Optics of semiconductors from meta-generalized-gradient-approximation-based time-dependent density-functional theory

We calculate the optical spectra of silicon, germanium, and zinc blende semiconductors in the adiabatic time-dependent density-functional formalism, making use of kinetic energy density-dependent meta-generalized-gradient-approximation (GGA)] exchange-correlation functionals. We find excellent agreement between theory and experiment. The success of the theory on this notoriously difficult problem is traced to the fact that the exchange-correlation kernel of meta-GGA supports a singularity of the form α/q(2) (where q is the wave vector and α is a constant), whereas previously employed approximations (e.g., local-density and generalized gradient approximations) do not. Thus, the use of the adiabatic meta-GGA opens a new path for handling the extreme nonlocality of the time-dependent exchange-correlation potential in solid-state systems.