Showing papers on "Orbital-free density functional theory published in 1986"

On the large‐gradient behavior of the density functional exchange energy

Abstract: A coordinate‐space model of the exchange hole density, previously introduced by the author, is extrapolated to the case of very strongly inhomogeneous systems (ie, large density gradients) As a result, we propose a new gradient‐corrected exchange energy functional for application to atomic and molecular problems The model provides theoretical estimates of the parameters in the functional, and these compare well with empirical values deduced from a least squares fit to exact atomic data

Nonlocal density functionals: Comparison with exact results for finite systems.

Abstract: The performance of approximations to the Hohenberg-Kohn-Sham density functionals is tested by comparing with essentially exact results for light atoms (the He isoelectronic series, Be, and Ne). The approximation schemes considered here are the effective gradient schemes due to Langreth and Mehl (LM), and the ``modified weighted-density'' (MWD) approximation due to Gunnarsson and Jones. Compared to the local density approximation the LM schemes give markedly better exchange-correlation energies and a certain improvement in the density profiles, effective potentials, and orbital eigenvalues. The MWD scheme gives good improvements of the exchange-correlation energies but improves the densities, potentials, and eigenvalues only for the He isoelectronic series. The sensitivity of the MWD scheme with respect to the model pair correlation used, as well as some additional approximations used in practical applications of the MWD scheme, are also analyzed.

Density functional theory of freezing with reference liquid

Abstract: The density functional theory of freezing is reformulated by introducing a reference liquid to describe the thermodynamic properties of the crystalline phase. The density of this liquid, which is a free parameter in the theory, is chosen so that the grand potential of the solid is stationary with respect to this parameter. The introduction of a reference liquid is shown to be equivalent to partial summation of higher-order terms of the perturbation series. The theory is applied to the hard sphere system. The calculated melting parameters as well as the properties of the high-density solid are in very good agreement with Monte Carlo results.

General functional relation between nucleon momentum and density distributions in nuclei

Abstract: It is shown on the basis of the Hohenberg-Kohn theorem that the nucleon momentum distribution is an unique functional of the local density distribution. A theoretical scheme in which density and momentum distributions enter equivalently as fundamental variables of the theory is suggested. The form of the momentum distribution proposed in the coherent density fluctuation model as a functional of the local density and its relation with the suggested theoretical scheme are discussed.

Analysis of the kinetic energy functional in density functional theory

Abstract: The density matrix that leads to a minimum kinetic energy for a given density is considered as a convex superposition of pure states. It is shown that the conditions of stationarity of the kinetic energy and collapse to the given density require that each of the pure state wave functions involved be a single determinant in the same eigenspace of a particular, n‐electron Hamiltonian and that all of the orbitals are eigenfunctions of the same effective one‐electron Hamiltonian. The potential function arises originally as a Lagrange multiplier associated with the density constraint. In some cases it can (at least in principle) be determined. The role of electron–electron interactions and possible treatment of excited states are considered.

Interatomic interactions in density functional theory

Abstract: The concept of an atom in a molecule in the context of density functional theory is used to analyze different levels of approximation to the description of interatomic interactions. Such an approach strongly suggests the use of Kohn–Sham atomic densities as an alternative to Hartree–Fock atomic densities in the electron gas model of Gordon and Kim. The results for rare gases and ionic crystals show that both densities lead to similar results.

Asymmetric rare gas pair potentials from energy density functionals

Abstract: The Thomas–Fermi density functional theory is applied to calculate repulsive interaction potentials for heteronuclear pairs of rare gas atoms. Our results are compared with other theoretical values as well as with available experimental data.

Non-local effects in the density functional treatment of the Wigner crystal

Abstract: The authors present a study of the effects of the non-local dependence of the exchange and correlation energy in the Wigner crystallisation of an electron system. Calculations are made in the density functional formalism, using the functional models recently developed by themselves. The non-local treatment gives higher values of rs for the transition than does the LDA, improving the comparison with computer simulations. Moreover, the unphysical shapes of the density distribution given by the LDA are completely corrected by their non-local model.

Local Approximations in the Applications of Density Functional Theory

Abstract: We present two examples of the use of local approximations in density functionals (DF) theory: 1) the estimation of the ionization potentials and spectroscopic terms for atoms and 2) the calculation of spin susceptibility for atoms in metals, and use them to review some current trends in the applications of DF. In the first case we stress that symmetry and statistics should be built into the basic formulation of the computational schemes in order to obtain realistic results. In the second example we show that DF allows the treatment of small regions of a material as a system in itself, provided the proper boundary conditions are considered for the density function and for the auxiliary Kohn-Sham wave functions. Some numerical results are given for several materials.

Interpretation of core-excitation (1s-π*) processes

Abstract: It follows from recent deductions of the HAM semiempirical MO method from density functional theory and Hartree–Fock, that HAM can be used to calculate electron affinities and core‐excitation energies. As an example trans‐butadiene is studied. Reasonable agreement with measurements is obtained.