The fully halogenated or hydrogenated B₁₂X₁₂^2- (X = H, F, Cl, Br and I) clusters are confirmed to be icosahedral. On the other hand, the bare B₁₂ cluster is shown to have a planar structure. A previous study showed that a transformation from an icosahedron to a plane happens when 5 to 7 iodine atoms are remained [P. Farràs et al., Chem. - Eur. J. 18, 13208-13212 (2012)]. Later, the transition was confirmed to be seven iodine atoms based on an infrared spectroscopy study [M. R. Fagiania et al., Chem. Phys. Lett. 625, 48-52 (2015)]. In this study, we investigated the effects of different halogen atoms on the opening of the B₁₂ icosahedral cage by means of density functional theory calculations. We found that the halogen elements do not have significant effects on the geometries of the clusters. The computed infrared (IR) spectra show similar representative peaks for all halogen doped clusters. Interestingly, we found a blue-shift in the IR spectra with the increase in the mass of the halogen atoms. Further, we compared the Gibbs free energies at different temperatures for different halogen atoms. The results show that the Gibbs free energy differences between open and close structures of B₁₂X₇^- become larger when heavier halogen atoms are presented. This interesting finding was subsequently investigated by the energy decomposition analysis.