The modeling of low-temperature plasma synthesis of low-dimensional carbon coatings remains a challenge, since the long-time spans must be simulated for structural relaxation. A proper theoretical method should be chosen to address possible charge-transfer processes. Considering the possibility of linear-chained carbon (LCC) synthesis simulation, a numerical study of the C-C bond breaking under slow argon-ion irradiation is performed for the model molecules of 2,2,3,3-tetramethylbutane (sp(3) hybridization), 1,2,3-butatriene (sp(2)), and 2-butyne (sp). Threshold energies of bond breaking are calculated for the carbon atoms in all three hybridizations. Three levels of theory are applied, and the results are compared with experiment. Based on the accuracy of the values obtained, an approach is proposed for modeling the ion-assisted plasma synthesis.