Failure of the local exchange approximation in the evaluation of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">H</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>ground state

Shore, Herbert B.; Rose, James H.; Zaremba, E.

doi:10.1103/physrevb.15.2858

Cited by 131 publications

(50 citation statements)

References 8 publications

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“…Despite the formal difficulties associated with direct calculations on the anion, the results for all of the atoms in Table 1 are in very good agreement with the experimental values, with a mean absolute error of just 0.18 eV. The accuracy of such estimates using conventional density-functional approximations and basis sets has been discussed widely in the literature 1,[3][4][5][6]8 and is well understood. In addition to the mean and mean absolute errors d and |d|, the linear regression parameters for a correlation plot between the calculated and experimental values, m, c and r 2 are also presented.…”

Section: Resultssupporting

confidence: 65%

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Atomic electron affinities and the role of symmetry between electron addition and subtraction in a corrected Koopmans approach

Teale

Proft

Geerlings

et al. 2014

Phys. Chem. Chem. Phys.

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The essential aspects of zero-temperature grand-canonical ensemble density-functional theory are reviewed in the context of spin-density-functional theory and are used to highlight the assumption of symmetry between electron addition and subtraction that underlies the corrected Koopmans approach of Tozer and De Proft (TDP) for computing electron affinities. The issue of symmetry is then investigated in a systematic study of atomic electron affinities, comparing TDP affinities with those from a conventional Koopmans evaluation and electronic energy differences. Although it cannot compete with affinities determined from energy differences, the TDP expression yields results that are a significant improvement over those from the conventional Koopmans expression. Key insight into the results from both expressions is provided by an analysis of plots of the electronic energy as a function of the number of electrons, which highlight the extent of symmetry between addition and subtraction. The accuracy of the TDP affinities is closely related to the nature of the orbitals involved in the electron addition and subtraction, being particularly poor in cases where there is a change in principal quantum number, but relatively accurate within a single manifold of orbitals. The analysis is then extended to a consideration of the ground state Mulliken electronegativity and chemical hardness. The findings further emphasize the key role of symmetry in determining the quality of the results.

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Section: Resultssupporting

confidence: 65%

“…The calculation of electron affinities remains a challenging and controversial issue for density-functional calculations [1][2][3][4][5][6][7][8][9] . In particular, local and semi-local approximate exchangecorrelation functionals typically provide a poor description of anionic species due to large self-interaction errors (SIEs).…”

Section: Introductionmentioning

confidence: 99%

Atomic electron affinities and the role of symmetry between electron addition and subtraction in a corrected Koopmans approach

Teale

Proft

Geerlings

et al. 2014

Phys. Chem. Chem. Phys.

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“…This anion has two electrons, just like He, but it is long known [SRZ77] that a standard DFT calculation, in the infinite basis-set limit, cannot bind two electrons. In fact, a fraction of an electron is lost to the continuum.…”

Section: Ks-dftmentioning

confidence: 99%

The Importance of Being Inconsistent

Wasserman

Nafziger

Jiang

et al. 2017

Annu. Rev. Phys. Chem.

114

156

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We review the role of self-consistency in density functional theory. We apply a recent analysis to both Kohn-Sham and orbital-free DFT, as well as to Partition-DFT, which generalizes all aspects of standard DFT. In each case, the analysis distinguishes between errors in approximate functionals versus errors in the self-consistent density. This yields insights into the origins of many errors in DFT calculations, especially those often attributed to self-interaction or delocalization error. In many classes of problems, errors can be substantially reduced by using 'better' densities. We review the history of these approaches, many of their applications, and give simple pedagogical examples.

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“…In such an extreme simplification, one expresses them as the one-particle fraction of the total spin-density n i (r) = n σi (r)/N σi where σ i is the spin of state i and N σi the number of particles with spin σ i . In such a scheme, the standard PZSIC functional is represented by the ADSIC functional : (9) where n = n ↑ + n ↓ . This is a spin-density functional and can be treated in the same manner as any LDA or GGA scheme.…”

Section: B Average Density Sicmentioning

confidence: 99%

“…Locality of the energy functional leads to a wrong asymptotic KS field. This is still a great hindrance in many applications, for instance a possibly large underestimation of IP and the absence of Rydberg or excitonic series in the static KS spectrum [9,10], the polarizability in chain molecules [11,12] or the spectral and fundamental gap in solids [13,14]. Another challenging application is the description of molecules or clusters deposited on surfaces [15,16].…”

Section: Introductionmentioning

confidence: 99%

Koopmans’ condition in self-interaction-corrected density-functional theory

et al. 2013

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We investigate from a practitioner's point of view the computation of the ionization potential (IP) within density functional theory (DFT). DFT with (semi-)local energy-density functionals is plagued by a self-interaction error which hampers the computation of IP from the single-particle energy of the highest occupied molecular orbital (HOMO). The problem may be cured by a self interaction correction (SIC) for which there exist various approximate treatments. We compare the performance of the SIC proposed by Perdew and Zunger with the very simple average-density SIC (ADSIC) for a large variety of atoms and molecules up to larger systems as carbon rings and chains. Both approaches to SIC provide a large improvement to the quality of the IP if calculated from the HOMO level. The surprising result is that the simple ADSIC performs even better than the original Perdew-Zunger SIC (PZSIC) in the majority of the studied cases.

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Failure of the local exchange approximation in the evaluation of theH−ground state

Cited by 131 publications

References 8 publications

Atomic electron affinities and the role of symmetry between electron addition and subtraction in a corrected Koopmans approach

Atomic electron affinities and the role of symmetry between electron addition and subtraction in a corrected Koopmans approach

The Importance of Being Inconsistent

Koopmans’ condition in self-interaction-corrected density-functional theory

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