The Carriers of the "Unidentified" Infrared Emission Features: Clues from Polycyclic Aromatic Hydrocarbons with Aliphatic Sidegroups

The "unidentified" infrared emission (UIE) features at 3.3, 6.2, 7.7, 8.6, and 11.3 $\mu$m are ubiquitously seen in various astrophysical regions. The UIE features are characteristic of the stretching and bending vibrations of aromatic hydrocarbons. The 3.3 $\mu$m feature resulting from aromatic C--H stretches is often accompanied by a weaker feature at 3.4 $\mu$m often attributed to aliphatic C--H stretches. The ratio of the observed intensity of the 3.3 $\mu$m aromatic C--H feature ($I_{3.3}$) to that of the 3.4 $\mu$m aliphatic C--H feature ($I_{3.4}$) allows one to estimate the aliphatic fraction (i.e. $N_{\rm C,aliph}/N_{\rm C,arom}$, the number of C atoms in aliphatic units to that in aromatic rings) of the UIE carriers, provided 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 ($A_{3.4}$) are known. In this article we summarize the computational results on $A_{3.3}$ and $A_{3.4}$ and their implications for the aromaticity and aliphaticity of the UIE carriers. We use density functional theory and second-order perturbation theory to derive $A_{3.3}$ and $A_{3.4}$ from the infrared vibrational spectra of seven PAHs with various aliphatic substituents (e.g., methyl-, dimethyl-, ethyl-, propyl-, butyl-PAHs, and PAHs with unsaturated alkyl-chains). The mean band strengths of the aromatic ($A_{3.3}$) and aliphatic ($A_{3.4}$) C--H stretches are derived and then employed to estimate the aliphatic fraction of the UIE carriers by comparing $A_{3.4}$/$A_{3.3}$ with $I_{3.4}$/$I_{3.3}$. We conclude that the UIE emitters are predominantly aromatic, as revealed by the observationally-derived ratio <$I_{3.4}$/$I_{3.3}$> ~ 0.12 and the computationally-derived ratio <$A_{3.4}$/$A_{3.3}$> ~ 1.76 which suggest an upper limit of $N_{\rm C,aliph}/N_{\rm C,arom}$ ~ 0.02 for the aliphatic fraction of the UIE carriers.