First-principles energy band calculation for undoped and S-doped TiO2 with anatase structure

The electronic structure of S-doped TiO₂ with an optimized anatase structure was calculated within the framework of the density functional theory (DFT). For the calculation we built four kinds of supercells; type-A and B supercells consist of 12 and 48 atoms and a centered Ti atom is substituted for an S atom, while type-C and D supercells consist of 12 and 48 atoms and a centered O atom is substituted for an S atom. The supercells (type-B and D) were employed to adjust the S-concentration in TiO₂ to an experimental value of a few %. The changes of the lattice parameters are not significant in the type-A and B supercells. The phase transition from the tetragonal to the orthorhombic occurs in the type-C and D supercells. In the small supercell (type-A), S-related states are located in the range of −1.6 to 0 eV, and the S-states are band-like. In contrast, in the large supercell (type-B), S-related states appeared at about 0.9 eV above the top of the valence band, and the S-states are atomic-like. The localization of the S-related states is remarkable in the type-B supercell. In the type-D supercell, the S-related states were merged with the top of the valence band, and as a result the band-gap energy is narrowed by 0.7 eV. Despite a low S-concentration (3%) in the type-D supercell, the S-related states are somewhat band-like.     

First-principles study on electronic structure of Sr2Bi2O5 crystal

The electronic structure of Sr₂Bi₂O₅ is calculated by the GGA approach. Both of the valence band maximum and the conduction band minimum are located at Γ-point. This means that Sr₂Bi₂O₅ is a direct band-gap material. The wide energy-band dispersions near the valence band maximum and the conduction band minimum predict that holes and electrons generated by band gap excitation have a high mobility. The conduction band is composed of Bi 6p, Sr 4d and O 2p energy states. On the other hand, the valence band can be divided into two energy regions ranging from −9.5 to −7.9 eV (lower valence band) and from −4.13 to 0 eV (upper valence band). The former mainly consists of Bi 6s states hybridizing with O 2s and O 2p states, and the latter is mainly constructed from O 2p states strongly interacting with Bi 6s and Bi 6p states.     

First-principles calculations of electronic, optical and elastic properties of ZnAl2S4 and ZnGa2O4

The optimized crystal structures, band structures, partial and total densities of states (DOS), dielectric functions, refractive indexes and elastic constants for ZnAl₂S₄ and ZnGa₂O₄ were calculated using the CASTEP module of Materials Studio package. Pressure effects were modeled by performing these calculations for different values of external hydrostatic pressure up to 50 GPa. Obtained dependencies of the unit cell volume on pressure were fitted by the Murnaghan equation of state, and the relative changes of different chemical bond lengths were approximated by quadratic functions of pressure. Variations of applied pressure were shown to produce considerable re-distribution of the electron densities around ions in both crystals, which is evidenced in different trends for the effective Mulliken charges of the constituting ions and changes of contour plots of the charge densities. The longitudinal and transverse sound velocities and Debye temperatures for both compounds were also estimated using the calculated elastic constants.     

High-temperature crystal structure and electronic properties of cesium niobate Cs2Nb4O11

The antiferroelectric material Cs₂Nb₄O₁₁ transforms at 165 °C from a low-temperature, antiferroelectric phase in space group Pnna to a high-temperature, paraelectric phase in space group Imma; the latter structure has been determined by single-crystal X-ray diffraction. The high-temperature lattice is comprised of niobium-centered tetrahedra and octahedra connected through shared vertices and edges; cesium atoms occupy channels afforded by the three-dimensional polyhedral network. Calculated band structures for both phases predict a bandgap of 3.1-3.2 eV, which is similar to that found experimentally through photoluminescence. The calculated band structure is also conducive to its observed photocatalytic properties.     

Band structure and optical spectra of RbNH4SO4 crystals

First-principal density functional theory (DFT) calculations of the band structure, density of states and dielectric functions ε(E) of the rubidium ammonium sulfate (RAS) crystal, RbNH₄SO₄, in the orthorhombic phase Pnma have been carried out using the CASTEP code. Valence electron bands of the crystal are flat in k-space, that responds to the relatively great effective mass, m*?5m_e. The top valence band of the crystal has been found to be the most flat, what might be an evidence of a weak chemical bonding of the sulfate complexes (SO₄) in the crystal and therefore for the predisposition to structural instability and phase transitions. The characteristic feature is that two top valence bands are originated almost entirely from p-electrons of oxygen. The bottom part of the conduction band is formed mainly by the hydrogen atoms, the higher parts of this band—by a mixed set of chemical elements and orbital moments. The calculated refractive indices in the range of crystal's transparency agree satisfactorily with the experiment considering that the infrared absorption is not taken into account in calculations.     

