Low-cost alternatives to the Bethe-Salpeter equation: Towards simple hybrid functionals for excitonic effects in solids

The Bethe-Salpeter equation (BSE) is the standard computational method for optical excitations in solids, including excitonic effects. In this paper we explore ways to reduce the computational cost of the BSE by simplifying the dielectrically screened Coulomb interaction: Instead of calculating the dielectric function from first principles, we replace it by a momentum-dependent model dielectric function or just by a single parameter. Combined with a semilocal exchange-correlation kernel, this defines an alternative class of hybrid functionals for solids within generalized time-dependent density-functional theory. We perform a systematic assessment of these simplified approaches and find that they yield optical absorption spectra and exciton binding energies of semiconductors and wide-gap insulators in close agreement with the standard BSE and with experiment. We also present applications to the perovskite material CsPbBr3 as an example of a more complex system.Y