In this thesis, the electronic, optical and phonon properties ofbulk TiC and it’s narrow nanowires are calculated by usingQuantum-Espresso/PWSCF computational packge in the framework of density functional theory with different approximtions for the exchange and correlation functionals. TiC nanowires are simulated in three different diameters whichstretched in the z crystallographic directions and and limited in x and y directions. According to the results this compound show metallic behavior in bulk structure but for the smallest diameters of the nanowires, againstthe bulk we received a semiconducting behavior. This deviation becomes negligible at higher diameters. In all cases the electronic properties results from optical calcultions are consistent with related properties which come from structural investigations. Bulk TiC has a maximum amount of refraction index value and this amount will be decreased by a reduction of nanowire diameters. Also, the optical results indicate that by increasing a size of nanowires, the ELLOS value increases toward the corresponding bulk value. In this thesis phonon calculations have been perfomed for bulk and ,due to computational restriction, only the first diameter of nanowires as a stable phase. By calculating the phonon modes of Brillouin zone, thermal properties, such asSpecific heat capacity, entropy and ect ,are calculated for both mentioned structures.

In this thesis, the structural, electronic, optical properties and elastic constants of Heusler compounds Co2CrZ(Z=Al,Ga) have been studied.Calculations were performed using the full-potential-linearized Argument Plane Wave(FP-LAPW) method in the framework of density functional theory with GGA,LSDA,WC.GGA and PBESOL approximations by Wien2k code.The lattice constants used in the calculations are 5.6787(A0)for Co2CrAl and 5.7235(A0)for Co2CrGa. In this research structural properties of Co2CrZ(Z=Al,Ga) such as lattice constants, bulk modulus and its derivative properties were calculated. Moreover electronic properties such as bandstructure, density of states and electron charge density were investigated. The results from bandstructure showed an indirect ban gap(0.4 A0) for Co2CrAl and also (0.2 A0) for Co2CrGa in spin-down states, so these compounds are half-mettal.Results of GGA approximation had good consistence with experimental results.Also we studied the elastic properties of these compounds and the results showed that Co2CrAl have more elastic resistivity than Co2CrGa.Optical properties revealed the adoption of the density of states and imaginary part of dielectric function and we obtainedrefractivity index 10 for both compounds.

In the present thesis the structural(Including the lattice constant, bulk modulus and the compressibility) , electronic and thermoelectric properties of the SiCFe3 compound at two various structural cubic and tetragonal phases were calculated. The calculations have been performed conducted using the pseudopotential method in the framework of the density functional theory with Pwscf code. The results obtained from the bulk modulus suggests that the bulk modulus of the SiCFe3 compound in the cubic phase is more related value for the tetragonal phase which means that the cubic phase is stronger than the tetragonal one. also the magnetic caclulations shows that the cubic phase has a non-magnetic property and the tetragonal phase has a ferromagnetic order which is the most stable phase.
Results coming from analysing the electronic properties of the SiCFe3 compound suggest that The SiCFe3 compound in both structural phases has a metallic behavior with no gap. Analysing the total and partial density of the systames shows that the conductivity mainly is due to the orbital 3d of the iron atom. Moreover the electron charge density shows type of that the bonds between the iron and carbon atoms is a covalent bond.Thermoelectric properties investiydions indicate that the cubic phase have the highest seebeck coefficient comparing to the tetragonal phase. Also results coming from the electric conductivity and the thermal conductivity suggest that the cubic phase thermoelectic devices has a higher efficiency comparing to the tetragonal one and -type doping give rise to better response
 

In this thesis, the structural, electronic and elastic properties of BeX(X=S,Se.Te) have been investigated. Calculations were performed by the Full Potential Linearized Augmented Plane Wave (FP-LAPW) method in the framework of density functional theory with LDA, PBEGGA, WCGGA , PBEsol-GGA and MBJ approximations and using Wien2k code. In this research, structural properties of BeX(X=S,Se.Te) such as lattice constant, bulk moduls and its derivative properties were calculated. Moreover electronic properties of BeX(X=S,Se.Te) such as band structure, density of states and electron charge density were investigated. The results of band structure calculations predict gap in ( Γ→X) for cubic stracture phase and indirect band gap in ( K→Γ) direction for hexagonal stracture phase. So these compounds are semiconductors.Amount of Calculated babd with MBJ approximation have good cosistantens with experimental results. In this compounds, acoording to changing S to Se Anion and them to Te (With increasing calcogean atomic number from 16 to 34 and then 52) , amount of band gap decreased. Then, We study the elastic properties of these compounds. The results obtained from elastic properties show that these compounds in sided Cubic structre phase and hexagonal have elastic resistivity. Finally we have investigated their different propertis of elastic calculation.

