Abstract: The time-dependent wave-packet method was employed to calculate the first full-dimensional state-to-state differential cross sections (DCS) for the title reaction with D₂O in the ground and the first symmetric (100) and asymmetric stretching (001) excited states. The calculated DCSs for these three initial states are strongly backward peaked at low collision energies. With the increase of collision energy, these DCSs become increasingly broader with the peak position shifting gradually to a smaller angle, consistent with the fact that the title reaction is a direct reaction via an abstraction mechanism. It is found that the (100) and (001) states not only have roughly the same integral cross sections, but also have essentially identical DCS, which are very close to that for the ground state at the same total energy of reaction. The reaction produces a small fraction of OD in the v=1 state, with the population close to the relative reactivity between the ground and vibrationally excited states, therefore confirming the experimental result of Zare et al. and the local mode pictureJ. Phys. Chem. 97 , 2204 (1993). Unexpectedly, the stretching excitation reduces the rotation excitation of product HD at the same total energy.