Theoretical study of infrared spectra of interstellar PAH molecules with
  N, NH & NH$_2$ incorporation
  This work presents theoretical calculations of infrared spectra of nitrogen
(N)-containing polycyclic aromatic hydrocarbon (PAH) molecules with
incorporation of N, NH and NH$_2$ using density functional theory (DFT). The
properties of their vibrational modes in 2--15 $\mu \rm m$ are investigated in
relation to the Unidentified Infrared (UIR) bands. It is found that neutral
PAHs, when incorporated with NH$_2$ and N (at inner positions), produce intense
infrared bands at 6.2, 7.7 and 8.6 $\mu \rm m$ that have been normally
attributed to ionized PAHs so far. The present results suggest that strong
bands at 6.2 and 11.2 $\mu \rm m$ can arise from the same charge state of some
N-containing PAHs, arguing that there might be some N-abundant astronomical
regions where the 6.2 to 11.2 $\mu \rm m$ band ratio is not a direct indicator
of PAHs' ionization. PAHs with NH$_2$ and N inside the carbon structure show
the UIR band features characteristic to star-forming regions as well as
reflection nebulae (Class A), whereas PAHs with N at the periphery have similar
spectra to the UIR bands seen in planetary nebulae and post-AGB stars (Class
B). The presence of N atom at the periphery of a PAH may attract H or H$^{+}$
to form N-H and N-H$_2$ bonds, exhibiting features near 2.9--3.0 $\mu \rm m$,
which are not yet observationally detected. The absence of such features in the
observations constrains the contribution of NH and NH$_2$ substituted PAHs that
could be better tested with concentrated observations in this range. However,
PAHs with N without H either at the periphery or inside the carbon structure do
not have the abundance constraint due to the absence of 2.9--3.0 $\mu \rm m$
features and are relevant in terms of positions of the UIR bands. Extensive
theoretical and experimental studies are required to obtain deeper insight.