Analysis of electronic structures of 3d transition metal-doped TiO2 based on band calculations

The electronic structures of titanium dioxide (TiO₂) doped with 3d transition metals (V, Cr, Mn, Fe, Co and Ni) have been analyzed by ab initio band calculations based on the density functional theory with the full-potential linearized-augmented-plane-wave method. When TiO₂ is doped with V, Cr, Mn, Fe, or Co, an electron occupied level occurs and the electrons are localized around each dopant. As the atomic number of the dopant increases the localized level shifts to lower energy. The energy of the localized level due to Co is sufficiently low to lie at the top of the valence band while the other metals produce midgap states. In contrast, the electrons from the Ni dopant are somewhat delocalized, thus significantly contributing to the formation of the valence band with the O p and Ti 3d electrons. Based on a comparison with the absorption and photoconductivity data previously reported, we show that the t_2g state of the dopant plays a significant role in the photoresponse of TiO₂ under visible light irradiation.     

A first-principles theoretical simulation on the electronic structures and optical absorption properties for O vacancy and Ni impurity in TiO2 photocatalysts

The band structures and optical absorption spectra of O vacancy and Ni ion doped anatase TiO₂ were successfully calculated and simulated by a plane wave pseudopotential method based on density functional theory (DFT). From the calculated results, a phenomenon of “impurity compensation” was found: the lower formation energy for O vacancy than Ni impurity indicated that introducing the intrinsic defect of O vacancy into Ni ion doped TiO₂ sample was very possible; the positive binding energy for the combination of O vacancy and Ni impurity indicated that two defects were apt to bind to each other; While Ni impurity produced the donor levels in the forbidden band of TiO₂, Ni impurity with O vacancy produced the acceptor levels upon which the excitation led to the photogenerated electrons with high energy and transferability. The combination of absorption spectra for O vacancy and Ni impurity with O vacancy models could reproduce the experimental measurement very well.     

Band structure calculations on the layered compounds FeGa2S4 and NiGa2S4

For the compounds FeGa₂S₄ and NiGa₂S₄ band structure calculations have been performed by the ab initio plane wave pseudo-potential method. The valence charge density distribution points to an ionic type of chemical bonding between the transition metal atoms and the ligand atoms. Two models for the pseudo-potentials are used to calculate the band structures: (a) only s and p electrons and (b) also the d-shells of the transition metal atoms are included in the pseudo-potentials. The differences between these two cases of band structures are discussed. Energy gap formation peculiarities are analysed for both crystals. Zak's elementary energy band concept is demonstrated for the energy spectra of the considered crystals.     

Electronic structure and chemical bonding of phosphorus-contained sulfides InPS4, TI3PS4, and Sn2P2S6

The electronic structure of phosphorus-contained sulfides InPS₄, Tl₃PS₄, and Sn₂P₂S₆ was investigated experimentally with X-ray spectroscopy and theoretically by quantum mechanical calculations. The partial densities of electron states calculated with the ab initio multiple scattering FEFF8 code correspond well to their experimental analogues—the X-ray K- and L_2,3-spectra of sulfur and phosphorus. The good agreement between theory and experiment was also achieved for K-absorption spectra of S and P in the investigated sulfides. In spite of the difference in the crystallographic structure of InPS₄, TI₃PS₄, and Sn₂P₂S₆ that influence the form of K-absorption spectra, the electronic structure of their valence bands are rather similar. This is due to the strong interaction of the P and S atoms, which are the nearest neighbors in the compounds studied. The electron densities of p- and s-states of phosphorus are shifted by about 3 eV to lower energies in comparison to the analogous electron states of sulfur. This is connected with the greater electro-negativity of sulfur, and is confirmed by the calculated electron charge transfer from P to S.     

Electronic structure and electric-field-gradients distribution in Y3Al5O12: An ab initio study

The periodic Hartree-Fock method has been applied to calculate the electronic structure of the yttrium aluminium garnet. We report on the results of the density of state calculations, the population analysis, as well as the electric-field-gradient distribution. A comparative analysis with the related structure α-Al₂O₃ was done. The calculations show that the Y₃Al₅O₁₂ crystal is more ionic than α-Al₂O₃.     

