Local Density Approximations in Quantum Chemistry and Solid State Physics de Jens Peder Dahl

Local Density Approximations in Quantum Chemistry and Solid State Physics

Jens Peder Dahl

John Avery

The· simplest picture of an atom, a molecule or a solid is the picture of its distribution of charge. It is obtained by specifying the positions of the atomic nuclei and by showing how the density, p(E), of the electronic charge-cloud varies from place to place. A much more detailed picture is provided by the many-electron wavefunction. This quantity shows not only the arrangement of the electrons with respect to the nuclei, but also the arrangement of the electrons with respect to each other, and it allows the evaluation of the total energy and other properties. The many-electron wavefunction is in principle obtained by solving the many-electron Schrodinger equation for the motion of the interacting electrons under the influ ence of the nuclei, but in practice the equation is unsolvable, and it is necessary to proceed by methods of approximation. Needless to say, .such methods will as a rule depend on the complexity of the system considered.

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Cuprins

Fundamental Theory.- Density Functional Theory and Local Potential Approximations from Momentum Space Considerations.- Aspects of Density Functional Theory.- On the Calculation of Potentials from Densities.- The Chemical Potential for Interacting Fermions in a Harmonic Potential.- Density, Total Energy and Chemical Potential of Atomic Ions and some Molecules.- Some Aspects of the Role of Single-Particle Density in Chemistry.- The Mechanics of and an Equation for the Electronic Charge Density.- The Qualitative Theory of the Current Density in Molecules.- The Constrained Search Approach, Mappings to External Potentials, and Virial-Like Theorems for Electron-Density and One-Matrix Energy-Functional Theories.- Self-Interaction Correction.- Some Approaches to Density Functional Theory.- Exchange-Correlation Energy Functionals in the Density Functional Formalism.- An Approach to Electron Correlation beyond the Local Spin Density Approximation.- Pair Correlation Energies and Local Spin-Density Functionals.- On the Extension of the Statistical Energy Expression to Multi-Determinantal Wave Functions.- The Weizsacker Term, its Corrections and Virial Partitioning in Density Functional Theory.- The Second Order Reduced Density Matrix and the Chemimal Bond.- Characteristic Function Approach to Density Matrix Calculations.- On the Systematic Assessment of Correlation Effects in Local Density Models.- Relativistic Density Functional Theory.- A Phase Space Approach to Energy Densities in Position Space.- Applications.- Application of the Hartree-Fock-Slater Method in Photoelectron Spectroscopy.- SCF-X?-SW Cluster Molecular-Orbital Models of Catalysts, Alloys, Magnetic Materials, and Superconductors.- Some Applications of the Density-Functional Formalism to Chemisorption.- Density Functional Calculations for Atomic Clusters.- Cohesive Energy, Spectroscopic, and Magnetic Properties of Small Clusters.- Calculations of Hyperfine Interactions in Transition Metal Compounds in the Local Density Approximation.- Local Density Approach to Surfaces and Adsorbed Layers.- Electron Densities in Solid Compounds.- Local Density Approximations for Relativistic Exchange Energies.- Relativistic Multiple Scattering X? Calculations.- Dirac Scattered Wave Calculations.- Theoretical Valence Charge Densities for Graphite, Diamond and LiC6.- Dependence of the Self-Consistent One-Electron Density of Anisotropic Semiconductors on Local Density Approximations.- ?-Ray Bragg and Compton Scattering Experiments Used as Tests of the Validity of the Local Density Approximation.- Multipole Expansion as an Alternative Representation of Charge Density.- Measured Electron Density Distributions in Crystals as a Basis for Band Structure Calculations.- Observation of Electron Distributions on Outermost Layers of Solid Surfaces by Penning Ionization Electron Spectroscopy.- Observations of Local Electron Distributions in Molecular Orbitals.- Accurate Hellmann-Feynman Force Method for the Study of the First and Second Derivatives of Potential Energy Hypersurface.- The Calculation of Spectroscopic Data by the SCC-X? Method.- On Correlated One-Electron Energies in the HFS and HFG Schemes.- On the Atomic Wavefunctions Generated by the Hartree-Fock-Slater Method X?HF and the Modified Hartree-Fock-Slater Method ?aHF which Includes Self Interaction Explicitly.- Ab-Initio Calculations Incorporating Desirable Options for Large Molecules and Solids: a Competitive Completely General Alternative to Local Density Methods for Many Systems.