Assessment of long-range-corrected exchange-correlation kernels for solids: accurate exciton binding energies via an empirically scaled Bootstrap kernel

In time-dependent density-functional theory, a family of exchange-correlation kernels, known as long-range-corrected (LRC) kernels, have shown promise in the calculation of excitonic effects in solids. We perform a systematic assessment of existing static LRC kernels (empirical LRC, Bootstrap, and jellium-with-a-gap model) for a range of semiconductors and insulators, focusing on optical spectra and exciton binding energies. We find that no LRC kernel is capable of simultaneously producing good optical spectra and quantitatively accurate exciton binding energies for both semiconductors and insulators. We propose a simple and universal, empirically scaled Bootstrap kernel which yields accurate exciton binding energies for all materials under consideration, with low computational cost.