The HCO + and DCO + molecules are commonly used as tracers in the interstellar medium. Therefore, accurate rotational rate coefficients of these systems with He and H 2 are crucial in non-local thermal equilibrium models. We determine in this work the rotational de-excitation rate coefficients of HCO + in collision with both para-and ortho-H 2 , and also analyse the isotopic effects by studying the case of DCO +. A new four-dimensional potential energy surface from ab initio calculations was developed for the HCO +-H 2 system, and adapted to the DCO +-H 2 case. These surfaces are then employed in close-coupling calculations to determine the rotational de-excitation cross-sections and rate coefficients for the lower rotational states of HCO + and DCO +. The new rate coefficients for HCO + + para-H 2 were compared with the available data, and a set of rate coefficients for HCO + + ortho-H 2 is also reported. The difference between the collision rates with ortho-and para-H 2 is found to be small. These calculations confirm that the use of the rate coefficients for HCO + + para-H 2 for estimating those for HCO + + ortho-H 2 as well as for DCO + + para-H 2 is a good approximation.< Leer menos