Low-cost alternatives to the Bethe-Salpeter equation: a simple hybrid functional for excitonic effects in solids*

The Bethe-Salpeter equation (BSE) is the standard computational method for optical excitations in solids, including excitonic effects. We 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 a new hybrid functional for solids within generalized TDDFT. 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 standard BSE. We also present applications to more complex systems.