The information entropy based on the occupation numbers has been found to play a central role in a description of electron correlation within the density-matrix functional theory [i-DMFT, see Phys. Rev. Lett. 2022, 128, 013001]. In this article, the i-DMFT method is applied to predict potential energy curves, equilibrium bond lengths, and harmonic vibrational frequencies for the hydrogen halides: HF, HCl, and HBr. The results are compared with other theoretical calculations and experimental spectroscopic data.