Showing papers on "Electronic structure published in 1972"

Electronic structure based on the local atomic environment for tight-binding bands

Abstract: Some new methods are presented for calculating the density of states n(E) and other aspects of electronic structure in a tight-binding band, without use of Bloch's theorem or the band structure E(k). The methods are therefore applicable to calculating the local density of states at surfaces, impurities etc. and relate the electronic structure to the local atomic environment. They depend on developing the Green function as an infinite continued fraction. There is no difficulty in obtaining n(E) in a few minutes computing time correct to the first 50 moments for an s-band and 10 moments for d-bands. The present paper discusses the methods and ideas, with specific applications to follow.

The Spectrum of Molecular Oxygen

Abstract: This is a critical review and compilation of the observed and predicted spectroscopic data on O2 and its ions O2−, O2+ and O22+ The ultraviolet, visible, infrared, Raman, microwave, and electron paramagnetic resonance spectra are included. Each electronic band system is discussed in detail, and tables of band origins and heads are given. The microwave and EPR data are also tabulated. Special subjects such as the dissociation energy of O2, perturbations, and predissociations are discussed. Potential energy curves are given, as well as f‐values, Franck‐Condon integrals, and other intensity factors. A summary table lists the molecular constants for all known electronic states of O2 and O2+ Electronic structure and theoretical calculations are also discussed.

Electronic Structure of Amorphous Si from Photoemission and Optical Studies

Abstract: Photoemission from and optical studies of amorphous Si samples, carefully prepared to minimize the influence of defects, are reported. Photoemission yield and energy distribution curves were obtained from 5.5 to 11.7 eV and reflectance data were measured from 0.4 to 11.8 eV. Optical constants were determined by a Kramers-Kronig analysis. No evidence was found to indicate that the wave vector $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$ provides a significant quantum number in amorphous Si.

Electronic structure of superheavy atoms

Abstract: We describe the status of the problem of the electron structure of superheavy atoms with nuclear charge Z > Zc ; here Zc≈170 is the critical value of the nuclear charge, at which the energy of the ground state of the 1S1/2 electron reaches the limit of the lower continuum of the solutions of the Dirac equation (∊ = - mec2) . We discuss the dependence of Zc on the nuclear radius R and on the character of the distribution of the electric charge inside the nucleus, and also the form of the wave functions at Z close to Zc . Owing to the Coulomb barrier , the state of the electron remains localized at Z > Zc , in spite of the fact that its energy approaches the continuum. An analysis of the polarization of the vacuum in a strong Coulomb field shows that a bare nucleus with supercritical charge Z > Zc produces spontaneously two positrons and, in addition a charge density with a total of two units of negative charge in the vacuum. The distribution of this density is localized in a region of dimension r ~ ħ/mec at the nucleus. The possibility of experimentally observing the effect of quasistatic production of positrons in the collision of two bare uranium nuclei (i.e., without electrons) is discussed. A brief review is presented of work on the motion of levels with increasing depth of the potential well in other relativistic equations (Kelin-Gordon, Proca, etc.).

Chemical Bonding of a Molecular Transition-Metal Ion in a Crystalline Environment

Abstract: A theoretical description of the chemical bonding of transition metals and other complex metal atoms in molecules and solids has been formulated in terms of a spin-unrestricted self-consistent-field cluster model. This model permits the accurate calculation, from first principles, of electronic energy levels and wave functions for the cluster, but requires relatively little computer time. The cluster, which may be a free polyatomic molecule, part of a macromolecule, or a polyatomic complex in an ordered or disordered solid, is geometrically partitioned into contiguous atomic, interatomic, and extramolecular regions. The one-electron Schr\"odinger equation is numerically integrated within each region in the partial-wave representation for spherically averaged and volume-averaged potentials which include Slater's $X\ensuremath{\alpha}$ statistical approximation to exchange correlation. The wave functions and their first derivatives are joined continuously throughout the cluster via multiple-scattered-wave theory similar to that developed originally by Korringa. The effects of a particular environment on the cluster are described by boundary conditions, e.g., the matching of the solutions of Schr\"odinger's equation in the extramolecular region to those within the atomic regions at an artificial spherical boundary surrounding the entire cluster. This numerical procedure is repeated, using the wave functions obtained at each iteration to generate a charge density and new potential, until self-consistency is attained. The model is illustrated for the tetrahedrally coordinated permanganate ion (Mn${\mathrm{O}}_{4}^{\ensuremath{-}}$) in the stabilizing field of a typical crystalline environment KMn${\mathrm{O}}_{4}$. The spin-unrestricted cluster calculation leads to a ground-state electronic structure of Mn${\mathrm{O}}_{4}^{\ensuremath{-}}$ which is consistent with the observed Van Vleck paramagnetism of permanganate crystals. Computer-generated contour maps of the cluster wave functions and charge densities are presented, showing the formation of directed chemical bonds. Both $\ensuremath{\pi}"$ and "$\ensuremath{\sigma}$ bonding" between oxygen $2p$ electrons and manganese $3d$ electrons are shown to be important. In conjunction with Slater's transition-state theory, which accurately describes the effects of orbital relaxation in optical transitions, the cluster model is used to interpret the measured optical properties of permanganate crystals. The characteristic purple color of KMn${\mathrm{O}}_{4}$ is shown to originate from the induced transfer of electrons between the oxygen ligands and central manganese atom in the Mn${\mathrm{O}}_{4}^{\ensuremath{-}}$ cluster. Finally, with the use of larger clusters, the theoretical model is extended to the chemical bonding of transition-metal impurities in semiconductors and transition metals which are the biologically active centers of certain enzymes and proteins.

