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\title{THE 2,4-CHALLENGE IN THE MICROWAVE SPECTRA OF 2,4-DIMETHYLTHIAZOLE AND 2,4-DIMETHYLFLUOROBENZENE: STRATEGY TO ASSIGN VERY LOW BARRIER METHYL INTERNAL ROTATION}

\author{\underline{\FirstName S. \LastName KHEMISSI},$^{1}$ \FirstName M. \LastName SCHWELL,$^{1}$ \FirstName I. \LastName KLEINER,$^{2}$ \FirstName H.~V.~L. \LastName NGUYEN$^{1,3}$}
\address{$^{1}$Univ Paris Est Creteil and Universit\'e Paris Cit\'e, CNRS, LISA, F-94010 Cr\'eteil, France, $^{2}$Universit\'e Paris Cit\'e and Univ Paris Est Creteil, CNRS, LISA, F-75013 Paris, France, $^{3}$Institut Universitaire de France (IUF), F-75231 Paris, France} 


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\fancyhead[C]{{\footnotesize \textit{HRMS, 28th Colloquium, Dijon, France,
  Aug. 28 - Sept. 1, 2023}}}
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\index{MW spectroscopy}
\index{2,4-dimethylfluorobenzene}
\index{2,4-dimethylthiazole}
\index{Low barrier}

The analysis and modeling of internal rotations with extremely low barriers is a challenging task in microwave spectroscopy. An almost free internal rotation hindered by a barrier less than 20 cm$^{-1}$ causes large torsional splittings in the spectrum. For molecules with two inequivalent methyl groups, the methyl rotations couple with each other, especially in aromatic molecules through $\pi$ conjugation, and all rotational lines split into quintets, making spectral assignment and modeling very difficult. The spectral analysis becomes even more complicated if additional effects are present such as the $^{14}$N nuclear quadrupole coupling, which causes quadrupole hyperfine splittings in addition to the torsional splittings.\footnote{\href{http://dx.doi.org/10.1515/psr-2020-0037}{doi.org/10.1515/psr-2020-0037}, H.V.L. Nguyen, I. Kleiner, \textit{Phys}. \textit{Sci}. \textit{Rev}. \textbf{7}, 679{$-$}726 (2020).} Probably for these reasons, a very limited number of studies on aromatic systems undergoing nearly barrier-free internal rotations have been reported.\footnote{\href{http://dx.doi.org/10.3390/molecules27123948}{doi.org/10.3390/molecules27123948}, H.V.L. Nguyen, W. Caminati, J.-U. Grabow, \textit{Molecules}. \textbf{27}, 3948 (2022).} \\
We will present here the challenges for two such molecules, 2,4-dimethylthiazole (24DMTA) and 2,4-dimethylfluorobenzene  (24DMFB).
The microwave spectra were recorded using a pulsed molecular jet Fourier transform microwave spectrometer operating in the frequency range from 2.0 to 26.5 GHz.\footnote{\href{http://dx.doi.org/10.1063/1.1147553}{doi.org/10.1063/1.1147553}, J.-U. Grabow, W. Stahl, H. Dreizler, \textit{Rev}. \textit{Sci}. \textit{Instrum}. \textbf{67}, 4072{$-$}4084(1996).} 
The experimental work was supported by quantum chemical calculations. For both molecules, the \textit{XIAM$_m_o_d$} program\footnote{\href{http://dx.doi.org/10.1063/1.5142401}{doi.org/10.1063/1.5142401}, S. Herbers, S.M. Fritz, P. Mishra, H.V.L. Nguyen, T.S. Zwier, \textit{J}. \textit{Chem}. \textit{Phys}. \textbf{152}, 074301 (2020).}$^{,}$\footnote{\href{http://dx.doi.org/10.1016/j.jms.2020.111289}{doi.org/10.1016/j.jms.2020.111289}, S. Herbers, H.V.L. Nguyen, \textit{J}. \textit{Mol}. \textit{Spectrosc}. \textbf{370}, 111289 (2020).} was used at the beginning to fit the first assigned lines, but it fails to predict new lines at higher \textit{J} and \textit{K} values, as well as to achieve the measurement accuracy of 2 kHz for the final data set.\footnote{\href{http://dx.doi.org/10.1515/zna-1990-0817}{doi.org/10.1515/zna-1990-0817}, J.-U. Grabow, W. Stahl, \textit{Z}. \textit{Naturforsch}. \textbf{45a}, 1043{$-$}1044 (1990).} 
To assign more lines, fitting each torsional species separately using odd power order parameters to get reliable predictions using the \textit{WS18} code\footnote{\href{http://dx.doi.org/10.1063/5.0049418}{doi.org/10.1063/5.0049418}, T. Nguyen, W. Stahl, H.V.L. Nguyen, I. Kleiner, \textit{J}. \textit{Chem}. \textit{Phys}. \textbf{154}, 204304 (2021).} and the \textit{SFLAMS} code,\textcolor{blue}{$^{4}$}} as well as checking the assigned frequencies by combination difference loops (Ritz cycles)\footnote{\href{http://dx.doi.org/10.1016/j.jms.2015.10.005}{doi.org/10.1016/j.jms.2015.10.005}, Y. Zhao, H.V.L. Nguyen, W. Stahl, J.T. Hougen, \textit{J}. \textit{Mol}. \textit{Spectrosc}. \textbf{318}, 91{$-$}100 (2015).} is the key to success. Finally, the \textit{BELGI-C$_s$-2Tops-hyperfine}\footnote{\href{http://dx.doi.org/10.1063/5.0049418}{doi.org/10.1063/5.0049418}, V. Van, T. Nguyen, W. Stahl, H.V.L. Nguyen, I. Kleiner, \textit{J}. \textit{Mol}. \textit{Struct}. \textbf{1207}, 127787 (2020).} and \textit{BELGI-C$_s$-2Tops}\footnote{\href{http://dx.doi.org/10.1016/j.jms.2011.07.005}{doi.org/10.1016/j.jms.2011.07.005}, M. Tudorie, I. Kleiner, J.T. Hougen, S. Melandri, L.W. Sutikdja, W. Stahl, \textit{J}. \textit{Mol}. \textit{Spectrosc}. \textbf{269}, 211{$-$}225 (2011).} programs were used for 24DMTA and 24DMFB, respectively, to decrease the standard deviation to measurement accuracy in a global fit. For 24DMTA, the barriers to internal rotation of the 2- and 4-methyl groups were determined to be 19.070(58) cm$^{-1}$ and 396.707(25) cm$^{-1}$, respectively. They are 3.23(40) cm$^{-1}$ and 227.039(51) cm$^{-1}$ for 24DMFB.

       
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