Since the discovery of the efficient luminescence of porous Si, a lot of effort has been devoted to the understanding of this phenomenon. Recently other Si-based luminescent materials have been synthesised, such as "nanocrystalline" Si/CaF2 multi-quantum wells (MQWs). A common feature of these nanocrystalline materials is that they contain small Si grains, passivated by hydrogen and/or oxygen. X-ray absorption measurements have recently suggested that the dimensions of the grains in the Si/CaF2 MQWs are smaller than 15 Angstrom. We have calculated, by linear combination of atomic orbitals, the electronic structure of different types of nanostructures, in order to compare our theoretical results to optical experiments performed on the MQWs, but also on porous Si. Here we present results on spherical Si clusters, Si (111) layers, and "nanocrystalline" layers, i.e. Si (111) layers divided into small grains. These nanocrystalline layers should model at least qualitatively the Si wells in the Si/CaF2 MQWs. The main result of our calculations is that the interaction between the wave functions of electrons belonging to adjacent grains in nanocrystalline materials decreases the band gap considerably, and has therefore to be included in the calculations.