We describe the results of quantum chemical calculations (DFT and MP2) on the intermolecular interactions involving ammonia and halofluoromethanes. The equilibrium C-X ... N geometries are linear and the X ... N distances are shorter than the sum of the van der Waals radii. The binding energies of CF3X ... NH3 increase from 2 to 6 kcal/mol on following the sequence X = Cl, Br, I. Also, progressive introduction of F atoms in methyliodides raises the interaction energy from 2 kcal/mol for CH3I to 6 kcal/mol for CF3I. Therefore, halogen bonding involving perfluorinated alkylhalides and appropriate donors can be comparable in strength to strong hydrogen bonding. This agrees with recent experimental observations, that also the former can drive the construction of supramolecular edifices overcoming the low affinity between perfluorocarbons and hydrocarbons. Calculation of the atomic charges by the Atoms in Molecules method indicates that the charge-transfer contribution to the interaction energy is much less important for the present systems than for dihalogen-ammonia complexes.