The occurrence of dihydrogen bonds in the complexes and dimers of complexes involving the main group elements is systematically investigated. The complexes of LiH, BH3, and AlH3 with HF, H2O, and NH3 as well as dimers of these complexes are studied using ab initio calculations at the MP2 level. The complexes having H ... H bonding are observed; however, in most of the cases they are not minima on their PES. The [H2OLiH](2) has a compact C-2h structure with a large dimerization energy where the H ... H bond exhibits features of a hydrogen bridge. The H ... H bond energy in [BH3HF](2), [BH3H2O](2), and [AlH3H2O](2) is analogous to the conventional moderate or weak hydrogen bond. The bonding features of these complexes and their dimers are analyzed using electron density topography. The structures of dimers are rationalized using molecular electrostatic potential maps. The decomposition analysis of interaction energies of dimers reveals the predominance of electrostatic contribution followed by charge transfer and polarization.