Showing papers by "Chalmers University of Technology published in 1976"

Exchange and correlation in atoms, molecules, and solids by the spin-density-functional formalism

Abstract: The aim of this paper is to advocate the usefulness of the spin-density-functional (SDF) formalism. The generalization of the Hohenberg-Kohn-Sham scheme to and SDF formalism is presented in its thermodynamic version. The ground-state formalism is extended to more general Hamiltonians and to the lowest excited state of each symmetry. A relation between the exchange-correlation functional and the pair correlation function is derived. It is used for the interpretation of approximate versions of the theory, in particular the local-spin-density (LSD) approximation, which is formally valid only in the limit of slow and weak spatial variation in the density. It is shown, however, to give good account for the exchange-correlation energy also in rather inhomogeneous situations, because only the spherical average of the exchange-correlation hole influences this energy, and because it fulfills the sum rule stating that this hole should contain only one charge unit. A further advantage of the LSD approximation is that it can be systematically improved. Calculations on the homogeneous spin-polarized electron liquid are reported on. These calculations provide data in the form of interpolation formulas for the exchange-correlation energy and potentials, to be used in the LSD approximation. The ground-state properties are obtained from the Galitskii-Migdal formula, which relates the total energy to the one-electron spectrum, obtained with a dynamical self-energy. The self-energy is calculated in an electron-plasmon model where the electron is assumed to couple to one single mode. The potential for excited states is obtained by identifying the quasiparticle peak in the spectrum. Correlation is found to significantly weaken the spin dependence of the potentials, compared with the result in the Hartree-Fock approximation. Charge and spin response functions are calculated in the long-wavelength limit. Correlation is found to be very important for properties which involve a change in the spinpolarization. For atoms, molecules, and solids the usefulness of the SDF formalism is discussed. In order to explore the range of applicability, a few applications of the LSD approximation are made on systems for which accurate solutions exist. The calculated ionization potentials, affinities, and excitation energies for atoms propose that the valence electrons are fairly well described, a typical error in the ionization energy being 1/2 eV. The exchange-correlation holes of two-electron ions are discussed. An application to the hydrogen molecule, using a minimum basis set, shows that the LSD approximation gives good results for the energy curve for all separations studied, in contrast to the spin-independent local approximation. In particular, the error in the binding energy is only 0.1 eV, and bond breaking is properly described. For solids, the SDF formalism provides a framework for band models of magnetism. An estimate of the splitting between spin-up and spin-down energy bands of a ferromagnetic transition metal shows that the LSD approximation gives a correction of the correct sign and order of magnitude to published $X\ensuremath{\alpha}$ results. To stimulate further use of the SDF formalism in the LSD approximation, the paper is self-contained and describes the necessary formulas and input data for the potentials.

Calculations of molecular ionization energies using a self‐consistent‐charge Hartree–Fock–Slater method

Abstract: A numerical-variational method for performing self-consistent molecular calculations in the Hartree-Fock-Slater (HFS) model is presented Molecular wavefunctions are expanded in terms of basis sets constructed from numerical HFS solutions of selected one-center atomlike problems Binding energies and wavefunctions for the molecules are generated using a discrete variational method for a given molecular potential In the self-consistent-charge (SCC) approximation to the complete self-consistent-field (SCF) method, results of a Mulliken population analysis of the molecular eigenfunctions are used in each iteration to produce 'atomic' occupation numbers The simplest SCC potential is then obtained from overlapping spherical atomlike charge distributions Molecular ionization energies are calculated using the transition-state procedure; results are given for CO, H2O, H2S, AlCl, InCl, and the Ni5O surface complex Agreement between experimental and theoretical ionization energies for the free-molecule valence levels is generally within 1 eV The simple SCC procedure gives a reasonably good approximation to the molecular potential, as shown by comparison with experiment, and with complete SCF calculations for CO, H2O, and H2S

Linearly polarized microstrip antennas

Abstract: An equivalent network for square and rectangular shaped microstrip radiating elements is derived. In order to simplify the problem the radiating element is considered as two slots separated by a transmission line of low characteristic impedance. The slots are characterized by their radiation pattern, directivity, and equivalent admittance. A design procedure for open circuit halfwave resonators and for arrays of such resonators is given. Finally, some antennas in the X band are designed and measured.

