Figure 4: Various modes of vibration at different frequencies: (a-b) bending, (c) symmetrical stretching, (d) asymmetrical stretching, (e-f) symmetrical stretching.
Electronic Properties
The electronic structure calculations have been carried out using CASTEP simulation code. The electronic density of states and band structure shown in figures (5-7) are calculated by utilizing LDA, PBE and HSE06 functionals, respectively. Figures (a) reveal band structures while figures (b) demonstrate corresponding DOS plots. In all figures (5-7) (a), it has been noticed that the electron-hole pair recombination took place at Γ (gamma) symmetry point of the first Brillouin Zone with a significant energy gap of magnitudes 6.35 eV, 6.81 eV and 7.58 eV using LDA, PBE and HSE06 functionals respectively, leading to the direct band gap insulating material. As depicted by the figure (5-7) (b), the density of states are found in wide range of energy, i.e., from 13.96 eV to -7.5 eV, 9.51 eV to -7.5 eV, and 15 eV to -7.5 eV for respective functionals. The highest edge of the valence band (VBM) is found on the Fermi level, which is set at zero energy, while lowest edges of the conduction bands (CBM) are noted at 6.35 eV, 6.81 eV and 7.58 eV for three different functionals, i.e., LDA, PBE and HSE06 respectively. 1s, 1s2 2s1, and 2s22p1 are the pseudo-states for H, Li, and B atoms respectively which are contributing in conduction mechanism. The highest value of band gap for HSE06 functional is due to underestimating the lattice constants as mentioned in structural properties section 3.1. Comparatively, it has been concluded that our theoretically estimated value of the band gap of 6.81 eV using PBE functional is ~4.1% smaller than the former experimental value of 7.1 eV reported for LiBH4 [27], which is an acceptable precision range. The value of band gap was found to be very close to the previously reported values of 6.80 eV and 6.95 eV by Miwa et al.and Ghellab et al. [31-32] respectively using diverse calculation codes. Figure 8 illustrates the behavior of atomic orbitals of each element of the studied compound. From this figure, it is seen that in the conduction band region, p -states of Li atoms mainly contribute between the energy range 7.0 eV to 12.5 eV. However, denser bands near the Fermi level and large peaks in density of states are seen due to p -state of B atoms and s -states of H atoms in energy range from -2.5 eV to 0 eV in the valence band. Thes -states of H and B atoms lie in lower region of the valence bands in between -7.5 eV to -5.2 eV energy range which look exactly similar to total density of states in this region of valence band.