Subsystem functionals and the missing ingredient of confinement physics in density functionals

Feng, Hao; Armiento, Rickard; Mattsson, Ann E.

doi:10.1103/physrevb.82.115103

Cited by 14 publications

(14 citation statements)

References 53 publications

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“…See Ref. 36 for additional properties of the HG. Further details regarding the HG relevant to this work can be found in Appendix C. The limit of slowly varying density is reached for w → 0, which opens the harmonic potential to infinite width, while keeping the chemical potential constant.…”

Section: E Hermite Gasmentioning

confidence: 99%

Quantum oscillations in the kinetic energy density: Gradient corrections from the Airy gas

2014

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We derive a closed form expression for the quantum corrections to the kinetic energy density (KED) in the Thomas-Fermi (TF) limit of a linear potential model system in three dimensions (the Airy gas). The universality of the expression is tested numerically in a number of three dimensional model systems: (i) jellium surfaces, (ii) confinement in a hydrogen-like potential (the Bohr atom), (iii) particles confined by an harmonic potential in one and (iv) all three dimensions, and (v) a system with a cosine potential (the Mathieu gas). Our results confirm that the usual gradient expansion of extended Thomas-Fermi theory (ETF) does not describe the quantum oscillations for systems that incorporate surface regions where the electron density drops off to zero. We find that the correction derived from the Airy gas is universally applicable to relevant spatial regions of systems of type (i), (ii), and (iv), but somewhat surprisingly not (iii). We discuss possible implications of our findings to the development of functionals for the kinetic energy density.

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Section: E Hermite Gasmentioning

confidence: 99%

Quantum oscillations in the kinetic energy density: Gradient corrections from the Airy gas

2014

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“…In a previous work we have therefore more closely investigated the error made by semi-local functionals for a confined electron gas. 18 In the present paper we extend this investigation to suggest a practical way to identify regions in space where a correction for the error due to electron confinement is needed by using the electron localization function (ELF). We also discuss how one can map a point in a real system onto the confined electron gas model, and how, in principle, such a mapping is intended to work for a real physical system (CuO).…”

Section: Introductionmentioning

confidence: 99%

“…A recent work by us 18 shows that all HO models can be classified by an occupation index α, which indicates how many quantum levels in the z dimension electrons can occupy. This index also gives a good quantification for the level of confinement: large values of α suggest a wide opening of the potential and thus a weak influence of confinement, whereas small values of α means that only a few quantum levels in z are occupied, implying a stronger confinement.…”

Section: The Elf As An Index Of Confinement Physicsmentioning

confidence: 99%

“…It has also been shown that while not performing as well as more specialized chemistry functionals, AM05 performs approximately as well as other semi-local functionals on a selection of chemical reaction energies. 15 It has previously been proposed by us [16][17][18] that the construction idea of the Armiento-Mattsson functional can be generalized to an arbitrary number of model systems and, in this way, describes a practical and semi-systematical way towards functionals with higher accuracy, for both solid state systems and systems containing free atoms and molecules. We want to emphasize that our ultimate goal is to construct a semi-local functional that gives high accuracy results both for traditional chemistry systems like individual atoms and molecules and traditional physics systems such as solids and liquids.…”

Section: Introductionmentioning

confidence: 99%

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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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“…In the QNA scheme the GGA-level problem is circumvented by utilizing the idea of subsystem functionals [ [45][46][47][48]. For each component of the alloy an elementspecific, atom-centered subsystem XC functional is developed and then the total XC functional can be expressed as a superposition…”

Section: Exact Muffin-tin Orbitals Calculationsmentioning

confidence: 99%

Gradient-level and nonlocal density functional descriptions of Cu-Au intermetallic compounds

et al. 2018

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Abstract. We use three gradient level and two nonlocal density functional approximations to study the thermodynamic properties of Cu-Au compounds. It is found that a well-designed gradient level approximation (quasi non-uniform approximation, QNA) reproduces the experimental equilibrium volumes and the formation energies of L12 and L10 phases. On the other hand, QNA predicts a non-existent β2 phase, which can be remedied only when employing the nonlocal hybrid-level Heyd-Scuseria-Ernzerhof (HSE06) or Perdew-Burke-Ernzerhof (PBE0) approximations. Gradient-level approximations lead to similar electronic structures for the Cu-Au compounds whereas hybrids shift the d-band towards negative energies and account for the complex d-d hybridization more accurately.

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Subsystem functionals and the missing ingredient of confinement physics in density functionals

Cited by 14 publications

References 53 publications

Quantum oscillations in the kinetic energy density: Gradient corrections from the Airy gas

Quantum oscillations in the kinetic energy density: Gradient corrections from the Airy gas

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

Gradient-level and nonlocal density functional descriptions of Cu-Au intermetallic compounds

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