In this paper, the optical properties of Lithium hydride (LiH), in rocksalt structure, with space group, Fm3m, in cubic (FCC) system, have been discussed. The theoretical background of the relation between the dielectric function, and, other optical constants has been examined. The real and imaginary parts of the dielectric function have also been scrutinized. The consequences of the exchange correlation potentials (GGA and GGA + U) applied to the absorption peaks and edges of the compound have also been spoken of. It was observed, at the application of GGA + U and GGA to the first absorption edge matched together; but there was overt difference in fine structure at higher energies due to the presence of the former exchange correlation approximation.
The Alkali hydrides compounds XH (X = Li, Na, K, Rb and Cs) are very simulating compounds in that they have the simplest electronic band structure. Alkali hydrides with complex hydrides are besides interesting for their capacity to store hydrogen [
In this present work, the optical properties of LiH are to be investigated, using full-potential linearized augmented plane wave (FP-LAPW), using GGA and GGA + U approximations with WIEN2k codes in the framework of density function theory (DFT) [
The optical properties can be derived from the dielectric function ε ( ω ) computed by density functional theory (DFT). Dielectric function is a three-dimensional tensor, which hinges on the symmetry of the crystal, and is calculated directly from the Kohn-Sham energy eigenvalues, ε k . In the Random Phase Approximation (RPA), the function, ε i j ( ω ) , can be expressed as [
ε i j = δ i j − 1 v ω 2 ∑ n , k ( − δ F ( ε ) δ ε ε n , k ) P i ; n , n , k P j ; n , n , k − 4 π v ω 2 ∑ P i ; c , v , k P j ; c , v , k ( ε c , k − ε v , k ) ( ε c , k − ε v , k ) 2 (1)
where V is a unit cell Volume, P n , m , k are momentum matrix elements between the bands n and m, for the point K of the crystal. F ( ε ) is a Fermi-Dirac distribution function:
F ( ε ) = 1 exp ( ε − ε F K B T ) + 1 (2)
where K B is Boltzmann constant.
The imaginary part, ε 2 ( ω ) , for the dielectric function ε ( ω ) = ε 1 ( ω ) + i ε 2 ( ω ) , can be calculated using momentum matrix [
The imaginary part of the dielectric function is indicative of real transfer between occupied and unoccupied states, thus the imaginary part then handles the attenuation, while the real part accounts for refraction; explicitly, the real part indicates scattering and loss in optical processes. At this point, it is apt to maintain that the conduction band is the imaginary part, while the valence band is the real part of the dielectric function.
The refractive index is one of the principles defining the characteristics of an optical material, while the extinction coefficient, K, illustrates the exponential decay of the amplitude of the electromagnetic waves. The refractive index and the extinction coefficients are intrinsically related, for they are derived from the same physical process. The refractive index and the extinction coefficient are tensors, and expressed as in Equations (3) and (4) below:
n i i ( ω ) = | ε i i ( ω ) | + R e ε i i ( ω ) 2 (3)
and
k i i ( ω ) = | ε i i ( ω ) | − R e ε i i ( ω ) 2 (4)
where n i i ( ω ) is the refractive index, and k i i ( ω ) is the extinction coefficient.
In optical experiments, n i i ( ω ) and k i i ( ω ) cannot be measured explicitly. The observables are reflectivity R i i ( ω ) , and the absorption coefficient A i i ( ω ) . The absorption coefficient describes how the intensity of light decays. It can be shown in Literature on electromagnetism that these quantities can be expressed as in Equation (5):
R i i ( ω ) = ( n i i ( ω ) − 1 ) 2 + k i i 2 ( ω ) ( n i i ( ω ) + 1 ) 2 + k i i 2 ( ω ) (5)
and
A i i ( ω ) = 2 ω k i i ( ω ) c (6)
To determine the optical properties of LiH, a self-scheme was used by solving the Kohn-Sham equation, employing FP-LAPW method, in the frame work of density theory along with GGA and GGA + U functionals [
The calculated complex dielectric function for LiH is depicted in
familiar method in the GGA calculations of scissor operation, shifting the empty conduction bands (imaginary part of the dielectric function) upwards to correspond with the experimental scissor operation was observed [
The imaginary part of the dielectric function obtained in this way depicts the absorption spectra of LiH. The black lines are for the GGA-PBE calculations, where the scissor operation was employed to correct the band gap error of this exchange-correlation functional [
The dielectric function of Lithium hydride (LiH), which is the underlying quantity relating to its electronic structure, and outlines its optical properties, has been calculated. It was observed that the application of the GGA + U approximation has very simple consequence for the simplicity of the band structure of alkali hydrides.
The authors declare no conflicts of interest.
Ofe, U., Amana, A.L. and Akonjom, N.A. (2021) GGA + U Study of the Optical Properties of LiH. Open Access Library Journal, 8: e7376. https://doi.org/10.4236/oalib.1107376