Atomic Sphere Radii Research Articles

First-principle studies of half-metallicities and magnetisms of the semi-Heusler alloys CoCrTe and CoCrSb

Half-metallic ferromagnet, in which the electrons with one spin band are metallic and the electrons with another spin band are semiconducting, is believed to be the most promising spin-injector material for spintronic devices, such as spin valves, spin filters, spin diodes, and magnetic tunnel junctions. The main advantages of half-metallic Heusler alloy over other half-metallic systems are their relatively high Curie temperatures and structural similarity to important binary semiconductors that are widely utilized in the industry. Thus far, half-metallicity has been predicted theoretically or confirmed experimentally in a limited number of Heusler alloys. Exploring new half-metallic Heusler alloys is necessary. In this study, the full-potential linearized augmented plane wave (FP_LAPW) method under density functional theory is utilized to investigate the electronic structures and magnetisms of semi-Heusler alloys CoCrTe and CoCrSb. In the calculations, the generalized gradient approximation (GGA) in the scheme of Perdew-Bueke-Ernzerhof is adopted to treat the exchange-correlation potential. The cutoff parameter is set to be Rmt Kmax =9, where Rmt is the smallest atomic sphere radius and Kmax is the maximum value of the reciprocal lattice vector. Meshes (131313 k-points) are used in the first Brillouin zone integration. Self-consistent calculations are considered to be convergent only when the integrated charge difference between the last two iterations is less than 110-4 e/cell. Spin-polarized calculations of the electronic structure for the semi-Heusler alloys CoCrTe and CoCrSb are performed. The calculations reveal that CoCrTe and CoCrSb at their equilibrium lattice constants are half-metallic ferromagnets with half-metallic gaps of 0.28 and 0.22 eV and total magnetic moments of 3.00 and 2.00 B per formula unit, respectively. The calculated integer total magnetic moments (in B) are consistent with the Slater-Pauling rule, Mt = Zt-18, where Zt denotes the total number of valence electrons and Mt means the total magnetic moment (in B) per formula unit. Moreover, the spin moment of the Cr atom is obviously larger than those of the Co, Te, and Sb atoms. Co, Te and Sb are all antiferromagnetically coupled to Cr for CoCrTe and CoCrSb. The electronic structures of CoCrTe and CoCrSb are also calculated as their lattice constants change from -13% to +13% relative to the equilibrium lattice constant. The calculated results indicate that CoCrTe and CoCrSb can maintain their half-metallicities and retain their total magnetic moments of 3.00 and 2.00 B per formula unit even as their lattice constants change from -11.4% to 9.0% and from -11.2% to 2.0%, respectively. The semi-Heusler alloys CoCrTe and CoCrSb should be useful in spintronics and other applications.

Theoretical Investigation on the Luminescence Transition Probabilities in the Phosphor ZnO:Cu

Optical properties of ZnO:Cu have been studied using the ASW (augmented spherical wave) band structure method and a supercell approximation to simulate copper impurities. The imaginary part of the dielectric function ϵ2(ω) is calculated in two different ways. In the first calculation, it is assumed that ϵ2(ω) is proportional to the joint density j(E) whereas in a second calculation the dependence of the dipole transitions on the wave vector is taken into account. The comparison of both calculations gives relative oscillator strengths for the different dipole transitions. Furthermore the influence of the choice of atomic sphere radii on the calculated j(E) is studied.

Determination of atomic sphere RADII for SCF-XαSW calculations

Abstract In molecules with no rings the requirement of tangent atomic spheres is not sufficient to fix uniquely all the atomic radii. An algorithm for the determination of tangent spheres for molecules is shown using a supplementary requirement that the atomic sphere radii should match as closely as possible the covalent radii of the corresponding atoms. If overlapping spheres are used a configuration of tangent spheres may nevertheless provide a useful point of departure for the determination of the radii of the overlapping spheres. In molecules with rings a configuration with tangent spheres in general does not exist. In this case the radii are chosen such that small gaps remain between spheres for atoms which are connected by chemical bonds.

SCF-Xα-SW calculations for small molecules using the optimization technique of atomic-sphere radii

SCF-Xα-SW calculations of structure parameters, normal-stretching-vibration frequencies and ionization energies of the small molecules N 2, O 2, F 2, CO, CH 2 and NH 3 have been performed using the atomic-sphere radii determined by a technique previously proposed on the basis of optimization of the virial theorem and minimization of total energy. The effectiveness of this optimization technique in the SCF-Xα-SW method has been confirmed by the improved agreement between the calculations and experimental data for all the cases. An extension of this technique to more complicated molecules is discussed using the H 2CO molecule as a test example.

