Strong and medium dihydrogen bonds of complexes for which binding energies amount to 10-20 kcal/mol were investigated. The calculations have been performed up to MP2/aug-cc-pVDZ//MP2/aug-cc-pVTZ level of theory for model systems of NH4+ . . . HBeH, NF3H+ . . . HBeH and NH4+ . . . HBeF. The results indicate that for the NF3H+ . . . HBeH complex there is a very short H (. . .) H intermolecular contact, much shorter than the sum of corresponding van der Waals radii. The analysis of geometrical and energetic data indicates partly covalent nature of H (. . .) H interaction. The characteristics of the bond critical points -the electron densities and their Laplacians - also confirm this conclusion. Additionally, the extrapolations of the values of interaction energies to the complete basis sets (CBSs) were performed here. (C) 2004 Elsevier B.V. All rights reserved.