X-ray photoemission band structure of some transition-metal oxides.

Abstract: The valence-band structures of MnO, CoO, NiO, ${\mathrm{Cu}}_{2}$O, CuO, and Re${\mathrm{O}}_{3}$ have been obtained by x-ray photoemission spectroscopy. It is found that in every case a narrow metal $d$ band lies above the center of the oxygen $2p$ valence band.

Self-Consistent Electronic Structure of Solid Surfaces

Abstract: We have developed a method for calculating electron states in the surface region of a semi-infinite solid taking full account of the three-dimensional nature of the lattice potential. The Schr\"odinger equation is integrated numerically in a region consisting of the last few atomic layers and the vacuum, and optimally matched to a linear combination of Bloch (pseudo) wave functions in the interior. The potential in the surface region is computed self-consistently from the valence-charge density by solving Poisson's equation, using a local approximation to the exchange and correlation contribution, and representing the cores by a model potential. As an illustration of the practical applicability of the method, the electronic structure of the (100) surface of Na has been calculated.

Calculation of Electronic Structure of Fe Base bcc Ferromagnetic Alloys in the Coherent Potential Approximation

Abstract: The electronic structure of Ni base ferromagnetic alloys with Co, Fe, Mn and Cr is discussed on the basis of the coherent potential approximation combined with the Hartree-Fock approximation for the electron-electron interaction. Calculations are carried out by use of a tight-binding single band model. With consistent choices of parameters the concentration dependences of the average magnetic moment of each constituent atom, the saturation magnetization, and the density of states at the Fermi level are calculated. The significance and limit of the coherent potential approximation for calculating the electronic structure of the ferromagnetic alloys are discussed in some detail.

Single-Electron Energies, Many-Electron Effects, and the Renormalized-Atom Scheme as Applied to Rare-Earth Metals

Abstract: A systematic investigation of certain electronic properties of the rare-earth metals is reported Calculations are performed within the framework of the renormalized-atom method in which Hartree-Fock free-atom solutions, with electronic configurations appropriate to the metal, are initially computed; the wave functions are then renormalized to the Wigner-Seitz sphere and used to construct $l$-dependent Hartree-Fock-Wigner-Seitz crystal potentials The following results are obtained: (i) Recent spectral information together with the free-atom solutions permits us to estimate the change in neutral-atom correlation energy associated with changing the $4f$ electron count; contrary to expectation, we find that correlation effects are more significant in a configuration with one fewer $4f$ and one more $5d$ electron (ii) Band extrema and Fermi levels are placed (iii) The positions of occupied and unoccupied $4f$ levels are estimated in both a one-electron approach and a multielectron method taking screening and relaxation effects into account in a definite way The one-electron approximation for the $4f$ levels fails badly in reproducing the results of recent photoemission experiments, while the multielectron calculations are in surprisingly good accord with experiment The effective Coulomb-interaction energy between two $4f$ electrons at the same site, the familiar $U$, is reduced from the single-particle value of approximately 27 eV to about 7 eV with the inclusion of multielectron effects (iv) Hartree-Fock values for the $4s$- and $5s$-shell exchange splittings are compared with soft-x-ray photoemission studies of the rare-earth fluorides and oxides; the calculated $4s$ splittings are roughly twice as large as experiment while, unexpectedly, the $5s$ results are in almost precise agreement

