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\title{CURRENT PROGRESS IN VARIATIONAL CALCULATIONS OF POLYATOMIC HYDROCARBONS (C$_2$H$_2$, CH$_4$, C$_2$H$_4$, C$_3$H$_4$, AND C$_2$H$_6$)}

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\author{\FirstName ALENA \LastName RODINA}
\address{Laboratory of Theoretical Spectroscopy, V.E. Zuev Institute of Atmospheric Optics SB RAS 1, Akademician Zuev Sq., Tomsk, 634055 Russia}

\author{\FirstName ANDREI V. \LastName NIKITIN}
\address{Laboratory of Theoretical Spectroscopy, V.E. Zuev Institute of Atmospheric Optics SB RAS 1, Akademician Zuev Sq., Tomsk, 634055 Russia, Faculty of Physics Tomsk State University 36, Lenin Ave., Tomsk, 634050 Russia}

\author{\FirstName ALEXANDER \LastName PROTASEVICH}
\address{Laboratory of Atmospheric Absorption Spectroscopy, V.E. Zuev Institute of Atmospheric Optics SB RAS 1, Akademician Zuev Sq., Tomsk, 634055 Russia}

\author{\FirstName OLEG \LastName EGOROV}
\address{Laboratory of Theoretical Spectroscopy, V.E. Zuev Institute of Atmospheric Optics SB RAS 1, Akademician Zuev Sq., Tomsk, 634055 Russia, Faculty of Physics Tomsk State University 36, Lenin Ave., Tomsk, 634050 Russia}

\author{\underline{\FirstName MICHA\"{E}L \LastName REY},
\underline{\FirstName DOMINIKA \LastName VIGLASKA}}
\address{Groupe de Spectrom\'etrie Mol\'eculaire et Atmosph\'erique UMR CNRS 7331, UFR Sciences BP 1039, 51687 Reims Cedex 2, France}

\author{\underline{\FirstName VLADIMIR \LastName TYUTEREV}}
\address{Faculty of Physics Tomsk State University 36, Lenin Ave., Tomsk, 634050 Russia}


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\fancyhead[C]{{\footnotesize \textit{HRMS, 28th Colloquium, Dijon, France,
  Aug. 28 - Sept. 1, 2023}}}
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\index{C2H2}
\index{CH4}
\index{C3H4}
\index{C2H4}
\index{C2H6}
\index{ab initio}
\index{Potential energy surface}
\index{Dipole moment surface}
\index{Variational calculations}


The prediction of the rovibrational energy levels of the acetylene molecule was studied using both the \textit{ab initio}\footnote{
\href{https://doi.org/10.1016/j.jqsrt.2022.108349}{doi:10.1016/j.jqsrt.2022.108349},
A. V. Nikitin, A. E. Protasevich, A. A. Rodina, M. Rey, A. Tajti, V. G. Tyuterev, \textit{J. Quant. Spectrosc. Radiat. Transfer.},
\textbf{292}, 108349, (2022).} and new empirically refined potential energy surfaces (PESs). 
The refinement of the PES was done by the fit of the available experimental data on the main $^{12}$C$_2$H$_2$ isotopologue. 
The quality of the refined PES was analyzed by the variational calculations of the rovibrational energy levels of four isotopologues ($^{13}$C$_2$H$_2$, $^{12}$C$_2$D$_2$, $^{13}$CH$^{12}$CH, and H$^{12}$C$^{12}$CD) 
including their isotopic shifts for some lower energy levels with \textit{J}$\geq$5. Although under the Born-Oppenheimer approximation the isotopic shift should be independent on the PES, we found that the refined PES gave more accurate results than those based on the \textit{ab initio} one. 
The accuracy of the isotopic shift calculation was estimated as an order of magnitude better than the accuracy of the energy levels calculation. 
In the case of CH$_4$, the rovibrational energy levels in the region of the tetradecade polyad were computed with a high accuracy using the \textit{ab initio} PES without any empirical corrections. 
It was found that the prediction of the vibrational energy levels up to 17000 cm$^{-1}$ strongly depended on shape of the PES. 

A novel methodology\footnote{
\href{https://doi.org/10.1063/5.0089097}{doi:10.1063/5.0089097},
M. Rey, \textit{J. Chem. Phys},\textbf{156}, 224103, (2022).} for computing parameters of the effective both Hamiltonian and dipole moment was applied with respect to C$_2$H$_4$. The obtained for each polyad effective parameters will be used to improve the assignment of the C$_2$H$_4$ absorption spectra, measured particularly, around 7000 cm$^{-1}$. 

The full-dimensional \textit{ab initio} PESs for two structural isomers of the hydrocarbon C$_3$H$_4$ (D$_{2d}$-propadiene and C$_{3v}$-propyne) were developed up to the 5$^{th}$ order inclusively. 
The application of the rigid (D$_{3d}$) approximation for the variational calculations of the line list of C$_2$H$_6$ was discussed with respect to the new contraction approach implemented in the variational TENSOR code and presented previously \textit{ab initio} PES and DMS\footnote{O. Egorov, M. Rey, A. V. Nikitin, D. Viglaska, \textit{27th Colloquium on High-Resolution Molecular Spectroscopy},
HRMS Cologne 2021 \textbf{A55}. https://hrms21.scg.ch.}.

This work was supported by the project of the Russian Scientific Foundation (RSF, No. 22-42-09022) and Agence Nationale de la Recherche (ANR, French National Research Agency, Grant No. 21-CE30-0053-01)

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