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\title{REVISITING THE GROUND STATE SYMMETRY OF C$_{60}^{+}$ VIA VUV PHOTOIONIZATION AND DFTB CALCULATIONS}

\author{\underline{\FirstName H.R. \LastName HRODMARSSON}}
\address{Laboratoire Interuniversitaire des Syst\`emes Atmosph\'eriques, CNRS UMR 7583, Universit\'e Paris-Est Cr\'eteil et Universit\'e
Paris Cit\'e, IPSL, 61 av. G\'en\'eral de Gaulle, 94010 Cr\'eteil, France}

\author{\FirstName M. \LastName RAPACIOLI, \FirstName F. \LastName SPIEGELMAN}
\address{Laboratoire de Chimie et Physique Quantiques LCPQ/FeRMI, UMR5626, Universit\'e de Toulouse (UPS) and CNRS, Toulouse, France}

\author{\FirstName G.A. \LastName GARCIA, \FirstName L. \LastName NAHON}
\address{Synchrotron SOLEIL, LOrme des Merisiers, St Aubin, BP 48, Gif sur Yvette, France}

\author{\FirstName J. \LastName BOUWMAN}
\address{Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, CO 80303,USA;
Department of Chemistry, University of Colorado, Boulder, CO 80309, USA;
Institute for Modeling Plasma, Atmospheres, and Cosmic Dust (IMPACT), University of Colorado, Boulder, CO 80303, USA.}

\author{\FirstName H. \LastName LINNARTZ}
\address{Laboratory for Astrophysics, Leiden Observatory, Leiden University, PO Box 9513, NL-2300 RA Leiden, The Netherlands}

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\fancyhead[C]{{\footnotesize \textit{HRMS, 28th Colloquium, Dijon, France,
  Aug. 28 - Sept. 1, 2023}}}
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Recently we reviewed and studied the photoionization dynamics of C$_{60}$ that are of great interest to the astrochemical community as four of the diffuse interstellar bands have been assigned to electronic transitions in the C$_{60}^+$ cation. However, there is still ambiguity about the absolute ground state symmetry of the C$_{60}^+$ cation and our previous analysis appeared to indicate D$_{3d}$ symmetry in stark contrast to theoretical predictions of D$_{5d}$ symmetry. We have revisited our experimental measurements to compare with theoretical works of the frequencies of the hg Jahn-Teller active modes which couple to the $^$2H$_u$ ground state of the C$_{60}^+$ cation. By reanalyzing our measured threshold photoelectron spectrum (TPES) of the ground state of C$_{60}$, we find a striking resemblance to the theoretical spectrum and we provide tentative assignments for many of the h$_g$ modes. In light of both the high temperature of our experiment and that the ab initio works could not account for anharmonicities, we also  performed Molecule Dynamics (MD) simulations with the Density Functional based Tight Binding (DFTB) potential to assess the effects of temperature on the vibrational bands of C$_{60}$ and C$_{60}^+$ and derive anharmonicity factors to aid the interpretation of our measured TPES and the comparisons to the ab initio spectrum. We showcase the complementarity of utilizing MD calculations to predict the anharmonicities at high temperatures expected in our experiment. This allows us to provide robust evidence for a D$_{5d}$ symmetric ground state of the C$_{60}^+$ cation, rather than a D$_{3d}$ symmetric minimum which has been proposed in other experiments. This allows us to assign the first adiabatic ionization transition and thus determine the ionization energy of C$_{60}$ with greater accuracy than has been achieved at 7.595 $\pm$ 0.003 eV; and postulate on the energetics of additional DIBs that could be assigned to C$_{60}^+$ in the future. 

       
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