Ab initio studies of complexes (HCCHH2)-H-..., (FCCHH2)-H-..., HCCH... HLi, (FCCHHLi)-H-..., (HCCHHBeH)-H-..., (FCCHHBeH)-H-..., (HCCHHBeF)-H-..., and (FCCHHBeF)-H-... with (HH)-H-... intermolecular binding contacts were carried out up to the MP2/6-311++G(3df,3pd)/MP2/aug-cc-pVQZ level of theory. Binding energies extrapolated to the complete basis set (CBS) limit indicate that the results obtained at the MP2/6-311++G(3df,3pd) level of theory are almost saturated. An analysis of the geometrical and energetic parameters was performed, indicating that the mote strongly bonded complexes could be classified as X-H+delta...-deltaH-Y dihydrogen bonds, whereas the weaker ones may belong to the X-H(...)sigma category. In the first case, the electrostatic and exchange contributions are the most important energetic terms, whereas in the second case, the correlation term also makes a sizable contribution to the overall dimer stability. The atoms in molecules (AIM) theory was also applied to explain the nature of all of the complexes. A complete analysis of the different parameters of the complexes shows that the stronger complexes may be classified as H bonded and that the weaker complexes my be classified as van der Waals complexes. However, there is no evident borderline between them, which indicates the ambiguous nature of dihydrogen-bonded complexes or the arbitrary character of the definitions used to categorize the molecular complexes.