Rotationally inelastic rate coefficients for C$_7$N$^{-}$ and C$_{10}$H$^{-}$ anions in collision with H$_2$ at interstellar conditions

The anions C$_7$N$^-$ and C$_{10}$H$^-$ are the two longest of the linear (C,N)-bearing and (C,H)-bearing chains which have so far been detected in the Interstellar Medium.

In order to glean information on their collision-induced rotational state-changing processes, we analyse the general features of new ab initio potentials describing the interaction of both linear anions with H$_2$, one of the most abundant partners in their ISM environment.

We employ an artificial neural network fit of the reduced-dimensionality potential energy surface for C$_7$N$^-$...H$_2$ interaction and discuss in detail the spatial features in terms of multipolar radial coefficients.

For the C$_{10}$H$^-$...H$_2$ interaction we use the initial grid of two dimensional raw points to generate by quadrature the Legendre expansion directly, further including the long-range terms as discussed in the main text.

Quantum scattering calculations are employed to obtain rotationally inelastic cross sections, for collision energies in the range of 10$^{-4}$ to 400 cm$^{-1}$.

From them we generate the corresponding inelastic rate coefficients as a function of temperature covering the range from 10 to 50 K.

The results for the rate coefficients for the longest cyanopolyyne are compared with the earlier results obtained for the smaller terms of the same series, also in collision with H$_2$.

We obtain that the inelastic rate coefficients for the long linear anions are all fairly large compared with the earlier systems.

The consequences of such findings on their non-equilibrium rotational populations in interstellar environments are illustrated in our conclusions.