The data set and the fit are described in detail in
(1) H. S. P. Müller, A. Maeda, F. Lewen, S. Schlemmer, I. R. Medvedev, and E. Herbst, 2024, Mol. Phys. 122, Art. No. e2262057.
The fit involves mainly data of the Coriolis coupled states v₄ = 1 and v₆ = 1, which are nearly degenerate, v₃ = 1, which is nearby, and the somewhat more distant v₂ = 1. Extensive rotational data from the millimeter to the terahertz region were taken from that work. Also included were ν₂ rovibrational data from
(2) D. McNaughton and D. N. Bruget, 1993, J. Mol. Spectrosc. 159, 340;
and ν₄, ν₆, and ν₃ rovibrational data from
(3) J. M. Flaud, W. J. Lafferty, A. Perrin, Y. S. Kim, H. Beckers, and H. Willner, 2008, J. Quant. Spectrosc. Radiat. Transfer 109, 995.
Furthermore, ground state rotational data were included as summarized by
(4) H. S. P. Müller, A. Maeda, S. Thorwirth, F. Lewen, S. Schlemmer, I. R. Medvedev, M. Winnewisser, F. C. De Lucia, and E. Herbst, 2019, Astron. Astrophys. 621, Art. No. A143.
See the ground state documentation (tag 046509) for details on these data. The signs of the Coriolis coupling parameters relative to those of the vibrational dipole moments have essentially negligible effects on the intensities in the rotational spectrum. But the signs of the Coriolis coupling parameters relative to those of the vibrational transition dipole moments have more pronounced effects on the intensities in the rovibrational spectrum. It was attempted in (1) to accomodate available information from (2) and (3).
The vibrational identifiers 0 to 4 represent v = 0, v₄ = 1, v₆ = 1, v₃ = 1, and v₂ = 1, respectively. Nominal transitions between two states occur in the entry of the upper states.
Frequencies with calculated uncertainties exceeding 0.1 MHz should be viewed with some caution.
The dipole moments in excited vibrational states differ marginally from those of the ground vibrational state. An experimental value for v₄ = 1 was determined by
(5) D. J. Bedwell and G. Duxbury, 1980, J. Mol. Spectrosc. 84, 531.
Spin-statistics were applied in the calculations. The ortho states are described by K_a odd, the para states by K_a even for vibrational states with A symmetry (v = 0, v₂ = 1, v₃ = 1). The ortho states are described by K_a even, the para states by K_a odd for vibrational states with B symmetry (v₄ = 1, v₆ = 1).
The partition function was calculated by summation over all rotational levels of these five vibrational states. The value should be insufficient by less than 10^–3 at 300 K while more pronounced deviations occur at 500 K.