  A systematic computational study on the structural, electronic, bonding, and
optical properties of orthorhombic ammonium azide (NH$_4$N$_3$) has been
performed using planewave pseudopotential (PW-PP) method based on density
functional theory (DFT). Semiempirical dispersion correction schemes have been
used to account for non-bonded interactions in molecular crystalline
NH$_4$N$_3$. The ground state lattice parameters and fractional co-ordinates
obtained using the dispersion correction schemes are in excellent agreement
with experimental results. We calculated the single crystal elastic constants
of NH$_4$N$_3$ and its sensitivity is interpreted through the observed ordering
of the elastic constants (C$_{33}$ $>$ C$_{11}$ $>$ C$_{22}$). The electronic
structure and optical properties were calculated using full potential
linearized augmented plane wave (FP-LAPW) approach with recently developed
functional of Tran-Blaha modified Becke-Johnson (TB-mBJ) potential. The TB-mBJ
electronic structure shows that NH$_4$N$_3$ is a direct band gap insulator with
a band gap of 5.08 eV, while the calculated band gap with standard generalized
gradient approximation is found to be 4.10 eV. The optical anisotropy is
analyzed through the calculated optical constants namely dielectric function
and refractive index along three different crystallographic axes. The
absorption spectra reveal that NH$_4$N$_3$ is sensitive to ultraviolet (UV)
light. Further, we also analyzed the detonation characteristics of the
NH$_4$N$_3$ using the reported heat of formation and calculated density.
NH$_4$N$_3$ is found to have a detonation velocity of 6.45 km/s and a
detonation pressure about 15.16 GPa computed by Kamlet-Jacobs empirical
equations.
