Local Spin Density Approximation Research Articles

Unlocking the Magnetic and Half-Metallic Properties of AMY2 (A = Cu, Ag; M = Sc, Ti, V, Cr, Mn, Fe; Y = S, Se) Compounds in Chalcopyrite Structure: An Ab Initio Study for Spintronics Applications

We present an investigation into the magnetism exhibited by AMY2 compounds characterized by a chalcopyrite structure, where A can be Cu or Ag, M can be Sc, Ti, V, Cr, Mn, or Fe, and Y can be either S or Se. By substituting M atoms at the Ga position of AGaY2 compounds, the magnetic properties were calculated using the full potential linearized augmented plane wave method under the generalized gradient approximation and local spin density approximation with the WIEN2K code. The obtained spin-polarized results confirmed the presence of ferromagnetic and half-metallic (HM) properties in AMY2 compounds (A = Cu, Ag; M = Ti, V, Cr, Mn; Y = S, Se), wherein the HM property is preserved through p-d hybridization of p states of Y (S, Se) atoms with d (t2g) states of M (M = Ti, V, Cr, Mn) atoms, and minimal contribution of −s states of A (A = Cu, Ag) atoms. The total magnetic moments for AMY2 compounds were calculated as 1.00, 2.00, 3.00, and 4.00 µB/f.u. for M = Ti, V, Cr, Mn, respectively. For AFeY2 compounds (A = Cu, Ag; Y = S, Se), electronic band structures for both up spin and down spin states were identical, suggesting antiferromagnetic behavior at equilibrium, while AScY2 compounds (A = Cu, Ag; Y = S, Se) exhibited nonmagnetic properties at equilibrium. Overall, the accurate HM properties of AMY2 materials suggest promising prospects for their utilization in spintronics and magnetic storage device applications.

Ab initio prediction of half-metallic and metallic ferromagnetism in ZnO:(Co,Cr) systems

Doping effects on the electronic and magnetic properties of Zn1−x (Co,Cr) x O systems are investigated within Local Spin Density Approximation and Hubbard U methods. Based on Density Functional Theory the spin-polarization band structures, density of states for investigated systems are calculated. Systematic analysis of the electronic properties shows that TM-doped ZnO has generated new energy levels in the vicinity of Fermi energy level. From first-principle calculations we obtained Cr-ZnO and Co-ZnO systems are metallic and half-metallic ferromagnetic materials, respectively. The obtained results for Cr-doped ZnO 128- and 192-atom supercell systems show magnetic properties with higher Curie temperature than room temperature. There are large local moments, ∼2.9 and ∼4.2 for Co and Cr dopants, respectively. Magnetic moments are related with two electron defects in the supercell structure and unpaired electrons of transition metal. The ferromagnetic and antiferromagnetic phases and the total energy are obtained for x = 2.08%, 3.125%, 4.16%, 6.25%, 8.3%, 12.5%, and 25% impurity concentrations for doped ZnO.

Comprehensive investigation of half Heusler alloy: Unveiling structural, electronic, magnetic, mechanical, thermodynamic, and transport properties

This study employs density functional theory (DFT) using Wien2k to comprehensively analyze the essential properties of two half-Heusler alloys, KCrSi and KCrGe. Our findings demonstrate that the ferromagnetic Type 2 configuration exhibits superior stability over non-magnetic and antiferromagnetic states for all KCrZ (Z = Si, Ge) alloys. These alloys exhibit complete spin polarization and half-metallic character, with calculated magnetic moments of 3 μB for both KCrSi and KCrGe. The Curie temperature (TC) is determined using the mean field approximation. Mechanical stability is assessed through second-order elastic constants (SOECs), and electronic properties are analyzed using local spin density approximation (LSDA), Perdew-Burke Generalized Gradient Approximation (PBE-GGA), and Tran-Blaha modified Becke-Johnson (TB-mBJ) schemes, confirming the retention of the half-metallic nature. The negative enthalpy of formation (ΔH) suggests material stability. The use of semi-classical Boltzmann theory, incorporated through the sophisticated scheme of BoltzTraP, explores transport coefficients. High pressures and temperature discrepancies in thermodynamics are considered by implementing the quasi-harmonic Debye approximation to illustrate stability. Finally, optical properties are summarized to assess the applicability of this alloy for optoelectronic applications. The overall characteristics of these particular alloys suggest potential applications in sustainable thermoelectric and optoelectronic features.

