Interaction potential of the OD(X2Π) radical is constructed by employing the CCSD(T) theory in combination with the correlationconsistent quintuple basis set, augccpV5Z, in the valence range. Using the potential, the spectroscopic parameters are accurately determined. The present D0, De, Re, ωe, ωeχe and Be values are of 44574, 46225 eV, 009702 nm, 2724923, 453534 and 100096 cm-1, respectively, which are in excellent agreement with the recent measurements wherever available. A total of 23 vibrational states have been found when J = 0 by solving the radial Schrdinger equation of nuclear motion. The complete vibrational levels, classical turning points, initial rotation and centrifugal distortion constants when J = 0 are reported for the first time, which are in good agreement with the available experimental results. The total and various partialwave cross sections are calculated for the elastic collisions of O and D atoms in their ground states at low and ultralow temperatures when the two atoms approach each other along the OD(X2Π) potential energy curve. The impact energy range covers a vange from 10×10-11 to 10 ×10-3a.u.. One shape resonance has been found in the total elastic cross sections. Contribution to the total elastic cross sections by each partial wave is investigated carefully. The results show that the shape of the total elastic cross sections is mainly dominated by the s partial wave. The shape resonances coming from the higher partial waves are covered up by the strong s partial wave cross sections.