Rovibrational energies, partition functions and equilibrium fractionation of the CO2 isotopologues

- A refined potential is obtained for CO2 by fitting to vibrational frequencies.
- Vibrational terms and rotational constants are computed for the stable isotopologues.
- Predicted values of the spectroscopic constants for unobserved bands are reported.
- Isotopologue partition functions are computed by direct summation over energies.
- Relative abundances of the isotopologues at thermodynamic equilibrium are determined.

Rovibrational energy levels, partition functions and relative abundances of the stable isotopologues of CO2 in gas phase at equilibrium are calculated using an empirical Morse-cosine potential energy surface (PES) refined by fitting to the updated pure (l2=0) vibrational frequencies observed for the main 12C16O2 isotopologue. The rovibrational energy levels are calculated variationally using a system of optimized hyperspherical normal coordinates, and from these the vibrational terms Gv and rotational constants Bv of the isotopologues are determined. The refined potential surface is shown to be clearly superior to the original potential surface, with the former reproducing the observed values of the spectroscopic constants Gv and Bv with accuracies of about 0.1 cm−1 and 0.00020 cm−1, respectively, for levels with l2≥0 up to 10,000 cm−1 above the ground state. The internal partition functions of the isotopologues are calculated by approximated direct summation over the rovibrational energies and compared with both previous partition sums and values obtained from analytical expressions based on the harmonic oscillator and rigid rotor models. The partition functions calculated by approximated direct summation are then used to determine the abundances of the CO2 isotopologues at thermodynamic equilibrium using the method developed by Wang et al. [74]. Significant variations in the relative abundances of some of the CO2 multiple substituted isotopologues at terrestrial temperatures with respect to those provided by the classical harmonic-based Urey theory are found, which may be of relevance in geochemical processes.