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\title{A NUMERICAL-TENSORIAL ``HYBRID'' NUCLEAR-MOTION HAMILTONIAN AND DIPOLE MOMENT FOR SPECTRA CALCULATION OF POLYATOMIC NONRIGID MOLECULES}

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\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}

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\author{\FirstName OLEG \LastName EGOROV, \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}


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\fancyhead[C]{{\footnotesize \textit{HRMS, 28th Colloquium, Dijon, France,
  Aug. 28 - Sept. 1, 2023}}}
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The analysis and modelling of high-resolution spectra of nonrigid molecules require a specific Hamiltonian 
and group-theoretical formulation which differs significantly  
from that of more familiar rigid systems. Within the framework of the Hougen-Bunker-Johns (HBJ) theory\footnote{J. T. Hougen, P. R. Bunker, J. W. C. Johns, J. Mol. Spectrosc., {\bf 34} (1970) 136}, this work  
is devoted to the construction of a nonrigid Hamiltonian based on a suitable combination of numerical calculations 
for the nonrigid part in conjunction with the irreducible tensor operator method for the rigid part.  A so-called ``hybrid'' model is thus introduced\footnote{M. Rey, D. Viglaska, O. Egorov, A. V. Nikitin, (2023, submitted).}.  
For the first time, a variational calculation from {\it ab initio} potential energy surfaces is performed using the hybrid formulation of the 
exact HBJ kinetic energy operator expressed in terms of vibrational, large-amplitude motion and rotational tensor operators through the use of both curvilinear and rectilinear coordinates. 
Group theory for nonrigid molecules plays a central role in the characterization of the overall tunnelling splittings 
and will be  discussed. The construction of the dipole moment operator will be also examined. 

Validation tests consisting in a careful convergence study of the energy levels as well as in a comparison of 
results obtained from independent computer codes are 
given for the nonrigid molecules CH$_2$, CH$_3$, NH$_3$ and H$_2$O$_2$. 
This work$-$combined with our recent method for constructing effective models\footnote{M. Rey, J. Chem. Phys. {\bf 156} (2022) 224103. \href{https://doi.org/10.1063/5.0089097}{doi.org/10.1063/5.0089097}}$-$will pave the way to the analysis of high-resolution spectra of larger nonrigid systems. 



This work is supported by the french Agence Nationale de la Recherche (ANR TEMMEX, Grant No. 21-CE30-0053-01) and the Russian Scientific Foundation (RSF, No. 22-42-09022).
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