Linear Combination Of Atomic Orbitals Method Research Articles

<i>Ab Initio</i> Local-Energy and Local-Stress Calculations for Materials Science and Engineering

Revealing atomic-scale distributions of energy and stress in defective or complex systems, based on the behavior of electrons, should contribute much to materials science and engineering, while only few practical ab initio methods were developed for this purpose. Thus, we developed computational techniques of local-energy and local-stress calculations within the plane-wave PAW (projector augmented wave)-GGA (generalized gradient approximation) framework. This is natural extension of ab initio energy-density and stress-density schemes, while the inherent gauge dependency is removed by integrating these densities in each local region where the contained gauge-dependent terms are integrated to be zero. In this overview, we explain our scheme with some details and discuss the concepts or physical meanings of local energy and local stress via the comparison with related schemes using similar densities, LCAO (linear combination of atomic orbitals) methods, Green’s function formulation implemented by multiple scattering or TB (tight-binding) methods, or EAM (embedded-atom method) potentials. We present recent applications to metallic surfaces, grain boundaries (GBs) with and without solute segregation, tensile tests of metallic GBs, local elastic constants of microstructures in alloys, and machine-learning based GB-energy prediction, where the local-energy and local-stress analyses provide novel aspects of phenomena, deep insights into the mechanism, and effective data for novel machine-learning based modelling. We discuss unsettled issues and future applications, especially for large-scale metallic systems.

Experimental and theoretical divulging of electronic structure and optical properties of Zn-doped SnSe thermoelectric materials

Electron momentum densities (EMDs) of undoped and Zn-doped SnSe are measured using a 100 mCi 241Am Compton spectrometer. Various density functional theories and hybrid exchange and correlation potentials (LDA, PBE, PBEsol, PBE0, and B3LYP) within the linear combinations of atomic orbitals (LCAO) calculations have been attempted to compute Compton profiles (CPs) and electronic structure of the doped and undoped SnSe. Among all the Compton line shapes predicted using first principles, B3LYP approximation-based EMDs are found to be in a better reconciliation with the CP measurements. Experimental data is also analyzed in terms of localization of Zn-d states. Going beyond the LCAO method, the density of state (DOS), energy bands, reflectance, dielectric constant, and absorption coefficient for Zn-doped (Sn0.97Zn0.03Se and Sn0.95Zn0.05Se) and undoped SnSe are computed using the FP-LAPW-mBJ method. It is seen that Sn-5s and Se-4p orbitals are responsible for the formation of the indirect band gap. Interestingly, Zn doping in SnSe (Sn0.97Zn0.03Se and Sn0.95Zn0.05Se) leads to interstitial bands in the low energy side of the conduction region leading to electron trapping centres and reduction of band gap (from 0.816 to 0.508eV in case of FP-LAPW-mBJ scheme and 1.152 to 0.510 eV in case of LCAO-B3LYP scheme). Our works evidently support the positive effect of Zn doping in enhancing the electronic and thermoelectric properties of the SnSe by forming interstitial bands. Apart from this, undoped and Zn-doped SnSe can also be used for solar cells as an absorber material and detection of ultraviolet (B and C) rays. Due to the formation of interstitial bands induced trapping centres, Zn-doped SnSe can also be uniquely employed in thermoluminescence devices (TLDs).

Triple-differential cross section for the twisted-electron-impact ionization of the water molecule

In this communication, we present the results of the triple differential cross-section (TDCS) for the (e,2e) process on H2O molecule for the plane wave and the twisted electron beam impact. The formalism is developed in the first Born approximation. We describe the plane/twisted wave, plane wave, the linear combination of atomic orbitals (LCAO) (self-consistent field LCAO method) and Coulomb wave for the incident electron, scattered electron, the molecular state of H2O, and the ejected electron, respectively. We investigate the angular profiles of the TDCS for the outer orbitals 1B1, 3A1, 1B2, and 2A1 of the water molecule. We compare the angular profiles of the TDCS for the different values of orbital angular momentum (OAM) number m of the twisted electron beam with that of the plane wave beam. We also study the TDCS for macroscopic H2O target to explore the effect of opening angle {\theta}p of the twisted electron beam on the TDCS. Our results clearly show the effect of the twisted electron's OAM number (m) and the opening angle {\theta}p on the TDCS of the water molecule.

