Theoretical studies of carbon isotopic fractionation in reactions of C with C2: dynamics, kinetics, and isotopologue equilibria

Abstract

Context. Our current understanding of interstellar carbon fractionation hinges on the interpretation of astrochemical kinetic models. Yet, the various reactions included carry large uncertainties in their (estimated) rate coefficients, notably those involving C with C2. Aims. We aim to supply theoretical thermal rate coefficients as a function of the temperature for the gas-phase isotope-exchange reactions 13C+12C2(X1Σg+,a3Πu)⇌13C12C(X1Σg+,a3Πu)+12C and 13C+13C12C(X1Σg+,a3Πu)⇌13C2(X1Σg+,a3Πu)+12C. Methods. By relying on the large masses of the atoms involved, we employ a variation of the quasi-classical trajectory method, with the previously obtained (mass-independent) potential energy surfaces of C3 dictating the forces between the colliding partners. Results. The calculated rate coefficients within the range of 25 ≤ T∕K ≤ 500 show a positive temperature dependence and are markedly different from previous theoretical estimates. While the forward reactions are fast and inherently exothermic owing to the lower zero-point energy content of the products, the reverse processes have temperature thresholds. For each reaction considered, analytic three-parameter Arrhenius-Kooij formulas are provided that readily interpolate and extrapolate the associated forward and backward rates. These forms can further be introduced in astrochemical networks. Apart from the proper kinetic attributes, we also provide equilibrium constants for these processes, confirming their prominence in the overall C fractionation chemistry. In this respect, the 13C+12C2(X1Σg+) and 13C+12C2(a3Πu) reactions are found to be particularly conspicuous, notably at the typical temperatures of dense molecular clouds. For these reactions and considering both equilibrium and time-dependent chemistry, theoretical 12C/13C ratios as a function of the gas kinetic temperature are also derived and shown to be consistent with available model chemistry and observational data on C2.