13,163 research outputs found

### Two Avenues to Self-Interaction Correction within Kohn-Sham Theory: Unitary Invariance is the Shortcut

The most widely-used density functionals for the exchange-correlation energy
are inexact for one-electron systems. Their self-interaction errors can be
severe in some applications. The problem is not only to correct the
self-interaction error, but to do so in a way that will not violate
size-consistency and will not go outside the standard Kohn-Sham density
functional theory. The solution via the optimized effective potential (OEP)
method will be discussed, first for the Perdew-Zunger self-interaction
correction (whose performance for molecules is briefly summarized) and then for
the more modern self-interaction corrections based upon unitarily-invariant
indicators of iso-orbital regions. For the latter approaches, the OEP
construction is greatly simplified. The kinetic-energy-based iso-orbital
indicator \tau^W_\sigma(\re)/\tau_\sigma(\re) will be discussed and plotted,
along with an alternative exchange-based indicator

### Localization and delocalization errors in density functional theory and implications for band-gap prediction

The band-gap problem and other systematic failures of approximate functionals
are explained from an analysis of total energy for fractional charges. The
deviation from the correct intrinsic linear behavior in finite systems leads to
delocalization and localization errors in large or bulk systems. Functionals
whose energy is convex for fractional charges such as LDA display an incorrect
apparent linearity in the bulk limit, due to the delocalization error. Concave
functionals also have an incorrect apparent linearity in the bulk calculation,
due to the localization error and imposed symmetry. This resolves an important
paradox and opens the possibility to obtain accurate band-gaps from DFT.Comment: 4 pages 4 figure

### Nonempirical Density Functionals Investigated for Jellium: Spin-Polarized Surfaces, Spherical Clusters, and Bulk Linear Response

Earlier tests show that the Tao-Perdew-Staroverov-Scuseria (TPSS)
nonempirical meta-generalized gradient approximation (meta-GGA) for the
exchange-correlation energy yields more accurate surface energies than the
local spin density (LSD) approximation for spin-unpolarized jellium. In this
study, work functions and surface energies of a jellium metal in the presence
of ``internal'' and external magnetic fields are calculated with LSD,
Perdew-Burke-Ernzerhof (PBE) GGA, and TPSS meta-GGA and its predecessor, the
nearly nonempirical Perdew-Kurth-Zupan-Blaha (PKZB) meta-GGA, using
self-consistent LSD orbitals and densities. The results show that: (i) For
normal bulk densities, the surface correlation energy is the same in TPSS as in
PBE, as it should be since TPSS strives to represent a self-correlation
correction to PBE; (ii) Normal surface density profiles can be scaled uniformly
to the low-density or strong-interaction limit, and TPSS provides an estimate
for that limit that is consistent with (but probably more accurate than) other
estimates; (iii) For both normal and low densities, TPSS provides the same
description of surface magnetism as PBE, suggesting that these approximations
may be generally equivalent for magnetism. The energies of jellium spheres with
up to 106 electrons are calculated using density functionals and compared to
those obtained with Diffusion Quantum Monte Carlo data, including our estimate
for the fixed-node correction. Finally we calculate the linear response of bulk
jellium using these density functionals, and find that not only LSD but also
PBE GGA and TPSS meta-GGA yield a linear-response in good agreement with that
of the Quantum Monte Carlo method, for wavevectors of the perturbing external
potential up to twice the Fermi wavevector.Comment: 14 pages, 9 figure

### Wavevector analysis of the jellium exchange-correlation surface energy in the random-phase approximation: detailed support for nonempirical density functionals

We report the first three-dimensional wavevector analysis of the jellium
exchange-correlation (xc) surface energy in the random-phase approximation
(RPA). The RPA accurately describes long-range xc effects which are challenging
for semi-local approximations, since it includes the universal small-wavevector
behavior derived by Langreth and Perdew. We use these rigorous RPA calculations
for jellium slabs to test RPA versions of nonempirical semi-local
density-functional approximations for the xc energy. The local spin density
approximation (LSDA) displays cancelling errors in the small and intermediate
wavevector regions. The PBE GGA improves the analysis for intermediate
wavevectors, but remains too low for small wavevectors (implying too-low
jellium xc surface energies). The nonempirical meta-generalized gradient
approximation of Tao, Perdew, Staroverov, and Scuseria (TPSS meta-GGA) gives a
realistic wavevector analysis, even for small wavevectors or long-range
effects. We also study the effects of slab thickness and of short-range
corrections to RPA.Comment: 7 pages, 7 figures, to appear in Phys. Rev.