The effects of V doping on the intrinsic properties of SmFe10Co2 alloys: A theoretical investigation

The present study focuses on the intrinsic properties of the SmFe10Co2-xVx (x = 0–2) alloys, which includes the SmFe10Co2 alloy, one of the most promising permanent magnets with the ThMn12 type of structure due to its large saturation magnetization (µ0Ms = 1.78 T), high Curie temperature (Tc = 859 K), and anisotropy field (µ0Ha = 12 T) experimentally obtained. Unfortunately, its low coercivity (<0.4 T) hinders its use in permanent magnet applications. The effect of V-doping on magnetization, magnetocrystalline anisotropy energy, and Curie temperature is investigated by electronic band structure calculations. The spin-polarized fully relativistic Korringa-Kohn-Rostoker (SPR-KKR) band structure method, which employs the coherent potential approximation (CPA) to deal with substitutional disorder, has been used. The Hubbard-U correction to local spin density approximation (LSDA + U) was used to account for the large correlation effects due to the 4f electronic states of Sm. The computed magnetic moments and magnetocrystalline anisotropy energies were compared with existing experimental data to validate the theoretical approach’s reliability. The exchange-coupling parameters from the Heisenberg model were used for obtaining the mean-field estimated Curie temperature. The magnetic anisotropy energy was separated into contributions from transition metals and Sm, and its relationships with the local environment, interatomic distances, and valence electron delocalization were analyzed. The suitability of the hypothetical SmFe10CoV alloy for permanent magnet manufacture was assessed using the calculated anisotropy field, magnetic hardness, and intrinsic magnetic properties.

Symmetry breaking and self-interaction correction in the chromium atom and dimer.

Density functional approximations to the exchange-correlation energy can often identify strongly correlated systems and estimate their energetics through energy-minimizing symmetry-breaking. In particular, the binding energy curve of the strongly correlated chromium dimer is described qualitatively by the local spin density approximation (LSDA) and almost quantitatively by the Perdew-Burke-Ernzerhof generalized gradient approximation (PBE-GGA), where the symmetry breaking is antiferromagnetic for both. Here, we show that a full Perdew-Zunger self-interaction-correction (SIC) to LSDA seems to go too far by creating an unphysical symmetry-broken state, with effectively zero magnetic moment but non-zero spin density on each atom, which lies ∼4eV below the antiferromagnetic solution. A similar symmetry-breaking, observed in the atom, better corresponds to the 3d↑↑4s↑3d↓↓4s↓ configuration than to the standard 3d↑↑↑↑↑4s↑. For this new solution, the total energy of the dimer at its observed bond length is higher than that of the separated atoms. These results can be regarded as qualitative evidence that the SIC needs to be scaled down in many-electron regions.

Real Structure, Magnetism and Chemical Bonding of SmSi3‐x

New metastable SmSi3‐x (x = 0‐0.05) is obtained by high‐pressure high‐temperature synthesis (9.5 GPa, 870‐1270 K). Powder diffraction data refinements reveal that the crystal structure of SmSi3 is isotypic to that of YbSi3 (space group I4/mmm, a = 7.23634(5) Å, c = 11.0854(1) Å). In the crystal structure, two types of Si2 dumbbells agglomerate into layers, which embed the samarium atoms. At ambient pressure, SmSi3 decomposes exothermally upon heating into Si and SmSi2‐x. Single‐crystal structure refinements of a specimen SmSi3‐x (x=0.05) reveal considerable electron density, which is not accounted for by the YbSi3 model. The additional maxima can be assigned to disorder which affects the samarium positions and induces silicon vacancies. Scanning transmission electron microscopy experiments evidence that the disorder can be attributed to extended defects. Magnetic measurements on SmSi3‐x reveal van Vleck paramagnetic behavior and antiferromagnetic ordering at low temperatures. Computations within the local spin density approximation (LSDA and LSDA+U) on the crystal structure of SmSi3 reproduce the anti­ferro­magnetic coupling as the favored long‐range order. Quantum chemical analysis of the chemical bonding in SmSi3 reveals two‐center two‐electron bonds within the Si2 dumbbells plus a total of a little less than four electrons in lone pairs at each silicon atom.

