to expand the PES function $V$ over a suitable angular expansion for any intermolecular distance $R$. In the simpler case of the [$\mathrm{HC_3N}$]{}– He system, this expansion is in the form: $$\label{eq:pot}
     V_{}(R,\theta_1) = \sum_{l_1}
     v_{l_1}(R)\,P_{l_1}(\cos\theta_1)\quad ,$$ where $P_{l_1}(\cos\theta_1)$ is a Legendre polynomial and $v_{l_1}(R)$ are the radial coefficients.

For the [$\mathrm{HC_3N}$]{}– [$\rm H_2$]{}system, the expansion becomes: $$\label{eq:pot2}
  V(R,\theta_1, \theta_2, \phi) = \sum_{l_1 l_2 l} v_{l_1 l_2 l}(R)
    s_{l_1 l_2 l}(\theta_1, \theta_2, \phi),$$ where the basis functions $s_{l_1 l_2 l}$ are products of spherical harmonics and are expressed in Eq. (A9) of @green75. Two new indices $l_2$ and $l$ are thus needed, associated respectively with the rotational angular momentum of [$\rm H_2$]{}and the total orbital angular momentum, see also eq. (A2) and (A5) of @green75.

Because the Legendre polynomials form a complete set, such expansions should always be possible. However, @chapman77 failed to converge above expansion (\[eq:pot\]) due to the steric hindrance of He by the impenetrable [$\mathrm{HC_3N}$]{}rod, and @green78 abandoned quantum calculations, resorting to quasi classical trajectories (QCT) studies. Similar difficulties arise for the interaction with H$_2$. Actually, as can be seen on figure \[fig:PES\] for small $R$ values, the interaction is moderate or possibly weakly attractive for $\theta_1 