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In this paper electronic structure, magnetic and optical properties of pure SnO₂ and  Sn_1-xCo_xO₂ (x= 6.25%, 12.5%, 18.75% and 25%)  samples and effect of Oxygen vacancies on those were investigated using density functional theory (DFT). Density of states and band structure curves show Co doping causes increase in energy surfaces near to the Fermi level. The results of this study showed the ground states of the 12.5% and 25% samples were ferromagnetic. The study of the effects of Oxygen vacancy on 12.5%Co doped- sample revealed that the introducing of vacancies causes increase in magnetic moment of the Co ions. The results were also showed that by increasing the Co concentration up to 12.5% the optical band gap decreases and then by more increasing of Co it increases. The intensity of the first peak in absorption curve increases and the intensity of the other peak above the 6eV decreases. The red shift of peak positions was also observed on absorption curves with increasing Co concentration to 12.5%.

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In this article, the electronic and structural properties of MgAl₂O₄ such as lattice constant, bulk modulus, compressibility, density; and optical propertieshave been investigated . Calculations were performed using the Full-Potential-Linearized Argument Plane Wave (FP-LAPW) method in the density functional theory framework by Wien2k  code. Structural properties and band gap have been studied with different approximations. Compared to experimental results,the results of structural properties withGGA-WCapproximation and the results of band gap withLDA approximation have been better compatibility, therefor; the MBJ method along with two mentioned approximations has been used later. The effect of pressure on MgAl₂O₄ have been investigated withMBJ+GGA(WC)approximation. The optical properties such as dielectric function, refraction index, extinction coefficient and energyloss function have been studied. The obtained results from band structure shows that MgAl₂O₄is an insulator and the band gap is equal to 7.67 eV. Therefraction indexis equal to 1.55. The obtained results have been in good agreement with other theory and experimental results.

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The entanglement is one of the  key features of the  quantum mechanics, that can be exploited for teleportation of quantum states. In this respect many solid state systems (e.g quantum dot) can be used quantum information processors. However, solid state modeling many-body systems is often calculation very difficult, so the approximation is used. In this work, the calculation of entanglement of  ground state of many-body systems by density functional theory  has been performed . For this purpose , first  the charge electronic density, has been calculated  than  the entanglement  has been  investigated by the linear entropy calculation. The investigated systems is the  Hooke’s atom is the system and after calculating the electric charge density of the system for different frequencies, we obtained of change entanglement system with frequency .The results indicated that with decreasing the frequency  in the  Hooke's atom model ,the potential was reduced and entanglement was according by also reduced.

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In the present work, we have studied and simulated the electronic, dynamical and elastic properties of the TaCRu₃ compound using QuantunEspreeso code within the framework of density functional theory and density functional perturbation theory in the generalized gradient approximation (GGA). We have concluded some properties of this compound such as metallic and magnetic behavior by obtaining the density of states and band structure.In order to study the dynamicaland elastic properties, at first we have calculated the phonon dispersion and phonondensity of the states and then obtained the elastic constants. Then the bulk,shear and young modulus, lames coefficients, poisons ratio, elastic heterogeneity parameter, Debye temperatureand also ductility parameter are calculated. We have compared the results with available experimental and theoretical data for this compound and also for the NbCRu₃ and VCRu₃ compounds. The lattice parameter is estimated about 2.62 % less than experimental data. For other calculated parameters, there are 0.12 and 22.9 as minimum and maximum percent difference between this work and others theoretical works. These values are predicable in the computational condensed matter physics

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Based on the density functional theory and the GGA approximation, by applying the improved potential of TB-mbJ the structural, electronic, optical, and thermodynamic properties of the XVSi semiconductor compounds (X = Co, Rh) and its [001] films Were studied. These two heusler compounds with the non-magnetic semiconductor behavior are stable in the MgAgAs-type cubic structure with F4-3m space group. Due to the good responses of the real and imaginary parts of the dielectric function for CoVSi and RhVSi in the visible spectrum range and the low electronic loss function, these two heuslers will be suitable for optical applications in this energy range. An examination of the stability phase diagram of [001] films showed that all 6 of its possible terminations would be thermodynamically stable. The electronic structure of these films indicates the emergence of half-metallic magnetic behavior only for two terms of V-Si: CoVSi [001] and   V-Si: RhVSi[001]. The responses of the dielectric function, as well as the absorption spectra of the two terms, are similar to those of the Bulk state, but with less intensity, while the electron loss in these two films is greater than that of the Bulk.

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In this article, the energy gap of 300 nitride compounds was analyzed and investigated using quantum simulations based on Density Functional Theory (DFT). The energy gaps of the compounds were calculated using two approximations, GGA-PBE and HSE06. The parameters considered in the machine learning studies were categorized into two groups: atomic and crystalline parameters. The atomic parameters include covalent radius, electronegativity, the number of valence electrons, and the first ionization energy. After collecting data on atomic features, a multiple linear regression model was fitted to the data. Subsequently, variable selection was performed using the stepwise regression method with the AICc criterion, and the effect size of various features was calculated. Additionally, to improve the accuracy of the model in predicting HSE06, three crystal features were incorporated into the model, and eight different models were fitted, each including one or more of these crystal features. The findings indicate that the model without any crystal variables has an adjusted coefficient of determination (R²) of 75.45%. However, with the inclusion of crystal features, the results improve significantly. Specifically, adding the PBE energy gap as a variable increases the R² to 99.03% (from 75.45% to 99.03%).

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In this study, quantum simulation calculations based on density functional theory (DFT) were used to investigate the electronic behavior and quantum capacitance of an AlN nanoribbon with a manganese magnetic impurity. The electronic results indicate that doping this nanoribbon with a manganese atom creates spin polarization around the Fermi level, and the density of states in the two spin channels differs around the Fermi level. Furthermore, the quantum capacitance of this compound and the surface electric charge density, arising from the accumulation of electric charge in the states around the Fermi level, were examined. All possible configurations for the position of the doped manganese atom were investigated. The results showed that the impurity atom's location significantly impacts the quantum capacitance and surface charge density of the compound compared to its pure state. The findings of this study can serve as a new foundation for utilizing nanoribbons doped with magnetic metals for charge and energy storage applications