Orthogonalized Linear Combination Of Atomic Orbitals Research Articles

Ab initio study of electronic structure, bonding and optical properties of ternary A2B2In (A = Ca, Eu and B = Pd, Pt) indides

Crystal structure, optical and electronic properties of metal rich intermetallic Ca2Pd2In, Ca2Pt2In, Eu2Pd2In and Eu2Pt2In compounds have been explored using density functional theory based orthogonalized linear combination of atomic orbitals (OLCAO) method and code. The local density approximation scheme has been employed to probe all the properties. The outcomes of the electronic structure revealed the conducting nature of ternary indides. Density of states plots of ternary indides exhibited an increased number of energy states moving from Ca2Pd2In, Ca2Pt2In, Eu2Pd2In to Eu2Pt2In at Fermi level which substantiate the metallic nature of these compounds. The localization index calculations reflected the highly delocalized states in the vicinity of Fermi level. The cationic behavior of Ca- and Eu-atoms and anionic character of Pd-, Pt-, In-atoms has been evaluated through the effective charge (Qα*) calculations. Bond order calculations indicated highest strength of Ca2Pt2In among the studied indides. Optical features in the form of complex dielectric function, optical conductivity and electron energy loss function have been thoroughly discoursed. Two eminent peaks in electron energy loss L(ω) spectra have been observed at 29.77 and 27.83 eV which are associated to the plasmonic resonance.

Comparative study on structural, electronic, optical and mechanical properties of normal and high pressure phases titanium dioxide using DFT

In this paper, a Self-consistent Orthogonalized linear combination of atomic orbitals (OLCAO) technique with a generalized gradient approximation such as Perdew–Burke–Ernzerhof Solid (GGA-PBE SOL) has been used to scrutinize the structural, optical, electronic and mechanical properties of normal pressure phase (Anatase and Rutile) and high pressure phase i.e., cubic (Fluorite and Pyrite) TiO2. Electronic and optical properties of normal pressure phases of TiO2 are also investigated using (Meta) MGGA-Tran and Blaha (TB09) and obtained results are a close approximation of experimental data. It is seen that the virtually synthesized structural parameter for cubic and tetragonal phases of TiO2 are consistent with experimental and theoretical data. From the effective mass of charge carriers (m*), it can be observed that pyrite TiO2 is having lower effective mass than the fluorite and hence shows higher photocatalytic activity than fluorite. Furthermore, it is seen that fluorite is more dense than anatase, rutile and pyrite TiO2. From the theoretical calculations on the optical properties, it can be concluded that optical absorption occursin the near UV region for high and normal pressue phases of TiO2. Again from the reflectivity characteristics R(ω), it can be concluded that TiO2 can be used as a coating material. Elastic constants, elastic compliance constants, mechanical properties are obtained for anatase, rutile, fluorite and pyrite TiO2. A comparison of the results with previously reported theoretical and experimental data shows that the calculated properties are in better agreement with the previously reported experimental and theoretical results.

First-Principles Calculation of Laser Crystal Multiplet Levels via Hybridized Density Functional Theory and Configuration Interaction within the OLCAO Method

Computation of highly-localized multiplet energy levels of transition metal dopants is essential to the design of materials such as laser host crystals. A purely first-principles density functional theory-configuration interaction (DFT-CI) hybrid computational method has been developed to accurately compute multiplet energy levels for single atoms of carbon, nitrogen, oxygen, sodium, aluminum, silicon, titanium, and chromium. The multiplet energy levels have been computed with close experimental agreement in terms of magnitude and degeneracy, and the method does not depend on empirical information (i.e. Racah parameters). The computed multiplet energy level results are distributed according to term symbols, which are then compared to experimentally-observed multiplet energy levels. The hybrid method consists of analytic computation of two-electron integrals via the DFT-based orthogonalized linear combination of atomic orbitals (OLCAO) method, which are subsequently used as input for the CI-based discrete variational multi-electron (DVME) method to obtain the multiplet energy values.Keywords: exchange-correlation; elecron repulsion integral; multiplet; DVME; OLCAO; density functional theory; configuration interaction

