A quantum chemistry study was carried out to investigate the strength and nature of halogen bond interactions in HXeH···XCCY complexes, where X = Cl, Br and Y = H, F, Cl, Br, CN, NC, C2H, CH3, OH, SH, NH2. Examination of the electrostatic potentials V(r) of the XCCY molecules reveals that the addition of substituents has a significant effect upon the most positive electrostatic potential on the surface of the interacting halogen atom. We found that the magnitude of atomic charges and multipole moments depends upon the halogen atom X and is rather sensitive to the electron-withdrawing/donating power of the remainder of the molecule. An excellent correlation was found between the most positive electrostatic potentials on the halogen atom and the interaction energies. For either HXeH···ClCCY or HXeH···BrCCY complexes, an approximate linear correlation between the interaction energies and halogens multipole moments are established, indicating that the electrostatic and polarization interactions are responsible for the stability of the complexes. According to energy decomposition analysis, it is revealed that the electrostatic interactions are the major source of the attraction in the HXeH···XCCY complexes. Furthermore, the changes in the electrostatic term are mainly responsible for the dependence of interaction energy on the halogen atom.