Deuterated Polycyclic Aromatic Hydrocarbons in the Interstellar Medium:
  The C--D Band Strengths of Multi-Deuterated Species
  Observationally, the interstellar gas-phase abundance of deuterium (D) is
considerably depleted and the missing D atoms are often postulated to have been
locked up into carbonaceous solids and polycyclic aromatic hydrocarbon (PAH)
molecules. An accurate knowledge of the fractional amount of D (relative to H)
tied up in carbon dust and PAHs has important cosmological implications since D
originated exclusively from the Big Bang and the present-day D abundance, after
accounting for the astration it has experienced during the Galactic evolution,
provides essential clues to the primordial nucleosynthesis and the cosmological
parameters. To quantitatively explore the extent to which PAHs could possibly
accommodate the observed D depletion, we have previously quantum-chemically
computed the infrared vibrational spectra of mono-deuterated PAHs and derived
the mean intrinsic band strengths of the 3.3 $\mu$m C--H stretch (A$_{3.3}$)
and the 4.4 $\mu$m C--D stretch (A$_{4.4}$). Here we extend our previous work
to multi-deuterated PAH species of different deuterations, sizes and
structures. We find that both the intrinsic band strengths A$_{3.3}$ and
A$_{4.4}$ and their ratios A$_{4.4}$/A$_{3.3}$ not only show little variations
among PAHs of different deuterations, sizes and structures, they are also
closely similar to that of mono-deuterated PAHs. Therefore, a PAH deuteration
level (i.e., the fraction of peripheral atoms attached to C atoms in the form
of D) of ~2.4% previously estimated from the observed 4.4 $\mu$m to 3.3 $\mu$m
band ratio based on the A$_{4.4}$/A$_{3.3}$ ratio of mono-deuterated PAHs is
robust.
