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We introduce a general method which allows reconstruction of electronic bandstructure of nanocrystals from ordinary real-space electronic structurecalculations. A comprehensive study of band structure of a realisticnanocrystal is given including full geometric and electronic relaxation withthe surface passivating groups. In particular, we combine this method withlarge scale density functional theory calculations to obtain insight into theluminescence properties of silicon nanocrystals of up to 3 nm in size dependingon the surface passivation and geometric distortion. We conclude that the bandstructure concept is applicable to silicon nanocrystals with diameter largerthan $\approx$ 2 nm with certain limitations. We also show how perturbationsdue to polarized surface groups or geometric distortion can lead toconsiderable moderation of momentum space selection rules.

Theoretical analysis of electronic band structure of 2-to-3-nm Si nanocrystals