The 3.3 $mu$m unidentified infrared emission feature is commonly attributed to C-H stretching band of aromatic molecules. Astronomical observations have shown that this feature is composed of two separate bands at 3.28 and 3.30 $mu$m and the origin of these two bands is unclear. In this paper, we perform vibrational analyses based on quantum mechanical calculations of 153 organic molecules, including both pure aromatic molecules and molecules with mixed aromatic/olefinic/aliphatic hydridizations. We find that many of the C-H stretching vibrational modes in polycyclic aromatic hydrocarbon (PAH) molecules are coupled. Even considering the un-coupled modes only, the correlation between the band intensity ratios and the structure of the PAH molecule is not observed and the 3.28 and 3.30 $mu$m features cannot be directly interpreted in the PAH model. Based on these results, the possible aromatic, olefinic and aliphatic origins of the 3.3 $mu$m feature are discussed. We suggest that the 3.28 $mu$m feature is assigned to aromatic C-H stretch whereas the 3.30 $mu$m feature is olefinic. From the ratio of these two features, the relative olefinic to aromatic content of the carrier can be determined.
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