Showing papers on "Orbital-free density functional theory published in 1988"

Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density

Abstract: A correlation-energy formula due to Colle and Salvetti [Theor. Chim. Acta 37, 329 (1975)], in which the correlation energy density is expressed in terms of the electron density and a Laplacian of the second-order Hartree-Fock density matrix, is restated as a formula involving the density and local kinetic-energy density. On insertion of gradient expansions for the local kinetic-energy density, density-functional formulas for the correlation energy and correlation potential are then obtained. Through numerical calculations on a number of atoms, positive ions, and molecules, of both open- and closed-shell type, it is demonstrated that these formulas, like the original Colle-Salvetti formulas, give correlation energies within a few percent.

Density-functional exchange-energy approximation with correct asymptotic behavior.

Abstract: Current gradient-corrected density-functional approximations for the exchange energies of atomic and molecular systems fail to reproduce the correct 1/r asymptotic behavior of the exchange-energy density. Here we report a gradient-corrected exchange-energy functional with the proper asymptotic limit. Our functional, containing only one parameter, fits the exact Hartree-Fock exchange energies of a wide variety of atomic systems with remarkable accuracy, surpassing the performance of previous functionals containing two parameters or more.

A combined density functional and configuration interaction method

Abstract: Correlation energies are divided into two parts. One contribution is given by a configuration interaction calculation in the space of the natural orbitals with occupation numbers larger than an arbitrary threshold u. The remaining part is obtained from a u-dependent functional of the electronic density. Representative examples (for which the existing spin-density functionals fail) are (1) the correlation energies in the He and Be series and (2) the contribution of the correlation energy to the dissociation energy of the first-row dimers. It is shown that even for large values of v the errors remain on the order of 0.01 hartree.

Some tests of an approximate density functional for the ground-state kinetic energy of a fermion system

Abstract: Any proposed approximation to the ground-state kinetic energy of a system of noninteracting fermions in terms of the particle density \ensuremath{\rho}(r) can be used to estimate the potential field v(r) that will give rise to a given \ensuremath{\rho}(r), or the \ensuremath{\rho}(r) that will result from placing a given number of particles in a given v(r). Comparison with exact quantum-mechanical calculations thus gives two possible types of tests for any proposed kinetic-energy functional. This paper reports such tests for a recently proposed nonlocal functional applicable to one-dimensional systems, comparing its predictions for several simple problems not only with the correct answers but also with the predictions of Thomas-Fermi and Thomas-Fermi-Weizs\"acker functionals, to which the new functional proves considerably superior. The comparisons yield useful insights on the virtues and defects of the new functional, and on the directions in which improvements should be sought. Particular attention is devoted to Friedel oscillations and shell structure. It is shown that functionals of the Thomas-Fermi-Weizs\"acker type can never predict multiple maxima in \ensuremath{\rho} if v has only a single minimum and no maxima; the new functional does not have this defect, though it yields density oscillations rather weaker than the exact quantum-mechanical calculations. A natural general inference from the present tests is that any satisfactory kinetic-energy functional must (as ours does) replace the entire Thomas-Fermi term by a nonlocal expression.

Density functionals for the energy of electronic systems: Explicit variational construction.

Abstract: A nonlinear transformation performs the Levy-constrained search formulation of the density functional for the electronic energy through a minimization of the energy with respect to a set of variational coefficients. The construction requires a complete set of arbitrary functions as the auxiliary basis. Truncation of the basis set provides an upper bound to the energy functional. Practical approaches to obtain accurate upper bounds to this functional are discussed, and a density-functional alternative to the standard Hartree-Fock method is described.

Statistical theory of electron densities

Abstract: An optimized Thomas–Fermi theory is proposed which retains the simplicity of the original theory and is a suitable reference theory for Monte Carlo density functional treatments of condensed materials. The key ingredient of the optimized theory is a neighborhood sampled potential which contains effects of the inhomogeneities in the one‐electron potential. In contrast to the traditional Thomas–Fermi approach, the optimized theory predicts a finite electron density in the vicinity of a nucleus. Consideration of the example of an ideal electron gas subject to a central Coulomb field indicates that implementation of the approach is straightforward. The optimized theory is found to fail completely when a classically forbidden region is approached. However, these circumstances are not of primary interest for calculations of interatomic forces. It is shown how the energy functional of the density may be constructed by integration of a generalized Hellmann–Feynman relation. This generalized Hellmann–Feynman relat...