Ab initio band structure calculations of the low-temperature phases of Ag2Se, Ag2Te and Ag3AuSe2

Ab initio band structure calculations were performed for the low-temperature modifications of the silver chalcogenides β-Ag₂Se, β-Ag₂Te and the ternary compound β-Ag₃AuSe₂ by the local spherical wave (LSW) method. Coordinates of the atoms of β-Ag₂Se and β-Ag₃AuSe₂ were obtained from refinements using X-ray powder data. The structures are characterized by three, four and five coordinations of silver by the chalcogen, a linear coordination of gold by Se, and by metal-metal distances only slightly larger than in the metals. The band structure calculations show that β-Ag₃AuSe₂ is a semiconductor, while β-Ag₂Se and β-Ag₂Te are semimetals with an overlap of about 0.1-0.2 eV. The Ag 4d and Au 5d states are strongly hybridized with the chalcogen p states all over the valence bands. β-Ag₂Se and β-Ag₂Te have a very low DOS in the energy range from about −0.1 to +0.5 eV. The calculated effective mass β-Ag₂Se is about 0.1-0.3 m_e for electrons and 0.75 m_e for holes, respectively.     

O-vacancy and surface on CeO2: A first-principles study

Atomic and electronic structures of CeO₂ (1 1 1), (1 1 0) and (1 0 0) surfaces are investigated using the first-principles density functional theory taking into account the on-site Coulomb interaction. Both the stoichiometric and O-deficient surfaces are examined in order to clarify the overall features. The CeO₂ (1 1 1) is found to be the most stable surface, followed by the (1 1 0) and (1 0 0) surfaces, consistent with experimental observations. Three surfaces exhibit different features of relaxation. Large relaxations are found at the (1 1 0) and (1 0 0) surfaces, while very small changes are observed at the (1 1 1) surface. It is found that the O-vacancy occurs more readily at the (1 1 0) surface as compared with the (1 1 1) surface. Furthermore, the formation energies of the O-vacancy in the surfaces are lower than that in the bulk. The energetically favorable O-vacancy locates in the second O-atomic layer for the (1 1 1) while at the surface layer for the (1 1 0). The excess electrons left with the removal of the O atom are distributed in the first two layers with certain (a considerable) fraction filling the Ce-4f states.     

The effects of O deficiency on the electronic structure of rutile TiO2

Ab initio density functional calculations (plane wave GGA, CASTEP) were performed to determine the effect of O deficiency on the electronic structure of rutile, TiO₂. O deficiency was introduced through either the removal of O or the insertion of interstitial Ti atoms. At physically realistic concentrations of O vacancies in the rutile lattice (i.e. 25% and less) O deficiency results in the population of the bottom of the conduction band, the location of the Ti 3d orbitals in the pure structure, increasingly with increasing vacancy concentration. We propose that this could be confused with the formation and population of gap states especially where O vacancies occur in isolated positions in the lattice. In contrast, Ti interstitials introduce a defect state into the energy gap, without an overall reduction in the size of the energy gap. O vacancies result in a spin polarized solution, whereas Ti interstitials do not.     

First-principles investigation of Mg2Ni phase and high/low temperature Mg2NiH4 complex hydrides

Using a density functional approach calculation, the structural, energetic and electronic properties of Mg₂Ni phase as well as its high/low temperature (HT/LT)-Mg₂NiH₄ complex hydrides are systematically investigated. The optimized structural parameters including lattice constants and atomic positions are very close to the experimental data determined from X-ray and neutron powder diffraction. A detailed study of the electronic structures including the energy band, density of states (DOS) and charge density distribution reveals the orbital hybridization and characteristics of bonding orbits within Mg₂Ni and its hydrides. Based on the calculated results of the reaction heat of hydrogenation, enthalpy of formation and energy cost to remove H atoms, it is found that the formation ability of LT-Mg₂NiH₄ is higher than that of the HT phase during the hydrogenation of Mg₂Ni alloy; moreover, LT-Mg₂NiH₄ has a relatively higher structural stability than HT phase, which is also well explained through the DOS and the charge distributions of HT/LT-Mg₂NiH₄ phases.     

First-principles studies on Ti3Si0.5Ge0.5C2 under pressure

The structural, electronic and elastic properties of Ti₃Si_0.5Ge_0.5C₂ have been investigated by using the pseudopotential plane-wave method within the density-functional theory. Our calculated equation of state (EOS) is consistent with the experimental results. The density of states (DOS) indicates that Ti₃Si_xGe_1−xC₂ (x=0, 0.5, 1.0) are metallic, and these compounds have nearly the same electrical conductivity. The elastic constants for Ti₃Si_0.5Ge_0.5C₂ are obtained at zero pressure, which is compared to Ti₃SiC₂ and Ti₃GeC₂. We can conclude that Ti₃Si_0.5Ge_0.5C₂ is brittle in nature by analyzing the ratio between bulk and shear moduli. There appears to be little effect on the electronic and elastic properties with the Ge substitution to Si atoms in Ti₃SiC₂.     