The band structure, heat of formation, and atomic interactions in titanium monophosphide

The Linear Muffin Tin Orbital (LMTO) method has been used to calculate the band structure and the heat of formation of titanium monophosphide. The phosphide is found to be metallic with a low state density at the Fermi level. The most important bonding interactions take place between the titanium d and the phosphorus p orbitals forming σ and π bonds. The valence electron density around the titanium atoms is higher in the directions of the d γ orbitals facing the nearest phosphorus atoms than in the directions of the d ε orbitals which largely point in the direction of the nearest titanium atoms. However, a peak in the state density just below the Fermi level and an increased electron density between the nearest titanium atoms indicate a certain amount of metal-metal interactions. The equilibrium average atomic sphere radius 1.533 Å calculated from the overall minimum in the total valence energy compares excellently with the value 1.547 Å derived from the experimental cell volume. The computed heat of formation is −249 kJ/mole which can be compared with the experimental value of −265 kJ/mole.

Optimization of atomic sphere radii in the scattered-wave Xα method: A second look at the water molecule

A method for determining the atomic sphere radii which strongly influence the results in the scattered-wave Xα method is proposed on the basis of optimization of the virial theorem and total energy minimization. Molecular structure calculations are carried out on the water molecule. The minimum energy geometry has been found for a bond distance of 0.960 Å and bond angle of 106.2°, which are very close to the experimental values and have never been well-explained by previous SW-Xα calculations. Good agreement between calculated ionization energies and the force constant and experimental results show the effectiveness of the proposed method.

A STUDY ON GROUND-STATE PROPERTIES OF hcp-WC BY FORCE THEOREM

We calculate the ground-state properties of hcp-WC material by local density functional theory and force theorem with LMTO-ASA approximation. Using the electronic pressure as a function of the lattice parameters, the equilibrium lattice constant, the bulk moduli and sound velocity have been calculated. It is found that the error of lattice constant is less than 10%. The effects of different ways for choosing; the atomic sphere radii on the calculated results are discussed. The bond characters of hcp-WC are also analyzed briefly in terms of the electronic partial pressures.

An SCF-MS-Xα study of the bonding and nuclear quadrupole coupling in diatomic halogens and interhalogens in the ground X1 Σ and B3 Π 0 excited states

SCF-MS- Xα calculations of the electronic structure of diatomic halogens and interhalogens XY (X = I, Br, Cl; Y = I, Br, Cl, F) have been used to investigate the bonding and nuclear quadrupole coupling in these molecules. Calculations have been carried out for the ground X 1 Σ electronic state, and for the excited B 3 Π 0 state in the case of I 2, Br 2, ICl and IBr. Good agreement (to within 10% in most cases) is obtained between the calculated and observed nuclear quadrupole coupling constants for the molecules in the ground state. For the excited state the agreement is not as good, but the calculation does reproduce the observed decrease in the coupling constants to less than one quarter of their ground state values, and analysis of the contributions to the field gradients clearly shows the reasons for this. The electric dipole moments and electric quadrupole moments of the molecules have also been calculated. However, these prove to be much more strongly dependent on the variables used in the calculation (atomic sphere radii, inclusion of d orbitals). The results of the calculations have also been used to test some of the assumptions made in the Townes and Dailey method of analysis of nuclear quadrupole coupling data.

Multiple scattering approach to the XANES theory of alkali halide crystals. I. Crystalline potential in the X‐Ray absorption spectra problem

AbstractTwo schemes of the crystalline potential for the slow electron in the conduction band of alkalihalides are proposed. The first one (semiempirical) is based on the assumption that in the case of an ion in the crystal one can use the same energy dependence of logarithmic derivatives (of radial solutions at the atomic sphere radius) as in the case of the isolated ion. The modifications required consist in some potential corrections, that are due to the Madelung field as well as to the relaxation and polarization response for both, hole and electron. The second model (ab initio) suggests the straightforward solution of Poisson's equation. Both approaches are compared, so it is found that they lead to satisfactory agreement for a wide energy interval in the continuum.

Theoretical calculations of carbon-13 NMR chemical shifts via the Xα-scattered wave method

The Xα-SW molecular-orbital method is applied to the calculation of carbon-13 NMR nuclear shielding constants in a series of small organic molecules. The application of perturbation theory within the Xα framework is discussed in order to place the equations used in the calculation of the shielding constants on firm theoretical ground. Use is made of a highly accurate mixed analytic-numerical method of integration in calculating the necessary matrix elements of 1/r, L/r3, and L. The results for both overlapping and nonoverlapping spheres calculations are shown to reproduce trends in experimental shielding constants remarkably well, but not the correct magnitudes. Calculated shielding constants are shown to be strongly dependent upon the carbon atomic-sphere radius, and the origins of this dependence are discussed in terms of discontinuities in the muffin–tin potential. An established method of choosing sphere radii based upon an initial approximation to the molecular charge density yields results which correlate well with experiment.

