The present study aims at a fundamental understanding of bonding characteristics of the C-Br and O-Br bonds. The target molecular systems are the isomeric CH3OBr/BrCH2OH system and their decomposition products. Calculations of geometries and frequencies at different density functional theory (DFT) and Hartree-Fock/MOller-Plesset (HF/MP2) levels have been performed. Results have been assessed and evaluated against those obtained at the coupled cluster single-double (Triplet) (CCSD(T)) level of theory. The characteristics of the C-Br and O-Br bonds have been identified via analysis of the electrostatic potential, natural bond orbital (NBO), and quantum theory of atoms in molecules (QTAIM). Analysis of the electrostatic potential (ESP) maps enabled the quantitative characterization of the Br sigma-holes. Its magnitude seems very sensitive to the environment and the charge accumulated in the adjacent centers. Some quantum topological parameters, namely delta(2), ellipticity at bond critical points and the Laplacian bond order, were computed and discussed. The potential energy function for internal rotation has been computed and Fourier transformed to characterize the conformational preferences and origin of the barriers. NBO energetic components for rotation about the C-Br and O-Br bonds as a function of torsion angle have been computed and displayed.