Vibrational Properties
The frequency vs phonon dispersion curves, and frequency vs density of states plots for the considered compound are shown beside each other in figure 2, wherein, the modes of vibrations are found to exist in the frequency range of 0 to 2500 cm-1 between the symmetry points G and Z of the first Brillouin zone. Figure 2 (a) depicts that there are no imaginary frequencies (soft modes) seen at gamma symmetry G. It is noteworthy that out of the possible 72 modes of vibrations, three belong to acoustic branches and remaining 69 modes of vibrations are associated with optical branches. The vibrational states seen in the frequency range of 0 to 400 cm-1 have been occurred due to the contribution of displacement of Li+and\({\ [\text{BH}_{4}]}^{-}\) ions. While, the vibrational states in the frequency range of 1050 to 1300 cm-1 are present due to contribution of B and H atoms. Finally, the H atom having least atomic mass portrays vibrational states in the frequency range 2300 to 2400 cm-1. Moreover, as shown in figure 2 (b) 1st dominant peak of density of state noted at a frequency of 250 cm-1 might belong to the displacements of Li+and\({\ [\text{BH}_{4}]}^{-}\) ions. Likewise, 2nd dominant peak (the highest peak) appeared at frequency of about 1000 cm-1, which is ought to become available due to the influence of B and H atoms. And that the third important peak, which is recognized as 2nd highest peak, noticed at frequency of about 2300 cm-1 might have appeared due to partaking of H atoms.