  The structural, electronic, optical and vibrational properties of LiN$_3$
under high pressure have been studied using plane wave pseudopotentials within
the generalized gradient approximation for the exchange and correlation
functional. The calculated lattice parameters agree quite well with
experiments. The calculated bulk modulus value is found to be 23.23 GPa which
is in good agreement with the experimental value of 20.5 GPa. Our calculations
reproduce well the trends in high pressure behavior of the structural
parameters. The present results show that the compressibility of LiN$_3$
crystal is anisotropic and the crystallographic b-axis is more compressible
when compared to a- and c-axis which is also consistent with the experiment.
The computed elastic constants clearly shows that LiN$_3$ is a mechanically
stable system and the calculated elastic constants follows the order C$_{33}$
$>$ C$_{11}$ $>$ C$_{22}$ implies that the LiN$_3$ lattice is stiffer along
c-axis and relatively weaker along b-axis. Under the application of pressure
the magnitude of the electronic band gap value decreases, indicating that the
system has the tendency to become semi conductor at high pressures. The optical
properties such as refractive index, absorption spectra and photo conductivity
along the three crystallographic directions have been calculated at ambient as
well as at high pressures. The calculated refractive index shows that the
system is optically anisotropic and the anisotropy increases with increase in
pressure. The observed peaks in the absorption and photo conductivity spectra
are found to shift towards the higher energy region as pressure increases which
imply that in LiN$_3$ decomposition is favored under pressure with the action
of light.

Materials Science