Ferromagnetism in silver-doped single-walled zinc oxide nanotubes

In this paper, the electronic and magnetic properties of single-walled ZnO:Ag nanotubes with a chirality of (6,0) were investigated. Ab initio simulations were carried out using Atomistic ToolKit computer code implementing density functional theory within the local spin density approximation. To obtain an accurate energy band gap for related systems, we used the Hubbard U semiempirical corrections. The introduction of the Ag atom into the ZnO nanotube structure changes the electronic structure, the energy gap decreases with the silver concentration. The calculated value of total magnetic moments of the Ag-doped single-walled ZnO NT system is 1.0 μB. Our results predict that Ag-doped ZnO NT can be a potential candidate for optoelectronic and spintronic devices.

First-principles simulations of magnetic properties of Co- and Ni-doped ZnSe

We purposed to analyze the theoretical ab initio study of ferromagnetism and to estimate Curie temperature of Co2+ and Ni2+ 3d transition metal (TM) ions doped Zn1-x TM x Se compounds for 12.5 % and 6.25 % concentrations of impurity TM(Co, Ni) atoms. The calculations are carried out using the norm-conserving Fritz-Haber-Institute ionic pseudopotentials based on density functional theory within the local spin density approximation and Hubbard U (U(Znd)=4.5 eV; U(Sep)=3.8 eV) corrections. The analysis of the total and partial electron density of states shows the half-metallic ferromagnetic behavior with a half-metallic bandgap. The theoretically obtained total magnetic moments of TM(Co, Ni) doped Zn1-x TM x Se systems are equal to 3 μB and 4 μB, correspondingly.

Doping effect on electronic and magnetic properties of Ag-doped single-walled (6,0) GaN nanotubes: First-principles study

The electronic and magnetic properties of GaN wurtzite, un-doped, and Ag-doped single-walled (6,0) chiral GaN nanotubes (SWGaNNT) were investigated using Density Functional Theory and Local Spin Density Approximation methods within Hubbard U semiempirical correction (DFT-LSDA + U). In a consecutive DFT-LSDA + U electronic structure simulation, the effects of defects on the nature and origin of ferromagnetism (FM) are studied for an Ag-doped SWGaNNT system. For the Ag-doped GaN nanotube configurations, the energy gap decreases with increasing concentration of impurity. The total energy calculations for doped systems show the stability of the ferromagnetic phase. In the case of the Ag-doping GaN NT system, the wide energy gap is decreasing and the total magnetic moment of this system is ∼2.0 μB. From first-principles calculations, an Ag-doped GaN nanosystem can be made into a magnetic ferromagnetic material, and it is an important candidate for spintronics device applications.

First-principles prediction of higher Curie temperature, metallic and half-metallic ferromagnetism in Zn1-x(Vx,Nix)O systems

The electronic and magnetic properties of Zn(V,Ni)O systems with 2.08 %, 4.16 %, 6.25 %, 8.3 %, and 12.5 % impurity concentrations were investigated based on ab initio simulations. The first-principles calculations were carried out using density functional theory and local spin density approximation by pseudopotential method. Analyzing the calculated density of states, the mechanism to stabilize the ferromagnetic phase in the 3d-metals doped ZnO systems is discussed. The analysis of the total density of states shows that the V-doped ZnO presents a metallic nature and Ni-doped ZnO exhibits a half-metallic character. First-principles calculations show that the stability of ferromagnetic or antiferromagnetic behaviors depends on impurity concentrations and impurity positions in related ZnO:V,Ni systems. Finally, we estimated and studied the Curie temperatures for V- and Ni-doped ZnO systems with different impurity concentrations. The Curie temperatures for VxZn1-xO and NixZn1-xO systems are higher than room temperature and these compounds are suitable ferromagnetic DMS materials for spintronic applications.

Unveiling the Robust Struct-Electromagnetic Characteristics of CdAB2 Chalcopyrite (A = Cr, Mn, Fe; B = P, As): A Comprehensive Ab-Initio Study

