functions of the energy.

Figure \[fig:sectionop\] also shows that ortho-[$\rm H_2$]{}inelastic cross-sections follow very closely the para-[$\rm H_2$]{}ones, including the position of resonances. Examination of all cross-sections reveals that the relative difference between $\sigma_{J_1J'_1}(E, \mbox{para})$ and $\sigma_{J_1J'_1}(E, \mbox{ortho})$ is less than $5\%$. This justifies *a posteriori* the much smaller amount of computational effort devoted to ortho-[$\rm H_2$]{}collisions as well as the neglect of $J_2 = 2$ closed para-[$\rm H_2$]{}channels. A detailed discussion of this behaviour is put forward in section \[sec:paraortho\].

Quantum rates and classical rates {#par:rates}
---------------------------------

The quantum collisional rates are calculated for $J_{1\rm up}\leq
15$, at astrophysically relevant temperatures, from 5 K to 100 K. We average the cross-sections described in the preceding section over the Maxwell distribution of velocities, up to a kinetic energy at least 10 times $kT$. The quantum calculations at the higher end of the energy range are approximated at the IOS level (see table \[tab:param\]), which is justified at these energies by the smallness of the rotational constant $B_{\rm HC_3N}$. Also we used a coarse energy grid for the IOS calculations because the energy dependence of the cross-sections becomes very smooth.

For values of $J_1 > 15$, the close coupling approach enters 