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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(1) H. S. P. Müller, 2021, unpublished.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.
Transition frequencies above 0.7 THz should be viewed
with some caution.
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.
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