Investigation on exchange and correlation holes in a strongly confined electron gas

Clark, S. J.; Rushton, Philip P.

doi:10.1088/0953-8984/16/28/006

Cited by 5 publications

(4 citation statements)

References 37 publications

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“…[47][48][49][50] Nekovee and co-workers 47,48 used the Variational Quantum Monte Carlo (VMC) method to investigate the xc energy density e xc (r) = n(r) xc (r) of strongly inhomogeneous electron gases subject to sinusoidal external potentials. Subtracting the xc energy density obtained by VMC from the one obtained by using LDA, e LDA xc − e VMC xc , negative errors were shown to arise in the center of the quantum wells, which is consistent with our results for HO gas.…”

Section: The Elf As An Index Of Confinement Physicsmentioning

confidence: 99%

Using the electron localization function to correct for confinement physics in semi-local density functional theory

Feng¹,

Armiento²,

Mattsson³

2014

The Journal of Chemical Physics

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We have previously proposed that further improved functionals for density functional theory can be constructed based on the Armiento-Mattsson subsystem functional scheme if, in addition to the uniform electron gas and surface models used in the Armiento-Mattsson 2005 functional, a model for the strongly confined electron gas is also added. However, of central importance for this scheme is an index that identifies regions in space where the correction provided by the confined electron gas should be applied. The electron localization function (ELF) is a well-known indicator of strongly localized electrons. We use a model of a confined electron gas based on the harmonic oscillator to show that regions with high ELF directly coincide with regions where common exchange energy functionals have large errors. This suggests that the harmonic oscillator model together with an index based on the ELF provides the crucial ingredients for future improved semi-local functionals. For a practical illustration of how the proposed scheme is intended to work for a physical system we discuss monoclinic cupric oxide, CuO. A thorough discussion of this system leads us to promote the cell geometry of CuO as a useful benchmark for future semi-local functionals. Very high ELF values are found in a shell around the O ions, and take its maximum value along the Cu-O directions. An estimate of the exchange functional error from the effect of electron confinement in these regions suggests a magnitude and sign that could account for the error in cell geometry. © 2014 AIP Publishing LLC. [http://dx

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Section: The Elf As An Index Of Confinement Physicsmentioning

confidence: 99%

Using the electron localization function to correct for confinement physics in semi-local density functional theory

Feng¹,

Armiento²,

Mattsson³

2014

The Journal of Chemical Physics

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“…In this paper, we will propose a new functional based on the exchange-correlation hole of the uniform electron gas, as parametrized by Gori-Giorgi and Perdew . The idea of directly modeling the exchange-correlation hole is very old and is the defining characteristic of the most venerable of all nonlocal functionals: the weighted density approximation (WDA). − Although the WDA has fallen out of favor, the trickle of papers that persists − suggest it is worth revisiting: the WDA gives more accurate highest-occupied orbital energies and band gaps − than the most of the density functionals that are commonly used in condensed matter physics. More importantly for our purposes, by directly modeling the exchange-correlation hole, we can design functionals with excellent formal and practical properties.…”

Section: Introductionmentioning

confidence: 99%

Symmetric Nonlocal Weighted Density Approximations from the Exchange-Correlation Hole of the Uniform Electron Gas

Cuevas-Saavedra

Chakraborty

Rabi

et al. 2012

J. Chem. Theory Comput.

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Nonlocal exchange-correlation energy functionals are constructed using the accurate model exchange-correlation hole for the uniform electron gas developed by Gori-Giorgi and Perdew. The exchange-correlation hole is constrained to be symmetric and normalized, so the resulting functionals can be viewed as symmetrized versions of the weighted density approximation; we call them two-point weighted density approximations. Even without optimization of parameters or functional forms, the exchange-correlation energies for small molecules are competitive with those of the best generalized gradient approximation functionals. Two-point weighted density approximations seem to be an interesting new direction for functional development. A more general version of the conditions that define the energy for fractional electron number and fractional spin are presented. These "generalized flat-planes" conditions are closely linked to the normalization of the spin-resolved exchange-correlation hole at noninteger electron number. This and many other properties of the exact exchange-correlation functional can be imposed straightforwardly and directly in symmetrized weighted density approximation.

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“…There has been significant interest in the weighted density approximation [61,62], mostly in condensed matter physics [50][51][52][53]57,[63][64][65][66][67], but also for the study of surfaces [58,[68][69][70][71] and metal clusters [49,72].…”

Section: Weighted Density Approximation (Wda)mentioning

confidence: 99%

Symmetric two-point weighted density approximation for exchange energies

2012

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We describe a symmetric, two-point, nonlocal weighted density approximation for the exchange energy of atoms and compare it to conventional density functionals and the conventional weighted density approximation. Even the simplest two-point weighted density approximation gives results comparable to the best generalized gradient approximations. Unlike those functionals, however, the two-point weighted density approximation is fully nonlocal, has no self-interaction error, approximately fulfills the Pauli principle, and preserves the uniform electron gas limit.

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Investigation on exchange and correlation holes in a strongly confined electron gas

Cited by 5 publications

References 37 publications

Using the electron localization function to correct for confinement physics in semi-local density functional theory

Using the electron localization function to correct for confinement physics in semi-local density functional theory

Symmetric Nonlocal Weighted Density Approximations from the Exchange-Correlation Hole of the Uniform Electron Gas

Symmetric two-point weighted density approximation for exchange energies

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