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Observationally, the interstellar gas-phase abundance of deuterium (D) isconsiderably depleted and the missing D atoms are often postulated to have beenlocked 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 Doriginated exclusively from the Big Bang and the present-day D abundance, afteraccounting for the astration it has experienced during the Galactic evolution,provides essential clues to the primordial nucleosynthesis and the cosmologicalparameters. To quantitatively explore the extent to which PAHs could possiblyaccommodate the observed D depletion, we have previously quantum-chemicallycomputed the infrared vibrational spectra of mono-deuterated PAHs and derivedthe 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 workto multi-deuterated PAH species of different deuterations, sizes andstructures. We find that both the intrinsic band strengths A$_{3.3}$ andA$_{4.4}$ and their ratios A$_{4.4}$/A$_{3.3}$ not only show little variationsamong PAHs of different deuterations, sizes and structures, they are alsoclosely similar to that of mono-deuterated PAHs. Therefore, a PAH deuterationlevel (i.e., the fraction of peripheral atoms attached to C atoms in the formof D) of ~2.4% previously estimated from the observed 4.4 $\mu$m to 3.3 $\mu$mband ratio based on the A$_{4.4}$/A$_{3.3}$ ratio of mono-deuterated PAHs isrobust.

Deuterated Polycyclic Aromatic Hydrocarbons in the Interstellar Medium: The C--D Band Strengths of Multi-Deuterated Species