Halogen hydride interactions between Z-X (Z = CN, NC and X = F, Cl, Br) as halogen donor and H Mg-Y (Y = H, F, Cl, Br, CH3) as electron donor have been investigated through the use of Becke three-parameter hybrid exchange with Lee Yang Parr correlation (B3LYP), second-order Moller -Plesset perturbation theory (MP2), and coupled-cluster single and double excitation (with triple excitations) [CCSD(T)] approaches. Geometry changes during the halogen hydride interaction are accompanied by a mutual polarization of both partners with some charge transfer occurring from the electron donor subunit. Interaction energies computed at MP2 level vary from -1.23 to -2.99 kJ/mol for Z-F center dot center dot center dot H-Mg-Y complexes, indicating that the fluorine interactions are relatively very weak but not negligible. Instead, for chlorine- and bromine-containing complexes the interaction energies span from 5.78 to a maximum of -26.42 kJ/mol, which intimate that the interactions are comparable to conventional hydrogen bonding. Moreover, the calculated interaction energy was found to increase in magnitude with increasing positive electrostatic potential on the extension of Z X bond. Analysis of geometric, vibrational frequency shift and the interaction energies indicates that, depending on the halogen, CN-X center dot center dot center dot H interactions are about 1.3-2.0 times stronger than NC-X center dot center dot center dot H interactions in which the halogen bonds to carbon. We also identified a clear dependence of the halogen hydride bond strength on the electron-donating or -withdrawing effect of the substituent in the H-Mg-Y subunits. Furthermore, the electronic and structural properties of the resulting complexes have been unveiled by means of the atoms in molecules (AIM) and natural bond orbital (NBO) analyses. Finally, several correlative relationships between interaction energies and various properties such as binding distance, frequency shift, molecular electrostatic potential, and intermolecular density at bond critical point have been checked for all studied systems.