Rotational Spectroscopy as a Tool to Study Vibration-Rotation Interaction: Investigations of $^{13}$CH$_3$CN and CH$_3$$^{13}$CN up to $v_8 = 2$ and a Search for $v_8 = 2$ Transitions toward Sagittarius B2(N)

Methyl cyanide, CH$_3$CN, is present in diverse regions in space, in particular in the warm parts of star-forming regions where it is a common molecule. Rotational transitions of $^{13}$CH$_3$CN and CH$3$$^{13}$CN in their $v_8 = 1$ lowest excited vibrational states ($E{\rm vib} \approx 520$ K) are quite prominent in Sagittarius B2(N). In order to be able to search for transitions of the next higher vibrational state $v_8 = 2$, we recorded spectra of samples enriched in $^{13}$CH$_3$CN and CH$_3$$^{13}$CN up to $v_8 = 2$ in the 35 to 1091~GHz region and reinvestigated existing spectra of CH$_3$CN in its natural isotopic composition between 1085 and 1200 GHz. Perturbations caused by near-degeneracies in $K = 4$ of $v_8 = 2^0$ and $K = 2$ of $v_8 = 2^{-2}$ yielded accurate information on the energy spacing of 22.93 and 21.79 cm$^{-1}$ between the $l$-components of $^{13}$CH$_3$CN and CH$_3$$^{13}$CN, respectively. Fermi-type interaction between $K = 13$ and 14 of $v_8 = 1^{-1}$ and $v_8 = 2^{+2}$ probe the energy differences between the two states of both isotopomers. In addition, a $ΔK \pm2$, $Δl \mp1$ interaction between the ground vibrational state of $^{13}$CH$_3$CN and $v_8 = 1^{+1}$ provides information on their energy spacing. Furthermore, we obtained improved or extended ground state rotational transition frequencies of $^{13}$CH$_3$$^{13}$CN and extensive data for $^{13}$CH$_3$C$^{15}$N and CH$_3$$^{13}$C$^{15}$N. Finally, we report the results of our search for transitions of $^{13}$CH$_3$CN and CH$_3$$^{13}$CN in their $v_8 = 2$ states toward Sagittarius B2(N).

💡 Research Summary

This paper presents a comprehensive laboratory and astronomical investigation of the ¹³C‑substituted isotopologues of methyl cyanide, 13CH₃CN and CH₃¹³CN, focusing on their vibrationally excited states up to ν₈ = 2. Using enriched samples (99 % ¹³C at the appropriate carbon position), the authors recorded rotational spectra over a very broad frequency range (35–1091 GHz) with three different spectrometer setups at the University of Cologne. In addition, archival high‑frequency data (1085–1200 GHz) of the main isotopologue in natural abundance were re‑examined to improve the coverage of high‑K transitions.

Methyl cyanide is a prolate symmetric top (A ≫ B) with a strong dipole moment (3.922 D). The doubly degenerate ν₈ bending mode (≈520 K) gives rise to l‑type splitting: ν₈ = 1 has l = ±1 components, while ν₈ = 2 possesses l = 0 and l = ±2 components. Because the Coriolis coupling constant ζ is close to unity (0.8775), the l = +1 (or +2) levels are pushed down in energy and the l = −1 (or −2) levels are pushed up, creating near‑degeneracies for states with the same K − l value. These near‑degeneracies enable q₂₂ interactions (ΔK = ±2, Δl = ∓2) and, at higher K, strong Fermi‑type resonances (ΔK = 0, Δl = ±3) between ν₈ = 1 and ν₈ = 2.

The authors exploited two specific perturbations to extract precise spectroscopic information. First, the near‑degeneracy of K = 4 (l = 0) and K = 2 (l = −2) in ν₈ = 2 produced observable q₂₂ splittings, from which the energy separation between the l‑components was determined to be 22.93 cm⁻¹ for 13CH₃CN and 21.79 cm⁻¹ for CH₃¹³CN. Second, a Fermi resonance involving K = 13–14 of ν₈ = 1⁻¹ and ν₈ = 2⁺² allowed a direct measurement of the energy gap between the two vibrational manifolds for both isotopologues. Additionally, a ΔK = ±2, Δl = ∓1 interaction between the ground state of 13CH₃CN and ν₈ = 1⁺¹ provided an independent check on the ground‑to‑excited‑state spacing.

All measured transition frequencies were fitted using Pickett’s SPFIT/SPCAT suite. The fit employed a conventional symmetric‑top Hamiltonian, including rotational, centrifugal‑distortion, and hyperfine (quadrupole) terms. Vibrational corrections were introduced as ΔX = X_i − X_0, which keeps the number of independent parameters low while preserving physical consistency across vibrational states. Interaction parameters (q₂₂, Fermi coupling constants, etc.) were added only when they significantly reduced the rms residuals and when their magnitudes were physically reasonable. The final spectroscopic models reproduce the laboratory data with rms deviations well within the experimental uncertainties.

Beyond the ν₈ = 2 analysis, the study extends the ground‑state line list of the doubly‑substituted isotopologue 13CH₃¹³CN and provides extensive new data for the ¹³C‑¹⁵N isotopologues 13CH₃C¹⁵N and CH₃¹³C¹⁵N, whose previous coverage was limited to ≈72 GHz.

The astronomical component uses ALMA observations of the high‑mass star‑forming region Sagittarius B2(N). Guided by the new laboratory frequencies, the authors searched for ν₈ = 2 transitions of 13CH₃CN and CH₃¹³CN. Although the predicted lines fall within the observed spectral windows, the current sensitivity (∼10 mK) is insufficient for a definitive detection; only upper limits on column densities are reported. Nevertheless, the work establishes the necessary spectroscopic foundation for future, deeper ALMA surveys targeting hot‑core chemistry and isotopic fractionation.

In summary, the paper delivers a high‑precision spectroscopic catalog for 13CH₃CN and CH₃¹³CN up to ν₈ = 2, quantifies key vibration‑rotation interaction mechanisms (q₂₂ and Fermi resonances), expands the data set for several other isotopologues, and demonstrates the relevance of these results for astrochemical studies of warm, dense environments such as Sgr B2(N).