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\title{ANALYSIS AND MODELING OF THE THRESHOLD PHOTOELECTRON SPECTRUM OF SiH$_2$ WITH MCTDH} 
\author{\FirstName N.\ L.\ \LastName CHEN, \FirstName B.\ \LastName GANS, \FirstName S.\ \LastName BOY\'E-P\'ERONNE, \FirstName L.\ H.\ \LastName COUDERT}
\address{Inst.\ des Sciences Mol\'eculaires d'Orsay, Univ.\ Paris-Saclay - CNRS, Orsay, France} 
\author{\FirstName J.-C.\ \LastName LOISON} 
\address{Institut des Sciences Mol\'eculaires, Universit\'e de Bordeaux, Bordeaux, France} 
\author{\FirstName G.\ A.\ \LastName GARCIA, \FirstName S.\ \LastName HARTWEG} 
\address{DESIRS beamline, Synchrotron SOLEIL, Gif-sur-Yvette, France} 
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\fancyhead[C]{{\footnotesize\textit{HRMS, 28th Colloquium, Dijon, France, Aug.\ 28 - Sep.\ 1, 2023}}}
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\begin{document}
\maketitle 
Although the ground $\widetilde{X}\,^{1\!}A_1$
electronic state of silylene SiH$_2$ is fairly well
characterized,\footnote{Clark, Ownes, Tennyson, and Yurchenko,
{\em J.\ Quant.\ Spec. Rad.\ Transf.}~{\bf 246} (2020) 106929}
fewer results are available about its first excited triplet
$\tilde{a}\,^{3\!}B_1$ electronic state and about its cationic
species ${\rm SiH}_2^+$.  The ground electronic state of the latter
is split into bent $\widetilde{X}^+\,^{2\!}A_1$ and linear
$\widetilde{A}^+\,^{2\!}B_1$ electronic states by the
Renner-Teller coupling.\footnote{Gu, Huang, Kong, and Liu,
{\em J.\ Mol.\ Struct.\ (Theochm)}~{\bf 253} (1992) 217}

Threshold photoelectron (TPE) spectroscopy has been used to
spectroscopically study the cationic species
$\mbox{SiH}_2^+$ of silylene produced through successive H atom
abstractions induced by fluorine atoms in gaseous silane.
The TPE spectrum, recorded at Synchrotron SOLEIL from
7.5 to 11.5~eV using VUV synchrotron radiation, displays
several sharp features and was modeled using wavepacket
propagation.\footnote{\label{viel}Viel, Eisfeld, Evenhuis,
and Manthe, {\em Chem.\ Phys.}~{\bf 347} (2008) 331; and Eroms,
Jungen, and Meyer, {\em J.\ Phys.\ Chem.\ A}~{\bf 114} (2010)
9893} $\omega$B97\-XD {\em ab initio} calculations were carried
out using cc-PVTZ correlation-consistent basis set functions
to retrieve 3-D potential energy surfaces for the various
electronic states. % involved in the TPE spectrum.
The ground
electronic state of the neutral (cation) is characterized
by an equilibrium bond length and a bond angle of 1.516~\AA\
and 92.2$^{\circ}$ (1.474~\AA\ and 121$^{\circ}$).  The MCTDH
method\footnote{\label{beck}Beck, J\"ackle, Worth, and Meyer,
{\em Phys.\ Rep.}~{\bf 324} (2000) 1; and Meyer, Graham,
and Worth, {\em Theor.\ Chem.\ Acc.}~{\bf 109} (2003) 251}
was first used to obtain the 3-D vibrational wavefunctions
of the neutral species $\widetilde{X}\,^{1\!}A_1$ and
$\tilde{a}\,^{3\!}B_1$ electronic states using propagation in
negative imaginary time. The wavefunctions thus obtained were
then time-propagated in the potential energy surfaces of the
coupled electronic states of the cationic species using also
MCTDH.\textsuperscript{\ref{viel},\ref{beck}} The threshold photoelectron
spectrum was at last computed as the Fourier transform of the
auto-correlation function.

In the poster, the results of the rovibronic energy calculations
will be reported and the experimental TPE spectrum will be
compared to the theoretical one. The importance of the Renner-Teller
coupling will be assessed and the vibrational temperature
which best reproduces the experimental spectrum will be evaluated.\end{document}
