Multiple-scattering Method Research Articles

Molecular photo cross sections with the LCGTO–Xα method using Stieltjes imaging

A method for calculating and symmetry analyzing total molecular photoionization cross sections is presented. The technique is based on the LCGTO–Xα method and employs Stieltjes imaging. It allows applications to molecular systems comparable in size to those treated so far with the continuum multiple-scattering Xα method, but avoids the pitfalls of the muffin-tin approximation to the electronic potential. Photo cross sections for valence ionization of CO are found in good agreement with experiment and with previous calculations. From a final state symmetry analysis for the 1π level, the absence of kσ* shape resonance which appears in the 4σ and the 5σ ionization channels is attributed to small transition moments. This is in contrast to a previous treatment where this difference has been rationalized as caused by a channel dependent final state potential. The photoionization cross sections for the four highest valence orbitals of benzene were calculated in better agreement with experiment than found in a previous Xα–SW treatment. The improvement is especially significant for the 1e1g(π) highest occupied molecular orbital where at least part of the experimentally observed structures are attributed to shape resonances. Some of the observed resonance features in the valence orbital photo cross sections of benzene were identified with resonances found in carbon K-shell ionization.

Multiple-scattering Green-function method for electronic-structure calculations of surfaces and coherent interfaces.

We present a formally exact solution of the multiple-scattering-theory (MST) equations for the case of semi-infinite and coherent doubly semi-infinite materials. For the case of semi-infinite materials (surfaces), we also present an alternative approach based upon the embedded-cluster method, which can be numerically as accurate as the exact method but is computationally easier to implement. The methods presented here satisfy the correct boundary conditions associated with semi-infinite materials and thus constitute a proper generalization of the Green-function formalism as applied to bulk systems, to the treatment of surfaces and interfaces. Specifically, the lack of translational invariance in directions perpendicular to the surface or interface is handled through the solution of a self-consistent equation for the scattering matrix, describing exactly the interaction of any chosen plane near the surface or interface with the rest of the material. The formalism is free of the introduction of extraneous conditions such as the artificial truncation of the free-particle propagator or the range of electron hopping elements, or the use of a complex potential. Furthermore, being based on a first-principles, MST Green-function method, the formalism is applicable to the treatment of a large number of physically important problems such as surface and/or interface regions formed by pure materials or concentrated alloys, the study of impurities of diverse kinds near such a region, and many others. Results for one-dimensional model systems as well as realistic three-dimensional materials are presented. The advantages, convergence properties, and restrictions of the formalisms are discussed and further work, currently in progress, is commented upon.

An exact band-structure method applied to the three-dimensional Mathieu problem

A method assigned to solve exactly the Schrodinger equation with non-muffin-tin crystal potential is numerically tested. The approach is based on the Green function technique. It differs from the conventional multiple-scattering methods in that the wave field psi k is sought at some points within a cell rather than at the boundaries. The empty lattice and three-dimensional Mathieu problems are studied with the emphasis on convergence properties. Generally, the convergence is governed by three independent parameters, resulting as a consequence of the truncation of some infinite series, namely, the expansions of the Green function, potential and wavefunction psi k sought. It is numerically shown that, by increasing the three parameters mentioned, the calculated energy eigenvalues approach the exact ones.

Polarized copperK-edge x-ray-absorption spectra inYBa2Cu3O7−y

The polarized copper K-edge x-ray-absorption near-edge spectra (XANES) in the high-${\mathit{T}}_{\mathit{c}}$ superconductor ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$ and related semiconductor oxide ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{6}$ were calculated. The initial states and the final bound states were obtained from the self-consistent-field discrete-variational X\ensuremath{\alpha} method (SCF DV-X\ensuremath{\alpha}). Continuum states were found by the multiple-scattering method using the muffin-tin truncation of the SCF DV-X\ensuremath{\alpha} potentials. XANES for each of the two Cu sites in these compounds were identified by using the calculated difference in Cu 1s ionization potentials. Features in XANES were interpreted with the help of the projected density of states and photoelectron trapping times. A quantitative comparison with the measured spectra leads us to assign shakedown features with relaxation energy of 8.3 eV and intensities of 20% and 12% of the total transition in the a-axis- and b-axis-polarized Cu K-edge XANES of ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$, respectively. This shakedown feature apparently involves ligand\ensuremath{\rightarrow}3d transitions in the core-hole excited state. It is found that this relaxation process is present in the metallic ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$ and absent in the semiconducting phase.