The Electron-Phonon Interaction in Normal Metals

Abstract: The influence of the electron-phonon many-body renormalization effects on the electron states in normal metals is reviewed. The emphasis is on the electron-phonon mass enhancement parameter λ. The occurrence or absence of renormalization effects is discussed for different electronic properties. After a review of theoretical and experimental methods of obtaining information about λ, numerical values for this quantity are given for the elements. Other sections deal with alloys, compounds, disordered and amorphous metals, anisotropy in λ and variations in λ under pressure. Finally, brief comments are given on the electron-electron and electron-magnon renormalization of the electron mass.

Hydrogen sensitivity of palladium--thin-oxide--silicon Schottky barriers

Abstract: It is shown that current transport through Schottky barriers formed by Pd on n-type silicon with a thin thermally grown oxide is sensitive to hydrogen in the ambient. It is shown that a transition from minority- to majority-carrier dominated current occurs with increasing hydrogen pressure.

Binding Energies for Different Adsorption Sites of Hydrogen on Simple Metals

Abstract: A self-consistent calculation for hydrogen chemisorption is reported, where the surface is described both by the jellium model and by a model that includes ion pseudopotentials to lowest order. It predicts that for H on Al(100) a bridge configuration is the most favorable (binding energy 1.9 eV), and that the activation energy for surface diffusion is 0.1-0.2 eV.

Many-body calculations of the hyperfine interaction of some excited states of alkali atoms, using approximate Brueckner or natural orbitals

Abstract: The theory of maximum-overlap or Brueckner orbitals and of natural Orbitals is reviewed for closed-shell systems. A technique is described to calculate approximate Brueckner or natural orbitals for systems with a single valence electron, and this is applied together with the linked-diagram expansion of effective operators to evaluate the hyperfine interaction of some excited states of alkali atoms. It is found that it is in this way possible to reproduce reasonably well also the highly perturbed interactions of the excitedd states, which is not possible in a low-order expansion based on HF orbitals. Numerical results are given for the 5d state in K and the 4d state in Rb, where good experimental information is available.

PFVIBAT—a computer program for plane frame vibration analysis by an exact method

Abstract: The described program PFVIBAT uses the exact displacement method to perform free and forced vibration analysis entirely within the differential equation theory of beams thus avoiding assumed modes and lumped masses. The frame may contain rigid bodies. Clamped, hinged, guided and rolling connections are allowed for. Consideration of rotatory inertia, shear deformation and second-order bending moments and shear forces as caused by static axial load is optional. Eigenfrequencies and modal masses are calculated with an accuracy that may be specified. Displacement and moment modes are plotted. Transient vibrations are studied.

The spin‐density‐functional formalism for quantum mechanical calculations: Test on diatomic molecules with an efficient numerical method

Abstract: The spin-density-functional (SDF) formalism with the local-spin-density (LSD) approximation is applied to a number of small molecules with the primary aim of testing the approximation for molecular applications. A new numerical method to solve the one-electron wave equation is developed, utilizing the special features of the SDF formalism. Energy curves, dissociation energies, and equilibrium distances for some diatomic molecules [H$sub 2$$sup +$($sup 2$$Sigma$$sup +$/sub g/, $sup 2$$Sigma$$sup +$/sub u/), H$sub 2$($sup 1$$Sigma$$sup +$/sub g/, $sup 3$$Sigma$$sup +$/sub u/), He$sub 2$$sup 2+$($sup 1$$Sigma$$sup +$/sub g/), and He$sub 2$($sup 1$$Sigma$$sup +$/sub g/)] and the vibrational frequencies of H$sub 2$. The deviations from the experimental results are typically $sup 1$/$sub 2$ eV for the energies and less than or equal to 0.1 A for the distances. The LSD approximation is discussed using the concept of an exchange-correlation hole and predictions about the applicability to other molecules are made. The LSD approximation is compared with the Hartree--Fock and multiple-scattering-X$alpha$ methods, and some difficulties in the latter methods are pointed out. It is argued that the SDF formalism within the LSD approximation has physical advantages compared to the Hartree--Fock and X$alpha$ methods and that it should provide a simple and useful method for a broad range of applications. (auth)

Discharge of MNOS structures at elevated temperatures

Abstract: The discharge behavior of MNOS structures without voltage applied, is investigated at temperatures from 25 to 300°C, for times from 10 min to about 1 week. The observed discharge behavior is explained by a theoretical model, including two discharge processes. The two processes are direct tunneling from traps and thermal excitation of these traps. It is shown that static retention times of more than 10 yr at 85°C is attainable. Also, discharge with voltage applied is investigated and shown to agree with the model when the voltage is small enough.

