  We present first-principles calculations of the quasiparticle band structures
of four isostructural semiconducting metal chalcogenides A$_2$B$_3$ (with A =
Sb, Bi and B = S, Se) of the stibnite family within the G$_0$W$_0$ approach. We
perform extensive convergence tests and identify a sensitivity of the
quasiparticle corrections to the structural parameters and to the semicore $d$
electrons. Our calculations indicate that all four chalcogenides exhibit direct
band gaps, if we exclude some indirect transitions marginally below the direct
gap. Relativistic spin-orbit effects are evaluated for the Kohn-Sham band
structures, and included as scissor corrections in the quasiparticle band gaps.
Our calculated band gaps are 1.5 eV (Sb$_2$S$_3$), 1.3 eV (Sb$_2$Se$_3$), 1.4
eV (Bi$_2$S$_3$) and 0.9 eV (Bi$_2$Se$_3$). By comparing our calculated gaps
with the ideal Shockley-Queisser value we find that all four chalcogenides are
promising as light sensitizers for nanostructured photovoltaics.
