Comparison of long-range corrected kernels and range-separated hybrids for excitons in solids

The most accurate theoretical method to describe excitons is the solution of the Bethe-Salpeter equation in the GW approximation (GW-BSE). However, because of its computation cost, time-dependent density functional theory (TDDFT) is becoming the alternative approach to GW-BSE to describe excitons in solids. Nowadays, the most efficient strategy to describe optical spectra of solids in TDDFT is to use long-range corrected exchange-correlation kernels on top of GW or scissor-corrected energies. In recent years, a different strategy based on range-separated hybrid functionals started to be developed in the framework of time-dependent generalised Kohn-Sham density functional theory (TDGKSDFT). Here, we compare the performance of long-range corrected kernels with range-separated hybrid functionals for the description of excitons in solids. This comparison has the purpose to weight the pros and cons of using range-separated hybrid functionals, giving new perspectives for theoretical developments of these functionals. We illustrate the comparison for the case of Si and LiF, representative of solid state excitons.