Time-dependent density-functional theory for periodic solids: assessment of excitonic exchange–correlation kernels

Abstract

We review recent theoretical and computational developments in time-dependent density-functional theory (TDDFT) for periodic insulators and semiconductors. To capture excitonic effects within a linear-response TDDFT framework requires using exchange–correlation (xc) kernels with a proper long-range behavior, which can be efficiently modeled with a class of so-called long-range corrected xc kernels. While attractive from a computational standpoint, these xc kernels have their limitations and require judicious use. We review the pros and cons of various xc kernels in the literature, and discuss an empirical scaling approach to obtain accurate exciton binding energies with TDDFT. We also discuss generalized TDDFT approaches for excitons using hybrid functionals.