Many‐Body Green's Functions for Finite, Nonuniform Systems: Applications to Closed Shell Atoms

Abstract: Ab initio calculations of natural orbitals, ionization potentials, and total ground state energies for the closed shell systems helium and beryllium are given using the technique of many‐body Green's functions. The necessary formalism for application of the Green's function theory to finite, nonuniform, many‐body systems is developed following the work of Layzer; connections with standard perturbation theory are made. The natural orbitals obtained were of high quality. Analysis of the diagrammatic expansion of the Green's function led to the surprising result that the main effect of the infinite‐order summations implicit in the solution of Dyson's equation was to ``renormalize'' the second‐order perturbation corrections.

Interaction of 25 keV Electrons with the Nucleic Acid Bases, Adenine, Thymine, and Uracil. I. Outer Shell Excitation

Abstract: The energy loss functions — Im(1/e) of thin films of the nucleic acid bases, adenine (C5N5H5), thymine (C5N2O2H6), and uracil (C4N2O2H4) have been determined in the range 2–50 eV from energy loss experiments with 25 keV electrons at room temperature. An analysis of the electronic structure of these materials in the region of outer shell excitation has been obtained in the form of determination of the dielectric constants e1 and e2 from a Kramers—Kronig analysis of the energy loss function. In the spectral region where ultraviolet absorption data exists (<10 eV), the calculated optical absorption coefficient μ is shown to be in good agreement with the optical measurements.

Coincidence Measurement of Quasifree Scattering of 9-keV Electrons on K and L Shells of Carbon

Abstract: Momentum distributions of electrons bound in the $K$ and $L$ shells of carbon have been separately measured. Data obtained from the angular distribution of coincidences between the two electrons outcoming in a quasifree ($e,2e$) process are compared with theoretical predictions.

Electronic structure of metal complexes containing π-cyclopentadienyl and related ligands. Part 1.—He(I) photoelectron spectra of some closed-shell metallocenes

Abstract: He I photoelectron spectra are reported for the metallocene species (C5H5)2V, (C5H5)2Cr, (C5H5)2Mn, (C5H5)2Co and (C5H5)2Ni, and for their 1,1′-dimethyl derivatives. The metal 3d ionisation structure is discussed in terms of ligand field theory. The unusual spectrum of (C5H4Me)2 Mn is interpreted in terms of a high-spin/low-spin equilibrium in the gas phase.

Inelastic collisions of fast charged particles with atoms: ionization of the aluminum l shell.

Abstract: Born-approximation calculations of the ionization of aluminum $L$-shell electrons have been performed using Hartree-Slater wave functions. Generalized oscillator strengths and proton energy-loss cross sections from threshold to ionized-electron energies of 128 Ry have been calculated. The results show a delayed maximum above threshold, and the ramifications of this phenomenon are discussed. Comparison is made with hydrogenic results and good agreement is found at intermediate and large energy loss, but the hydrogenic calculation is totally inadequate near threshold. The implications of this for stopping-power calculations and subshell corrections is discussed. The Bethe asymptotic cross section is obtained and the variation of parameters therein is investigated.

Photoelectron Spectroscopic Investigation of the Electronic Structure of Nitromethane and Nitrobenzene

Abstract: The electronic structure of nitromethane and nitrobenzene has been studied by high‐resolution HeI photoelectron spectroscopy and quantum chemical calculations of the INDO type. The spectra of CH3NO2 and CD3NO2 exhibit six ionization bands below 21 eV. The transitions to the ground and first excited ionic states have extensive vibrational structure which has been identified as the symmetric NO2 bending mode. The spectra of C6H5NO2 and C6D5NO2 contain at least 10 ionization bands below 21 eV with resolved vibrational structure only in the transition to the ground ionic state. The most loosely bound MO of nitromethane has been identified as the 5a1 NO2–σ bonding orbital, and that of nitrobenzene as the b1 ring‐π orbital. The nonbonding a2 π orbital has been assigned to the second and fourth ionization bands in these respective molecules. Using the MO ordering found here, the 198 mμ absorption band of nitromethane is assigned to the π*(2b1)← σ(5a1) transition and the long wavelength bands of nitrobenzene are ...

