Showing papers on "Electronic structure published in 1980"

Quantum theory of molecular electronic structure

Abstract: With the increasing availability of powerful computers, attempts to calculate the electronic structure and properties of molecules by the direct ab initio solution of a many-body Schrodinger equation have received a great stimulus. The authors review the mainstream developments in quantum chemistry and give a straightforward account of some of the many-body techniques borrowed, with appropriate modifications, from other areas of physics-field theory, nuclear theory and solid-state theory. After a historical introduction, the traditional approach based on the self-consistent field and the method of configuration interaction is developed in detail. This is followed by the introduction of the cluster expansion, various types of correlated electron-pair theory, and diagrammatic perturbation methods. Finally, propagator and Green function techniques are reviewed, not only as a means of calculating transition energies but also as an alternative approach to the determination of the electronic ground state.

The Recursive Solution of the Schrodinger Equation

Abstract: Publisher Summary The chapter presents a study on the recursive solution of the Schrodinger equation. The local environment approach to the electronic structure of solids requires an alternative to band theory for solving the Schrodinger equation. In the limit of weak interaction between electrons and atoms, for example in simple metals, the electronic structure is determined by the long-range periodicity of the atomic potentials. Band theory exploits this aspect of the physics to express electronic properties of the solid as a coherent superposition of the electronic properties of all the atoms. When the electrons interact strongly with the atoms, this picture breaks down and properties no longer depend on long-range periodicity, but rather on only the first few shells of neighbors of each atom. The d electrons in transition metals are prime examples of this regime. While band theory is still a valid, formal solution to the Schrodinger equation, the physics is better understood by means of a solution that explicitly accounts for the role of local environment. This chapter presents a discussion on such a method of solution of the Schrodinger equation. The recursive solution of the Schrodinger equation is well adapted to the digital computer. The chapter is organized in order of sophistication of the applications. The elementary part finishes with Green functions. The topics apply to particular kinds of calculations, such as local density of states, energy differences, and photocurrents.

Electronic Structure from the Point of View of the Local Atomic Environment

Abstract: Publisher Summary The chapter presents a study on electronic structure from the perspective of the local atomic environment. The chapter begins by discussing fundamental ideas, such as throwing out k space, the invariance theorem, and mathematics of the Green functions. Several aspects of solid state physics, where the model of perfect lattice periodicity is simply not appropriate are a part of the discussion. It must be emphasized that the density functional theory is purely concerned with the ground state, that the eigenfunctions Ψn are only a device for calculating the kinetic energy, and that the energy values En do not have any direct physical significance in contrast to the Landau quasi-particle energies, which are genuine excitation energies of the system. The chapter presents a summary on the basic results of the density functional formalism without proof and considers a system in its ground state of stationary nuclei with an electron density p(r). The chapter discusses the special and important type of perturbation or rather difference calculation, namely, switching on or off a coupling interaction between two subsystems, or between an adsorbed atom and the adsorbate surface. The chapter presents the calculation of the coupling energy.

Electrons at the Fermi surface

Abstract: Lifshitz, I. M. and Kaganov, M. I. Geometric concepts in the electron theory of metals. -- Wilkins, J. W. Understanding quasi-particles. -- Chambers, R. G. The generalized path-integral approach to transport problems. -- Pippard, A. B. The Shoenberg effect (magnetic interaction). -- Mackintosh, A. R. and Andersen, O. K. The electronic structure of transition metals. -- Lonzarich, G. G. Fermi surface studies of ground-state and magnetic excitations in itinerant electron ferromagnets. -- Fawcett, E. et al. The effect of strain on the Fermi surface. -- Coleridge, P. T. The de Haas-van Alphen effect in dilute alloys. -- Springford, M. Electron quasi-particle lifetimes in metals. -- Higgins, R. J. and Lowndes, D. H. Waveshape analysis in the de Haas-van Alphen effect. -- Coleridge, P. T. and Templeton, I. M. High precision measurements of de Haas-van Alphen frequencies.

Electronic structure of magnetic impurities calculated from first principles

Abstract: The electronic structure of magnetic $3d$ impurities in Cu and Ag is calculated self-consistently from first principles. Using the density functional theory the exchange and correlation is treated in the local spin-density approximation of von Barth and Hedin. Our method is based on the Kohn-Korringa-Rostocker Green's-function method and the impurity is described by a single perturbed muffin-tin potential in an otherwise periodic lattice. We give results for the local density of states, the magnetic moments, and the phase shifts at the Fermi energy for the $3d$ impurities in Cu and Ag. Our results are in qualitative agreement with the Anderson model, however modifications due to the host band structure are important, especially for Mn and Fe in Cu. For all cases studied, the exchange integral $I$ lies between 0.65 and 0.8 eV.