We present a comprehensive investigation of the electromagnetic properties of CdAB2 compounds, where A represents Cr, Mn, or Fe, and B denotes P or As. To investigate the spin-polarized behavior of these compounds the A atoms were substituted at the Group IV (Ge) position in CdGeB2 in the chalcopyrite crystal structure. Our results reveal that all the CdAB2 compounds exhibit compelling spin-splitting of energy states near the Fermi level (EF). Notably, CdAB2 materials with A = Cr and Mn exhibit intriguing half-metallic ferromagnetic (HMF) characteristics, with the calculated total magnetic moments of 2.00 and 3.00 µB/f.u., respectively. The HMF properties originated in CdAB2 (A = Cr and Mn; B = P, As) these compounds owing to the hybridization of partially filled -3d(t2g) states of A atoms with the p-states of B (P, As) atoms, with minor contributions from Cd’s-like states. In contrast, CdFeB2 displays distinct behavior, demonstrating spin-splitting of energy levels around the EF indicative of a stable ferromagnetic (FM) state and the absence of HMF at their equilibrium volume. The calculated total magnetic moments for CdFeP2 and CdFeAs2 are about 1.83 (1.64 µB/f.u.) and 1.94 µB/f.u. (1.84 µB/f.u.) under generalized gradient approximation (GGA) (local spin density approximation (LSDA)) approximations, respectively. Perhaps these CdAB2 compounds (A = Cr and Mn; B = P, As) with HMF characteristic within both LSDA and GGA formalisms makes them highly promising candidates for spin injectors in the spintronic device applications. Furthermore, their semiconducting nature renders CdCrB2 and CdMnB2 materials compatible with silicon and other semiconducting lattices, enhancing their potential practical applications in the spintronic technologies. In conclusion, this study presents a thorough exploration of the robust electronic and magnetic properties of CdAB2 chalcopyrites, offering exciting prospects for their utilization in the future spintronic applications.

Electronic structure of SrFe1−x(Mn,Co)xO3-δ: A CPA case study

A new methodology is suggested for determining and using the Coulomb interaction parameter U(t2g), taking into account the different energy localizations of t2g and eg states in disordered transition metal perovskite-like oxides, based on the local spin density approximation with Coulomb interaction correction method and the coherent potential approximation. The adjustment of U(t2g)’s relies on the best coincidence of the experimental and calculated maxima in X-ray absorption/reflection spectra at simultaneous demand for the calculated magnetic moments to closely correspond to their experimental values in cubic oxides SrFeO3, SrMnO3, and SrCoO3. Then, the obtained U’s are utilized in order to construct the Green functions for calculating the electronic properties of strongly correlated perovskite-like solid solutions within the coherent potential method. The high efficiency of the proposed methodology has been demonstrated by a close coincidence of the experimentally observed and calculated X-ray emission/absorption spectra, magnetic moments, density of states at the Fermi level, and electronic conductivity in the disordered non-stoichiometric SrFeO3-δ, SrFe0.75Mn0.25O3-δ, and SrFe0.85Co0.15O3-δ phases. The composition SrFe0.85Co0.15O3-δ is proposed as a promising electrode material with enhanced characteristics of electric transport.

Study of structural, elastic, mechanical, electronic and magnetic properties of FeX (X=Pt, Pd) austenitic and martensitic phases

All studied properties of FeX (X = Pt, Pd) in austenitic and martensitic phases are investigated within Local Spin Density Approximation as exchange functional. The structural parameters at equilibrium for ferromagnetic tetragonal FePt and FePd a = 3.911 Å, c = 3.842 Å and a = 3.816 Å, c = 3.736 Å, and the lattice constant for ferromagnetic cubic FePt and FePd a = 4.9304 Å and a = 4.905 Å agree well with their available theoretical and experimental data. FePd and FePt formation enthalpy of the martensitic phase was −12625.73 eV and −39414.97 eV, while in the austenitic phase it was −12625.33 eV and −39413.97 eV. The rock-salt FePd (tetragonal FePt) is more stable than tetragonal FePd (rock-salt FePt). For both compounds, the anisotropy is more pronounced in the martensitic phase.

Simulation of the Adsorption and Diffusion of Lithium Atoms on Defective Graphene for a Li-Ion Battery