Correspondence between the surface integral and linear combination of atomic orbitals methods for ionic-covalent interactions in mutual neutralization processes involving H−/D−

The surface integral method for estimating ionic-covalent interactions in diatomic systems been successful in producing cross sections for mutual neutralization (MN) in reasonable agreement with experimental results for branching fractions between final states in systems such as ${\mathrm{O}}^{+}\text{/}{\mathrm{O}}^{\ensuremath{-}}$ and ${\mathrm{N}}^{+}\text{/}{\mathrm{O}}^{\ensuremath{-}}$. However, for simpler cases of MN involving ${\mathrm{H}}^{\ensuremath{-}}$ or ${\mathrm{D}}^{\ensuremath{-}}$, such as ${\mathrm{Li}}^{+}\text{/}{\mathrm{D}}^{\ensuremath{-}}$ and ${\mathrm{Na}}^{+}\text{/}{\mathrm{D}}^{\ensuremath{-}}$, it has not produced results that are in agreement with experiments and other theoretical calculations; in particular, for ${\mathrm{Li}}^{+}\text{/}{\mathrm{D}}^{\ensuremath{-}}$ calculations predict the wrong ordering of importance of final channels, including the incorrect most populated channel. The reason for this anomaly is investigated, and a leading constant to the asymptotic ${\mathrm{H}}^{\ensuremath{-}}$ wave function is found that is different by roughly a factor of $1\text{/}\sqrt{2}$ from that which has been used in previous calculations with the surface integral method involving ${\mathrm{H}}^{\ensuremath{-}}$ or ${\mathrm{D}}^{\ensuremath{-}}$. With this correction, far better agreement with both experimental results and calculations with full quantum and linear combination of atomic orbitals (LCAO) methods is obtained. Further, it is shown that the surface integral method and LCAO methods have the same asymptotic behavior, in contrast to previous claims. This result suggests the surface integral method, which is comparatively easy to calculate, has greater potential for estimating MN processes than earlier comparisons had suggested.

Electronic response of rare-earth magnetic-refrigeration compounds GdX2 (X = Fe and Co)

We present the Compton profiles (CPs) of rare-earth-transition metal compounds GdX2 (X = Fe and Co) using 740 GBq 137Cs Compton spectrometer. To compare the experimental momentum densities, we have also computed the CPs, electronic band structure, density of states (DOS) and Mulliken population (MP) using linear combination of atomic orbitals (LCAO) method. Local density and generalized gradient approximations within density functional theory (DFT) along with the hybridization of Hartree-Fock and DFT (B3LYP and PBE0) have been considered under the framework of LCAO scheme. It is seen that the LCAO-B3LYP based momentum densities give a better agreement with the experimental data for both the compounds. The energy bands and DOS for both the spin-up and spin-down states show metallic like character of the reported intermetallic compounds. The localization of 3d electrons of Co and Fe has also been discussed in terms of equally normalized CPs and MP data. Discussion on magnetization using LCAO method is also included.

Electron momentum distribution and electronic response of ceramic borides

Isotropic Compton profiles of transition metal based ceramics TaB and VB have been measured using 137Cs (661.65keV) γ-ray Compton spectrometer. The experimental momentum densities are compared with those deduced using linear combination of atomic orbitals (LCAO) with Hartree-Fock (HF), density functional theory (DFT) with Wu-Cohen generalized gradient approximation (WCGGA) and also the hybridization of HF and DFT (namely B3PW and PBE0) schemes. It is found that LCAO-DFT-WCGGA scheme based profiles give an overall better agreement with the experimental data, for both the borides. In addition, we have computed the Mulliken's population (MP) charge transfer data, energy bands, density of states and Fermi surface topology of both the borides using full potential-linearized augmented plane wave (FP-LAPW) and LCAO methods with DFT-WCGGA scheme. Cross-overs of Fermi level by the energy bands corresponding to B-2p and valence d-states of transition metals lead to metallic character in both the compounds. Equal-valence-electron-density profiles and MP analysis suggest more ionic character of VB than that of TaB.