General theory of electronic transport in molecular crystals. I. Local linear electron–phonon coupling

Abstract: An improved general theory of electronic transport in molecular crystals with local linear electron–phonon coupling is presented. It is valid for arbitrary electronic and phonon bandwidths and for arbitrary electron–phonon coupling strength, yielding small‐polaron theory for narrow electronic bands and strong coupling, and semiconductor theory for wide electronic bands and weak coupling. Detailed results are derived for electronic excitations fully clothed with phonons and having a bandwidth no larger than the phonon frequency; the electronic and phonon densities of states are taken as Gaussian for simplicity. The dependence of the diffusion coefficient on temperature and on the other parameters is analyzed thoroughly. The calculated behavior provides a rational interpretation of observed trends in the magnitude and temperature dependence of charge‐carrier drift mobilities in molecular crystals.

The electronic structure of small nickel atom clusters

Abstract: The ground state electronic structure of small nickel atom clusters (Nin, n=1–6) has been calculated using the ab initio effective core potential self‐consistent field (SCF) method in a Gaussian expansion basis. The electronic configuration of the nickel atoms in the clusters is found to be very close to 3d94s1. The ground state electronic configurations for Nin generally have n unpaired 3d electrons in molecular orbitals (MO’s) spanning the same irreducible representations as the 4s atomic orbitals while the n 4s electrons fill their MO’s in accord with a simple three‐dimensional Huckel model with overlap. Exceptions to this description are found in the cases of linear systems where the 3d holes prefer δ over σ symmetry and in octahedral Ni6 where a different preferred set of 3d holes is obtained. The SCF ground state wave functions correspond roughly to a model in which the 3d electrons can be viewed as weakly interacting localized 3d9 units. The clusters are bound together primarily by the 4s electrons with the 4p orbital contribution increasing in importance with cluster size and dimensionality. The binding energy per nickel atom generally increases as the size of the cluster increases, although at six atoms this quantity has not yet converged with cluster size. The density of states diagram for the occupied one electron energy levels in Ni6 is found to be very different from the corresponding types of diagrams obtained in the muffin tin (MT)–Xα method for small nickel atom clusters. This difference is examined in detail, with consideration given to the effects of relaxation energy and to the different orbital level filling criteria used in the two methods.

Molecular electronic property density functions: The nuclear magnetic shielding density

Abstract: The general concept of a density function for a molecular electronic property is considered. The origin dependence of some electric and magnetic property densities is investigated and the nuclear magnetic shielding density function is used as a typical example. Density difference maps which reflect the changes in this electronic property upon molecule formation and bond extension are shown for the HF molecule and the related systems, the H atom and F− ion.

Quantum chemistry by random walk: Higher accuracy

Abstract: The random walk method of solving the Schrodinger equation is extended to allow the calculation of eigenvalues of atomic and molecular systems with higher accuracy. The combination of direct calculation of the difference δ between a true wave function ψ and a trial wave function ψo with importance sampling greatly reduces systematic and statistical error. The method is illustrated with calculations for ground‐state hydrogen and helium atoms using trial wave functions from variational calculations. The energies obtained are 20 to 100 times more accurate than those of the corresponding variational calculations.

Geometrical and electronic structure of Si(001) and Si(111) surfaces: A status report

Abstract: A critical review of recent studies of the geometrical and electronic structure of the Si(001) and Si(111) surfaces is given. Emphasis is placed on low‐energy electron diffraction (LEED) studies of the geometrical structure, photoelectron spectroscopy studies of the electronic structure, and theoretical studies of the electronic and geometric structure of the Si(111)–(2×1), Si(111)–(7×7), Si(111)–(1×1)X, and Si(001)–(2×1) surfaces.

Electronic magnetic and cohesive properties of some nickel-aluminium compounds

Abstract: A method developed recently by Williams and co-workers (1979) for the calculation of electronic structure and cohesive properties is applied to Ni3Al, NiAl and Al3Ni and is generalised to make possible the performance of self-consistent spin-polarised calculations which are applied to Ni3Al. Results are given for the densities of states, the magnetic moment and its pressure derivative, lattice constants, bulk modulus and the heats of formation, and are compared with experimental data. In an attempt to isolate dominating binding forces, the heats of formation are decomposed into site- and angular-momentum contributions.

Electronic structure of lanthanum perovskites with 3d transition elements

Abstract: The systematics of the electronic structure of $\mathrm{La}B{\mathrm{O}}_{3}$ perovskite oxides, where the $B$ element scans the $3d$ transition-metal series from Ti to Co, are examined. X-ray photoelectron spectra of valence bands and shallow core states are presented and compared with theoretical molecular cluster and free-ion multiplet models. Self-consistent ionic configurations are obtained from the embedded cluster calculations, which differ from the assumptions of crystal-field theory due to metal-oxygen covalency. The prospect for more rigorous many-electron models is discussed.

