234 research outputs found
Equivalence of two approaches for the inhomogeneous density in the canonical ensemble
In this article we show that the inhomogeneous density obtained from a
density-functional theory of classical fluids in the canonical ensemble (CE),
recently presented by White et al [Phys. Rev. Lett. 84 (2000) 1220], is
equivalent to first order to the result of the series expansion of the CE
inhomogeneous density introduced by Gonzalez et al [Phys. Rev. Lett. 79 (1997)
2466].Comment: 6 pages, RevTe
Unscreened Coulomb repulsion in the one dimensional electron gas
A tight binding model of electrons interacting via bare Coulomb repulsion is
numerically investigated by use of the Density Matrix Renormalization Group
method which we prove applicable also to very long range potentials. From the
analysis of the elementary excitations, of the spin and charge correlation
functions and of the momentum distribution, a picture consistent with the
formation of a one dimensional "Wigner crystal" emerges, in quantitative
agreement with a previous bosonization study. At finite doping, Umklapp
scattering is shown to be ineffective in the presence of long range forces.Comment: RevTex, 5 pages with 8 eps figures. To be published on Phys. Rev.
Symmetry of the Atomic Electron Density in Hartree, Hartree-Fock, and Density Functional Theory
The density of an atom in a state of well-defined angular momentum has a
specific finite spherical harmonic content, without and with interactions.
Approximate single-particle schemes, such as the Hartree, Hartree-Fock, and
Local Density Approximations, generally violate this feature. We analyze, by
means of perturbation theory, the degree of this violation and show that it is
small. The correct symmetry of the density can be assured by a
constrained-search formulation without significantly altering the calculated
energies. We compare our procedure to the (different) common practice of
spherically averaging the self-consistent potential. Kohn-Sham density
functional theory with the exact exchange-correlation potential has the correct
finite spherical harmonic content in its density; but the corresponding exact
single particle potential and wavefunctions contain an infinite number of
spherical harmonics.Comment: 11 pages, 6 figures. Expanded discussion of spherical harmonic
expansion of Hartree density. Some typos corrected, references adde
Occupation numbers in density-functional calculations
It is the intention of this paper to rigorously clarify the role of the
occupation numbers in the current practical applications of the density
functional formalism. In these calculations one has to decide how to distribute
a given, fixed number of electrons over a set of single-particle orbitals. The
conventional choice is to have orbitals below the Fermi level completely
occupied and the orbitals above the Fermi level empty. Although there is a
certain confusion in literature why this choice is superior to any others, the
general belief is that it can justified by treating the occupation numbers as
variational parameters and then applying Janak's theorem or similar reasoning.
We demonstrate that there is a serious flaw in those arguments,mainly the
kinetic energy and therefore the exchange-correlation potential are not
differentiable with respect to density for arbitrary occupation numbers. It is
rigorously shown that in the present context of the density functional
calculations there is no freedom to vary the occupation numbers. The occupation
numbers cannot be considered as variational parameters.Comment: 10 pages, Revtex, accepted for publication by Phys.Rev.
Effective action and density functional theory
The effective action for the charge density and the photon field is proposed
as a generalization of the density functional. A simple definition is given for
the density functional, as the functional Legendre transform of the generator
functional of connected Green functions for the density and the photon field,
offering systematic approximation schemes. The leading order of the
perturbation expansion reproduces the Hartree-Fock equation. A renormalization
group motivated method is introduced to turn on the Coulomb interaction
gradually and to find corrections to the Hartree-Fock and the Kohn-Sham
schemes.Comment: New references and a numerical algorithm added, to appear in Phys.
Rev. B. 30 pages, no figure
Thermal Density Functional Theory in Context
This chapter introduces thermal density functional theory, starting from the
ground-state theory and assuming a background in quantum mechanics and
statistical mechanics. We review the foundations of density functional theory
(DFT) by illustrating some of its key reformulations. The basics of DFT for
thermal ensembles are explained in this context, as are tools useful for
analysis and development of approximations. We close by discussing some key
ideas relating thermal DFT and the ground state. This review emphasizes thermal
DFT's strengths as a consistent and general framework.Comment: Submitted to Spring Verlag as chapter in "Computational Challenges in
Warm Dense Matter", F. Graziani et al. ed
Computational Physics on Graphics Processing Units
The use of graphics processing units for scientific computations is an
emerging strategy that can significantly speed up various different algorithms.
In this review, we discuss advances made in the field of computational physics,
focusing on classical molecular dynamics, and on quantum simulations for
electronic structure calculations using the density functional theory, wave
function techniques, and quantum field theory.Comment: Proceedings of the 11th International Conference, PARA 2012,
Helsinki, Finland, June 10-13, 201
Ab initio atomistic thermodynamics and statistical mechanics of surface properties and functions
Previous and present "academic" research aiming at atomic scale understanding
is mainly concerned with the study of individual molecular processes possibly
underlying materials science applications. Appealing properties of an
individual process are then frequently discussed in terms of their direct
importance for the envisioned material function, or reciprocally, the function
of materials is somehow believed to be understandable by essentially one
prominent elementary process only. What is often overlooked in this approach is
that in macroscopic systems of technological relevance typically a large number
of distinct atomic scale processes take place. Which of them are decisive for
observable system properties and functions is then not only determined by the
detailed individual properties of each process alone, but in many, if not most
cases also the interplay of all processes, i.e. how they act together, plays a
crucial role. For a "predictive materials science modeling with microscopic
understanding", a description that treats the statistical interplay of a large
number of microscopically well-described elementary processes must therefore be
applied. Modern electronic structure theory methods such as DFT have become a
standard tool for the accurate description of individual molecular processes.
Here, we discuss the present status of emerging methodologies which attempt to
achieve a (hopefully seamless) match of DFT with concepts from statistical
mechanics or thermodynamics, in order to also address the interplay of the
various molecular processes. The new quality of, and the novel insights that
can be gained by, such techniques is illustrated by how they allow the
description of crystal surfaces in contact with realistic gas-phase
environments.Comment: 24 pages including 17 figures, related publications can be found at
http://www.fhi-berlin.mpg.de/th/paper.htm
Chemical Bonding in Solids
This chapter discusses the various classes of hydride compounds, with a special focus on saline and metallic hydrides as well as oxyhydrides. It includes the following topics: thermodynamic stability, crystal chemistry, synthesis, and physical properties. The chapter also highlights recent progress in understanding hydride ion mobility in alkaline earth hydrides. It further deals with hydride compounds and in particular those containing alkali, alkaline earth, and transition and rare earth metals. The saline hydrides, that is, AH and AeH2 (with A=Li, Na, K, Rb, and Cs; Ae=Mg, Ca, Sr, and Ba) are proper ionic materials, in which hydrogen is present as hydride anions, H−. Saline hydrides show many similarities with their halide analogues, especially concerning crystal and electronic structures and, perhaps to a lesser extent, physical attributes such as brittleness, hardness, and optical properties
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