  Nanocrystals of AgInS$_2$ demonstrate giant Stokes shifts ~ 1 eV, the nature
of which is still not clearly understood. We propose a theoretical model of
this phenomenon bringing together several different mechanisms previously
considered only separately. We take into account the contribution of
electron-electron interaction with the hybrid density functional theory, as
well as the renormalization of energy spectrum due to the electron-phonon
coupling. Furthermore, we consider the presence of at least one point defect
responsible for hole trapping and the formation of a localized polaron state.
Our numerical simulations show that photoluminescence due to the recombination
of a non-trapped electron and a trapped hole results in the giant Stokes shift
in AgInS$_2$ nanocrystal, which is in close agreement with the recent
experimental results.