A Density Functional Theory based Analysis on the Electronic, Mechanical, and Optical Properties of Cubic TiO2

Abstract This paper presents an analysis on electronic, mechanical and optical properties of cubic titanium dioxide using Orthogonalized Linear Combinations of Atomic Orbitals (OLCAO) basis set under the framework of Density Functional Theory. The structural property, namely lattice constant ‘a’, and the electronic properties such as, the band diagram, density of states (DOS) have been studied and analyzed. Whereas, the mechanical properties like, bulk moduli, Shear moduli, Young’s Moduli, poison’s ratio have also been investigated thoroughly. Moreover, optical properties such as refractive index, extinction co- efficient, reflectivity, absorption coefficient have been studied and analyzed thoroughly. The results are compared with previous theoretical and experimental results. It is found that, DFT based simulation produces results which are approximation to experimental results, whereas, the calculated values of elastic constants are better than the previous theoretical and experimental values.

Ab initio electronic structure, bonding and optical properties of two relatively new ceramics Hf2Al3C4 and Hf3Al3C5: A comparative study

The structural, electronic and optical properties of the ternary carbides Hf2Al3C4 and Hf3Al3C5 are studied via first principles orthogonalized linear combination of atomic orbitals (OLCAO) method. Results on crystal structure, interatomic bonding, band structure, total and partial density of states (DOS), localization index (LI), effective charge (Q*), bond order (BO), dielectric function (ε), optical conductivity (σ) and electron energy loss function are presented and discussed in detail. The band structure plots show the conducting nature of Hf2Al3C4 and Hf3Al3C5 carbides. DOS results disclose that the total number of states at Fermi level N(EF) are 1.89 and 2.38 states/(eV unit cell) for Hf2Al3C4 and Hf3Al3C5 respectively. The Q* calculations show an average charge transfer of 0.723 and 0.711 electrons from Hf and 0.809 and 0.807 electrons from Al to C sites in Hf2Al3C4 and Hf3Al3C5 respectively. The BO results provide the dominating role of Al–C bonds with BO value of 6.62 (BO% = 59%) and 6.66 (BO% = 49%) for Hf2Al3C4 and Hf3Al3C5 respectively and are considered responsible for the crystals cohesion. The LI results reflect the presence of highly delocalized states in the vicinity of the Fermi level. The dielectric function plots of the real (ɛ1(ℏω)) and imaginary (ɛ2(ℏω)) parts show the anisotropic behavior of Hf2Al3C4 and Hf3Al3C5. The results on optical conductivity (σ) support the trends observed in dielectric functions. The electron energy loss functions reveal the presence of sharp peaks both in ab-plane and along c-axis around 20 eV in Hf2Al3C4 and Hf3Al3C5 ternary carbides.

Structure, electronic, mechanical and optical properties of ternary YAl3C3 carbide

The electronic structure, mechanical and optical properties of ternary yttrium aluminum carbide (YAl3C3) has been studied by first principles approach. The crystal structure and elastic properties are studied by using Vienna ab initio simulation package (VASP). An orthogonalized linear combination of atomic orbitals (OLCAO) method based on the density functional theory (DFT) is implemented to elucidate the electronic structure and optical properties of ternary YAl3C3 carbide. The YAl3C3 carbide exhibits a narrow indirect band gap, Eg=0.12eV which shows its poor metallic and/or semiconductor behavior. The effective charge (Q*) calculation reveals more charge transfer from Al-sites as compared to Y-sites which indicates dominant ionic character of Al-sites. The analysis of structure and bond order (BO) calculations show that the Al–C bonds in the basal plane are much stronger as compared to Al–C bonds along the c-axis. The Al–C bonds lying in the basal plane have main contribution into the overall stiffness of YAl3C3 carbide. The effective mass of charge carriers (electrons and holes) and inter-band optical properties (complex dielectric function and optical conductivity) are also studied which show high degree of anisotropy in YAl3C3.

