Dihydrogen-bonded systems MH· · ·HX (M Li, Na and X F, Cl, Br) have been studied at HF, DFT/B3LYP and MP2 level of theory. Some of these complexes are found to be stationary points with two degenerated imaginary frequencies, while the others are considered as minima in the potential energy surface (PES). In order to eliminate the basis set superposition error (BSSE) and have a better description of such stationary points, counterpoise correction (CP) has been applied to the whole surface, obtaining the CP-corrected PES for each system. These BSSE-free PES's present a new minimum with different topology, i.e. number of imaginary frequencies. Two different groups of complexes can be distinguished, depending on dihydrogen bond strength and electrostatic or covalent contributions. To analyse these interactions, calculations in the framework of atoms in molecules (AIM) theory have been performed, as well as a discussion about charge transfer.KEY WORDS: Dihydrogen bond (DHB); basis set superposition error (BSSE); counterpoise correction (CP); atoms in molecules (AIM) theory.