Superhydrogenated Polycyclic Aromatic Hydrocarbon Molecules: Vibrational
  Spectra in the Infrared
  Superhydrogenated polycyclic aromatic hydrocarbons (PAHs) may be present in
H-rich and ultraviolet-poor benign regions. The addition of excess H atoms to
PAHs converts the aromatic bonds into aliphatic bonds, the strongest of which
falls near 3.4 $\mu$m. Therefore, superhydrogenated PAHs are often hypothesized
as a carrier of the 3.4 $\mu$m emission feature which typically accompanies the
stronger 3.3 $\mu$m aromatic C--H stretching feature. To assess this
hypothesis, we use density function theory to compute the IR vibrational
spectra of superhydrogenated PAHs and their ions of various sizes (ranging from
benzene, naphthalene to perylene and coronene) and of various degrees of
hydrogenation (ranging from minimal hydrogenation to heavy hydrogenation). For
each molecule, we derive the intrinsic oscillator strengths of the 3.3 $\mu$m
aromatic C--H stretch ($A_{3.3}$) and the 3.4 $\mu$m aliphatic C--H stretch
($A_{3.4}$). By comparing the computationally-derived mean ratio of $\langle
A_{3.4}/A_{3.3}\rangle\sim1.98$ with the mean ratio of the observed intensities
$\langle I_{3.4}/I_{3.3}\rangle\sim0.12$, we find that the degree of
superhydrogenation --- the fraction of C atoms attached with excess H atoms ---
is only $\sim2.2\%$ for neutral PAHs which predominantly emit the 3.3 and 3.4
$\mu$m features. We also determine for each molecule the intrinsic band
strengths of the 6.2 $\mu$m aromatic C--C stretch ($A_{6.2}$) and the 6.85
$\mu$m aliphatic C--H deformation ($A_{6.85}$). We derive the degree of
superhydrogenation from the mean ratio of the observed intensities $\langle
I_{6.85}/I_{6.2}\rangle\sim0.10$ and $\langle A_{6.85}/A_{6.2}\rangle\sim1.53$
for neutrals and $\langle A_{6.85}/A_{6.2}\rangle\sim1.23$ for cations to be
$\lesssim 3.1\%$ for neutrals and $\lesssim 8.6\%$ for cations. We conclude
that astrophysical PAHs are primarily aromatic and are only marginally
superhydrogenated.