Electronic structure, mechanical, and optical properties of CaO·Al2O3 system: a first principles approach

A comprehensive study of the structure, bonding, mechanical and optical properties of five stable phases within the calcium aluminate (Ca–Al–O) series with different CaO to Al2O3 proportions has been carried out using the density functional theory based orthogonalized linear combination of atomic orbitals (OLCAO) method. The phases are C3A, C12A7-crystal, CA, CA2, and CA6 and the oxygen deficient C12A7-electride phase. These five stable phases are wide band gap insulators with energy gap values ranging from 3.85 to 4.62 eV. The charge neutral C12A7-crystal has localized defective states in the gap whereas the C12A7-electride phase has a region of metallic bands of about 2 eV wide in the gap. Effective charge and bond order calculations reveal intimate details of electronic structure and bonding in relation to the aluminate contents in the series. It is shown that Al–O bonds dominate the Ca–O bonds in determining the crystal strength with CA6 having the highest and C12A7 having the lowest bond order density. Calculations of elastic coefficients and mechanical properties in these crystals show a high degree of diversity and anisotropic behavior consistent with the bond order calculations. The refractive index values from optical properties calculations are in good agreement with available literature. Other results furnish more insights for the Ca–Al–O series and provide the opportunity for further investigations on similar or more complicated quaternary systems with potential novel properties.

OLCAO based Electronic Structure Calculations and Optical Properties of Ni_3Ga Intermetallic Alloy System

The first-principles orthogonalized linear combination of atomic orbitals (OLCAO) method has been employed to study the electronic structure and optical properties of the Ni3Ga intermetallic alloy system. To see the effects of ordering, we have simulated the ordered (L12) and disorder models. The calculated optical conductivity of the ordered phase is rich in structures and in reasonable agreement with the experimental data, while the conductivity spectrum of the disordered phase shows a single broadened peak. It is found that the average charge transfer from Ga to Ni in the ordered phase was greater (0.376 electrons per atom) as compared to the disordered phase (0.234 electrons per atom). The localization index (LI) calculations show that in case of the ordered phase there were localized states present below as well as above the Fermi-level. Localization of states is also present in the disordered phase, but both the models have shown different behavior. Other results on the band structure, density of states, and dielectric functions have also been discussed and described in detail.

Atomic structure, energetics, and chemical bonding of Y doped Σ13 grain boundaries in α-Al2O3

The atomic structure, energetics and chemical bonding state of pristine and Y doped Σ13, (104) grain boundaries in α-Al2O3 were investigated by aberration-corrected Z-contrast scanning transmission electron microscopy combined with first-principles calculations. Combining observations from two orthogonal directions parallel to the grain boundary plane, we found that Y atoms segregate into specific atomic sites and form two-dimensionally ordered structure. We performed first-principles calculations to estimate stable atomic sites for Y segregation, and it was found that the calculation results are in good agreement with the experimental results. Local chemical bonding states at the core of the boundary were investigated by a first-principles orthogonalized linear combination of atomic orbitals (OLCAO) method, and Y atoms and neighboring O atoms were found to evince strong ionic character while O–Al back bonds evince strong covalent character.