Electronic structure of CeF3 and TbF3 by valence-band XPS and theory

Electronic structures of the rare earth trifluorides CeF₃ () and TbF₃ (Pnma) were examined by high-resolution valence-band X-ray photoelectron spectroscopy (VB-XPS) and all-electron periodic-crystal DFT theory including the spin-polarization (SP) combined with spin-orbit (SO) coupling using a second-variational treatment. Calculations using the Perdew-Burke-Ernzerhof (PBE) functional and the LDA+U method were carried out and compared. The results show that a complete analysis does require a full DFT-SP-SO treatment to obtain a quantitative account for the observed VB-XPS spectra, with an additional insight of the theory with regard to the nature of the topmost orbitals, and the bonding-antibonding character of orbitals within the VB and sub-VB levels. The band structure at the bottom of the conduction band (BCB) shows a strong dispersion in TbF₃ but not in CeF₃, predicting photoconductivity in TbF₃.     

Crystal growth and the electronic structure of Tl3PbCl5

Total and partial densities of states of constituent atoms of two tetragonal phases of Tl₃PbCl₅ (space groups P4₁2₁2 and P4₁) have been calculated using the full potential linearized augmented plane wave (FP-LAPW) method and Korringa-Kohn-Rostoker method within coherent potential approximation (KKR-CPA). The results obtained reveal the similarity of occupations of the valence band and the conduction band in the both tetragonal phases of Tl₃PbCl₅. The FP-LAPW and KKR-CPA data indicate that the valence band of Tl₃PbCl₅ is dominated by contributions of the Cl 3p-like states, which contribute mainly to the top and the central portion of the valence band with also significant contributions throughout the whole valence-band region. Further, the bottom of the valence band of Tl₃PbCl₅ is composed mainly of the Tl 6s-like states, while the bottom of the conduction band is dominated by contributions of the empty Pb 6p-like states. The KKR-CPA results allow to assume that the width of the valence band increases somewhat while band gap, E_g, decreases when changing the crystal structure from P4₁2₁2 to P4₁. The X-ray photoelectron core-level and valence-band spectra for pristine and Ar⁺-ion-irradiated surfaces of a Tl₃PbCl₅ monocrystal grown by the Bridgman-Stockbarger method have been measured.     

Electronic states of lanthanide in the ternary thiogallate CaGa2S4

The electronic states of lanthanide (Ln) doped CaGa₂S₄ are investigated by the molecular orbital calculations for a spherical cluster of LnCa₈Ga₁₂S₂₄ using the FORTRAN program DVSCAT on the basis of the Discrete Variational method with Xα potentials (DV-Xα). In view of the SCF convergence, the Ln-doped lattice should contract to 85-90% of the mother crystal around the Ln atom for the lightweight lanthanides from Ce to Sm. On the other hand, the lattice contraction is very small for the heavyweight lanthanides, especially for Er, Tm and Yb in contrast to the generally known lanthanide contraction for Ln³⁺ ions. This is probably attributed to the effective charges of Ln atoms calculated here to be less than +1 for all lanthanides contrary to the chemically accepted value of +3. The energy level scheme of 4f and 5d related molecular orbitals is proposed for each Ln substituting Ca in CaGa₂S₄, showing that the optical processes relating to the 5d→4f transition must be complicated especially for the lightweight Ln-doped CaGa₂S₄.     

Physical properties of the cubic spinel LiMn2O4

We have performed an ab initio study of structural, electronic, magnetic, vibrational and thermal properties of the cubic spinel LiMn₂O₄ by employing the density functional theory, the linear-response formalism, and the plane-wave pseudopotential method. An analysis of the electronic structure with the help of electronic density of states shows that the density of states at the Fermi level (N (E_F)) is found to be governed by the Mn 3d electrons with some contributions from the 2p states of O atoms. It is important to note that the contribution of Mn 3d states to N(_EF)$N\left(E_F\right)$ is as much as 85%. From our phonon calculations, we have obtained that the main contribution to phonon density of states (below 250 cm⁻¹) comes from the coupled motion of Mn and O atoms while phonon modes between 250 cm⁻¹ and 375 cm⁻¹ are characterized by the vibrations of all the three types of atoms. The contribution from Li increases rapidly at higher frequency (above 375 cm⁻¹) due to the light mass of this atom. Finally, the specific heat and the Debye temperature at 300 K are calculated to be 249.29 J/mol K and 820.80 K respectively.     

Ab initio study of phonons in the rutile structure of TiO2

The local-density approximation is used to find the phonon dispersion relations, total and partial phonon density of states for TiO₂ crystal of rutile structure. For that the Hellmann-Feynman forces were computed and direct method applied. Some thermodynamic quantities are also presented. Calculated results are analyzed and compared with the experimental neutron scattering and optic data. Good agreement has been achieved. A giant LO/TO splitting is observed for A_2u and E_u modes.