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We present fully ab initio calculations of van der Waals coefficients for two different situations: (i) the interaction between hydrogenated silicon clusters and (ii) the interactions between these nanostructures and a nonmetallic surface (a silicon or a silicon carbide surface). The methods used are very efficient and allow the calculation of systems containing hundreds of atoms. The results obtained are further analyzed and understood with the help of simple models. These models can be of interest for molecular-dynamics simulations of silicon nanostructures on surfaces, where they can give a very fast yet sufficiently accurate determination of the van der Waals interaction at large separations.