  We present a theoretical study of the formation of self-trapped excitons
(STEs) and the associated broadband emission in metal-halide perovskites
Cs$_4$SnBr$_6$ and Cs$_2$AgInCl$_6$, using time-dependent density functional
theory (TDDFT) with the dielectric-dependent hybrid (DDH) functional. Our
approach allows for an accurate description of the excitonic effect and
geometry relaxation in the electronic excited states and yields optical gap,
STE emission energy, and emission spectra in reasonable agreement with
experiments. We point out the significance of considering geometry relaxations
in the electronic excited state by showing that the exciton-phonon coupling
computed in the ground-state atomic geometry is insufficient to describe the
physical properties of STEs. Overall, we find that TDDFT with the DDH hybrid
functional is a suitable approach for the study of the formation of STEs in
perovskite and provides insights for designing metal-halide perovskites with
tailored emission properties.
