Ab initio molecular orbital calculations were used to determine the structure and vibrational frequencies of the cyclic glycerol trimer, which represents the region of medium-range ordering in liquid and supercooled glycerol. The calculations reproduced the experimentally observed low-frequency Raman scattering peak (or the "boson peak") at similar to 50 per centimeter, which suggests that the peak results from the localized collective motions of the cooperatively hydrogen-bonded hydroxyl groups. The calculations also suggest that the fast relaxation process may result from the translational motion of each glycerol molecule in the cyclic structure. On the basis of these results, a model of the glass transition was developed.