Polycyclic Aromatic Hydrocarbons with Aliphatic Sidegroups: Intensity Scaling for the C-H Stretching Modes and Astrophysical Implications

The so-called unidentified infrared emission (UIE) features at 3.3, 6.2, 7.7, 8.6, and 11.3 $\mu$m ubiquitously seen in a wide variety of astrophysical regions are generally attributed to polycyclic aromatic hydrocarbon (PAH) molecules. Astronomical PAHs may have an aliphatic component as revealed by the detection in many UIE sources of the aliphatic C-H stretching feature at 3.4 $\mu$m. The ratio of the observed intensity of the 3.4 $\mu$m feature to that of the 3.3 $\mu$m aromatic C-H feature allows one to estimate the aliphatic fraction of the UIE carriers. This requires the knowledge of 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 ($A_{3.4}$). Lacking experimental data on $A_{3.3}$ and $A_{3.4}$ for the UIE candidate materials, one often has to rely on quantum-chemical computations. Although the second-order Moller-Plesset (MP2) perturbation theory with a large basis set is more accurate than the B3LYP density functional theory, MP2 is computationally very demanding and impractical for large molecules. Based on methylated PAHs, we show here that, by scaling the band strengths computed at an inexpensive level (e.g., B3LYP/6-31G*) we are able to obtain band strengths as accurate as that computed at far more expensive levels (e.g., MP2/6-311+G(3df,3pd)).