Entanglement role as an essential resource in quantum information, research intensive way to determine that provides quantitative and qualitative aspects. Many solid-state systems (such as quantum dots) can be used as quantum information processors. One of the useful methods for modeling these systems,is density functional theory. To calculate the entanglement using density functional theory, be a function of density functional theory define appropriate interaction wave function. Density functional theory, each measure of entanglement function of expected values ; this procedure is a direct relationship between entanglement and energy derivatives of the coefficients of the quantum system based introduces is that the relationship between entanglement and quantum phase transition. In this project, the helium atom entanglement Kinoshita calculated for the wave function so that the results indicate that the amount of helium atom entanglement tended to increase with increasing energy. Also, the radial wave function entanglement for Hydrogen-like calculation results show that by increasing the number of quantum entanglement is a tendency to decrease.

In this thesis, the structural, electronic and optical properties of Na2S have been investigated. Calculations were performed by the Full Potential Linearized Augmented Plane Wave (FP-LAPW) method in the framework of density functional theory with LDA, PBEGGA, WCGGA and PBEsol-GGA approximations and using Wien2k code. In this research, structural properties of Na2S such as lattice constant, bulk modulus and its derivative and optical properties were calculated. Moreover electronic properties of Na2S such as band structure, density of states and electron charge density were investigated. The obtained results from band structure showed a direct gap at point, expressing Na2S as a semiconductor. Optical properties revealed the adoption of the band structure and imaginary part of dielecric function and rough equality of optical gap with band gap in all three phases. The refractive indices obtained from the real part of dielectriec function are bout 2.2. Moreover obtained bulk modulus at hexagonal phase is 4 time larger than two other phases, that show solidity of crystal in this phase is lesser than other phases. Obtained results are in a good agreement with experimental results.

In this thesis, structural, electronical, phononic and thermal properties of FeAl compounds in two and regulary phases have been investigated. Calculations have been performed by using PWscf computational package which is based on Density function theory and Psudo-potentials method.
At the present study, in addition to lattice parameters, bulk modulus and linear compressibility which are structural properties aspects of the compound, phononic and thermal properties have been calculated as well.
The obtained results from Bulk-moduls calculations indicate that stifness of FeAl compound B2 phases is higer than Do3 phases.
The band structure calculation show that FeAl in both mentioned phases has a metallic 3d-iron and 3p-aluminum atomic orbitals have been observed within density of state calculation that is an evidence to presence of covalent bonding between Fe-Al atoms of the system the in-plane charge density plot represents strong FeAl bonding at Do3 structural phase to B2 phase in comparison.
Witin LDA and LSDA functionals a frecuency gap have been calculated for B2 structural phase, while corresponding gap has been calculations vanished during GGA+sp.
In B2 phase at low temprature constant volume specific heat capacity of the compound has a T3 behavior while converges to classical Dulon-Petit value for higher tempratures.
The results are in good agreement with the experimental data when results.
 

In this thesis, the structural, electronic and optical properties of calcium carbonate in different phases have been investigated. Calculations were performed by using pseudopotential approach, within density functional theory framework and PWscf code. The pseudopotentials applied here are generated using norm-conserving and ultrasoft condition within LDA and GGA for exchange correlation functional. The results of the compressibility indicate that as the pressure increases from hexagonal to orthorhombic phase the hardness of compound is increased. Study of the band structures suggests that this compound is an insulator in hexagonal, orthorhombic (aragonite) and orthorhombic (vaterite) phases. The results of he optical properties of hexagonal, orthorhombic (aragonite) and orthorhombic (vaterite) phases reveal the conformity between band structure and the imaginary part of dielectriec function, and the band gap and optical gap are almost equal. The refractive indexes obtained from the real part of dielectriec function in hexagonal phase are 1.455 and 1.274 in xx and zz directions, respectively, in orthorhombic (aragonite) phase are 1.487, 1.456 and 1.366 in xx, yy and zz directions, respectively and in orthorhombic (vaterite) phase are 1.373, 1.374 and 1.433 in xx, yy and zz directions, respectively. The results are well consistent with other available data.

In this thesis, the structural, electronic, optical, phononic and thermodynamic properties of WS2 have been investigated. Calculations were performed by using pseudopotential approach, within density functional theory framework and PWscf code. The pseudopotentials applied here are generated using norm-conserving and ultrasoft conditions and the exchange correlation functional is of the types LDA and GGA. Study of the band structures suggests that this compound is a semiconductor with a band gap of 1.35 (eV). The results of the optical properties reveal the conformity between band structure and imaginary part of dielectriec function, and the band gap and optical gap are almost equal. The refractive indices obtained from the real part of dielectriec function are 3.662 and 2.556 in xx and zz directions, respectively. With study of thermodynamic properties we understand that the low temprerature dependence of the heat capacity become close to 3NKB (Dulong-Petit law). The specific heat and entropy of this mixture at room temperature were calculated 65.221 (j/k.mol) and 68.757 (j/k.mol), respectively.