Based on the density functional theory (DFT) with allowance for spin polarization or the local spin density approximation (LSDA), we calculate the adsorption and diffusion properties of a lithium atom on a graphene ( ) monolayer with monovacancy ( ) as the anode material for an -ion battery. The DFT LSDA calculations are performed in relaxed 5 × 5 and 6 × 6 supercells and based on graphene with the monovacancy + lithium adatom complex . Based on the calculated values of the adsorption energy of the lithium atom , the energetically stable location of the lithium adatom is determined on a monolayer of supercells in and . The calculation results show that the adatom energetically prefers to be adsorbed in the pit position (H-site) rather than adsorbed from above (T-site) of the carbon atom in the monolayer. The DFT LSDA calculated electronic band structure and local total and partial magnetic moment of supercell atoms are consistent with the calculations performed by the generalized gradient approximation (GGA)-PBE functional for the H-, B-, and T-sites of graphene. Taking into account the experimentally obtained diffusion coefficients of lithium in two-layer graphene in the struc-tural packing of an AB package and the temperature (263–333 K) dependence of Li diffusion in two-layer graphene, which is described by the Arrhenius law, the diffusion activation energy of is calculated at con-centrations of = 0.06–0.51 in LixC12 graphene in the AB packaging.

Vertical detachment energies of ammonia cluster anions using self-interaction-corrected methods.

Systems with weakly bound extra electrons impose great challenges to semilocal density functional approximations (DFAs), which suffer from self-interaction errors. Small ammonia clusters are one such example of weakly bound anions where the extra electron is weakly bound. We applied two self-interaction correction (SIC) schemes, viz., the well-known Perdew-Zunger and the recently developed locally scaled SIC (LSIC) with the local spin density approximation (LSDA), Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA), and the SCAN meta-GGA functionals to calculate the vertical detachment energies (VDEs) of small ammonia cluster anions (NH3)n-. Our results show that the LSIC significantly reduces the errors in calculations of VDE with LSDA and PBE-GGA functionals leading to better agreement with the reference values calculated with coupled cluster singles and doubles with perturbative triples [CCSD(T)]. Accurate prediction of VDE as an absolute of the highest occupied molecular orbital (HOMO) is challenging for DFAs. Our results show that VDEs estimated from the negative of HOMO eigenvalues with the LSIC-LSDA and Perdew-Zunger SIC-PBE are within 11meV of the reference CCSD(T) results. The LSIC method performs consistently well for the VDE estimates, from both the total energy differences and the absolute HOMO eigenvalues.

Photoferroic prospective of multiferroic HoMnO3 compound, evaluated on the base of the DFT study of its magnetic, electronic, and optical properties

In this work, non-collinear spin density functional theory based all-electron full-potential linearized augmented plane wave electronic structure method have been employed to study magnetic, electronic, and optical properties of multiferroic HoMnO3 compound in order to evaluate its potential to be used in photovoltaic applications. Exchange and correlation effects of the Ho 4f- and Mn 3d-electrons were treated on the base of the local spin density approximation including effective Hubbard (Ueff) correction. We concluded that the ground state magnetic structure should be described by Γ3 irreducible representation of the P63cm space group, for both the Mn and the Ho magnetic sub-lattices. The calculated indirect and direct band gaps, corresponding to the transition from the O 2p-to the Mn 3d-states, are found to be 1.25 eV and 1.4 eV, respectively, in very good agreement with the experimental findings. Calculated dielectric tensor spectra are found to be in satisfactory agreement with the experiment as well. On the base of these results, we investigated photoferroic properties of the HoMnO3 by calculating its absorption coefficient spectrum and the effective mass tensor of the photogenerated electrons and holes. By comparing results with those of isostructural LuMnO3 and the YMnO3 multiferroics, we concluded that the HoMnO3 exhibits similar photoferroic properties, a fact that classifies it as a material suitable for photovoltaic applications.

First-principles study of structural and electronic properties of ZnSe with wurtzite structure

Using Density Functional Theory (DFT) and Local Spin Density Approximation (LSDA) the structural and electronic properties of pure ZnSe wurtzite compound were theoretically investigated. The Hubbard U semiempirical correction has also been used to improve the underestimated DFT calculated band gap. From the DFT+LSDA+U method obtained that the wide of band gap is 2.7 eV and this result is closer to the available experimental results. Current studies reveal that the maximum of valence band and the minimum of conduction band located at the Γ (0, 0, 0) symmetry point on the Brillouin zone. Accurate investigation of the electronic structure of studied material is helpful for the technical applications.

Spin-state gaps and self-interaction-corrected density functional approximations: Octahedral Fe(II) complexes as case study.