Theoretical calculations of x-ray-absorption spectra of copper in La2CuO4 and related oxide compounds.

We report the results of theoretical calculations of copper K-edge x-ray-absorption near-edge spectra (XANES) in ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$ and related oxides ${\mathrm{Cu}}_{2}$O, CuO, and ${\mathrm{KCuO}}_{2}$. The final bound states were obtained from the self-consistent-field discrete-variational X\ensuremath{\alpha} method (SCF DV X\ensuremath{\alpha}), and continuum states were found by the multiple-scattering method using the muffin-tin truncation of the SCF DV X\ensuremath{\alpha} potentials. Composition of the final-state wave functions was analyzed. The 1s ionization potentials of the three reference compounds obtained from the SCF DV X\ensuremath{\alpha} transition-state calculations were used to set up the relative energy scale for the calculated cross section. The principal features of measured Cu K-edge XANES for ${\mathrm{Cu}}_{2}$O, CuO, and ${\mathrm{KCuO}}_{2}$ were reproduced satisfactorily by our calculations along with their relative energy positions. Our calculated polarized XANES of ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$ were compared with measured spectra, and two shakeup features were identified with radiation polarized along the crystal c axis. By quantitatively comparing the measured spectra with a model based on our calculated cross sections, their intensities were found to be \ensuremath{\sim}24% and 10% of the main transition with shakeup energies of 5.7 and 9.5 eV, respectively. We suggest that these multielectron excitation features involve Cu 3d\ensuremath{\rightarrow}4p transitions.

Multiple small-angle neutron scattering characterization of the densification of ceramics: application to microporous silica

Multiple small-angle neutron scattering was used to characterize the microstructure evolution of porous silica as a function of thermal processing. This new technique offers a statistically significant determination of microstructure morphology in the 0.08–10 μm range, which was previously inaccessible without increasing the resolution of the currently available scattering spectroscopy beamlines. All of the scatterers, which in the present work are pores within ceramic bodies, are measured whether they are open or closed. Earlier mercury porosimetry and nitrogen desorption measurements of the microporous silica system indicated that there are two major populations of pores in this material, differing in pore size by approximately an order of magnitude. In this work, it was found that densification during the intermediate stages of sintering is accompanied by coarsening to radii > 0.22 μm within the population of large pores in microporous silica. In the late stages of sintering, there are no detectable pores with radii > 0.08 μm, and radii of gyration equal to 33 and 28 nm were measured. Finally, Monte Carlo simulations were carried out to complement the neutron-scattering measurements, to predict the influence on the results of the bimodal distribution, and to explore the sensitivity of the multiple-scattering method.

A refined LEED structural determination for the surface designated Ni (111)–(2 × 2)–S

A new intensity analysis with low-energy electron diffraction is reported for the (2 × 2) surface structure obtained by the adsorption of H2S on the (111) surface of nickel. Intensity-versus-energy curves were measured with a video LEED analyzer for 10 diffracted beams at normal incidence, and comparisons were made with intensity curves calculated with multiple-scattering methods for models in which S atoms chemisorb at three-fold coordinated adsorption sites, but with the possibilities of both lateral and vertical relaxations in the local metallic structure. Small adsorbate-induced relaxations are found, but the dominant structural feature is that the S atoms adsorb above the "expected" adsorption sites (i.e. those which continue the regular fee packing) with a 1.50 Å spacing between the S layer and the top-most Ni layer. The S–Ni bond length of 2.10 Å agrees to within 0.02 Å of a prediction using a current bond length – bond order relation, but this value is smaller than two other recent measurements by SEXAFS and ion scattering by 0.06 and 0.10 Å, respectively. This analysis also finds the first two Ni layer spacings are expanded from the bulk value by 2 to 3%. Keywords: LEED, surface structure, S chemisorption, Ni(III) surface.

