We have recently demonstrated that simple classical molecular dynamics methods are capable of nearly quantitatively reproducing most of the intermolecular and intramolecular infrared (IR) spectroscopy of water [H. Ahlborn, X. Ji, B. Space, and P. B. Moore, J. Chem. Phys. 111, 10622 (1999)]. Here it is demonstrated that the result is robust by quantitatively reproducing experimentally measured D2O IR spectroscopy utilizing the same models. This suggests that the quantum effects associated with light atom motion are relatively unimportant. Instantaneous normal mode (INM) theory and the time correlation function (TCF) methodology are used in a complimentary fashion to analyze the molecular origin of the IR spectroscopy of deuterated water (D2O). The TCF methods demonstrate that our models of the dynamics and the system dipole are reasonable by successful quantitative comparison of the theoretical spectrum with experimental results. INM methodology is then employed to analyze what condensed phase motions are responsible for the observed O-D stretching line shapes. It is surprising that classical models can reproduce the complex spectroscopy of both liquid H2O and D2O, and this result implies that the motions responsible for the signal must be effectively harmonic in nature. This assertion is supported by the drastic impact that is seen on both the intensity and line shape through the choice of detailed balance correction factor that is used to quantum correct the classical vibrational line shape.