The chiral self-discrimination of twelve molecules showing axial chirality has been studied. They included peroxides, hydrazines, carboxylic acids, amides, and allenes. The homo and heterochiral dimers of the selected compounds, that present two hydrogen bonds, have been studied by means of density functional theory (B3LYP/6-31+G**) and ab initio (MP2/6-31+G** and MP2/6-311++G**) methods. The energetic differences found for the complexes of each compound have been rationalized based on their electron density maps and the natural bond orbital analysis. In some cases, intermolecular oxygen-oxygen interactions have been found and interpreted as additional stabilizing contacts.