A new general methodology for deriving effective Hamiltonians for atoms and molecules. Application to the transferability of atomic potentials in the hydrocarbon series

Abstract: A new general methodology for deriving, from first principles, effective Hamiltonians by Fourier techniques is presented. The Fock operator is shown to be a particular one‐electron effective Hamiltonian. Other one‐electron effective Hamiltonians are suggested. The methodology is applied to a first study of the transferability of atomic potentials in the hydrocarbon series.

Ultraviolet resonance Raman excitation profiles of pyrimidine nucleotides

Abstract: A semiempirical theoretical method for calculating the resonant Raman excitation profiles (RREP) from the measured absorption profile is developed and applied to measurements on pyrimidine mononucleotides. The method is general and provides a way of checking the consistency of a measured RREP with a measured absorption profile. From this treatment one obtains Δej, the shift in the equilibrium position of the normal coordinate Qj when the molecule is excited to the eth (resonant) electronic state. This quantity is useful in the estimation of the excited state geometry. Some error in our calculated values of Δej may result because changes in the excited state normal‐mode frequencies have not been included in our evaluation of the Franck–Condon factors.

Self-consistent linearized augmented-plane-wave study of the electronic structure and superconductivity of fcc lanthanum under pressure

Abstract: We report the results of a linearized augmented-plane-wave calculation of the electronic structure of fcc La at three lattice constants corresponding to ambient pressure, 50, and 120 kbars. The Kohn-Sham-Gaspar approximation for exchange and correlation is used and the potential is allowed a fully non-muffin-tin form. The f bands lie approx.2--2.5 eV above the Fermi level and are approx.1 eV wide, resulting in a very small (0.05 electrons) localized f occupation. Under pressure the f bands rise and broaden appreciably, resulting in only a slight increase in f occupation. The rigid-muffin-tin approximation for the electron-phonon interaction lambda overestimates the superconducting transition temperature T/sub c/ by 40%, but we find that the drastic increase in T/sub c/ under pressure can be attributed primarily to changes in the electronic stiffness eta. Structural transitions which occur at 25 and 53 kbars may be related to changes in Fermi-surface topology which we find to occur approximately at these pressures.

Applicability of self‐consistent field techniques based on the complex coordinate method to metastable electronic states

Abstract: Hartree–Fock theory is applied to resonance states of an atomic Hamiltonian under the complex coordinate transformation. It is concluded that for shape resonances restricted Hartree–Fock theory provides a useful and practical approach to the problem of computing the complex resonance energy. Numerical results are presented for the low‐energy 2P shape resonance in e–Be scattering. With properly chosen basis functions the resonance energy obtained in these calculations is practically independent of the phase of the complex scaling parameter for a wide range of values. Application of this technique to molecular resonances is discussed. The widths of Feshbach resonances cannot be obtained from the theory in its present form, but it is suggested that a complex coordinate form of multiconfiguration self‐consistent field theory may be appropriate for that case.

Photoexcitation and ionization in molecular oxygen - Theoretical studies of electronic transitions in the discrete and continuous spectral intervals

Abstract: Theoretical studies of valence-electron (1πg, 1πu, 3σg) photoexcitation and ionization cross sections in molecular oxygen are reported employing separated-channel static-exchange calculations and the Stieltjes–Tchebycheff moment-theory technique. As in previously reported investigations of photoexcitation and ionization in small molecules following this approach, canonical Hartree–Fock orbitals, large Gaussian basis sets, and many-electron eigenstates of correct symmetry are used in defining appropriate noncentral static-exchange potentials and in computations of the appropriate discrete and continuum transition strengths. It is particularly important in molecular oxygen to incorporate the appropriate ionic parentages of the various photoionization multiplet states in order to obtain the correct partial-channel cross sections. The calculated discrete series associated with 1πg excitation are found to be in good agreement with available experimental assignments and previously reported theoretical studies, and the predicted states associated with 1πu and 3σg excitations are in general accord with assignments for the higher series based on spectral and quantum-defect analysis. Although the observed photoelectron spectra and photoionization cross sections are relatively complex, the calculated total vertical electronic photoabsorption cross section and the partial-channel photoionization cross sections for production of X 2πg, a 4πu, A 2πu, 2 2πu, 3 3IIu, b 4∑g-, and B 2∑g-, ionic states are found to be in good accord with recent synchrotron radiation, line-source, electron-impact, and (e,2e) dipole oscillator-strength measurements when proper account is taken of the parentages of the various multiplet states. The partial-channel cross sections exhibit resonancelike structures that can be attributed to contributions from diabatic valencelike virtual states that appear in the appropriate photoionization continua, rather that in the corresponding discrete spectral intervals. These features in the dipole spectrum of molecular oxygen are discussed and are contrasted and compared with the results of previously reported related studies in molecular nitrogen and carbon monoxide.