Bridging density-functional and many-body perturbation theory

Orbital-density dependence in electronic-structure functionals

Andrea Ferretti, Ismaila Dabo, Matteo Cococcioni, Nicola Marzari

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

Energy functionals which depend explicitly on orbital densities, rather than on the total charge density, appear when applying self-interaction corrections to density-functional theory; this is, e.g., the case for Perdew-Zunger and Koopmans-compliant functionals. In these formulations the total energy is not invariant under unitary rotations of the orbitals, and local, orbital-dependent potentials emerge. We argue that this is not a shortcoming, and that instead these potentials can provide, in a functional form, a simplified quasiparticle approximation to the spectral potential, i.e., the local, frequency-dependent contraction of the many-body self-energy that is sufficient to describe exactly the spectral function. As such, orbital-density-dependent functionals have the flexibility to accurately describe both total energies and quasiparticle excitations in the electronic-structure problem. In addition, and at variance with the Kohn-Sham case, orbital-dependent potentials do not require nonanalytic derivative discontinuities. We present numerical solutions based on the frequency-dependent Sham-Schlüter equation to support this view, and examine some of the existing functionals in this perspective, highlighting the very close agreement between exact and approximate orbital-dependent potentials.

Original languageEnglish (US)
Article number195134
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume89
Issue number19
DOIs
StatePublished - May 27 2014

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Charge density
functionals
Electronic structure
Density functional theory
perturbation theory
electronic structure
Derivatives
orbitals
energy
contraction
discontinuity
flexibility
density functional theory
formulations
approximation
excitation
interactions

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Electronic, Optical and Magnetic Materials

Cite this

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abstract = "Energy functionals which depend explicitly on orbital densities, rather than on the total charge density, appear when applying self-interaction corrections to density-functional theory; this is, e.g., the case for Perdew-Zunger and Koopmans-compliant functionals. In these formulations the total energy is not invariant under unitary rotations of the orbitals, and local, orbital-dependent potentials emerge. We argue that this is not a shortcoming, and that instead these potentials can provide, in a functional form, a simplified quasiparticle approximation to the spectral potential, i.e., the local, frequency-dependent contraction of the many-body self-energy that is sufficient to describe exactly the spectral function. As such, orbital-density-dependent functionals have the flexibility to accurately describe both total energies and quasiparticle excitations in the electronic-structure problem. In addition, and at variance with the Kohn-Sham case, orbital-dependent potentials do not require nonanalytic derivative discontinuities. We present numerical solutions based on the frequency-dependent Sham-Schl{\"u}ter equation to support this view, and examine some of the existing functionals in this perspective, highlighting the very close agreement between exact and approximate orbital-dependent potentials.",
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Bridging density-functional and many-body perturbation theory : Orbital-density dependence in electronic-structure functionals. / Ferretti, Andrea; Dabo, Ismaila; Cococcioni, Matteo; Marzari, Nicola.

In: Physical Review B - Condensed Matter and Materials Physics, Vol. 89, No. 19, 195134, 27.05.2014.

Research output: Contribution to journalArticle

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T2 - Orbital-density dependence in electronic-structure functionals

AU - Ferretti, Andrea

AU - Dabo, Ismaila

AU - Cococcioni, Matteo

AU - Marzari, Nicola

PY - 2014/5/27

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