In this paper, the optical properties of CaH 2, in orthorhombic structure, with space group, , in crystal system (Co 2Si-type) have been investigated carefully. The theoretical milieu of the correlation between the dielectric function with other optical constants has been investigated. The real and the imaginary parts of the dielectric function have besides, been inspected accurately. The outcome of the exchange correlation potentials implemented (GGA and GGA + U) to the absorption peaks and edges of this insulator (CaH 2), have also, been determined. It was noticed that the application of GGA + U results in the shift of the first absorption peak caused by the conduction band (imaginary part), thus resulting in the band correlation.
The electronic band structure and the structural property (Lattice constant) of CaH2 in orthorhombic structure, with space group, P n m a , in crystal system (Co2Si-type) have been computed, using the density functional theory. The Kohn-Sham equation was solved, using the full-potential linearized augmented plane wave (FP-LAPW) [
In this current work, the optical properties of CaH2 are to be examined, using full-potential linearized augmented plane (FP-LAPW), GGA and GGA + U approximations, with WIEN2K codes in the frame work of density functional theory (DFT).
The dielectric function describes what an electric field such as oscillating light wave does to a material. The Dielectric function is a three-dimensional tensor which depends on the symmetry of crystal, and can be 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 ε F is a Fermi level.
The imaginary part of the dielectric function is calculated in order to understand the optical properties of CaH2. The study of the optical properties is pivotal for understanding of the electronic structure of materials [
ε ( ω ) = ε 1 ( ω ) + i ε 2 ( ω ) (3)
The imaginary part ε 2 ( ω ) of the dielectric function can be calculated using momentum matrix elements [
At this point, it is apropos to mention that the imaginary part of the dielectric function, also, is indicative of real transfers between the occupied and unoccupied states, thus the imaginary part then, controls the attenuation, while the real part explains refraction. In other words, the real part marks scattering and loss in optical processes.
The refractive index determines how much light is bent or refracted, when entering a material. The refractive and extinction coefficients are intrinsically related, for they are derived from the same physical process. The refractive index and the extinction coefficients are tensors, and are expressed as
n i i ( ω ) = | ε i i ( ω ) | + R e ε i i ( ω ) 2 (4)
and
k i i ( ω ) = | ε i i ( ω ) | − R e ε i i ( ω ) 2 (5)
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 measurable quantities are reflectivity R i i ( ω ) , and the absorption coefficient A i i ( ω ) . It can be shown in Literature on electromagnetism that these quantities can be expressed as [
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 ) (6)
and
A i i ( ω ) = 2 ω k i i ( ω ) c (7)
To eschew verbosity, the detailed computational method is presented in the electronic and structural properties of CaH2, using GGA and GGA + U approximations, with WIEN2K codes [
The calculated dielectric function for CaH2 is portrayed in
The black solid lines are for GGA-PBE and the dash line for GGA + U calculations. It was observed that the compound has one leading absorption peak at 5.6 eV and one minor one at 4.5 eV. It was also noticed that implementation of the GGA + U functional induces the alteration in the first absorption peak caused by the shift in the conduction band.
The dielectric function of Sodium hydride (NaH), which is the fundamental quantity that appertains to the electronic structure, and defines its optical properties, has been determined. It was observed that the hydrogen embedded in the compound, including the XC, GGA + U, applied changes its band gaps, thus making it more insulating.
This work was supported by the Department of Physics, Veritas University Abuja.
The data that support the findings of this study are available from the corresponding author upon reasonable request.
The authors declare no conflicts of interest.
Ofe, U., Amana, A.L. and Akonjom, N.A. (2021) GGA + U Approximation: An Improved Density Functional Theory of Optical Properties of CaH2. Open Access Library Journal, 8: e7293. https://doi.org/10.4236/oalib.1107293