Spectroscopic properties of crystalline elemental boron and the implications on B11C–CBC

Elemental boron is a complicated material that involves a variety of phases with puzzling structures that are still controversial to this day. The allotropes of solid elemental boron include six crystalline phases (α-rhombohedral, β-rhombohedral, α-tetragonal, β-tetragonal, γ-orthorhombic, and α-Ga type), amorphous phases, and nanoscale structures. In the present work, the electronic structure and spectroscopic properties [X-ray absorption near edge structure (XANES) and optical dielectric functions] of the six crystalline phases were studied via the ab initio orthogonalized linear combination of atomic orbitals (OLCAO) method. The calculated XANES and dielectric functions of the α- and β-rhombohedral phases agree well with experiment. Based on this agreement, we predict the XANES spectra and dielectric functions for the other four crystalline phases. Each of the calculated XANES spectra of the five phases that have icosahedral units or clusters of icosahedra show a characteristic set of peak features in the energy range from 190 to 215 eV. These characteristic features were also observed in the XANES spectra of the icosahedron-containing B11C–CBC, a typical boron-rich compound.

Electronic structure and optical conductivities of 20 MAX-phase compounds

The electronic structure and optical conductivities of 20 so-called MAX phases Ti${}_{3}$AC${}_{2}$ (A $=$ Al, Si, Ge), Ti${}_{2}$AC (A $=$ Al, Ga, In, Si, Ge, Sn, P, As, S), Ti${}_{2}$AlN, M${}_{2}$AlC (M $=$ V, Nb, Cr), and Ta${}_{n}$${}_{+1}$AlC${}_{n}$ ($n$ $=$ 1 to 4) are studied using the first-principles orthogonalized linear combination of atomic orbitals (OLCAO) method. The calculated results include total and partial density of states, effective charge on each atom, and quantitative bond order values. Also calculated are directionally resolved interband optical conductivities. By analyzing such results regarding these phases (that have different atomic compositions and layered structures) several important features on structural stability and electrical conductivities are identified and compared with experimental data. We confirm the trend of increasing $N$(${E}_{f}$) (total density of states at the Fermi level ${E}_{f}$) as the number of valence electrons of the composing elements increases. The local feature of total density of states (TDOS) near ${E}_{f}$ is used to predict structural stability. The calculated effective charge on each atom shows that the M (transition-metal) atoms always lose charge to the X (C or N) atoms, whereas the A-group atoms mostly gain charge but some lose charge. Bond order values are obtained and critically analyzed for all types of interatomic bonds in all the 20 MAX phases.

X-ray absorption near edge structure/electron energy loss near edge structurecalculation using the supercell orthogonalized linear combination of atomic orbitalsmethod

Over the last eight years, a large number of x-ray absorption near edge structure (XANES)and/or electron energy loss near edge structure (ELNES) spectroscopic calculations forcomplex oxides and nitrides have been performed using the supercell-OLCAO (orthogonalizedlinear combination of atomic orbitals) method, obtaining results in very good agreementwith experiments. The method takes into account the core-hole effect and includes thedipole matrix elements calculated from ab initio wavefunctions. In this paper, we describethe method in considerable detail, emphasizing the special advantages of this method forlarge complex systems. Selected results are reviewed and several hitherto unpublishedresults are also presented. These include the Y K edge of Y ions segregated to the core of aΣ31 grain boundary in alumina, O K edges of water molecules, C K edges in different types ofsingle walled carbon nanotubes, and the Co K edge in the cyanocobalamin (vitaminB12) molecule. On the basis of these results, it is argued that the interpretation of specificfeatures of the calculated XANES/ELNES edges is not simple for complex material systemsbecause of the delocalized nature of the conduction band states. The long-standing notionof the ‘fingerprinting’ technique for spectral interpretation of experimental data is nottenable. A better approach is to fully characterize the structure under study, using eithercrystalline data or accurate ab initio modeling. Comparison between calculatedXANES/ELNES spectra and available measurements enables us to ascertain the validity ofthe modeled structure. For complex crystals or structures, it is necessary to use theweighted sum of the spectra from structurally nonequivalent sites for comparison with themeasured data. Future application of the supercell-OLCAO method to complexbiomolecular systems is also discussed.

