Radiative electronic attachment to a ro-vibrating diatomic molecule: Benchmark study of CN$^-$

We study the process of radiative electronic attachment (REA) to linear molecules of astrophysical interest and consider in detail the reaction CN+e$^-\to$CN$^-$+$\hbar\omega$. The treatment is based on first-principles only and takes into account the rotational and vibrational motion of the diatomic molecule. The energy-dependent transition dipole moment between the continuum and bond electron is obtained for various molecular geometries using the complex Kohn variational method. The benchmark calculation for the formation of CN$^-$ by REA has produced a low rate coefficient of about $10^{-15}$cm$^3/$s at 30 K. This confirms the idea that the simplest observed negative ion CN$^-$ can not be formed by the process of radiative electron attachment. Note that the same type of treatment could be equivalently used to study photodetachment of a ro-vibrating linear negative ion.