Carbon K-shell near-edge structure: Multiple scattering and band-theory calculations.

The carbon K-shell near-edge absorption fine structure of both diamond and graphite has been calculated by the multiple-scattering method and by a single-particle self-consistent pseudo-atomic-orbital band-theory method. We compare the results of these two calculations with experiment, and show that they both give agreement with the experimental near-edge structure.

Multiple-scattering Green-function method for space-filling cell potentials.

It is shown that the equations of multiple-scattering theory (MST) originally derived for scattering off collections of muffin-tin (MT) potentials, i.e., potential cells bounded by non overlapping spheres, remain valid in the case of arbitrarily shaped, non overlapping, and particularly space-filling potential cells. Specifically, it is shown that in the angular momentum representation the total scattering (transition) matrix, the Greenfunction, the Bloch function for a translationally invariant material, and the Lloyd formula for the change in the integrated density of states have forms that are invariant with respect to the partition of a given potential into non overlapping cells, and with respect to the choice of the cell centers. Ananalytic proof is provided for the vanishing of near-field corrections (NFC's)long conjectured to arise when the spheres bounding individual cells over lap one another or adjacent potentials. Thus, the well-known MST expressions, originally derived for the case of MT potentials, for obtaining the solution of the Schroedinger equation and hence determining the band structure and the charge density of materials, ordered or disordered, are rigorously valid in the completely general case of arbitrarily shaped cells. The differences between this work and previous attempts to generalize MST to non-MT space-filling potentials aremore » discussed. It is pointed out that in calculations involving non-MT potential cells, particular attention must be paid to the question of convergence of expansions in angular momentum eigenstates. This convergence is tested numerically in terms of cluster calculations and through the calculation of the electronic structure of elemental bcc Nb and fcc Zr and Rh.« less

Impurity levels, impurity bands, excited impurity bands, and band tails: The electronic density of states in quantum wells and heterostructures.

We have investigated in quantum wells (QW's) and heterostructures (HS's) the modification of the electronic structure near the band edge, which is induced by selective doping. The density of states has been calculated as a function of the relevant parameters, namely, carrier and impurity concentrations (and depletion concentrations for HS's), QW width, and impurity position. Using a multiple-scattering method which includes a finite-range screened potential and impurity concentration to all orders, we have succeeded in obtaining ground-state and excited-state impurity bands (IB's). We observed these bands merging gradually with the lowest conduction subband as the impurity concentration is increased, leading to the formation of a band tail into the energy gap. Other main results obtained for different values of the parameters are the binding energy for a single impurity, the widths and energy shifts of ground- and excited-state IB's, and the contribution of the electron-impurity interaction to the gap shrinkage in the band-tail regime. Our results are compared with experiments and other theories.

Electronic structure, hyperfine interactions, and radial densities in the Fe1+ tetrahedral sulfide as calculated by the multiple-scattering method.

Spin-polarized multiple-scattering calculations have been performed for the ${\mathrm{FeS}}_{4}^{7\mathrm{\ensuremath{-}}}$ cluster in order to investigate the uncommon ${\mathrm{Fe}}^{1+}$ charge state observed in ZnS. The calculated electronic structure, charge and spin densities, and atomic populations are used to interpret the measured hyperfine interactions. The overall good agreement between theory and experiment supports the presence of monovalent--charge-state ${\mathrm{Fe}}^{1+}$ in the M\"ossbauer spectra emitted by $^{57}\mathrm{Co}$ diluted in ZnS.