FIRST-PRINCIPLES STUDY OF GAMMA-Si3N4 WITH GENERALIZED GRADIENT APPROXIMATION AND LOCAL DENSITY APPROXIMATION

The electronic structure, and optical and mechanical properties of gamma- Si 3 N 4 are calculated by means of the plane-wave pseudo-potential method (PWP) with generalized gradient approximation (GGA) and local density approximation (LDA). The calculated values are in good agreement with experimental results. A comparative investigation reveals that the band gap calculated by GGA agrees better with the experimental value than by the other methods, while the calculated bulk modulus by LDA is comparable with that by the method of orthogonalized linear combinations of atomic orbitals (OLCAO). Our results indicate that a satisfactory calculation of the structures and properties of gamma- Si 3 N 4 could be achieved by combining GGA and LDA methods.

Density functional calculations of the electronic structure and optical properties of aluminosilicate polymorphs (Al2SiO5)

The density functional theory (DFT) based orthogonalized linear combination of atomic orbitals (OLCAO) method is used to study the electronic structure and spectroscopic properties of three alumino silicate polymorphs (Al 2 SiO 5 ), andalusite, sillimanite, and kyanite. These polymorphs are precursors to mullite, which is an excellent refractory material. The electronic structure results include the band structure, total and partial density of states, bond order, and Mullikan effective charge (Q*), whereas the spectroscopic properties include X-ray absorption near-edge-structure (XANES), and the complex optical dielectric functions (e 1 + ie 2 ) for each polymorph. For the XANES calculations, we use a supercell approach and account for the electron-core hole interaction. Our calculations show that the polymorphs are insulators with direct band gaps of 5.05, 5.21, and 5.80 eV for andalusite, sillimanite, and kyanite, respectively. The calculated refractive indices (n) for each material are in agreement with experimental values from the literature. Results on the XANES spectral calculations ( K -edge and L -edge) for all crystallographically nonequivalent ions in the polymorphs are presented. It is shown that to achieve excellent agreement with the experimentally measured spectrum, a weighted sum of the spectra from crystallographically inequivalent sites must be used. The analysis of the XANES spectra based on differences in the local bonding environments are provided.

Peak assignments of ELNES and XANES using overlap population diagrams

The usefulness of overlap population (OP) diagrams for peak assignments of an electron energy loss near-edge structure (ELNES) and an X-ray absorption near-edge structure (XANES) is demonstrated. Mg-K, L 2,3, and O-K edges of MgO are taken as examples. Theoretical calculations are performed using a first-principles orthogonalized linear combination of atomic orbitals (OLCAO) method. A core-hole is included explicitly, and a large supercell is used to minimize artificial interactions among the core-holes in adjacent cells. All experimental spectra are quantitatively reproduced by the calculations. The OP diagrams for a selected pair of atomic orbitals are computed in order to provide proper assignments for each peak in ELNES and XANES. They are interpreted in terms of interactions among Mg–Mg and Mg–O bonds. Results are found to be consistent to our previous conclusion, which was obtained using a cluster method [T. Mizoguchi, et al., Phys. Rev. B 61 (2000) 2180]. The powerful combination of the OP diagram and a high-energy resolution ELNES to obtain fine electronic structures is also demonstrated.

Theoretical and Experimental Ti-K NEXAFS of Various Ti-Oxides

Near-edge structure of X-ray absorption spectrum (NEXAFS) of various Ti-oxides were investigated by combined with first principles orthogonalized linear combinations of atomic orbitals (OLCAO) method. From experimental and theoretical studies on the NEXAFS of the tetravalent and trivalent Ti-oxides, including rutile, anatase, brookite, columbite, and Ti2O3, it was found that the valence state of Ti can be identified by regarding the positions of the spectral onset and the shoulder in the main-peak of Ti-K NEXAFS.