A new approach to second order corrections based on density functional theory

Abstract: An approximate relation between the static-density response function and the fukui function is used to develop a perturbation approach within the framework of density functional theory. It is shown that the approximate relation describes correctly the equivalence between the representation of the energy in terms of the electronic density and the external potential, and the representation in terms of the number of electrons and the external potential. The perturbation scheme is applied to calculate the first and second order corrections to the energy of a two-electron atom. The results show that the present approach incorporates part of the correlation energy.

The formulation and use of density functional theory.

Abstract: Density functional theory, in a form useful for the study of the electronic structure of atoms, molecules and condensed matter, can be systematically derived and formulated avoiding either practical or formal inconsistencies and without the limitations imposed by working at a Hartree-Fock like level. The theory is developed, after considering the properties of the density operators, with particular emphasis in three aspects: a) definitions and existence theorems, b) rules for constructing density functionals and c) methodology. Some examples will be given: illustrating the use of multi-configuration techniques in DFT, as we have in fact generalized the formulation of density functional theory in a form suitable for multiconfiguration calculations and for the calculation of (electric, magnetic and chemical) response functions. The method allows the direct calculation of intermediate and mixed valence states, spectra (and not just the energy eigenvalues and their differences) and, in general, of the elementary excitations of the system.

The Energy Density Functional Theory: Present Status-Reflections

Abstract: In this year all many-body theorists celebrate the 60th anniversary of the energy density functional theory. Sixty years ago, in 1927 Thomas1 and Fermi2 proposed independently the approximate, statistical model for a many-electron atom christened later by their names - the Thomas-Fermi model - and originated the modern rigorous theory.

Thomas–Fermi theory from a perturbative treatment of the hydrogenic limit energy density functional: A possible link to local density functional theory

Abstract: A perturbation expansion which connects the hydrogenic limit energy density functional to the Thomas–Fermi functional is discussed. This perturbation series, where the Coulomb energy density functional is treated as the perturbation to the hydrogenic limit functional, is, in fact, the q = (N/Z) expansion of Thomas–Fermi theory. A truncated form of the first-order correction to the functional provides further insight into the model which treats the ground state energy as a local functional of the electron density.

The kinetic energy density functional for fast-varying densities

Abstract: The expression of the von Weizsacker term consisting of the kinetic energy density of an inhomogeneous fermion gap is derived from a variational standpoint when the density varies rapidly. It may provide insight or severe as a starting point for a Kohn-Sham-type self-consistent calculation in density functional theory.

Toward a simple density functional theory of nonuniform solids

Abstract: With analogy to the “highly accurate” summation of cluster diagrams for hard sphere fluids a la Carnahan-Starling, a simple real space free-energy density functional for arbitrary potential systems is proposed, based on a generalization of the second virial coefficient to inhomogeneous systems, which when applied to ordered and amorphous solid hard-sphere systems yields pressures in remarkable agreement with experiment. Possibilities for corrections and extensions toward a simple density functional theory of nonuniform solids are noted.

Calculation of the Hubbard-Type Many Body Interaction Parameters using Constrained Density Functional Theory

Abstract: The constrained density functional approach is used to calculate the energy surface as a function of local charge fluctuations in La2CuO4. This energy surface is then mapped onto a self consistent mean field solution of the Hubbard model which allows extraction of the Coulomb interaction parameters when combined with oneelectron parameters derived from band structure results. The present calculations indicate that La2CuO4 is intermediate between the extreme spin or charge fluctuation regimes. This severly restricts the range of parameter space for theories of quasiparticles, optical excitations and possible pairing mechanism based on the extended Hubbard model.

The Formulation of Density Functional Theory

Abstract: We have generalized the formulation of density functional theory in a form suitable for multiconfiguration calculations, and for the calculation of electric and magnetic response functions. The method allows the direct calculation of mixed valence states, spectra (and not just the energy eigenvalues and their differences) and in general, of the elementary excitations of the system.