An isotopic independent fit was performed by
(1) H. S. P. Müller, 2021, unpublished.
Data of the ⁴⁸Ti main isotopic species in v = 0 were reported by
(2) K.-I. Namiki, S. Saito, J. C. Robinson, and T. C. Steimle, 1998, J. Mol. Spectrosc. 191, 176.
The essentially negligible Λ-splitting was ignored; 40 kHz uncertainties were used for the two transitions, as for the remaining data.
Extensive v = 0 isotopic data for ⁴⁶TiO, ⁴⁷TiO, ⁴⁹TiO, and ⁵⁰TiO were taken from
(3) A. P. Lincowski, D. T. Halfen, and L. M. Ziurys, 2016, Astrophys. J., 833, 9;
The ⁴⁷TiO and ⁴⁹TiO data displayed resolved Ti hyperfine splitting throughout.
Additional v = 0 TiO, ⁴⁶TiO, and ⁵⁰TiO data were published by
(4) P. Kania, T. F. Giesen, H. S. P. Müller, S. Schlemmer, and S. Brünken, 2008, 33rd Int. Conf. Infrared, Millimeter, Terahertz Waves, 1.
Two TiO transition frequencies in v = 1 and five Ti¹⁸O, v = 0 were taken from
(5) A. A. Breier, B. Waßmuth, G. W. Fuchs, J. Gauss, and T. F. Giesen, 2019, J. Mol. Spectrosc. 355, 46.
Extensive, accurate infrared data were reported by
(6) D. Witsch, A. A. Breier, E. Döring, K. M. T. Yamada, T. F. Giesen, and G. W. Fuchs, 2021, J. Mol. Spectrosc. 377, Art. No. 111439.
Some transitions with large residual were omitted.
The transition frequencies are probably reliable thoroughout.
Please note: The hyperfine structure of the Ω = 2 fine structure component is perturbed by the low-lying a ¹Δ electronic state. This perturbation is modeled well by an effective parameter in the ground vibrational state, but may be different in excited vibrational states. The calculated hyperfine patterns of the Ω = 2 component should thus be viewed with caution. Vibrational changes in the hyperfine patterns of the Ω = 1 and 3 components are probably small.
The partition function was evaluated by summation over the first 10 vibrational states. The partition function is converged (in the ground electronic state !) at 2000 K to order 0.0001, and at 3000 K to order 0.01.
Please note that Hund's case (b) quantum numbers are used, as is generally the case in the CDMS. The quantum numbers are N, Λ, v, and J, as expected. The Ω = 1, 2, and 3 transitions appear at increasing frequency for a given J; this is also apparent from the lower state energies. More specifically,
Ω = 1: N = J + 1, Ω = 2: N = J, Ω = 3: N = J – 1, for J ≤ 3.
Ω = 1: N = J, Ω = 2: N = J + 1, Ω = 3: N = J – 1, for 4 ≤ J ≤ 29.
Ω = 1: N = J – 1, Ω = 2: N = J + 1, Ω = 3: N = J, for 30 ≤ J ≤ 40.
Ω = 1: N = J – 1, Ω = 2: N = J, Ω = 3: N = J + 1, for 41 ≤ J; which means that now Hund's (b) quanta are good quantum numbers.
The the ground state dipole moment was taken from
(7) T. C. Steimle and W. Virgo, 2003, Chem. Phys. Lett. 381, 30. Vibrational corrections to the dipole moment may be non-negligible, isotopic or rotational corrections probably are.