Analytic methods for the calculation of the electronic structure of solids.

Andersen's atomic-sphere approximation has been utilized with approximations based upon linear-combination of atomic orbitals (LCAO) theory to obtain approximate energy-band parameters for solids. Simple analytic expressions for the bandwidth and position of the band center have been derived that require only free-atom wave functions evaluated at the Wigner-Seitz atomic-sphere radius. For convenience, the method has been named the atomic surface method (ASM). The following simple analytic expressions for the band parameters have been derived from the ASM: (i) The bandwidth is equal to the product of ${\ensuremath{\Elzxh}}^{2}$/m, the gradient of the electron density at the atomic-sphere radius, and the surface area of the sphere; (ii) the average band energy is shifted from the atomic-term-value energy by an amount given by the product of the bandwidth, electron density at the atomic-sphere radius, and atomic-sphere volume. The theory has been applied without adjustable parameters to the transition metals and f-shell metals with use of tabulated Hartree-Fock wave functions and is in reasonable agreement with full band-structure calculations. The same analysis is applied to atomic core states under compression and is also in reasonable agreement with complete band-structure calculations. The 2s and 2p states of Na and Al have been calculated to the point where they merge with the conduction band as free-electron states. These bandwidths and shifts are also written in terms of the atomic term values by using the asymptotic form of the radial wave function. Finally, the LCAO energy bands of Ni are calculated with use of the ASM parameters. The average d-band energy relative to the conduction-band minimum and the hybridization of the conduction band with the d band are calculated with use of the asymptotic form of the radial wave function, giving approximate energy bands entirely in terms of free-atom parameters.

Applicability of the SCF-Xα-SW method in the study of the stability of doubly positive microclusters: N++2

The effect of the overlapping sphere modification of the muffin-tin SCF-Xα-SW scheme on the potential energy curve of N++ 2 is discussed. Overlapping spheres are used whereby the atomic sphere radii are uniformly increased by 30 per cent with respect to the tangent sphere situation. This procedure which has previously been shown to be successful in predicting equilibrium bond lengths for ground-state molecules, now for the doubly ionized N2 molecule results in a potential energy curve in fair agreement with other published data. In particular the so-obtained potential energy curve shows a distinct minimum, whereas the uncorrected muffin-tin scheme gives rise to a repulsive potential energy curve.

Augmented Gaussian-orbital basis for atomic-cluster calculations within the density-functional formalism: Application toCu2

The principle of augmentation, used to introduce inner-atom core structure into slowly varying basis functions, is applied to Gaussian orbitals to define a new basis set for highly accurate total-energy calculations for atomic clusters within the density-functional formalism. Diffuse Gaussian-orbital tails are matched continuously and differentiably to inner-atom numeric radial functions at the atomic-sphere radius. Major advantages of Gaussian-orbital basis sets are acquired without the need for numerous Gaussians of large exponent for the core region. The numeric functions used inside the atom permit essentially exact solutions for that region. Procedures are described which recover use of the efficient integral algorithms for the Gaussian-orbital-tail matrix elements. The interactions over the structured inner-atom region are treated by efficient integrand smoothing and integration procedures for the sphere. The new augmented Gaussian basis removes the primary limitations on the use of Gaussian orbitals for heavy atoms. As an illustration the method is applied to the copper dimer in an all-electron framework within the local-spin-density approximation (LSDA). The calculated binding energy, equilibrium separation, and first ionization potential of ${\mathrm{Cu}}_{2}$ are within 2% of experiment within the $X\ensuremath{\alpha}$ model. Excitation energies are better described within more recent refined exchange-correlation functionals. These all-electron results show the LSDA model predicts a slightly contracted bond length for ${\mathrm{Cu}}_{2}$, consistent with bulk LSDA calculations for the $3d$ transition-metal series.

The electronic structure of WF 6 elucidated by SCF-Xα-SW calculations

SCF-Xα-SW calculations have been performed to determine the ground state electronic structure of WF 6. The energies of the lowest excited states have been estimated using the transition state procedure, and an assignment of the electronic absorption spectrum is proposed. Parallels are drawn to the electronic structure of the tungsten bronzes. In addition, an alternative and straightforward method for choosing atomic sphere radii in Xα-SW calculations is devised.

Non-empirical versus empirical choices for overlapping-sphere radii ratios in SCF-Xα-SW calculations on ClO4-and SO2

Two non-empirical schemes for establishing ratios of atomic sphere radii for Xα-SW calculations are proposed and compared with known methods of partitioning molecules into atomic fragments along paths of maximum change in electrostatic potential or charge density. In the initial Xα-SW molecular charge distribution, the radius of a sphere around each atom containing the atomic number of electrons is shown to be constant within a few per cent no matter what atomic charges are assumed in constructing the charge distribution. This contrasts with the radius of a sphere containing the number of electrons put in for the atom in calculating its atomic charge density, which shows a significant inverse variation with the assumed charge. Ionization energies for ClO4 - and SO2 are calculated using ratios of sphere radii established both from the atomic number sphere sizes and from Slater's empirical atomic radii. The results are compared with experiment and with HF-LCAO calculations. The Xα-SW calculations using atom...

