Hydro-nitrogen solids are potential high energy density materials (HEDMs) due to high mass ratio of nitrogen which find wide range of applications as propellants and explosives. In the present work, we report the structural and vibrational properties of Tetramethyl Ammonium Azide (TMAA) and HydroZonium Azide(HZA) using density functional theory calculations by treating weak intermolecular interactions. The obtained ground state parameters using vdW-TS method are in good agreement with the experimental data. The pressure dependent lattice constants, compressibility and equation of state are discussed. The obtained equilibrium bulk moduli show the soft nature of these materials. The compressibility curves reveal that these compounds are highly compressible along crystallographic a-axis.We have also calculated the zone-center phonon frequencies and made a complete analysis of vibrational spectra at ambient as well as at high pressure. Contraction and elongation of C-H and N-H (NH₃ stretching) bonds under pressure lead to blue- and red-shift of the frequencies in the mid-IR region for TMAA and HZA compounds, respectively