Locality of correlation in density functional theory

Burke, Kieron; Cancio, Antonio C.; Gould, Tim; Pittalis, Stefano

doi:10.1063/1.4959126

Cited by 51 publications

(72 citation statements)

References 92 publications

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“…other properties (e.g, ) of both closed-shell and open-subshell cases. This approach has previously been shown to reproduce well the properties of atoms 14,29 . The code is available on request.…”

Section: Model For the Factor In Eq (6); Ionization Potentials Omentioning

confidence: 83%

“…A simple model that accommodates these various physical conditions is Our calculations are carried out in the atomic code pyAtom, which is a python/scipy/numpy implementation of DFT in spherical geometries. We construct the Kohn-Sham orbitals and energies of the atoms and atomic ions using a spherically-symmetric Kohn-Sham potential produced by ensemble averaging 14,28 , that reproduces by construction correct density variables (e.g., ) and…”

Section: Model For the Factor In Eq (6); Ionization Potentials Omentioning

confidence: 99%

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Simple self-interaction correction to random-phase-approximation-like correlation energies

2019

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The random phase approximation (RPA) is exact for the exchange energy of a many-electron ground state, but RPA makes the correlation energy too negative by about 0.5 eV/electron. That large short-range error, which tends to cancel out of iso-electronic energy differences, is largely corrected by an exchange-correlation kernel, or (as in RPA+) by an additive local or semilocal correction. RPA+ is by construction exact for the homogeneous electron gas, and it is also accurate for the jellium surface. RPA+ often gives realistic total energies for atoms or solids in which spinpolarization corrections are absent or small. RPA and RPA+ also yield realistic singlet binding energy curves for H2 and N2, and thus RPA+ yields correct total energies even for spin-unpolarized atoms with fractional spins and strong correlation, as in stretched H2 or N2. However, RPA and RPA+ can be very wrong for spin-polarized one-electron systems (especially for stretched H2 + ), and also for the spin-polarization energies of atoms. The spin-polarization energy is often a small part of the total energy of an atom, but important for ionization energies, electron affinities, and the atomization energies of molecules. Here we propose a computationally efficient generalized RPA+ (gRPA+) that changes RPA+ only for spin-polarized systems by making gRPA+ exact for all oneelectron densities, in the same simple semilocal way that the correlation energy densities of many meta-generalized gradent approximations are made self-correlation free. By construction, gRPA+ does not degrade the exact RPA+ description of jellium. gRPA+ is found to greatly improve upon RPA and RPA+ for the ionization energies and electron affinities of light atoms. Many versions of RPA with an approximate exchange-correlation kernel fail to be exact for all one-electron densities, and they can also be self-interaction corrected in this way.

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Section: Model For the Factor In Eq (6); Ionization Potentials Omentioning

confidence: 83%

Section: Model For the Factor In Eq (6); Ionization Potentials Omentioning

confidence: 99%

Simple self-interaction correction to random-phase-approximation-like correlation energies

2019

Self Cite

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“…The overall trend for the total exchange‐correlation contribution is gathered in Figure , showing that C, O, and S yield minima placed at

λ_{x} \sim 0.6 - 0.7

, while for Si that minimum is found at

λ_{x} = 1

, mostly due to the PT2 correlation contribution being somewhat lower than expected in that case. Actually, if we compare the atomic correlation energies provided by the PBE‐QIDH model, when one feeds the model with the PBE, PBE0, PBEH&H, or HF‐PBE orbitals, with respect to reference values, we found that relative errors are reasonably comprised between

19 and 26

%.…”

Section: Resultsmentioning

confidence: 99%

Determining the role of the underlying orbital‐dependence of PBE0‐DH and PBE‐QIDH double‐hybrid density functionals

et al. 2017

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We study the orbital-dependence of three (parameter-free) double-hybrid density functionals, namely the PBE0-DH, the PBE-QIDH models, and the SOS1-PBE-QIDH spin-opposite-scaled variant of the latter. To do it, we feed all their energy terms with different sets of orbitals obtained previously from self-consistent density functional theory calculations using several exchange-correlation functionals (e.g., PBE, PBE0, PBEH&H), or directly with HF-PBE orbitals, to see their effect on selected datasets for atomization and reaction energies, the latter proned to marked self-interaction errors. We find that the PBE-QIDH double-hybrid model shows a great consistency, as the best results are always obtained for the set of orbitals corresponding to its hybrid scheme, which prompts us to recommend this model without any other fitting or reparameterization. © 2017 Wiley Periodicals, Inc.

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“…Using the self-consistent density for each functional and nearly-exact correlation energies 17 for the rare-gas atoms Ne, Ar, Kr, and Xe, we have computed the relative errors of the various correlation energy functionals in Fig. 1.…”

Section: Correlation Energy At High Density: Analytic Derivationmentioning

confidence: 99%

“…Correlation energy for neutral rare-gas atoms (Ne, Ar, Kr, Xe) with atomic number Z. The numbers are from reference calculation (taken from Ref 17…”

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confidence: 99%

Perdew-Zunger self-interaction correction: How wrong for uniform densities and large-Z atoms?

Santra

Perdew

2019

The Journal of Chemical Physics

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Semi-local density functionals for the exchange-correlation energy of a many-electron system cannot be exact for all one-electron densities. In 1981, Perdew and Zunger (PZ) subtracted the fully-nonlocal self-interaction error orbital-by-orbital, making the corrected functional exact for all collections of separated one-electron densities, and making no correction to the exact functional. Although the PZ self-interaction correction (SIC) eliminates many errors of semi-local functionals, it is often worse for equilibrium properties of sp-bonded molecules and solids. Non-empirical semi-local functionals are usually designed to be exact for electron gases of uniform density, and thus also make 0% error for neutral atoms in the limit of large atomic number Z, but PZ SIC is not so designed. For localized SIC orbitals, we show analytically that the LSDA-SIC correlation energy per electron of the uniform gas in the high-density limit makes an error of -50% in the spinunpolarized case, and -100% in the fully-spin-polarized case. Then we extrapolate from the Ne, Ar, Kr, and Xe atoms to estimate the relative errors of the PZ SIC exchange-correlation energies (with localized SIC orbitals) in the limit of large atomic number: about +5.5% for the local spin density approximation (LSDA-SIC), and about -3.5% for nonempirical generalized gradient (PBE-SIC) and meta-generalized gradient (SCAN-SIC) approximations. The SIC errors are considerably larger than those that have been estimated for LSDA-SIC by approximating the localized SIC orbitals for the uniform gas, and may explain the errors of PZ SIC for equilibrium properties, opening the door to a generalized SIC that is more widely accurate.

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Locality of correlation in density functional theory

Cited by 51 publications

References 92 publications

Simple self-interaction correction to random-phase-approximation-like correlation energies

Simple self-interaction correction to random-phase-approximation-like correlation energies

Determining the role of the underlying orbital‐dependence of PBE0‐DH and PBE‐QIDH double‐hybrid density functionals

Perdew-Zunger self-interaction correction: How wrong for uniform densities and large-Z atoms?

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