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A thorough characterization of the γ, β, and glass phases of deuterated 1,1,2,2 tetrachloroethane (C2D2Cl4) via nuclear quadrupole resonance and Molecular Dynamic Simulations (MDSs) is reported. The presence of molecular reorientations was experimentally observed in the glass phase and in the β phase. In the β phase, and from MDS, these reorientations are attributed to two possible movements, i.e., a 180? reorientation around the C2 molecular symmetry axis and a reorientation of the molecule between two non-equivalent positions. In the glass phase, the spin-lattice relaxation time T¹ is of the order of 16 times lower than in the crystalline phase and varies as T-1 below 100 K in good agreement with the strong quadrupolar relaxation observed in amorphous materials and in the glassy state of molecular organic systems. The activation energy of molecular reorientations in the glass phase (19 kJ/mol) is comparable to that observed in the glassy crystal of a "molecular cousin" compound, Freon 112 (C2F2Cl4), for the secondary β-relaxation. Moreover, the on-site orientational motion of tetrachloroethane molecules offers a new indirect evidence of the prominent role of such orientational disorder in glassy dynamics. [ABSTRACT FROM AUTHOR]