Excitons in solids with time-dependent density-functional theory: the long-range corrected kernel and beyond

Time-dependent density-functional theory (TDDFT) can describe the optical properties of solids in principle more efficiently than the Bethe-Salpeter equation, but the construction of good approximations to the exchange-correlation (xc) kernel is challenging. Since the long-range ($ -1/q^2 $) behavior is a key for producing bound excitons in solids, many long-range corrected (LRC) xc kernels have been proposed, among them the so-called "bootstrap" kernel. However, closely related LRC-type kernels have been reported in the literature to yield conflicting results. Here, we reveal the origin of the confusion, present a new choice-free LRC kernel which yields exciton binding energies of semiconductors and insulators accurately and efficiently, and discuss the general limitations of LRC-type xc kernels. This work was supported by NSF Grant DMR-1408904