The 11.3 $\mu$m emission feature is a prominent member of the family of unidentified infrared emission (UIE) bands and is frequently attributed to out-of-plane bending modes of polycyclic aromatic hydrocarbon (PAH) molecules. We have performed quantum mechanical calculations of 60 neutral PAH molecules and found that it is difficult to reconcile the observed astronomical feature with any or a mix of these PAH molecules. We have further analyzed the fitting of spectra of several astronomical objects by the NASA PAH database program and found that reasonable fittings to the observed spectra are only possible by including significant contributions from oxygen and/or magnesium containing molecules in the mix. A mixed of pure PAH molecules, even including units of different sizes, geometry and charged states, is unable to fit the astronomical spectra. Preliminary theoretical results on the vibrational spectra of simple molecules with mixed aromatic/aliphatic structures show that these structures have consistent bundles of vibrational modes and could be viable carriers of the UIE bands.