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)).
