Relativistic effects in structural chemistry

We propose a simple scheme for decomposition of molecular functions into single‐center components The problem of three‐dimensional integration in molecular systems thus reduces to a sum of one‐center, atomic‐like integrations which are treated using standard numerical techniques in spherical polar coordinates The resulting method is tested on representative diatomic and polyatomic systems for which we obtain five‐ or six‐figure accuracy using a few thousand integration points per atom

A multicenter numerical integration scheme for polyatomic molecules

How can the fundamental band gap of an insulator be predicted? As a difference of ground-state energies, the fundamental gap seems to fall within the reach of density functional theory, yet the predicted gaps from band structure calculations within the local density approximation (LDA) are about 40% too small. It is argued here that even the exact Kohn-Sham potential veff(r), which generates the exact density in a self-consistent-field calculation, generates a band structure which underestimates the gap. Within the context of the band gap problem, several recent developments in the density-functional theory of many-electron systems are reviewed: (1) The Langreth-Mehl approximation to the Kohn-Sham exchange-correlation energy and potential, based upon the Langreth-Perdew wavevector analysis of the density gradient expansion. This functional leads to more accurate ground-state energies and densities than those of the LDA with little change in the calculated band structures of solids. (2) The derivative discontinuity of the exchange-correlation energy, which is responsible for substantial underestimation of the fundamental gap by even the exact Kohn-Sham potential. (3) The self-interaction correction, which yields accurate gaps in insulators only by virtue of its orbital-dependent potential. (4) The density response function of the uniform electron gas, which suggests that the LDA gives a good estimate of the exact Kohn-Sham potential for a semiconductor with a weak periodic potential. In short, several very different (but admittedly approximate) numerical calculations suggest that most of the error in the LDA fundamental gap would persist in the gap of the exact Kohn-Sham band structure. This error would persist in any attempt to calculate the gap from LDA total energy differences for clusters of increasing size.

Density functional theory and the band gap problem

A measure of non-classicality of quantum states based on the volume of the negative part of the Wigner function is proposed. We analyse this quantity for Fock states, squeezed displaced Fock states and cat-like states defined as coherent superposition of two Gaussian wavepackets.

https://iopscience.iop.org/article/10.1088/1464-4266/6/10/003/pdf

Negativity of the Wigner function as an indicator of non-classicality

On degeneracy, near-degeneracy and density functional theory

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.

Local Density Approximations in Quantum Chemistry and Solid State Physics

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Understanding Molecular Properties

We show that a free quantum particle in two dimensions with zero angular momentum (s wave) in the form of a ring-shaped wave packet feels an attraction towards the center of the ring, leading first to a contraction followed by an expansion. An experiment to demonstrate this effect is also outlined.

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In- and outbound spreading of a free-particle s-wave.

The rise of atomic theory the birth of quantum mechanics wave mechanics particle in a box quantum-mechanical operators the free particle the harmonic oscillator the central-field problem the hydrogen atom the spinning electron the periodic table by electron counting the variational method diatomic molecules vibration and rotation of diatomic molecules atomic term symbols atomic terms, wavefunctions and energies electronic terms of diatomic molecules the Hartree-Fock method density-functional theory.

Jens Peder Dahl

Papers

Local Density Approximations in Quantum Chemistry and Solid State Physics

Understanding Molecular Properties

In- and outbound spreading of a free-particle s-wave.

Introduction to the quantum world of atoms and molecules: solutions manual

Introduction to the Quantum World of Atoms and Molecules