The H + +D 2 → HD+ D + reaction has been theoretically investigated by means of an exact quantum mechanical approach, a quasiclassical trajectory method, and two statistical methods based in the propagation of either wave functions or trajectories. The study addresses the possible changes on the overall dynamics of the title reaction when the D 2 diatom is rotationally excited to its v =0, j =1 state. In addition, the reactivity for the ground rotational state on two different potential energy surfaces ͑PESs͒, namely, the surface by Aguado et al. ͓J. Chem. Phys. 112, 1240 ͑2000͔͒ and the PES by Kamisaka et al. ͓J. Chem. Phys. 116, 654 ͑2002͔͒, is examined. Reaction probabilities and cross sections at 0.524 and 0.1 eV collision energies are calculated. The major differences with respect to the reaction initiated with D 2 in its ground rovibrational state are observed for the lowest collision energy E c = 0.1 eV. Differential cross sections have been found to depend to some extend on the PES employed. In addition, at E c = 0.1 eV further discrepancies in the total and rotational cross sections are noticeable.