High energy Compton spectroscopy and electronic structure of Laves phase ZrFe 2

Abstract We present the first-ever experimental Compton profile of Laves phase ZrFe2 using indigenous 20 Ci 137Cs Compton spectrometer. To annotate the experimental electron momentum density, we have calculated the theoretical Compton profiles using density functional theory (DFT) and hybridization of Hartree–Fock and DFT within linear combination of atomic orbitals (LCAO) method. The spin-polarized energy bands and density of states are computed using LCAO and full potential-linearized augmented plane wave methods. The revised Perdew-Burke-Ernzerhof functional (for solids) based theoretical profile gives a marginally better agreement with the experimental profile as compared to other approximations considered in the present work. The Fermi surface topology of ZrFe2 is explained in terms of majority- and minority-spin energy bands.

Electronic and optical properties of ceramic Sc2O3 and Y2O3: Compton spectroscopy and first principles calculations

We present the first-ever experimental Compton profiles (CPs) of Sc2O3 and Y2O3 using 740 GBq 137Cs Compton spectrometer. The experimental momentum densities have been compared with the theoretical CPs computed using linear combination of atomic orbitals (LCAO) within density functional theory (DFT). Further, the energy bands, density of states (DOS) and Mulliken's population (MP) data have been calculated using LCAO method with different exchange and correlation approximations. In addition, the energy bands, DOS, valence charge density (VCD), dielectric function, absorption coefficient and refractive index have also been computed using full potential linearized augmented plane wave (FP-LAPW) method with revised functional of Perdew–Becke–Ernzerhof for solids (PBEsol) and modified Becke Johnson (mBJ) approximations. Both the ab-initio calculations predict wide band gaps in Sc2O3 and Y2O3. The band gaps deduced from FP-LAPW (with mBJ) are found to be close to available experimental data. The VCD and MP data show more ionic character of Sc2O3 than Y2O3. The ceramic properties of both the sesquioxides are explained in terms of their electronic and optical properties.

Electronic and optical response of zirconium sulphoselenides: Compton spectroscopy and first-principles calculations

We present the first-ever experimental Compton profiles (CPs) of ZrSSe2 and ZrS1.5Se1.5 using 100 mCi 241Am Compton spectrometer. To analyze the experimental momentum densities, we have computed for the first-time the CPs, energy bands and density of states using linear combination of atomic orbitals (LCAO) method. To model the exchange and correlation effects within LCAO approach, we have considered Hartree–Fock (HF), density functional theory (DFT) with revised functional of Perdew–Becke–Ernzerhof (PBEsol) and hybridization of HF and DFT. Going beyond computation of electronic properties using LCAO method, we have also derived electronic and optical properties using the modified Becke–Johnson (mBJ) potential within full potential linearized augmented plane wave (FP-LAPW) method. There is notable decrease in the energy band gap on replacing S by Se atoms in ZrSSe2 to obtain ZrS1.5Se1.5 composition, which is mainly attributed to readjustment of Zr–4d, S–3p and Se–4p states. It is seen that the CPs based on hybridization of HF and DFT show a better agreement with the experimental profiles than those based on individual HF and DFT-GGA-PBEsol schemes. The optical properties computed using FP-LAPW-mBJ method unambiguously depict feasibility of using both the sulphoselenides in photovoltaics and also utility of ZrS1.5Se1.5 in the field of non-linear optics.

A Simple Demonstration of Atomic and Molecular Orbitals Using Circular Magnets

A quite simple and inexpensive technique is described here to represent the approximate shapes of atomic orbitals and the molecular orbitals formed by them following the principles of the linear combination of atomic orbitals (LCAO) method. Molecular orbitals of a few simple molecules can also be pictorially represented. Instructors can employ the method to demonstrate the application of the LCAO method, which can help students better understand the bonding principle.

Comparison of Finite Element Approach and LCAO Analysis with SIWB Method for a Molecule Including an Anion in a Discrete Variational Density Functional Theory

For proper anion description, the author developed the SIWB (surrounding or solid Coulomb-potential-induced well for basis set) method for a linear combination of atomic orbitals (LCAO) calculated numerically in a discrete variational (DV) density functional theory (DFT). In the DV method, a relatively deep (such as −1 Eh) well potential is added to the potential for electrons to generate stable atomic orbital basis functions, where the depth and radius of the well are not definitely determined. Meanwhile, the SIWB method uniquely determines the well radius and the well depth, which is relatively shallow (such as −0.34 Eh). In this article, calculations of the one-electron wave function for a molecule containing an anion were performed using the finite element method (FEM). The FEM results were compared not only to results from the usual LCAO method with a relatively deep well, but also to those from the improved LCAO method with the SIWB scheme (denoted as LCAO−SIWB). It was shown that the FEM results for the anion are consistent with the LCAO−SIWB results.

