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\title{SNAPS \& HUBS}

\author{\underline{\FirstName R. \LastName T\'OBI\'AS}}
\address{MTA-ELTE Complex Chemical Systems Research Group,
         H-1518 Budapest 112, P.O. Box 32, Hungary}
         
\author{\FirstName A. G. \LastName CS\'ASZ\'AR}
\address{Institute of Chemistry, ELTE E\"otv\"os Lor\'and University,
                    H-1117 Budapest, P\'azm\'any P\'eter s\'et\'any 1/A, Hungary \& 
         MTA-ELTE Complex Chemical Systems Research Group,
                           H-1518 Budapest 112, P.O. Box 32, Hungary}
         
\author{\FirstName M. L. \LastName DIOUF, 
        \FirstName P. \LastName BLOEM, 
        \FirstName F. M. J. \LastName COZIJN, 
        \FirstName W. \LastName UBACHS}
\address{Department of Physics and Astronomy, LaserLaB, Vrije Universiteit, 
       De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands}



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\fancyhead[C]{{\footnotesize \textit{HRMS, 28th Colloquium, Dijon, France,
  Aug. 28 - Sept. 1, 2023}}}
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The theory of spectroscopic networks%
\footnote{A. G. Cs\'asz\'ar and T. Furtenbacher. \emph{J. Mol. Spectrosc.}, \textbf{266}, 
          99--103, (2011), \href{https://doi.org/10.1016/j.jms.2011.03.031}{DOI}.}
offers a powerful instrument for the intelligent design and validation of precision-%
spectroscopy experiments, as well as the subsequent derivation of accurate rovibrational 
energies,%
\footnote{\label{20ToFuSiCs} R. T\'obi\'as, T. Furtenbacher, I. Simk\'o, A. G. Cs\'asz\'ar, 
M. L. Diouf, F. M. J. Cozijn, J. M. A. Staa, E. J. Salumbides, and W. Ubachs, 
\emph{Nat. Commun.}, \textbf{11}, 1708 (2020), 
\href{https://doi.org/10.1038/s41467-020-15430-6}{DOI}.}$^,$%
\footnote{M. L. Diouf, R. T\'obi\'as, I. Simk\'o, F. M. J. Cozijn, E. J. Salumbides, 
          W. Ubachs, and A. G. Cs\'asz\'ar. \emph{J. Phys. Chem. Ref. Data}, 
          \textbf{50}, 023106 (2021) 
\href{https://doi.org/10.1063/5.0052744}{DOI}.}$^,$%
\footnote{M. L. Diouf, R. T\'obi\'as, T. S. van der Schaaf, F. M. J. Cozijn, 
          E. J. Salumbides, A. G. Cs\'asz\'ar, and W. Ubachs. \emph{Mol. Phys.}, 
          \emph{120}, e2050430 (2022)
\href{https://doi.org/10.1080/00268976.2022.2050430}{DOI}.}$^,$%
\footnote{R. T\'obi\'as, M. L. Diouf, P. Bloem, F. M. J. Cozijn, 
          W. Ubachs, and A. G. Cs\'asz\'ar, \emph{Nat. Chem.} 
          \emph{to be submitted} (2023).}
in particular those associated with hubs (high-degree nodes) of the network. 
Through a joint experimental and theoretical approach, absolute energies have been determined 
for a large number of hubs in the experimental spectroscopic networks of H$_2^{~16}$O and 
H$_2^{~18}$O, with an accuracy of a few times 10$^{-7}$ cm$^{-1}$. 
The Lamb-dip measurements utilized two noise-immune cavity-enhanced optical heterodyne 
molecular spectroscopy (NICE-OHMS) apparata%
\footnote{F. M. J. Cozijn, P. Dupr\'e, E. J. Salumbides, K. S. E. Eikema, and W. Ubachs, 
          \emph{Phys. Rev. Lett.}, \textbf{120}, 153002 (2018)
\href{https://doi.org/10.1103/PhysRevLett.120.153002}{DOI}.}$^,$%
\footnote{F. Cozijn, M. Diouf, and W. Ubachs. arXiv preprint, arXiv:2303.17818 (2023),
\href{https://doi.org/10.48550/arXiv.2303.17818}{Link}.}
and three probe lasers covering different wavenumber ranges. 
The observed lines, whose lower states belong to the vibrational ground state and the 
bending fundamental, were selected \emph{via} the spectroscopic-network-assisted precision 
spectroscopy (SNAPS) approach.\footref{20ToFuSiCs}
The accurately known energy levels are involved in thousands of unique transitions already 
measured, though at much lower accuracy, for H$_2^{~16}$O and H$_2^{~18}$O. 
From the ultraprecise absolute energies a large number of benchmark-quality predicted 
transitions has been deduced, which could be employed as frequency standards in 
high-resolution Fourier-transform infrared spectroscopy.


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