Accurate prediction of a spin-state energy difference is crucial for understanding the spin crossover phenomena and is very challenging for density functional approximations, especially for local and semi-local approximations due to delocalization errors. Here, we investigate the effect of the self-interaction error removal from the local spin density approximation (LSDA) and Perdew-Burke-Ernzerhof generalized gradient approximation on the spin-state gaps of Fe(II) complexes with various ligands using recently developed locally scaled self-interaction correction (LSIC) by Zope et al. [J. Chem. Phys. 151, 214108 (2019)]. The LSIC method is exact for one-electron density, recovers the uniform electron gas limit of the underlying functional, and approaches the well-known Perdew-Zunger self-interaction correction (PZSIC) as a particular case when the scaling factor is set to unity. Our results, when compared with reference diffusion Monte Carlo results, show that the PZSIC method significantly overestimates spin-state gaps favoring low spin states for all ligands and does not improve upon density functional approximations. The perturbative LSIC-LSDA using PZSIC densities significantly improves the gaps with a mean absolute error of 0.51eV but slightly overcorrects for the stronger CO ligands. The quasi-self-consistent LSIC-LSDA, such as coupled-cluster single double and perturbative triple [CCSD(T)], gives a correct signof spin-state gaps for all ligands with a mean absolute error of 0.56eV, comparable to that of CCSD(T) (0.49eV).

First principles study on electronic, magnetic and optical properties of Gd2NiMnO6

The double perovskite oxide materials have various applications in light absorber, solid oxide fuel cells, electrode materials for electrochemical energy devices, solid state thermoelectric devices, etc. The calculations of electronic, optical and magnetic properties of Gd2NiMnO6 (GNMO) double perovskite are aimed in the present work. GNMO crystallizes in monoclinic structure with P21/n (14) space group. Implementing first principles density functional theory, we have reported the spin-polarised electronic band structure, density of states (DOS), optical absorption property and magnetic moment of GNMO double perovskite. Furthermore, the effect of on-site d-d Coulomb interaction energy (Ueff) on the electronic and optical properties were investigated by applying a range of Hubbard parameters from 0 to 6 eV on Ni-3d and Mn-3d orbitals within the local spin density approximation (LSDA) and generalised gradient approximation (GGA). Interestingly, on applying Ueff in this range, band gap of GNMO enhanced progressively in both majority and minority spins and also for Ueff = 4 and 6 eV implemented on Ni-3d and Mn-3d orbits, respectively, we observe the band gap value 1.16 and 2.12 eV for the spin-up and spin-down states which is in good agreement with the previously reported experimental band gap value (1.5 eV). In this regard, the electronic structure and light absorption of GNMO have been analysed for Ueff = 4 and 6 eV implemented on Ni-3d and Mn-3d orbits, respectively. The calculations revealed suitable narrow band gap and large visible light absorption coefficient in GNMO, which are extremely desired for the high photovoltaic performance.

Theoretical validation of experimental properties of TiO2 prepared through organometallic precursors

Our TiO2 thin films were elaborated using spray pyrolysis technique. The spray solutions were prepared by two titanium precursors: titanium (IV) propoxide and titanium chloride. The elaborated thin films were analyzed with different characterization techniques such as X‐ray diffraction (XRD), Raman spectroscopy, scanning electron microscopy (SEM), and UV–visible spectroscopy. These characterizations showed that the change of precursors from titanium chloride to titanium propoxide has a significant impact on all TiO2 properties. The structural characterizations showed the formation of anatase TiO2 and the crystallization improvement when the precursor changed from titanium chloride to titanium (IV) propoxide, which proves the superiority of our TiO2 thin layers made without any type of annealing in comparison with other previous studies. The SEM images showed an improvement of the surface quality of the TiO2 thin layers with the change of TiO2 precursors' solution. The obtained optical properties confirmed the semiconducting properties of TiO2 prepared by titanium propoxide with a large band gap equal to 3.28 eV and shifted to 3.18 eV. The refractive index increases from ~1.75 to ~2.14, while the porosity decreases. To confirm the experimental results, the Wien2K code, founded on the full‐potential linearized augmented plane wave (FP‐LAPW), has been used. The theoretical study has been done by applying the generalized gradient approximation (GGA), the modified Beck‐Johnson (MBJ) exchange potential, and the local spin density approximation + Hubbard's parameter U (LSDA + U). The theoretical results varied with the variation of approximations. The obtained properties were improved with LSDA + U and acquired the real values of Eg, n, and k for anatase TiO2 (like Eg = 3.214 eV). The obtained experimental and theoretical results could be considered superposable or better than other ones recently published.