5,472 research outputs found
Treatments of the exchange energy in density-functional theory
Following a recent work [Gal, Phys. Rev. A 64, 062503 (2001)], a simple
derivation of the density-functional correction of the Hartree-Fock equations,
the Hartree-Fock-Kohn-Sham equations, is presented, completing an integrated
view of quantum mechanical theories, in which the Kohn-Sham equations, the
Hartree-Fock-Kohn-Sham equations and the ground-state Schrodinger equation
formally stem from a common ground: density-functional theory, through its
Euler equation for the ground-state density. Along similar lines, the Kohn-Sham
formulation of the Hartree-Fock approach is also considered. Further, it is
pointed out that the exchange energy of density-functional theory built from
the Kohn-Sham orbitals can be given by degree-two homogeneous N-particle
density functionals (N=1,2,...), forming a sequence of degree-two homogeneous
exchange-energy density functionals, the first element of which is minus the
classical Coulomb-repulsion energy functional.Comment: 19 pages; original manuscript from 2001 (v1) revised for publication,
with presentation substantially improved, some errors corrected, plus an
additional summarizing figure (Appendix B) include
Preparation of monotectic alloys having a controlled microstructure by directional solidification under dopant-induced interface breakdown
Monotectic alloys having aligned spherical particles of rods of the minor component dispersed in a matrix of the major component are prepared by forming a melt containing predetermined amounts of the major and minor components of a chosen monotectic system, providing in the melt a dopant capable of breaking down the liquid solid interface for the chosen alloy, and directionally solidfying the melt at a selected temperature gradient and a selected rate of movement of the liquid-solid interface (growth rate). Shaping of the minor component into spheres or rods and the spacing between them are controlled by the amount of dopant and the temperature gradient and growth rate values. Specific alloy systems include Al Bi, Al Pb and Zn Bi, using a transition element such as iron
Fractional spins and static correlation error in density functional theory
Electronic states with fractional spins arise in systems with large static
correlation (strongly correlated systems). Such fractional-spin states are
shown to be ensembles of degenerate ground states with normal spins. It is
proven here that the energy of the exact functional for fractional-spin states
is a constant, equal to the energy of the comprising degenerate pure spin
states. Dramatic deviations from this exact constancy condition exist with all
approximate functionals, leading to large static correlation errors for
strongly correlated systems, such as chemical bond dissociation and band
structure of Mott insulators. This is demonstrated with numerical calculations
for several molecular systems. Approximating the constancy behavior for
fractional spins should be a major aim in functional constructions and should
open the frontier for DFT to describe strongly correlated systems. The key
results are also shown to apply in reduced density-matrix functional theory.Comment: 6 pages, 4 figure
Kohn-Sham Exchange Potential for a Metallic Surface
The behavior of the surface barrier that forms at the metal-vacuum interface
is important for several fields of surface science. Within the Density
Functional Theory framework, this surface barrier has two non-trivial
components: exchange and correlation. Exact results are provided for the
exchange component, for a jellium metal-vacuum interface, in a slab geometry.
The Kohn-Sham exact-exchange potential has been generated by using
the Optimized Effective Potential method, through an accurate numerical
solution, imposing the correct boundary condition. It has been proved
analytically, and confirmed numerically, that ; this conclusion is not affected by the inclusion of correlation
effects. Also, the exact-exchange potential develops a shoulder-like structure
close to the interface, on the vacuum side. The issue of the classical image
potential is discussed.Comment: Phys. Rev. Lett. (to appear
Fractional charge perspective on the band-gap in density-functional theory
The calculation of the band-gap by density-functional theory (DFT) methods is
examined by considering the behavior of the energy as a function of number of
electrons. It is found that the incorrect band-gap prediction with most
approximate functionals originates mainly from errors in describing systems
with fractional charges. Formulas for the energy derivatives with respect to
number of electrons are derived which clarify the role of optimized effective
potentials in prediction of the band-gap. Calculations with a recent functional
that has much improved behavior for fractional charges give a good prediction
of the energy gap and also for finite systems.