Electronic Structure of Oxo-Bridged Iron(III) Dimers

Abstract: Magnetic susceptibility results and extensive electronic, infrared, and Mi:issbauer spectral data are presented for enH_2[(FeHEDT A)_2O]· 6H_2O_3, Na_4[(FeEDTA)_2O]· 12H_2O, FeHEDTA· H_2O, and NaFeEDT A· 3H_2O (HEDTA = N-hydroxoethylethylenediaminetriacetate, EDTA = ethylenediaminetetraacetate, and enH_2^(2+) = ethylenediammonium cation). The magnetic and spectral data establish an electronic structural model for the oxo-bridged dimers in which pairs of S = 5/2 Fe(III) ions interact antiferromagnetically, with J ≃ -95 cm^(-1). The oxo-bridged dimers show marked intensity enhancement of the one-center Fe(III) ligand-field bands. There are also several uv bands which are interpreted as arising from simultaneous electronic excitations of Fe(III) pairs. A simple high-spin ligand-field model modified by spin-spin interaction is judged to be considerably more appropriate than the Dunitz-Orgel molecular orbital approach as a vehicle for describing oxo-bridged Fe(IIl) dimers.

Electronic Structure of CsCl-Type Transition Metal Alloys

Abstract: Transition metal alloys have a tendency to make a stable ordered lattice of the CsCl-type, when the average number of conduction electrons (including d-electrons) is the same as that of Cr. The electronic structures of VMn, TiFe and ScCo are investigated by the self-consistent KKR method, to clarify the stability of these alloys. It is found that the density-of-states of these alloys has a deep valley in the middle region, by which bonding and antibonding orbitals are well separated, and the Fermi energy lies in the valley. The electronic structure of ordered alloy ScCu is also investigated. Here the narrow d-bands of Cu are situated well below the d-bands of Sc, and s-, p-electrons are polarized by about 0.6/atom at the Cu-cell. Thus, the ionic bond seems to be important to make a stable ordered lattice of ScCu. § I. Introduction

Study of the Electronic Structure of Molecules. XVII. Analysis of the Formation of the Acetylene, Ethylene, and Ethane Molecules in the Hartree-Fock Model

Abstract: The electronic density and energy of the C2H2, C2H4, and C2H6 molecules are computed in the Hartree‐Fock approximation and the results compared. Each molecule is computed at three different carbon‐carbon internuclear distances, namely, those experimentally known for the equilibrium geometry in C2H2, C2H4, and C2H6. The comparison is extended by reporting computations on the lowest singlet state of the C2 molecule. The analysis is performed by making use of Mulliken's electron population analysis and our technique for partitioning the energy (bond energy analysis). For C2H4 we have also considered the twisted configuration (where one CH2 group is perpendicular to the other) and for C2H6 we have considered both staggered and eclipsed configurations (and therefore, we are in a position to add a few comments on the barrier to internal rotation). The basis set is sufficiently large and extended so as to be near to the Hartree‐Fock limit for all the computations reported. The binding energy computed in the Hart...

Spin–Spin Coupling between Geminal and Vicinal Protons

Abstract: The geminal (HCH) and vicinal (HCCH) proton spin–spin coupling constants are of fundamental importance in the applications of nuclear magnetic resonance (NMR) spectroscopy in structural and conformational analysis, since they are extremely sensitive to fine details of steric and electronic molecular structure. The nature of the dependence of the constants on individual structural factors (bond length, valence and dihedral angles, electronic structure of the substituents and their orientation, etc.) has been examined in detail. At present a priori theoretical calculations do not allow an exact description of these relations and therefore a semiempirical approach, based on general qualitative relations found by quantum-mechanical calculations, is very promising. The bibliography includes 293 references.

The electronic state of cerium in some CeRh3 − xPdx alloys

Abstract: The room temperature lattice spacings and magnetic susceptibilities of some alloys represented by the general formula, CeRh3 − xPdx, have been measured. The results indicate that in the composition range x = 0 to x = 2.36 (59% Pd∗) the cerium atoms are in the four valent state (the 4ƒ0 configuration), whereas from igc = 2.36 tox = 3 (75 % Pd), the effective valency of the cerium atoms increases to a value of 3.45 at CePd3 (the 4ƒ0.55 configuration). The behaviour of the magnetic susceptibility in this latter composition range suggests that the 4ƒ electrons are not localised in character but can be described by a nonmagnetic, virtual bound state.