### Climbing the Density Functional Ladder: Non-Empirical Meta-Generalized Gradient Approximation Designed for Molecules and Solids

The electron density, its gradient, and the Kohn-Sham orbital kinetic energy
density are the local ingredients of a meta-generalized gradient approximation
(meta-GGA). We construct a meta-GGA density functional for the
exchange-correlation energy that satisfies exact constraints without empirical
parameters. The exchange and correlation terms respect {\it two} paradigms:
one- or two-electron densities and slowly-varying densities, and so describe
both molecules and solids with high accuracy, as shown by extensive numerical
tests. This functional completes the third rung of ``Jacob's ladder'' of
approximations, above the local spin density and GGA rungs.Comment: 4 pages, 1 figure, 1 table. updated with minor and yet necessary
corrections. New references are adde

### A natural orbital functional for the many-electron problem

The exchange-correlation energy in Kohn-Sham density functional theory is
expressed as a functional of the electronic density and the Kohn-Sham orbitals.
An alternative to Kohn-Sham theory is to express the energy as a functional of
the reduced first-order density matrix or equivalently the natural orbitals. In
the former approach the unknown part of the functional contains both a kinetic
and a potential contribution whereas in the latter approach it contains only a
potential energy and consequently has simpler scaling properties. We present an
approximate, simple and parameter-free functional of the natural orbitals,
based solely on scaling arguments and the near satisfaction of a sum rule. Our
tests on atoms show that it yields on average more accurate energies and charge
densities than the Hartree Fock method, the local density approximation and the
generalized gradient approximations

### Exchange and Correlation in Open Systems of Fluctuating Electron Number

While the exact total energy of a separated open system varies linearly as a
function of average electron number between adjacent integers, the energy
predicted by semi-local density functional approximations curves upward and the
exact-exchange-only or Hartree-Fock energy downward. As a result, semi-local
density functionals fail for separated open systems of fluctuating electron
number, as in stretched molecular ions A$_2^{+}$ and in solid transition metal
oxides. We develop an exact-exchange theory and an exchange-hole sum rule that
explain these failures and we propose a way to correct them via a local hybrid
functional.Comment: 4 pages, 2 figure

### Ab initio pseudopotential study of Fe, Co, and Ni employing the spin-polarized LAPW approach

The ground-state properties of Fe, Co, and Ni are studied with the
linear-augmented-plane-wave (LAPW) method and norm-conserving pseudopotentials.
The calculated lattice constant, bulk modulus, and magnetic moment with both
the local-spin-density approximation (LSDA) and the generalized gradient
approximation (GGA) are in good agreement with those of all-electron
calculations, respectively. The GGA results show a substantial improvement over
the LSDA results, i.e., better agreement with experiment. The accurate
treatment of the nonlinear core-valence exchange and correlation interaction is
found to be essential for the determination of the magnetic properties of 3d
transition metals. The present study demonstrates the successful application of
the LAPW pseudopotential approach to the calculation of ground-state properties
of magnetic 3d transition metals.Comment: RevTeX, 14 pages, 2 figures in uufiles for

### A More Accurate Generalized Gradient Approximation for Solids

We present a new nonempirical density functional generalized gradient
approximation (GGA) that gives significant improvements for lattice constants,
crystal structures, and metal surface energies over the most popular
Perdew-Burke-Ernzerhof (PBE) GGA. The new functional is based on a diffuse
radial cutoff for the exchange-hole in real space, and the analytic gradient
expansion of the exchange energy for small gradients. There are no adjustable
parameters, the constraining conditions of PBE are maintained, and the
functional is easily implemented in existing codes.Comment: 5 pages, corrected the errors of the sublimation energy of Ih ic

### Exact exchange optimized effective potential and self-compression of stabilized jellium clusters

In this work, we have used the exchange-only optimized effective potential in
the self-consistent calculations of the density functional Kohn-Sham equations
for simple metal clusters in stabilized jellium model with self-compression.
The results for the closed-shell clusters of Al, Li, Na, K, and Cs with $N=$2,
8, 18, 20, 34, and 40 show that the clusters are 3% more compressed here than
in the local spin density approximation. On the other hand, in the LSDA,
neglecting the correlation results in a contraction by 1.4%.Comment: 7 pages, RevTex, 5 eps figures, 2 table

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