A many-body calculation of the hyperfine interaction in the lowest 2 S and 2 P states of li-like systems

Abstract: A non-relativistic perturbation method of Brueckner-Goldstone type is used to calculate the hyperfine interactions in the lowest2 S and2 P states of the Li-like systems, Li, Be+, B2+, C3+, N4+, O5+ and F6+. The effect of the polarization of the closed shell is treated to all orders of perturbation, while the correlation effect is calculated in the lowest order, i.e. in the third order of the perturbation expansion. Experimental data are at present available only for Li, Be+ and F6+, and the agreement with the calculated values is in these cases very good, usually within the experimental uncertainties. This implies that the predictions made in the remaining cases should be quite reliable, which may simplify the experimental determination of these quantities. Theoretical values are also given for the quadrupole interaction, which can be used to determine the nuclear quadrupole moments, when accurate experimental information becomes available.

Nuclear Deformations, Level Assignments and Static Nuclear Moments of Isotopes in the Region 72Hf-77Ir

Abstract: A comparison is made between experimental and theoretical level assignments and static electromagnetic moments of nuclei in the region 72Hf-77Ir. The theoretical calculations are based on the modified oscillator model. Equilibrium deformation values, and 4, are determined for doubly-even and odd-mass nuclei from the minima in the potential energy surfaces. The influence of the different parameters entering the expressions for the magnetic dipole moment is analysed. The electric quadrupole and hexadecapole moments are calculated on the assumption that the nucleus is a homogeneously charged body with a sharp surface and a shape corresponding to that of an equipotential surface. In some selected cases, the electric multipole moments are evaluated by use of the single-particle wave functions.

Reinforced Concrete Corners and Joints Subjected to Bending Moment

Abstract: In this investigation simple and rational methods for design of the reinforcement in corners and joints are developed. Proposals for design rules are based on tests with monotonic one-way loading to failure. The reinforcement details must satisfy the fundamental requirements of strength, limited cracking, ductility, and simplicity of construction. The main emphasis of the experimental work has been placed on the study of frame corners subjected to positive moments, i.e., moments that cause tensile stresses on the inside of the corner. Other types of joints are also studied, such as corners in retaining walls and T-joints. Different causes of failure in corners and joints are examined. Special attention is devoted to diagonal tension crack failure. Simple expressions are derived for the analysis of this type of failure on the basis of truss analogies. Proposals are put forward for simple and functional reinforcement layouts for corners and some common types of joints in reinforced concrete structures subjected to bending moment.

Internal stresses and activation volumes from the stress relaxation behavior of polyethylene at low deformations

Abstract: Internal stress levels and values of the activation volume have been evaluated from the kinetics of stress relaxation in annealed samples of LD and HD polyethylene. The initial deformation of the samples was varied, the maximum values amounting to ca. 1%. The temperature of the experiments was 24°C for LDPE, and 24°, 50°, and 69°C for HDPE. The internal stress level was found to be approximately proportional to the initial deformation and independent of the temperature used. Such internal stresses appear to be introduced upon deformation, since permanent stresses had been removed by careful annealing. The activation volume (v) was found to satisfy the relation vσ* ≈ 10kT, where σ* is the effective stress, i.e., the difference between the applied and internal stress, k is Boltzmann's constant, and T is the absolute temperature. This is in good agreement with results reported elsewhere for a wide variety of materials. This relation applies primarily to the exponential flow portion of the relaxation curves, but by a simple transformation the power‐law region can also be encompassed. Copyright © 1976 John Wiley & Sons, Inc.

Polymorphism of Metals. III. Theory of the Temperature-Pressure Phase Diagram of Iron

Abstract: The temperature-pressure phase diagram of iron is analysed in terms of the microscopic contributions to the free energy, i.e. vibrational, electronic and magnetic excitations. It is shown that the thermodynamic data, when combined with other experimental and theoretical information, require persistent disordered localized magnetic moments in the paramagnetic bcc, fcc and liquid phases but not so for the hcp phase. The bcc-fcc transitions are mainly caused by differences in the electronic and magnetic free energies while the vibrational part plays a minor role.