Investigation of the muffin-tin approximations for potential and charge density in the MS-X? method by means of calculations of H2O

By detailed analysis of results for H2O it is shown that both approximations, the muffin-tin approximation of the potential as well as the muffin-tin approximation of the charge density, severely influence the results. Their effects are of the same order of magnitude. Good results for molecular total energies are achieved by roughly compensating the effects from the two approximations, not by minimizing them. The total energy changes drastically when radius or position of the outer sphere are varied. Equilibrium distances strongly depend on the choice of the atomic sphere radii and always are calculated too large, not due to the charge density approximation, but due to the potential approximation. In order to lay hold of angular properties, the sphere radii have to be chosen in a completely different way than for total energies.

SCF-X αSW calculations on PH3 using a nonempirical scheme for choosing overlapping-sphere radii

Detailed results of two SCF-X αSW calculations on PH3, one with phosphorus d-type partial waves (2) and one without (1), are presented and compared with the best Hartree-Fock calculations. Ionization energies for the 5a1, 2e, and 4a1 levels, respectively, are 10.61, 13.42, and 20.55 eV from 1 and 10.37, 13.60, and 20.22 eV from 2, in better agreement with the experimental values of 10.59 and 13.5 eV for the first two levels than any previous first-principles calculation. Total energies are −342.6114 and −342.6449 hartree from 1 and 2, respectively. Contour maps of the valence-level wavefunctions and total valence charge density are presented; phosphorus d functions are found to contribute significantly (about 15%) only to the wavefunction for the 2e level, their effect being to promote better P–H overlap. Overlapping atomic sphere radii for the above calculations were chosen by a nonempirical scheme involving satisfaction of the virial theorem and the relative sizes of spheres around each atom which enclose the atomic number of electrons in the initial X αSW molecular charge distribution. Results of several complete PH3 calculations with varying sphere radii, hydrogen α parameter, and outer sphere position, and their role in developing the scheme for choosing radii, are discussed. Overlapping of the spheres improves the quantitative agreement of the eigenvalues with experiment, but the ordering and semiquantitative spacing of the levels are insensitive to variation in any of the above parameters.

Multiple scattering method based on overlapping atomic spheres with application to the TCNQ molecule

The theoretical foundation of the self-consistent statistical exchange (X α) multiple scattering method based on overlapping atomic spheres is presented. After discussing the principal assumptions and approximations, the theory is illustrated by a study of the electronic structure of the TCNQ molecule. Satisfactory results are obtained for the energy level structure and electronic charge distribution if the atomic sphere radii are chosen in accordance with the following guidelines: (a) the calculated first ionization energy should agree with experiment; and (b) the calculated virial coefficient should be equal to −2. The present work suggests that the overlapping sphere model can be used to obtain realistic electronic structures for large planar organic molecules as well as for arrays of such molecules.

Low-temperature thermostatics of face-centered-cubic metallic hydrogen

The thermostatic properties of a high-symmetry phase of metallic hydrogen with atomic sphere radius between 0.1 and 1.5 bohr are studied, with special emphasis accorded to electronic screening and quantum proton motion. The electron-proton and proton-proton interactions receive a perturbation treatment based on the Singwi dielectric function, while the proton motion is handled by self-consistent harmonic approximation. Quantum behavior is found to be less pronounced than expected, and nuclear magnetism is absent. The phonon spectrum is, however, affected by screening and large proton motion. The zero-point vibrational energy and the superconducting critical temperature are below previous estimates. The crystalline-defect formation energies are a few times the Debye energy, which implies that defects contribute significantly to melting at the lower particle densities.

Non-Muffin-Tin Augmented-Plane-Wave Method for Diamond and Zinc-Blende Lattices

The augmented-plane-wave method is adapted to the diamond and zinc-blende lattices by including both "nonflat" and "nonspherical" corrections to the usual "muffin-tin" potential. The former are treated exactly while the latter are treated perturbatively. The method is tested for silicon where "nonflat" corrections are as large as 3.4 eV with "nonspherical" corrections less than 0.4 eV. Plane wave convergence is superior to the orthogonalized-plane-wave method. The atomic-sphere radius was varied from $2.15{a}_{0} \mathrm{to} 1.35{a}_{0}$ with energy changes of less than 0.03 eV. Nonflat matrix elements are easily computed by use of a spherical-harmonic expansion of the potential due to point charges. Multipole-lattice-sum coefficients are given for the fcc, diamond, and zinc-blende lattices.