We selected a few $\left\{\theta_2,\phi\right\}$ orientation sets, bearing in mind that the dependence of the final PES with the orientation of [$\rm H_2$]{}is weak. In terms of spherical harmonics, the PES depends only on $Y_{l_2m_2}(\theta_2,\phi)$, with $l_2=0,2,4,\ldots$ and $m_2=0,1,2,\ldots$, $|m_2|\leq l_2$. Terms in $Y_{l_2m_2}$ and $Y_{l_2 -m_2}$ are equal by symmetry. Previous studies [@faure05a; @wernli06] have shown that terms with $l_2> 2$ are small, and we consequently truncated the $Y_{l_2m_2}$ series to $l_2\leq 2$. Hence, only four basis functions remain for the orientation of [$\rm H_2$]{}: $Y_{00},Y_{20},Y_{21}$ and $Y_{22}$.

Under this assumption, the whole [$\mathrm{HC_3N}$]{}– [$\rm H_2$]{}surface can be obtained knowing its value for four sets of $\left\{\theta_2, \phi\right\}$ angles at each value of $R$. We selected actually five sets, having thus an over-determined system allowing for the monitoring of the accuracy of the $l_2$ truncation. Consequently, we determined five independent PES, each being constructed similarly to the [$\mathrm{HC_3N}$]{}– He one as a bicubic spline fit over an irregular grid in $\left\{R,
\theta_1\right\}$ coordinates. The angular mesh is slightly denser than for the [$\mathrm{HC_3N}$]{}– He PES for small $R$ distances to account for more severe steric hindrance effects involving [$\rm H_2$]{}. In total, we computed 3420 $\left\{R, \theta_1, \theta_2, \phi\right\}$ 