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{\it Ab-initio} study of structural and vibrational properties of KN$_3$ under pressure

Structural stability and vibrational properties of KN$_3$ have been studied under pressure using the first principles calculations based on the density functional theory (DFT) as well as with semi empirical dispersion correction to the DFT to treat van der Waals interactions. The structural properties calculated through the dispersion correction are in good agreement with the experimental results when compared with the standard density functional theory. The lattice mode and the azide ion bending mode frequencies are found to be well reproduced by our calculations. As pressure increases, the E$_g$ mode gets softened as observed in the experiment. Despite the softening of E$_g$ mode, the enhancement of intramolecular interactions keeps the lattice stable.