Our results indicate it is possible, within DFT, to have a functional whose
eigenvalues or derivatives accurately predict the band-gap
Exchange parameters from approximate self-interaction correction scheme
The approximate atomic self-interaction corrections (ASIC) method to density
functional theory is put to the test by calculating the exchange interaction
for a number of prototypical materials, critical to local exchange and
correlation functionals. ASIC total energy calculations are mapped onto an
Heisenberg pair-wise interaction and the exchange constants J are compared to
those obtained with other methods. In general the ASIC scheme drastically
improves the bandstructure, which for almost all the cases investigated
resemble closely available photo-emission data. In contrast the results for the
exchange parameters are less satisfactory. Although ASIC performs reasonably
well for systems where the magnetism originates from half-filled bands, it
suffers from similar problems than those of LDA for other situations. In
particular the exchange constants are still overestimated. This reflects a
subtle interplay between exchange and correlation energy, not captured by the
ASIC.Comment: 10 page
Orbital-Free Density Functional Theory: Kinetic Potentials and Ab-Initio Local Pseudopotentials
In the density functional (DF) theory of Kohn and Sham, the kinetic energy of
the ground state of a system of noninteracting electrons in a general external
field is calculated using a set of orbitals. Orbital free methods attempt to
calculate this directly from the electron density by approximating the
universal but unknown kinetic energy density functional. However simple local
approximations are inaccurate and it has proved very difficult to devise
generally accurate nonlocal approximations. We focus instead on the kinetic
potential, the functional derivative of the kinetic energy DF, which appears in
the Euler equation for the electron density. We argue that the kinetic
potential is more local and more amenable to simple physically motivated
approximations in many relevant cases, and describe two pathways by which the
value of the kinetic energy can be efficiently calculated. We propose two
nonlocal orbital free kinetic potentials that reduce to known exact forms for
both slowly varying and rapidly varying perturbations and also reproduce exact
results for the linear response of the density of the homogeneous system to
small perturbations. A simple and systematic approach for generating accurate
and weak ab-initio local pseudopotentials which produce a smooth slowly varying
valence component of the electron density is proposed for use in orbital free
DF calculations of molecules and solids. The use of these local
pseudopotentials further minimizes the possible errors from the kinetic
potentials. Our theory yields results for the total energies and ionization
energies of atoms, and for the shell structure in the atomic radial density
profiles that are in very good agreement with calculations using the full
Kohn-Sham theory.Comment: To be published in Phys. Rev.
Determination of the gaseous hydrogen ductile-brittle transition in copper-nickel alloys
A series of copper-nickel alloys were fabricated, notched tensile specimens machined for each alloy, and the specimens tested in 34.5 MPa hydrogen and in air. A notched tensile ratio was determined for each alloy and the hydrogen environment embrittlement (HEE) determined for the alloys of 47.7 weight percent nickel to 73.5 weight percent nickel. Stacking fault probability and stacking fault energies were determined for each alloy using the x ray diffraction line shift and line profiles technique. Hydrogen environment embrittlement was determined to be influenced by stacking fault energies; however, the correlation is believed to be indirect and only partially responsible for the HEE behavior of these alloys
Novel properties of the Kohn-Sham exchange potential for open systems: application to the two-dimensional electron gas
The properties of the Kohn-Sham (KS) exchange potential for open systems in
thermodynamical equilibrium, where the number of particles is non-conserved,
are analyzed with the Optimized Effective Potential (OEP) method of Density
Functional Theory (DFT) at zero temperature. The quasi two-dimensional electron
gas (2DEG) is used as an illustrative example. The main findings are that the
KS exchange potential builds a significant barrier-like structure under slight
population of the second subband, and that both the asymptotic value of the KS
exchange potential and the inter-subband energy jump discontinuously at the
one-subband (1S) -> two-subband (2S) transition. The results obtained in this
system offer new insights on open problems of semiconductors, such as the
band-gap underestimation and the band-gap renormalization by photo-excited
carriers.Comment: 7 pages, 3 figures, uses epl.cls(included), accepted for publication
in Europhysics Letter
Closed-form expressions for correlated density matrices: application to dispersive interactions and example of (He)2
Empirically correlated density matrices of N-electron systems are
investigated. Exact closed-form expressions are derived for the one- and
two-electron reduced density matrices from a general pairwise correlated wave
function. Approximate expressions are proposed which reflect dispersive
interactions between closed-shell centro-symmetric subsystems. Said expressions
clearly illustrate the consequences of second-order correlation effects on the
reduced density matrices. Application is made to a simple example: the (He)2
system. Reduced density matrices are explicitly calculated, correct to second
order in correlation, and compared with approximations of independent electrons
and independent electron pairs. The models proposed allow for variational
calculations of interaction energies and equilibrium distance as well as a
clear interpretation of dispersive effects on electron distributions. Both
exchange and second order correlation effects are shown to play a critical role
on the quality of the results.Comment: 22 page
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