Simplified model to treat the electron attachment of complex molecules

We present a theoretical approach to evaluate cross sections for dissociative electron attachment to polyatomic molecules. Starting from the Bardsley-O'Malley theory developed for diatomic targets, we extend the formalism of resonant scattering to polyatomic molecules. By inspecting the variation of resonance energies with respect to normal coordinates, a generalized dissociation coordinate is introduced for polyatomic molecules. Using the local complex potential model, the present \textit{ab inito} model gives a reasonable estimate for dissociative attachment cross sections with modest computational efforts. The model is applied to the H$_2$CN molecule, which is considered as a precursor in the formation of the CN$^-$ anion observed in the IRC~+10216 carbon star. The computed rate coefficient suggests that the dissociative electron attachment of H$_2$CN may not be an efficient reaction to form CN$^-$ in the circumstellar envelope of IRC +10216.