  Excitons are bound electron-hole pairs that dominate the optical response of
semiconductors and insulators, especially in materials where the Coulomb
interaction is weakly screened. Light absorption (including excitonic effects)
has been studied extensively using first-principles calculations, but methods
for computing radiative recombination and light emission are still being
developed. Here we show a unified ab initio approach to compute exciton
radiative recombination in materials ranging from bulk crystals to
nanostructures and molecules. We derive the rate of exciton radiative
recombination in bulk crystals, isolated systems, and in one- and
two-dimensional materials, using Fermi's golden rule within the Bethe-Salpeter
equation approach. We present benchmark calculations of radiative lifetimes in
a GaAs crystal and in gas-phase organic molecules. Our work provides a general
method for studying exciton recombination and light emission in bulk,
nanostructured and molecular materials from first principles.