In this thesis, the structural, electronic, phononic and thermodynamic properties of GaBi in different phases have been investigated. Calculations were performed by using pseudopotential approach, within the density functional theory framework and PWscf code. The pseudopotentials applied here are generated using norm-conserving and ultrasoftmethodfor theexchange-correlation part of the LDA and GGA functionals. Results revealed that the GaBi is a semi-metal material. Relativistic calculations suggest that the GaBicompound in zincblende phasehas a negative band gap, and in other, RockSalt and CsCl,phases hasa metallic behavior. The results of the compressibility indicate that a zincblende phasecompressibility is more than RS phase and is less than CsCl phase. Bythe study of thermodynamic properties of the zincblendephase, weconcluded that the hightemperature dependence of the heat capacity becomes close to 3Nk_Bvalue which is consistent with the amount of classical Dulong–Petit law.

In this thesis, the structural, electronic, optical, phononic and thermodynamic properties of HgTe compound in different phases have been investigated. Calculations were performed by using pseudopotential approach, within density functional theory framework and PWscf code. The pseudopotentials applied here are generated using norm-conserving condition within LDA and GGA for exchange-correlation functional. The results of the compressibility indicate that as the pressure increased from ZincBlend to CsCl phase the hardness of compound is increased. The calculations of band structure show that this compound is a semiconductor with zero band gap in stable ZincBlend phase and is a semiconductor with small indirect band gap in a Hexagonal phase. Furthermore, by some calculations, the electronic properties of high pressure rocksalt, orthorhombic, and CsCl phases are revealed to have metallic character. The results obtained from optical properties of ZincBlend and Hexagonal phases show the conformity between imaginary part of dielectric function and band structure, and in addition, proximate equality between band gap and optical gap. The refractive index obtained from the real part of dielectric function in ZincBlend phase is 3.413 and in Hexagonal phase is 3.192 and 3.339 in x and z direction, respectively. The study of thermodynamic properties of ZincBlend and rocksalt phases reveals that in the low temperature limit, the heat capacity exhibits a first order dependence on temperature. At high temperatures, it becomes close to 3Nk_B (Dulong –Petit law).

In this thesis, two-dimensional phononic crystal comprising of steel cylinder in water investigated. Three cross sections for cylinder are considered using finite element method(EFM). We plot equifrequency surface of the first band by projection of three-dimension (kx, ky, ω) on kx-ky plane. Because of convex of equifrequency around edge of the first Brillouin Zone, we guess negative effective phononic mass and so negative refraction. Moreover, the negative refraction behaviors are demonstrated by the simulation of a phononic crystal slab. The results show the maximum intensity for phononic crystal with circle, square and triangle cross section, 1.15MHz, 1.11MHz and 1.27MHz, respectively. The dependence of intensity and focal point distance on the slab thickness and distance between source and the slab and the effect of incident angle on the negative refractive investigated. The results are in good agreement with other works.

 Entanglement is one of the main features that can be used to transfer quantum states. In this relation, many solid-state systems (for example quantum dots ) can be used as quantum information processors. However, accurate modeling of solid-state, many-body systems is often difficult, therefore approximations are used. In This project the method of calculating the entanglement of the ground state of many-body systems are discussed, by using density functional theory. To do this we first calculate the electric charge density and then the required entanglement using linear entropy. The system under investigation is Hooke’s atom, whose density of electric charge for different frequencies is calculated first, then the entanglement variations with frequency is studied. The results indicate that as the frequency decreases in Hooke’s atom, its potential and also its entanglement decrease.

In this thesis, the structural, electronic, optical, phononic and thermodynamic properties of GaP in different phases have been investigated. Calculations were performed by using pseudopotential approach, within density functional theory framework and PWscf code. The pseudopotentials applied here are generated using norm-conserving condition within LDA and GGA for exchange correlation functional. The results of the compressibility indicate that as the pressure increased from Zincblend to Cmcm phase the hardness of compound is increased. Investigation of Energy –Volume curves shows that the cinnabar phase is metastable. Study of the band structures suggests that this compound is a semiconductor in Zincblend and Cinnabar phase and is a metal in Cmcm phase. The results of he optical properties of Zincblend and Cinnabar phase reveal the conformity between band structure and imaginary part of dielectriec function, and the band gap and optical gap are almost equal. The refractive index obtained from the real part of dielectriec function in Zincblend is 3.306 and in Cinnabar phase is 4.235 and 3.808 in xx and zz direction, respectively. With study of thermodynamic properties of Zincblend and Cinnabar phase we understand that the low temprerature dependence of the heat capacity become close to 3Nk_B (Dulong –Petit law).