To the best of our knowledge, the only available collisional rates are those of @green78 for the rotational excitation of HC$_3$N by He below 100 K. In cold and dense clouds, however, the most abundant colliding partner is H$_2$. In such environments, para-[$\rm H_2$]{}is only populated in the $J=0$ level and may be treated as a spherical body. @green78 and @dickinson82 postulated that the collisional cross-sections with para-[$\rm H_2$]{}$(J=0)$ are similar to those with He (assuming thus an identical interaction and insensitivity of the scattering to the reduced mass). As a result, rates for excitation by para-[$\rm H_2$]{}were estimated by scaling the rates for excitation by He while rates involving ortho-[$\rm H_2$]{}were not considered.

In the present study, we have computed new rate coefficients for rotational excitation of [$\mathrm{HC_3N}$]{}by He, para-[$\rm H_2$]{}($J=0$) and ortho-[$\rm H_2$]{}($J=1$), in the temperature range 5$-$20 K for He and 5$-$100 K for H$_2$. A comparison between the different partners is presented and the collisional selection rules are investigated in detail. The next section describes details of the PES calculations. The cross-section and rate calculations are presented in Section \[sec:cross\]. A discussion and a first application of these rates is given in Section \[sec:disc\]. Conclusions are 