Compton scattering study and electronic structure of different phases of NH4NO3

In this paper, we present energy bands, density of states and the nature of hydrogen bonding in different temperature-dependent phases of NH4NO3, namely phases II (357–398 K), III (305–357 K) and IV (257–305 K), using the full potential linearized augmented plane wave and linear combination of atomic orbitals (LCAO) methods. Both band structure calculations show the insulating character of the II–IV phases of NH4NO3. In addition, we have reported the isotropic Compton profile of NH4NO3(IV) measured using 661.65 keV γ-radiation from a 137Cs isotope. The experimental momentum density has been compared with that based on density functional theory (DFT) and Hartree–Fock schemes within the LCAO method. It is seen that the LCAO with hybridization of DFT and Hartree–Fock (so-called B3LYP) gives better agreement with the present Compton profile measurement.

Spin splitting in bulk wurtzite AlN under biaxial strain

The spin-splitting energies in biaxially strained bulk wurtzite material AlN are calculated using the linear combination of atomic orbital (LCAO) method, and the equi-spin-splitting distributions in k-space near the minimum-spin-splitting (MSS) surfaces are illustrated. These data are compared with those derived analytically by two-band k · p (2KP) model. It is found that the results from these two methods are in good agreement for small k. However, the ellipsoidal MSS surface under biaxial compressive strain does not exist in the 2KP model, because the data points are far from the Γ point. Instead, three basic shapes of the MSS surface occur in the wurtzite Brillouin zone: a hyperboloid of two sheets, a hexagonal cone, and a hyperboloid of one sheet, evaluated from the LCAO method across the range of biaxial strains from compressive to tensile.

Electronic structure and elastic properties of TiB2 and ZrB2

We investigate the electronic structure and elastic properties of TiB2 and ZrB2. The electronic properties are computed within the framework of density functional theory (DFT) based on linear combination of atomic orbitals (LCAO), full potential linearized augmented plane wave (FP-LAPW) and projector augmented wave (PAW) methods while the elastic properties are calculated using the PAW method. The calculated electronic and elastic properties of TiB2 and ZrB2 are found to be in good agreement with earlier data. In addition, the theoretical directional and spherically averaged Compton profiles of TiB2 and ZrB2 are also computed using the LCAO method. The spherically averaged theoretical values are compared with the first-ever measurement on polycrystalline ZrB2. To estimate the charge transfer in ZrB2, ionic model based calculations have also been performed which suggest transfer of electron from Zr to B atoms.

Electronic and Optical Modeling of Solar Cell Compounds CuGaSe2 and CuInSe2

We present dielectric-function-related optical properties such as absorption coefficient, refractive index, and reflectivity of the semiconducting chalcopyrites CuGaSe2 and CuInSe2. The optical properties were calculated in the framework of density functional theory (DFT) using linear combination of atomic orbitals (LCAO) and full-potential linearized augmented plane wave (FP-LAPW) methods. The calculated spectral dependence of complex dielectric functions is interpreted in terms of interband transitions within energy bands of both chalcopyrites; for example, the lowest energy peak in the \( \varepsilon_{2} (\omega ) \) spectra for CuGaSe2 corresponds to interband transitions from Ga/Se-4p → Ga-4s while that for CuInSe2 emerges as due to transition between Se-4p → In-5s bands. The calculated dielectric constant, \( \varepsilon_{1} (0) \), for CuInSe2 is higher than that of CuGaSe2. The electronic structure of both compounds is reasonably interpreted by the LCAO (DFT) method. The optical properties computed using the FP-LAPW model (with scissor correction) are close to the spectroscopic ellipsometry data available in the literature.

