Time-dependent density-functional approaches for excitons: the pros and cons of long-range corrected exchange-correlation kernels

Time-dependent density-functional theory (TDDFT) is, in principle, more efficient than the Bethe-Salpeter equation for calculating the optical properties of semiconductors and insulators. However, finding accurate exchange-correlation (xc) kernels for describing excitons is quite challenging: standard local and semilocal approximations lack the proper long-range behavior and do not produce bound excitons. This talk presents a systematic assessment of a class of long-range corrected (LRC) xc kernels which have shown promise for excitonic effects. It is found that no existing LRC kernel is capable of simultaneously producing good optical spectra and quantitatively accurate exciton binding energies for both semiconductors and insulators. We discuss strategies to improve the TDDFT treatment of excitons via semiempirical LRC xc kernels and screened hybrid approaches.