  The 11.2 $\mu$m emission band belongs to the family of the `Unidentified'
Infrared (UIR) emission bands seen in many astronomical environments. In this
work we present a theoretical interpretation of the band characteristics and
profile variation for a number of astrophysical sources in which the carriers
are subject to a range of physical conditions. The results of Density
Functional Theory (DFT) calculations for the solo out-of-plane (OOP)
vibrational bending modes of large polycyclic aromatic hydrocarbon (PAH)
molecules are used as input for a detailed emission model which includes the
temperature and mass dependence of PAH band wavelength, and a PAH mass
distribution that varies with object. Comparison of the model with astronomical
spectra indicates that the 11.2 $\mu$m band asymmetry and profile variation can
be explained principally in terms of the mass distribution of neutral PAHs with
a small contribution from anharmonic effects.
