H_2$]{}bond separation $r_{\rm HH}= 1.44876$ Bohr obtained by averaging over the ground-state vibrational wave-function, similarly to previous calculations [@hodges04; @faure05; @wernli06]. For [$\mathrm{HC_3N}$]{}, as vibrational wave-functions are not readily available from the literature, we resorted to experimental geometries deduced from the rotational spectrum of [$\mathrm{HC_3N}$]{}and its isotopologues (@thor00; see also Table 5.8 in @gordy). The resulting bond separations are the following: $r_{\mathrm{HC_1}}= 1.998385$; $r_{\mathrm{C_1C_2}}=2.276364$;$r_{\mathrm{C_2C_3}}= 2.606688$; $r_{\mathrm{C_3N}}= 2.189625$, and should be close to vibrationally averaged values.

For the [$\mathrm{HC_3N}$]{}– He collision, only two coordinates are needed to fully determine the overall geometry. Let $\vec{R}$ be the vector between the center of mass of [$\mathrm{HC_3N}$]{}and He. The two coordinates are the distance $R=|\vec{R}|$ and the angle $\theta_1$ between the [$\mathrm{HC_3N}$]{}rod and the vector ***R***. In our conventions, $\theta_1 = 0$ corresponds to an approach towards the H end of the [$\mathrm{HC_3N}$]{}rod. For the collision with H$_2$, two more angles have to be added, $\theta_2$ and $\phi$, that respectively orient the [$\rm H_2$]{}molecule in the rod-***R*** plane and out of the plane. The [$\mathrm{HC_3N}$]{}– He PES has thus two degrees of freedom, the [$\mathrm{HC_3N}$]{}– [$\rm H_2$]{}four degrees of freedom.

As we aim to solve close coupling equations for the scattering, we need ultimately 