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\title{DUO: A GENERAL MULTI-STATE PROGRAM FOR SOLVING THE NUCLEAR MOTION SCHR\"{O}DINGER EQUATION FOR DIATOMIC MOLECULES WITH ARBITRARY COUPLINGS}

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\author{\underline{\FirstName   S.N. \LastName YURCHENKO},
\underline{\FirstName J. \LastName TENNYSON},
\underline{\FirstName C.A.  \LastName BOWESMAN},
\underline{\FirstName R.P.  \LastName BRADY},
\underline{\FirstName M.  \LastName PEZZELLA},
\underline{\FirstName G.  \LastName MITEV},
\FirstName W.  \LastName SOMOGYI,
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\address{Department of Physics and Astronomy, University College London, Gower Street, WC1E 6BT London, United Kingdom}
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\fancyhead[C]{{\footnotesize \textit{HRMS, 28th Colloquium, Dijon, France,
  Aug. 28 - Sept. 1, 2023}}}
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\textsc{Duo} is a general, user-friendly program for computing rotational, rovibrational and rovibronic spectra of  diatomic molecules.\footnote{ \citeref{S.N. Yurchenko, L. Lodi, J. Tennyson, and A.V. Stolyarov}{\href{http://dx.doi.org/10.1016/j.cpc.2015.12.021}{Duo: A general program for calculating spectra of diatomic molecules}}{Comput. Phys. Commun.}{202}{262}{2016} } \textsc{Duo} solves the Schr\"{o}dinger equation for the general case of an arbitrary number and type of couplings between electronic states (typical for open-shell diatomics and excited states). Possible couplings include spin-orbit, angular momenta, spin-rotational and spin-spin.

\textsc{Duo} requires user-specified potential energy curves and, if relevant, dipole moment, coupling and correction curves. From these it computes energy levels, line positions and line intensities.  \textsc{Duo} can refine potential energy and coupling curves to best reproduce reference data such as experimental energy levels or line positions. \textsc{Duo} is provided as a free-access Fortran 2003 program.\footnote{\href{https://github.com/exomol/Duo/}{https://github.com/exomol/Duo/}} \textsc{Duo} has been used for many studies of diatomics including \href{http://dx.doi.org/10.1093/mnras/sty1524}{AlH}, \href{http://dx.doi.org/10.1093/mnras/stv507}{AlO}, \href{http://dx.doi.org/10.1093/mnras/stac3757}{AlCl}, \href{http://dx.doi.org/10.1093/mnras/sty2050}{C$_2$}, \href{http://dx.doi.org/10.1093/mnras/stac371}{CaH}, \href{http://dx.doi.org/10.3847/1538-4365/ab85cb}{CaO}, \href{http://dx.doi.org/10.1093/mnras/stac1634}{HF}, \href{http://dx.doi.org/10.1093/mnras/stac1634}{HCl}, \href{http://dx.doi.org/10.1093/mnras/stac371}{MgH}, \href{http://dx.doi.org/10.1093/mnras/stz912}{MgO}, \href{http://dx.doi.org/10.1093/mnras/stab3357}{NaO}, \href{http://dx.doi.org/10.1093/mnras/stab1154}{NO}, \href{http://dx.doi.org/10.1093/mnras/sty939}{NS}, \href{http://dx.doi.org/10.1093/mnras/stx2229}{PO}, \href{http://dx.doi.org/10.1093/mnras/stx2229}{PS}, \href{http://dx.doi.org/10.1093/mnras/stz2517}{SH}, \href{http://dx.doi.org/10.1093/mnras/stac2004}{SiN}, \href{http://dx.doi.org/10.1093/mnras/stx2738}{SiH}, \href{http://dx.doi.org/10.1093/mnras/stab3267}{SiO}, \href{http://dx.doi.org/10.1039/D2CP03051A}{SO}, \href{http://dx.doi.org/10.1093/mnras/stz1818}{TiO}, \href{http://dx.doi.org/10.1093/mnras/stw1969}{VO}, as part of the ExoMol project.\footnote{\citeref{J. Tennyson and S.N. Yurchenko}{\href{https://doi.org/10.1093/astrogeo/atab102}{ExoMol at 10}}{Astron. Geophys.}{62}{6}{2021}} In this presentation, we report recent \textsc{Duo} updates, including implementations of

\begin{itemize}
  \item Non-adiabatic couplings;
  \item \href{http://dx.doi.org/10.1063/5.0105965}{Hyperfine effects}, such as hyperfine resolved spectra and refinement;
  \item Reduced radial density analysis;
  \item Treatment of continuum states;
  \item \href{http://dx.doi.org/10.1093/rasti/rzad014}{Pre-dissociation effects};
  \item \href{http://dx.doi.org/10.1063/5.0063256}{Quadrupole} and magnetic spectra; %\footnote{\citeref{W. Somogyi, S. N. Yurchenko, and A. Yachmenev}{Calculation of electric quadrupole linestrengths for diatomic molecules: Application to the H$_2$, CO, HF, and O$_2$ molecules}{J. Chem. Phys.}{155}{214303}{2021}}
  \item \href{http://dx.doi.org/10.1093/mnras/stac1634}{Photo-absorption cross-sections}.
\end{itemize}

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