Theoretical active impurity levels of iron, chromium, and manganese for photorefractive effects in barium titanate

Using the self-consistent field multiple-scattering Xα method, we calculate and discuss the 3d energy levels, which are potentially photorefractively active for substitutional iron, chromium, and manganese ions in BaTiO3 relative to the valence band edge. Moreover, we examine the almost intrinsic defect formed by an oxygen vacancy associated with titanium.

Inverse photoemission from Ag(111) calculated by a multiple-scattering method.

Calculations of angle-resolved ultraviolet bremsstrahlung isochromats, using a multiple-scattering method, are presented for the first time for Ag(111). Good agreement is found with experimental data, both for surface- and bulk-derived spectral structures.

Summary Abstract: Off-normal and azimuthal photoelectron diffraction studies of the system C(2×2)S–Ni(001) by the multiple-scattering method

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Calculated metalloid Knight shifts for Ni3B and Ni3P compounds

The Knight shifts for the metalloid site in Ni3B and Ni3P alloys were calculated by using the multiple-scattering Green function method for a cluster of atoms with the metalloid atom in the centre and twelve Ni neighbours. The results support the large difference of the Knight-shift values found in recent experiments on these two compounds.

A study of the covalent bonding in hexaiodoiridate complex ions

The Multiple Scattering (MS-Χα) method is used in order to study important charge transfer processes in hexaiodoiridate complex ions. Iridium (IV) complexes are predicted to exhibit more covalent character than iridium complexes with lower oxidation states. Experimental photoelectron and theoretical results also predict an increase in the binding energy of the Ir (4f) levels with an increase in the oxidation state of iridium.

QUANTUM DEFECT THEORY——THEORETICAL MULTIPLE-SCATTERING CALCULATIONS

Molecular Rydberg states and their adjoint continuum can be described in an unified manner by a compact set of slightly energy-dependent parameters in quantum defect theory. Here, we present a multiple-scattering method to calculate these physical parameters. As illustrative examples, calculations for H2 and NO are carried out.

MSXα calculation of the electronic structure of Cu+ and Ag+ ions in lithium chloride single crystal

The multiple-scattering Xα method applied to an embedded (MCl6)5− cluster (M=Ag,Cu) is used to describe the electronic structure of Ag+ and Cu+ in the LiCl crystal. Several calculations have been performed with different impurity–ligand distances in order to reach the equilibrium distance. The vibrational energy of the breathing mode is deduced from the total energy variation of the cluster vs the bond distance. The multiplet level diagrams obtained after a calculation of spin-orbit interactions are shown and compared with the spectroscopic features.

Cross-section analysis of surface and bulk phonons by electron scattering from Cu(100).

High-resolution electron energy-loss measurements at off-specular directions on a clean Cu(100) surface ($\overline{\ensuremath{\Gamma}}\ensuremath{-}\overline{X}$ direction) demonstrate the presence of both surface and bulk phonon excitations. We present what we believe to be the first detailed cross-section analysis of surface and bulk phonon excitations on the Cu(100) surface. The data are shown to be in very good agreement with calculations based on the multiple-scattering slab method. The achievement of experimental phonon intensities one to two orders of magnitude higher than previously obtained is also demonstrated.

The noble gas atoms as impurities in silicon

Ground state one-electron energies have been calculated for the substitutional and interstitial helium, neon, and argon impurities in silicon by use of the self-consistent-field multiple-scattering Xα method within the framework of the Watson-sphere-terminated molecular cluster model. The substitutional noble gas atoms are found to inhibit the rebonding of the first neighbor's dangling bonds through orthogonality repulsion. The interstitial nobel gas atoms induce empty shallow levels close to the bottom of the conduction band. We tentatively relate these levels to the emission bands observed for silicon crystals implanted with helium, neon, and argon.