First-principles Calculation of L<SUB>3</SUB> X-ray Absorption Near Edge Structures (XANES) and Electron Energy Loss Near Edge Structures (ELNES) of GaN and InN Polymorphs

First principles calculations of L3 XANES/ELNES of GaN and InN with both wurtzite and zinc-blende structures have been made using OLCAO (orthogonalized linear combinations of atomic orbitals) method. Supercells with more than 100 atoms were employed. A core-hole was rigorously included in the calculation, and the photo absorption cross section (PACS) between the initial and final states was computed. Quantitative reproduction of experimental spectrum that is available in literature can be found when the PACS was computed. Although spectral shapes of two phases look similar, characteristic differences are predicted to appear at the first peak of the L3 XANES/ELNES. The first peak is notably broader in the zinc-blende phases. The origin of the broadness is analyzed using partial density of unoccupied states (PDOS) and Mulliken charge. We then conclude that the broadness can be related to greater covalency of the zinc-blende phase as compared to the wurtzite phase.

Ab‐initio Calculation of Yttrium Substitutional Impurities in alpha‐Al2O3

Yttrium has a very low solubility in bulk α‐Al2 O3 and a great propensity for segregation to the grain boundaries in polycrystalline Al2O3. The segregation of yttrium influ‐ences many properties of the material. To understand the nature of the chemical bonding of yttrium within Al2O3, we have, as a first step, conducted an ab‐initio self‐consistent calculation for a yttrium impurity atom replacing an aluminum atom in Al2O3. We have used the first‐principles orthogonalized linear combination of atomic orbitals (OLCAO) method and a supercell with 120 atoms in the hexagonal lattice. The relaxation of the nearby atoms, be‐cause of the presence of yttrium, is studied via total energy calculation within the local density approximation. The nearest‐neighbor oxygen atoms of yttrium move outward by 8% and the next‐nearest‐neighbor aluminum atoms move inward by 5% of the respective separations in the undistorted lattice. A substitutional energy of 4.79 eV is obtained. The yttrium impurity introduces three defect states in the gap near the conduction band edge, thus natu‐rally explaining the “donor effect.” Two of the defect states are degenerate, and all three are derived mainly from the Y4d orbitals with very different local symmetries. The effec‐tive‐charge and bond‐order calculations show a substantial covalent bonding character between yttrium and the re‐laxed oxygen and aluminum atoms in the host.

Calculation of optical excitations in cubic semiconductors. I. Electronic structure and linear response.

The electronic structures and the linear optical dielectric functions of 18 cubic semiconductors are studied by the first-principles orthogonalized linear-combination-of-atomic-orbitals (OLCAO) method in the local-density approximation. The crystals studied include the group-IV semiconductors C, Si, and Ge; the III-V compounds AlP, AlAs, AlSb, GaP, GaAs, GaSb, InP, InAs, InSb; and the II-VI semiconductors ZnS, ZnSe, ZnTe, CdS, CdSe, and CdTe. Results are presented for the band structures, for the density of states, and for the real and imaginary parts of the linear dielectric functions for photon energies up to 12 eV. The results are compared with other existing calculations and experimental data. Some interesting correlations and trends among the 18 semiconductors studied are pointed out, and possible problems with the optical excitation calculation are discussed. These results provide the groundwork for the calculation of nonlinear optical properties on these crystals using the full band-structure approach in the two papers to follow. It is argued that optical excitations in semiconductors can be efficiently carried out using the OLCAO method without resorting to empirical methods or model studies. The present calculation gives band gaps larger than the well-converged result of first-principles pseudopotential calculations. The consequence of this difference on the optical properties is discussed.

ENERGY BANDS AND OPTICAL PROPERTIES OF CdTe

The energy bands of CdTe are studied using the method of Orthogonalized Linear Com-bination of Atomic Orbitals (OLCAO). The risults are in good agreement with that given by methods of LAPW, LMTO-ASA and NL-EPM. Some physical quantities related to the optical properties of CdTe are also described. These are the imaginary component of optical dielec-tric function ∈2(ω), and that of high frequency conductivity σ1(ω), and the optical reflectivity R(∈)