, with improved dielectric functions as result