Excitons in solids with time-dependent density-functional theory: the bootstrap kernel and beyond

Time-dependent density-functional theory (TDDFT) is an efficient method to describe the optical properties of solids. Lately, a series of bootstrap-type exchange-correlation (xc) kernels have been reported to produce accurate excitons in solids, but different bootstrap-type kernels exist in the literature, with mixed results. In this presentation, we review and clarify the status of the bootstrap kernels and present a new empirical TDDFT xc kernel to compute excitonic properties of semiconductors and insulators efficiently and accurately. We also discuss the recently proposed nonempirical screened exactexchange (SXX) approach for excitonic properties, which can be viewed as a first step towards an excitonic hybrid TDDFT functional. SXX performs well for bound excitons and continuum spectra in both small-gap semiconductors and large-gap insulators, with a computational cost much lower than that of solving the Bethe-Salpeter equation. This work was supported by NSF Grant DMR-1408904.