Example Aminoacetonitrile, H₂NCH₂CN

Coriolis interaction between v₁₁ = 1 and v₁₈ = 1

This example deals with the combined fit of rotational and rovibrational transitions associated with the four lowest vibrational states of aminoacetonitrile, which are v = 0, v₁₁ = 1 (A'; E_vib = 210.576 cm^–1), v₁₈ = 1 (A"; E_vib = 244.892 cm^–1), and v₁₇ = 1 (A"; E_vib = 368.105 cm^–1).
Aspects in this example are the treatment of the Coriolis interaction between v₁₁ = 1 and v₁₈ = 1 and likely interactions involving v₁₇ = 1.

The data set is based on
1) M. Melosso, A. Belloche, M.-A. Martin-Drumel, O. Pirali, F. Tamassia, L. Bizzocchi, R. T. Garrod, H. S. P. Müller, K. M. Menten, L. Dore, and C. Puzzarini,
Far-infrared laboratory spectroscopy of aminoacetonitrile and first interstellar detection of its vibrationally excited transitions,
Astron. Astrophys. 641 (2020) Art. No. A160.
A pdf file (AAN-vibs_2020.pdf) is available in this directory.
The spfit files are available in the directory background_files.
The catalog files and other auxiliary files used or generated by spcat or necessary for the various incarnations of the CDMS are in the directories gs, 11_18, and 17.

Additional data were taken from
2) C. Degli Esposti, L. Dore, M. Melosso, K. Kobayashi, C. Fujita, and H. Ozeki,
Millimeter-wave and Submillimeter-wave Spectra of Aminoacetonitrile in the ThreeLowest Vibrational Excited States,
Astrophys. J. Suppl. Ser. 230 (2017) Art. No. 26;
from
3) Y. Motoki, Y. Tsunoda, H. Ozeki, and K. Kobayashi
Submillimeter-wave Spectrum of Aminoacetonitrile and its Deuterated Isotopologues, Possible Precursors of the Simplest Amino Acid Glycine,
Astrophys. J. Suppl. Ser. 209 (2013) Art. No. 23;
and from references therein. Please note that the treatment here uses all of the available hyperfine structure information.
There is an additional account on the rotational spectrum of aminoacetonitrile by
4) L. Kolesniková, E. R. Alonso, S. Mata, and J. L. Alonso,
Rotational Spectra in 29 Vibrationally Excited States of Interstellar Aminoacetonitrile,
Astrophys. J. Suppl. Ser. 229 (2017) Art. No. 26.
As the title implies, many more vibrational states were covered in this work, but the frequency coverage is more limited, and no interactions were treated.

The energy difference between v₁₁ = 1 and v₁₈ = 1 is 34.316 cm^–1, which may appear as a lot. Nevertheless, non-resonant, but also resonant interactions are possible between levels differing not too much in K_a. The list below is probably not complete.

• ΔK_a = 4 interactions are possible for
  K_a = 7/3 with a resonant interaction at J = 37/38 for the levels differing in K_c by 5; and
  K_a = 4/8 with a pronounced resonance calculated at J = 61/62 for the levels differing in K_c by 3.
• ΔK_a = 3 interactions are possible for
  K_a = 8/5 with a pronounced resonance calculated at J = 72 for the K_c = J – K_a + 1 levels; and
  K_a = 6/9 with a resonance calculated at J = 66/67 for the K_c = J – K_a + 1 levels.
• ΔK_a = 2 interactions are possible for
  K_a = 10/8 with a pronounced resonance calculated at J = 113 for the levels differing in K_c by 3; and
  K_a = 11/9 with a pronounced resonance calculated at J = 119/120 for the levels differing in K_c by 3; and
  K_a = 10/12 with a pronounced resonance calculated at J = 105/106 for the levels differing in K_c by 1.
• ΔK_a = 1 interactions are possible for
  K_a = 25/24 with a resonant interaction calculated at J = 149/150; and
  K_a = 26/25 with a resonant interaction calculated at J = 124/125; and
  K_a = 27/26 with a resonant interaction calculated at J = 94/95; and
  K_a = 28/27 with a resonant interaction calculated at J = 49/50; and
  K_a = 28/29 with no resonant interaction up to J = 165.

The far-infrared transitions reach K_a = 25 in ν₁₈. Therefore, G_a is not determined directly, meaning through (near) resonant ΔK_a = 0 interactions. Instead, the largest effect is probably caused by the non-resonant ΔK_a = 0 interactions, which shift K_a levels of v₁₁ = 1 down and those of v₁₈ = 1 up. It may well be that (near) resonant ΔK_a = 2 interactions are important also. We also point out that the highest K_a levels in ν₁₈ reach the region of strongest ΔK_a = 1 interactions. It is therefore not surprising that G_b became determinable. The effects are, however, not particularly large. This, in combination with a not so small uncertainty and correlations with other parameters, caused the fit to require quite a few iterations to reach the minimum. It is useful in such cases, to adjust the parameter first manually, and float it with reduced variability in the first few iterations.

Comparison of purely K-dependent parameters (MHz):
A₀: 30246.5; D_K,0: 0.714.
Δ₁₁(A): –228.3; Δ₁₈(A): +381.3; Δ₁₁(D_K): –0.155; Δ₁₈(D_K): +0.149; according to Kolesniková et al.
Δ₁₁(A): +33.1; Δ₁₈(A): +119.8; Δ₁₁(D_K): –0.064; Δ₁₈(D_K): +0.065; according to Degli Esposti et al.
Δ₁₁(A): +54.9; Δ₁₈(A): 98.0; Δ₁₁(D_K): 0.0; Δ₁₈(D_K): –0.0006; according to Melosso et al.
Δ₁₁(A): +51.7; Δ₁₈(A): 101.3; Δ₁₁(D_K): 0.0; Δ₁₈(D_K): 0.0; here.

Please note that v₁₇ = 1 is not an isolated state, as v₁₁ = 2 is quite close. v₁₁ = v₁₈ = 1 is farther away, but a classical Fermi interaction is possible.