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.

Combined model for 15N, 13C, and spin-state chemistry in molecular clouds

“…For example for our Reaction (5) in the forward direction ( 13 C + C 2 → 12 C + 13 CC), we obtain a rate coefficient of 2.89 × 10 −10 cm −3 at 10 K, whereas the fit of Rocha & Linnartz (2021) gives 1.52 × 10 −11 cm −3 -though it is to be noted that the rate coefficients of Rocha & Linnartz (2021) were calculated for higher temperatures (upward of 25 K) than we consider here (10 K in most simulations). We tested the effect of switching to the Rocha & Linnartz (2021) rate coefficients for their reactions (2) and (3) (with the C 2 variants in the X 1 Σ + g state) by running new variants of simulations S1, S2, and S3 with the rate coefficients of the reactions in question switched to the Rocha & Linnartz (2021) values. We found that the effects on the simulation results are highly dependent on the physical conditions.…”

“…In model S3, the rate coefficients of these reactions play only a very minor role, but in the highdensity and low-temperature environment of model S1 we obtain variations of up to an order of magnitude in the 12 C/ 13 C ratios of C 2 (and typically a factor of a few for other ratios) depending on the choice of the rate coefficients. The reason why the Rocha & Linnartz (2021) coefficients are so much lower than ours, or those of Loison et al (2020), is unknown at present and hence we have not included their rate coefficients in the bulk of the analysis presented here. However, these tests highlight that constraining the rate coefficients of critical reactions is of great importance for the predictions of chemical models, and further experimental and theoretical work on this is called for.…”