We present calculations of the one- and two-particle excitations in silicon
nanocrystals. The one-particle properties are handled in the GW approximat
ion, and the excitonic gap is obtained from the Bethe-Salpeter equation. We
develop a tight binding version of these methods to treat clusters up to 2
75 atoms. The self-energy and Coulomb corrections almost exactly cancel eac
h other for crystallites with radius larger than 0.6 nm. The result of this
cancellation is that one-particle calculations give quite accurate values
for the excitonic gap of crystallites in the most studied range of sizes.