The characteristics of low-valence derivatives (monohydrides and monofluorides) of boron, aluminum (group 13 of the periodic system), nitrogen, and phosphorus (group 15 of the periodic system) have been investigated. Several aspects of these derivatives have been studied such as the energy gap between their singlet and triplet configuration, their proton affinity in the different parts of the molecule, and their ability as hydrogen bond accepters. The geometries and energies of all the monomers and complexes have been fully optimized using a hybrid method (B3LYP) and the second-order Moller-Plesset (MP2) levels with the 6-311++G** basis set. In addition, the G2 and MCSCF methodologies were also used. The natural population analysis and the natural bond orbital analysis have been used to evaluate the charge transfer and second-order interaction energies, respectively. Topological properties of the electron density have been characterized using the atoms in molecules methodology. Our results show surprisingly strong hydrogen bonds for the boron derivatives. By use of principal component analysis, it was possible to express, the interaction energy as a function of the acidity or basicity and the softness of the molecules involved in the complexes following Pearson's model. As well, it was found, by the natural bond orbital analysis, that the charge is transferred by a n(HBA) --> sigma*(HBD) donor-acceptor interaction, similar to standard hydrogen bonds. Moreover, different correlations have been found between the interaction energies and the second-order interaction energies or the charge-transfer calculated for both of the parameters, from the natural bond orbital analysis. The slopes of those correlations vary with the group of the periodic system to which the accepting atom belongs.