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\title{ANALYSIS OF THE HOT BANDS OF METHYLAMINE: $3$\nu_{15}$\leftarrow$\nu_{15}$, $4$\nu_{15}$\leftarrow$\nu_{15}$ AND $\nu_9$\leftarrow$\nu_{15}$}

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\author{\underline{\FirstName I. \LastName GULACZYK},
  \FirstName M. \LastName KREGLEWSKI}
\address{Faculty of Chemistry, Adam Mickiewicz University in Poznan, Poland}
\author{\FirstName I. \LastName KLEINER}
\address{Universite Paris Cite and Univ Paris Est Creteil, CNRS, LISA, 75013, Paris, France}


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\fancyhead[C]{{\footnotesize \textit{HRMS, 28th Colloquium, Dijon, France,
  Aug. 28 - Sept. 1, 2023}}}
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Methylamine is a molecule performing two large amplitude motions: CH$_3$ internal rotation and NH$_2$ inversion. These two large amplitude motions are strongly coupled and give rise to a rotation-inversion-torsion structure in the vibrational states. The rovibrational spectrum of the methylamine molecule has been extensively studied both experimentally and theoretically. The analyses of infrared bands such as inversion ($\nu_ 9$) or CN stretching ($\nu_8$) show significant perturbations from highly excited torsional states. In order to untangle the interactions in the $700$ - $1200$ cm$^{-1}$ region of the methylamine spectrum, it is crucial to assign the dark states, which are the third and fourth excited torsional states ($3$\nu_{15}$ and $4$\nu_{15}$). These states can be experimentally observed as hot bands from the first excited torsional bands in the range $360$ - $720$ cm$^{-1}$. In the same range a hot band to the excited inversion state was discovered and since the intensities of three hot bands are similar, they must be analyzed jointly.
The spectra were recorded with a resolution of $0.00125$ cm$^{-1}$ using Bruker IFS-120HR spectrometer at the University of Oulu. 
The accurate energy levels of the first excited torsional state, $\nu_{15}$,\footnote{\ I. Gulaczyk, M. Kreglewski, V-M. Horneman, J. Mol. Spectrosc. 342 (2017) 25-30.}$^$\footnote{\ I. Gulaczyk, M. Kreglewski, JQSRT 252 (2020) 107097.} were used as reference values for lower state combination differences in the assignments of the third and fourth torsional hot bands, $3$\nu_{15}$\leftarrow$\nu_{15}$, $4$\nu_{15}$\leftarrow$\nu_{15}$, as well as in the hot inversion-torsional band, $\nu_9$\leftarrow$\nu_{15}$}.
On the basis of the predicted energy levels for the third and fourth excited torsional states, many transitions of the hot torsional bands: $3$\nu_{15}$\leftarrow$\nu_{15}$, $4$\nu_{15}$\leftarrow$\nu_{15}$, not assigned previously, have been identified. Many transitions belonging to the inversion-torsion hot band, $\nu_9$\leftarrow$\nu_{15}$}, have been assigned too. All the assignments were confirmed by the Lower State Combination Differences. Only experimental data of inversion-torsion hot band,  $\nu_9$\leftarrow$\nu_{15}$}, could be fitted to a single state model based on the group theoretical formalism of Hougen and Ohashi\footnote{\ N. Ohashi and J.T. Hougen, J. Mol. Spectrosc. 121, (1987) 474.}. The transitions belonging to the hot torsional bands ($3$\nu_{15}$\leftarrow$\nu_{15}$, $4$\nu_{15}$\leftarrow$\nu_{15}$) require another approach like a "hybrid" Hamiltonian model\footnote{\ I. Kleiner, J.T. Hougen, J. Phys. Chem. A 119 (2015) 10664.}$^$\footnote{\ I. Kleiner, J.T. Hougen, J. Mol. Spectrosc. 368 (2020) 111255.}, thus the analysis is still in progress.


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