Compton scattering study and electronic properties of vanadium carbide: A validation of hybrid functional

In this paper, we have reported the isotropic Compton profile of VC measured using high energy (661.65 keV) γ-radiations from a 137Cs isotope. To compare the experimental momentum densities, we have also employed the linear combination of atomic orbitals (LCAO). In addition, energy bands, density of states and Fermi surface topology of VC have been computed using FP-LAPW and LCAO methods. It is seen that the LCAO with hybridization of density functional theory and Hartree–Fock (so called B3LYP) gives a better agreement with the present Compton profile experiment. This shows validation of an exact exchange part in hybrid density functional. On the basis of energy bands, we have discussed the microscopic origin for the anomalous behavior of hardness of VC. The relative nature of bonding in VC and NbC is also discussed in terms of valence charge densities and Mulliken′s population analysis. To establish the role of Compton profiles in computation of cohesive properties of refractory materials, we have also calculated for the first time the cohesive energy using the present experimental Compton profile and compared it with the existing data.

Characterizing CA 2 and CA 6 using ELNES

Calcium aluminates, compounds in the CaO–Al 2O 3 phase system, are used in high-temperature cements and refractory oxides and have wide range of potential technological applications due to their interesting optical, electrical, thermal, and mechanical properties. They are used in both crystalline and glassy form; the glass is an isotropic material while the crystalline materials may be highly anisotropic. This paper will consider two particular crystalline materials, CA 2 and CA 6, but the results should be applicable to all calcium aluminates. Although CA 2 and CA 6 crystals contain the same chemical species, Ca, Al, and O, the coordination and local environments of these species are different in the two structures and hence they show very different energy-loss near-edge structures (ELNES) when examined by electron energy-loss spectroscopy (EELS) in the TEM. The data obtained using ELNES can effectively provide a fingerprint for each compound and a map for their electronic structure. Once such fingerprints are obtained, they can be used to identify nano-sized particles/grains or material at interfaces and grain boundaries. In the present study, the local symmetry fingerprints for CA 2 and CA 6 structures are reported combining experimental spectra with electronic-structure calculations that allow the different features in the spectra to be interpreted. Al-L 2,3 and O-K edge core-loss spectra from CA 2 and CA 6 were measured experimentally using electron energy-loss spectroscopy in a monochromated scanning transmission electron microscope. The near-edge structures were calculated for the different phases using the orthogonalized linear combination of atomic-orbitals method, and took account of core–hole interactions. It is shown that CA 2 and CA 6 structures exhibit distinctive experimental ELNES fingerprints so that these two phases can be separately identified even when present in small volumes.

Electronic structure of AlAs: A Compton profile study

The electronic structure of AlAs through a Compton profile study is presented in this paper. Theoretical calculations are performed following the linear combination of atomic orbitals (LCAO) method and the empirical pseudopotential method (EPM). In LCAO method, to treat exchange and correlation two cases are considered. In the first case, the exchange function of Becke and the correlation function of Perdew and Wang on the basis of generalized gradient approximation (PW-GGA) is adopted. In the second case, the hybrid function B3PW is adopted. Measurement of Compton profile on the polycrystalline AlAs is performed using 59.54 keV gamma-rays. The spherically averaged theoretical Compton profiles are in good agreement with the measurement. The best agreement is, however, shown by the EPM. The anisotropies predicted by B3PW and the EPM are smaller than those from the PW-GGA calculation. On the basis of equal-valence-electron-density profiles, it is found that AlAs is more covalent compared to AlN. The charge transfer model suggests transfer of 0.6e − from Al to As on compound formation.

Novel Band Structures and Transport Properties from Graphene Nanoribbons with Armchair Edges

Using an empirical linear combination of atomic orbitals method (LCAO) based on the sp3 tight-binding scheme, we studied the band structures of graphene nanoribbons with armchair edges terminated by H atoms and found that the band gap exhibits the size dependence and the ‘family’ behaviors, in which a metallic graphene nanoribbon and two semiconducting graphene nanoribbons coexist in a ‘family’. On the basis of Pichard’s transfer matrix technique, we calculated the conductance of the graphene nanoribbons and interestingly found that the steplike curves of conductance display conductance plateaus in the integer multiples of G0 = 2e2/h and the conductance gap emerges in the semiconducting graphene nanoribbon. Meanwhile, a side needle is located on the conductance curve at zero energy in the metallic graphene nanoribbon, which is attributed to degeneration of eigenstates at zero energy. Additionally, we showed that edge states do not have a notable contribution to the conductance because of the strong locali...

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.