  We report on a common fragment ion formed during the
electron-ionization-induced fragmentation of three different three-ring
polycyclic aromatic hydrocarbons (PAHs), fluorene (C$_{13}$H$_{10}$),
9,10-dihydrophenanthrene (C$_{14}$H$_{12}$), and 9,10-dihydroanthracene
(C$_{14}$H$_{12}$). The infrared spectra of the mass-isolated product ions with
$m/z=165$ were obtained in a Fourier transform ion cyclotron resonance mass
spectrometer whose cell was placed inside the optical cavity of an infrared
free-electron laser, thus providing the high photon fluence required for
efficient infrared multiple-photon dissociation. The infrared spectra of the
$m/z=165$ species generated from the three different precursors were found to
be similar, suggesting the formation of a single C$_{13}$H$_{9}^+$ isomer.
Theoretical calculations using density functional theory (DFT) revealed the
fragment's identity as the closed-shell fluorenyl cation. Decomposition
pathways from each parent precursor to the fluorenyl ion are proposed on the
basis of DFT calculations. The identification of a single fragmentation product
from three different PAHs supports the notion of the existence of common
decomposition pathways of PAHs in general and can aid in understanding the
fragmentation chemistry of astronomical PAH species.
