The Diep and Johnson (DJ) H 2 -H 2 potential energy surface (PES) obtained from the first principles [P. Diep, K. Johnson, J. Chem. Phys. 113, 3480 (2000); 114, 222 (2000)], has been adjusted through appropriate rotation of the three-dimensional coordinate system and applied to low-temperature (T < 300 K) HD+o-/p-H 2 collisions of astrophysical interest. A non-reactive quantum mechanical close-coupling method is used to carry out the computation for the total rotational state-to-state cross sections σ j1j2→j ′ 1 j ′ 2 (ǫ) and corresponding thermal rate coefficients k j1j2→j ′ 1 j ′ 2 (T ). A rather satisfactory agreement has been obtained between our results computed with the modified DJ PES and with the newer H 4 PES [A.