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)

TL;DR

This study extends rotational spectroscopy of CH$_3$CN and its isotopologs to the $v_8=2$ vibrational state using $^{13}$C-enriched samples, delivering extensive spectra from $35$ to $1091$ GHz (and $1083$–$1200$ GHz from JPL data) and refining the ground and excited-state parameters through SPCAT/SPFIT fits that include vibration–rotation interactions and perturbations from near-degeneracies. The authors report precise energy spacings between $l$ components for $v_8=2$ ($^{13}$CH$_3$CN: $E(8^{2^2})-E(8^{2^0}) \\approx 22.93$ cm$^{-1}$; CH$_3$$^{13}$CN: \\approx 21.79$ cm$^{-1}$) and observe Fermi-type resonances with $v_8=1^{-1}$ and $v_8=2^{+2}$ levels, enabling improved quantum-chemical benchmarks for overtone bending states. They also present refined data for $v_8=1$ and $v=0$ across multiple isotopologs, plus line lists for doubly substituted species, and conduct an astrophysical search toward Sgr B2(N) with LTE modeling that yields no secure detection but suggests these high-vibrational transitions may be detectable in warm, dense regions with cleaner spectra. Overall, the work delivers high-precision spectroscopic parameters and comprehensive line catalogs that enhance astrochemical identifications and inform future searches for vibrationally excited methyl cyanide in space.

Abstract

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).

Figures (10)

• Figure 1: Model of the methyl cyanide molecule with the $\nu _8$ displacement vectors. The C atoms are shown in gray, the H atoms in light gray, and the N atom in blue. The $a$-axis is along the CCN atoms and is also the symmetry axis. The lengths of the $\nu _8$ displacement vectors are exaggerated.
• Figure 2: $J = K$ energy levels of methyl cyanide $\varv = 0$ on the left and the doubly degenerate $\varv _8 = 1$ on the right; with the latter separated into their $l = +1$ and $l = -1$ substates. Levels with $k - l \equiv 0$ mod 3 have A symmetry while all others have E symmetry. A symmetry levels are shown with thicker lines. The Coriolis interaction between the two $l = \pm1$ substates of $\varv _8 = 1$ with the lowest order parameter $A\zeta$ shifts $l = +1$ down in energy and $l = -1$ up in energy, causing levels in $\varv _8 = 1$ having the same $K - l$ to be close in energy, facilitating $q_{22}$ interaction. Note the proximity of $K = 12$ of $\varv _8 = 1^{+1}$ to $K = 14$ of $\varv = 0$. The $K = 0$, 1, and 2 levels of $\varv _8 = 1^{+1}$ are so close in energy that their lines in the figure appear as one.
• Figure 3: Low-$K$ energy level structure of the triply degenerate $\varv _8 = 2$ of $^{13}$CH$_3$CN on the left and of CH$_3$$^{13}$CN on the right, separated into their $l = 0$, $l = -2$, and $l = +2$ substates. Here, the hypothetical $J = 0$ level energies are shown. The Coriolis interaction between the two $l = \pm2$ substates of $\varv _8 = 2$ shifts the $l = +2$ levels down in energy and the $l = -2$ levels up in energy, causing levels having the same $K - l$ to be close in energy, as indicated by magenta lines, facilitating again $q_{22}$ interaction, similer to $\varv _8 = 1$. Note that $K = 4$ of $l = 0$ and $K = 2$ of $l = -2$ are very close in energy with the former being slightly lower than the latter in the case of $^{13}$CH$_3$CN whereas it is opposite in the case of CH$_3$$^{13}$CN. Note also that for $l = +2$$K = 1$, 2, and 3 are lower in energy than $K = 0$.
• Figure 4: Section of the submillimeter spectrum of $^{13}$CH$_3$CN in the region of the $\varv _8 = 2$$J = 44 - 43$ transitions on the upper trace and of CH$_3^{13}$CN in the region of $\varv _8 = 2$$J = 43 - 42$ on the lower trace. The $k$ values of the different $l$ substates are indicated centered above or below the line, for $l = 0$ without a sign, and in different colors; see \ref{['intro-spec']} for the definition of $k$. The patterns of both isotopomers are quite similar, in particular with the decrease in frequency for increasing $k$ in the case of $l = +2$ (red); two lines appear for $k = +2$ because the respective levels are split by $q_{22}$ interaction, see also \ref{['intro-spec']}. Note, however, that $k = -2$ (in green) occurs at the high frequency edge on the upper trace, whereas it occurs near the low frequency part on the lower trace. Similarly, $k = 4$ (in blue) is near the high frequency edge on the lower trace, whereas it is slightly off the low frequency edge of the upper trace. This is caused by the near-degeneracy of $k = -2$ and $k = 4$ together with the $q_{22}$ interaction, see also \ref{['v8_eq_2_low-K_egy']}.
• Figure 5: Section of the $J = K$ energy levels of $^{13}$CH$_3$CN $\varv _8 = 1$ on the left and $\varv _8 = 2$ on the right displaying the $K$ levels around their interactions. Levels having the same $K - l$ in $\varv _8 = 1$ are close in energy, and this occurs also within $\varv _8 = 2$. Energy levels with $K = 13$ or 14 in $\varv _8 = 1^{-1}$ and in $\varv _8 = 2^{+2}$ are close in energy, giving rise to Fermi-type interaction ($\Delta K = \Delta J = 0$, $\Delta l = \pm3$). In addition, $K = 13$ of $\varv _8 = 1^{-1}$ and $K = 11$ of $\varv _8 = 2^{0}$ get close in energy, as do $K = 15$ of $\varv _8 = 1^{+1}$ and $K = 13$ of $\varv _8 = 2^{+2}$; see also \ref{['v8eq2-results']}.