ExoMol Line Lists -- LXII: Ro-Vibrational Energy Levels and Line-Strengths for the Propadienediylidene (C3) in its Ground Electronic State

Improved opacities are needed for modelling the atmospheres and evolution of cool carbon-rich stars and extra-solar planets; in particular, contributions made by the astrophysically important propadienediylidene (C$_3$) molecule need, at a minimum, to be determined using a line list which includes all significant transitions in the energy range of interest. We report variational calculations giving ro-vibrational energy levels and corresponding line-strengths for $^{12}$C$_3$, $^{12}$C$^{13}$C$^{12}$C and $^{12}$C$^{12}$C$^{13}$C. In the $^{12}$C$_3$ case we obtain 2166503 ro-vibrational state energies $\le$ 20000 cm$^{-1}$ for the electronic $\tilde{X}^1 Σ_g^+$ ground-state. Comparison with experiment indicates a maximum error of +/- 0.03 cm$^{-1}$ in calculated positions of lines involving an upper state energy $\lesssim$ 4000 cm$^{-1}$. For lines with upper state energies $\gtrsim$ 4000 cm$^{-1}$ to have comparable line-position accuracies, conical intersections would need to be accounted for in an adopted potential energy surface. Line lists and associated opacities are provided in the ExoMol Database http://www.exomol.com ).