  We report a detailed first principles study on the structural, elastic,
vibrational and thermodynamic properties of layered structure energetic alkali
metal azides KN$_3$ and RbN$_3$. All the calculations were carried out by means
of plane wave pseudopotential method with and without including van der Waals
interactions. The calculated ground state structural properties are improved to
a greater extent by the inclusion of dispersion corrections, implies that the
van der Waals interactions play a major role on the physical properties of
these systems. The elastic constants and the related bulk mechanical properties
for the tetragonal KN$_3$ and RbN$_3$ have been calculated using both the
methods and found that the compounds are mechanically stable systems. The
magnitude of the calculated elastic constants increases in the order RbN$_3$
$<$ KN$_3$ implying higher elastic stiffness for KN$_3$, the fact also
confirmed by the higher values of bulk, shear and Young's moduli of KN$_3$ than
RbN$_3$. Moreover, the calculated elastic constants follows the inequality
C$_{33}$ $<$ C$_{11}$ which indicates the presence of more number of
intermolecular interactions along a-axis over c-axis of the azide lattices. A
correlation has been proposed to relate the calculated elastic constants to the
decomposition phenomena for the metal azides. The experimentally reported
vibrational frequencies at the gamma point were exactly reproduced by the
present calculations. In addition, we also present the thermodynamic properties
such as heat capacity which compares well with the experiment.
