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\title{SPECTRA OF THE FORMALDEHYDE MOLECULE IN THE RANGE 3800$-$5100 CM$^{-1}$}

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\author{\FirstName ALENA \LastName RODINA, \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}

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\author{\underline{\FirstName MICHA\"{E}L \LastName REY}}
\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 LAURENT \LastName MANCERON }}
\address{Universit\'e Paris-Est Cr\'eteil, CNRS, LISA, F-75013 Paris, France.}

\author{\FirstName ALEXANDER \LastName PROTASEVICH, \underline{\FirstName VLADIMIR \LastName TYUTEREV}}
\address{Laboratory of Theoretical Spectroscopy, V.E. Zuev Institute of Atmospheric Optics SB RAS 
1, Akademician Zuev Sq., Tomsk, 634055 Russia}
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\fancyhead[C]{{\footnotesize \textit{HRMS, 28th Colloquium, Dijon, France,
  Aug. 28 - Sept. 1, 2023}}}
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A comprehensive study of vibration-rotation spectral patterns of the formaldehyde molecule will be reported. Vibrational energy 
levels of H$_2$CO were computed using variational nuclear motion calculations from {\it ab initio} and empirically optimized full 6-dimensional 
potential energy surfaces in the electronic ground state. {\it Ab initio} calculations were carried out using extended electronic structure 
coupled-cluster method accounting for the dynamic electron correlations including triple and quadruple excitations as well as relativistic 
and diagonal Born-Oppenheimer corrections\footnote{A.V. Nikitin, A.E. Protasevich, A.A. Rodina, M. Rey, A. Tajti, Vl.G. Tyuterev Y, J. Quant. Spectrosc. Radiat. Transfer 260, 107478 (2021).}. 
Effective Hamiltonian and effective dipole transition moments for the ro-vibrational polyads 
were derived from the {\it ab initio} surfaces using high-order contact transformations (CT) 
\footnote{V. Tyuterev, S. Tashkun, M. Rey, A. Nikitin, Mol. Phys., 120, issue 15-16 art. no. e2096140 (2022)}$^,$\footnote{M. Rey, J. Chem. Phys, 292, 108349 (2022)}. 
The analyses of experimental spectra recorded 
at T=160$-$165 K and various pressures were performed for the region of the 3-rd vibrational polyad. The experimental setup was described 
in Ref.\footnote{F.K. Tchana, F. Willaert, X. Landsheere, J.-M. Flaud, L.Lago, M. Chapuis, C. Herbeaux, P. Roy, L. Manceron, Review Scientif. Instrum. 84, 093101 (2013).}. 
The line positions and intensities were obtained by nonlinear least-squares fits with the 
SpectraPlot software\footnote{A. V. Nikitin, R. V. Kochanov, Optic. Atmos. 24, 931-941 (2011).} and analyzed using the 
CT-models for the effective Hamiltonian and effective dipole transition moments. Fifteen new vibrational levels were derived from these analyses 
in a good agreement with calculations$^1$. In the range 4500$-$4700 cm$^{-1}$, a line list with the quantum identification was produced. It can be 
useful for a global modelling of the formaldehyde spectra and for an improvement of the line parameters 
in the databases\footnote{I.E. Gordon et al., J. Quant. Spectrosc. Radiat. Transfer 277, art. no. 107949 (2022). }$^,$\footnote{T. Delahaye, et al., 
J. Mol. Spectrosc. 380, art. no. 111510 (2021).}$^,$\footnote{M. Rey, A. Nikitin, Y. Babikov, V. Tyuterev,  J. Mol. Spectrosc, 327, 138-158 (2016)}.


This work was supported by 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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