Showing papers on "Orbital-free density functional theory published in 1987"

Rational function representation for accurate exchange energy functionals

Abstract: A representation of the exchange energy functional as the product of a homogeneous gas functional and a rational function approximation in the density gradient is developed and shown to describe accurately both the total exchange energy and the local exchange energy density of atomic systems. For the atoms H through Kr, the error in the total exchange energy is generally <0.02 hartree except for Cr through Zn where it is <0.21 hartree.

Density functional rationale of chemical reaction coordinate

Abstract: A dynamical partitioning of the reaction field is proposed in order to study the electron density flow along the reaction coordinate. The density functional is constructed in a universal form, and a one-to-one correspondence is established between the density matrix and the electron density. The density functional is free from the constraints of N or v representability and is treated as a thermodynamic function that obeys the principle of maximum entropy. The functional derivative of the density functional with respect to the electron density is introduced as a response operator. The reaction paths are combinations of the dynamical processes of the electron density; the corresponding response operators and new type of thermodynamic functions and potentials are defined and shown to be useful. The characteristic features of the chemical reaction coordinate is discussed in terms of the new thermodynamic quantities. The importance of the softest vibrational mode as the chemical reactivity index is rationalized in terms of the density functional theory.

Method of local‐scaling transformations and density functional theory in quantum chemistry. III. The energy density functional: Spin‐restricted approach

Abstract: The rigorous derivation of the energy density functional is proposed within the framework of the spinfree, or spin-restricted formulation of the energy density functional theory. It is shown particularly that the kinetic energy density functional is given by a sum of the Weizsacker term and the so-called “modified” Thomas–Fermi one. The variational principle is formulated for the energy density functional theory in terms of the Euler–Lagrange equation, and the virial theorem is proposed.

Density matrices and density functionals : proceedings of the A. John Coleman symposium

Abstract: A Tribute to A. John Coleman - The "Tame" Mathematician.- Reduced Density Matrices: 1929-1989.- Some Aspects on the Development of the Theory of Reduced Density Matrices and the Representability Problem.- Representability Conditions.- On the Diagonal N-Representability Problem.- Fermion N-Representability Conditions Generated by a Decomposition of the 1-Particle Identity Operator onto Mutually Orthogonal Projection Operators.- The Unitarily Invariant Decomposition of Hermitian Operators.- Building Up N-Electron States with Symplectic Symmetry.- Time Dependent Antisymmetrized Geminal Power Theory Using a Coherent State Formulation.- Griffiths Inequalities for Fermion Systems.- Entropy of Reduced Density Matrices.- A Lower Bound to the Ground State Energy of a Boson System With Fermion Source.- Reduced Density Operators, Their Related von Neumann Density Operators, Close Cousins of These, and Their Physical Interpretation.- Theory and Practice of the Spin-Adapted Reduced Hamiltonians (SRH).- Variational Principle with Built-In Pure State N-Representability Conditions. The N-Electron Case.- Wigner Distributions as Representations of the Density Matrix.- Inter-Relationships Between Various Representations of One-Matrices and Related Densities: A Road Map and an Example ..- Current Problems in Density Functional Theory.- The Interface Between Reduced Density Matrices and Density Functional Theory.- The Physics Underlying the Langreth-Mehl Scheme for Non-Uniform Systems.- Understanding Energy Differences in Density Functional Theory.- Density Functional Calculations of Molecular Bond Energies.- Non-Local Effects on Atomic and Molecular Correlation Energies Studied with a Gradient-Corrected Density Functional.- An Evaluation of Local Electron Correlation Corrections and Non-Local Exchange Corrections to the Hartree-Fock-Slater Method from Calculations on Bond Energies and Electronic Spectra of Molecular Systems.- Correlation Energy Functionals of One-Matrices and Hartree-Fock Densities.- Some Remarks on Scaling Relations in Density Functional Theory.- Deduction of Semiempirical MO Methods from Density Functional Theory.- Charge and Spin Densities in Molecular Solids: Local Density Functional Calculations Versus Experiment.- A Functional of the Two-Particle Density Matrix for the Approximate Calculation of the Electronic Correlation Energy.- Extracules, Intracules, Correlation Holes, Potentials, Coefficients and All That.- The Exact Schroedinger Equation for the Electron Density.- Adiabatic Separation, Broken Symmetries and Geometry Optimization.- Asymptotic Results for Density Matrices and Electron Density in Atoms and Nearly Spherical Molecules.- An Algorithm for Calculating Isoelectronic Changes in Energies, Densities, and One-Matrices.- Atoms and Ions in the Limit of Large Nuclear Charge.- Improved Thomas-Fermi Theory for Atoms.- A Bond Energy from Quantum Mechanics.- Measured Electron Densities and Band Structure Calculations.- X-ray Orthonormal Orbital Model for Crystallography.

Density functional theory formalism

Abstract: A derivation and formulation of density functional theory, which eliminates the formal and practical inconsistencies and limitations of previous theories and allows its extension to stationary states other than the ground state, is given. The theory presented here can also be stated as a series of three theorems that define a family of its mathematical forms, as far as the physical content of the third theorem can either be implicitly incorporated in the density functional or explicitly in the procedure to find a solution to the equations. Examples of both cases are discussed, including the statement of configuration interaction procedure in density functional form.

Quantum chemistry in phase space: Some current trends

Abstract: Recent developments in the phase space formalisms within density functional theory are discussed. The phase space distribution function corresponding to a ground state electron density, obtained through an entropy maximization procedure, leads to good quality momentum density and first order reduced density matrix. Calculations of Compton profiles and exchange energies with different kinetic energy functionals show interesting results.

Density functional theory and electronic structure

Abstract: We have tried to present a brief account of the activities in the realm of the DFT.Study of the band structure has aimed at the understanding of the single particle behaviour of a many body system. All the first principle self-consistent band structure methods are based on the foundations of the DFT.Therefore it is important to understand the physical meaning of the DFT bands via the Janak's theorem. In other words the band structure is an important practical aspect of the DFT.We have mentioned some of the successes and failures of it.

Current Problems in Density Functional Theory

Abstract: I was pleased to be given an opportunity to talk about density functional theory, especially on this occasion honouring John Coleman. This symposium is a tribute to his influential role in the development of the mathematical theory of density matrices, a subject to which he has made many contributions and which remains a fruitful line of inquiry in mathematics, physics and chemistry. There are obvious philosophical and formal links between the subjects of density matrices and density functionals and it is therefore appropriate that a symposium be held to explore and hopefully elucidate these relationships.