  We have investigated the effect of hydrostatic pressure and temperature on
phase stability of hydro-nitrogen solids using dispersion corrected Density
Functional Theory calculations. From our total energy calculations, Ammonium
Azide (AA) is found to be the thermodynamic ground state of N$_4$H$_4$
compounds in preference to Trans-Tetrazene (TTZ), Hydro-Nitrogen Solid-1
(HNS-1) and HNS-2 phases. We have carried out a detailed study on structure and
lattice dynamics of the equilibrium phase (AA). AA undergoes a phase transition
to TTZ at around $\sim$ 39-43 GPa followed by TTZ to HNS-1 at around 80-90 GPa
under the studied temperature range of 0-650 K. The accelerated and decelerated
compression of $a$ and $c$ lattice constants suggest that the ambient phase of
AA transforms to a tetragonal phase and then to a low symmetry structure with
less anisotropy up on further compression. We have noticed that the angle made
by Type-II azides with $c$-axis shows a rapid decrease and reaches a minimum
value at 12 GPa, and thereafter increases up to 50 GPa. Softening of the shear
elastic moduli is suggestive of a mechanical instability of AA under high
pressure. In addition, we have also performed density functional perturbation
theory calculations to obtain the vibrational spectrum of AA at ambient as well
as at high pressures. Further, we have made a complete assignment of all the
vibrational modes which is in good agreement with the experimental observations
at ambient pressure. Also the calculated pressure dependent IR spectra show
that the N-H stretching frequencies undergo a red and blue-shift corresponding
to strengthening and weakening of hydrogen bonding, respectively below and
above 4 GPa.
