The Renner-Teller effect splits the two Σ components of the CCH bending mode ν₄ (≈ 600 cm^–1) of C₃H such that the lower component ²Σ^μ is only 27.2 cm^–1 above the lowest rotational state (N = 1, J = 0.5, F = 0 of the ²Π_1/2 ladder). This leads to considerable Coriolis interaction, as shown by
(1) S. Yamamoto, S. Saito, H. Suzuki, S. Deguchi, N. Kaifu, S.-I. Ishikawa, and M. Ohishi, 1990, Astrophys. J. 348, 363. In the case of CC¹³CH, this enegy difference is 27.00 cm^–1.
In the present fit, all five isotopomers studied by laboratory spectroscopy were fit together in order to constrain some higher order constants and the ¹H hyperfine splitting. This is reflected in the code for the quantum number format.
C₃H and C₃D experimental lines were taken from (1).
Additional C₃H millimeter transitions come from
(2) C. A. Gottlieb, J. M. Vrtilek, E. W. Gottlieb, P. Thaddeus, and Å. Hjalmarson, 1985, Astrophys. J. 294, L55.
Further C₃H low frequency transitions were taken from astronomical observations by
(3) N. Kaifu, M. Ohishi, K. Kawaguchi, S. Saito, S. Yamamoto, T. Miyaji, K. Miyazawa, S.-I. Ishikawa, C. Noumara, S. Harasawa, M. Okuda, and H. Suzuki, 2004, Publ. Astron. Soc. Japan 56, 69.
Data for the three ¹³C species were taken from
(4) M. Kanada, S. Yamamoto, S. Saito, and Y. Osamura, 1996, J. Chem. Phys. 104, 2192.
Predictions for low N transitions should be viewed with some caution mainly because of the uncertainties in the ¹³C hyperfine parameters. Increasing caution is advised for extrapolations beyond the experimentally accessed ~330 GHz.
The state numbers 0 and 1 refer to the ground vibrational state and the excited v₄ = 1, ²Σ^μ state, respectively.
The dipole moment was assumed to be the same as for the main isotopomer, see e037501.cat.
A substantial transition dipole moment between v = 0 and v₄ = 1 can be expected – a value of 0.5 D was assumed in (1). However, because of the large uncertainty of the band origin, rovibrational transitions were omitted from the prediction.