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Title: Construction of exchange-correlation functionals through interpolation between the non-interacting and the strong-correlation limit

Abstract

Drawing on the adiabatic connection of density functional theory, exchange-correlation functionals of Kohn-Sham density functional theory are constructed which interpolate between the extreme limits of the electron-electron interaction strength. The first limit is the non-interacting one, where there is only exchange. The second limit is the strong correlated one, characterized as the minimum of the electron-electron repulsion energy. The exchange-correlation energy in the strong-correlation limit is approximated through a model for the exchange-correlation hole that is referred to as nonlocal-radius model [L. O. Wagner and P. Gori-Giorgi, Phys. Rev. A 90, 052512 (2014)]. Using the non-interacting and strong-correlated extremes, various interpolation schemes are presented that yield new approximations to the adiabatic connection and thus to the exchange-correlation energy. Some of them rely on empiricism while others do not. Several of the proposed approximations yield the exact exchange-correlation energy for one-electron systems where local and semi-local approximations often fail badly. Other proposed approximations generalize existing global hybrids by using a fraction of the exchange-correlation energy in the strong-correlation limit to replace an equal fraction of the semi-local approximation to the exchange-correlation energy in the strong-correlation limit. The performance of the proposed approximations is evaluated for molecular atomization energies, total atomic energies,more » and ionization potentials.« less

Authors:
;  [1];  [2]
  1. Département de Chimie, Université de Montréal, C.P. 6128, Succursale A, Montréal, Québec H3C 3J7 (Canada)
  2. Department of Chemistry, Technische Universität Berlin, Strasse des 17 Juni, Berlin (Germany)
Publication Date:
OSTI Identifier:
22489627
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Chemical Physics; Journal Volume: 143; Journal Issue: 12; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; 97 MATHEMATICAL METHODS AND COMPUTING; APPROXIMATIONS; ATOMIZATION; DENSITY FUNCTIONAL METHOD; ELECTRON CORRELATION; ELECTRON-ELECTRON COLLISIONS; ELECTRON-ELECTRON INTERACTIONS; ELECTRONS; HYBRIDIZATION; INTERPOLATION; NUCLEAR ENERGY

Citation Formats

Zhou, Yongxi, Ernzerhof, Matthias, E-mail: Matthias.Ernzerhof@UMontreal.ca, and Bahmann, Hilke. Construction of exchange-correlation functionals through interpolation between the non-interacting and the strong-correlation limit. United States: N. p., 2015. Web. doi:10.1063/1.4931160.
Zhou, Yongxi, Ernzerhof, Matthias, E-mail: Matthias.Ernzerhof@UMontreal.ca, & Bahmann, Hilke. Construction of exchange-correlation functionals through interpolation between the non-interacting and the strong-correlation limit. United States. doi:10.1063/1.4931160.
Zhou, Yongxi, Ernzerhof, Matthias, E-mail: Matthias.Ernzerhof@UMontreal.ca, and Bahmann, Hilke. 2015. "Construction of exchange-correlation functionals through interpolation between the non-interacting and the strong-correlation limit". United States. doi:10.1063/1.4931160.
@article{osti_22489627,
title = {Construction of exchange-correlation functionals through interpolation between the non-interacting and the strong-correlation limit},
author = {Zhou, Yongxi and Ernzerhof, Matthias, E-mail: Matthias.Ernzerhof@UMontreal.ca and Bahmann, Hilke},
abstractNote = {Drawing on the adiabatic connection of density functional theory, exchange-correlation functionals of Kohn-Sham density functional theory are constructed which interpolate between the extreme limits of the electron-electron interaction strength. The first limit is the non-interacting one, where there is only exchange. The second limit is the strong correlated one, characterized as the minimum of the electron-electron repulsion energy. The exchange-correlation energy in the strong-correlation limit is approximated through a model for the exchange-correlation hole that is referred to as nonlocal-radius model [L. O. Wagner and P. Gori-Giorgi, Phys. Rev. A 90, 052512 (2014)]. Using the non-interacting and strong-correlated extremes, various interpolation schemes are presented that yield new approximations to the adiabatic connection and thus to the exchange-correlation energy. Some of them rely on empiricism while others do not. Several of the proposed approximations yield the exact exchange-correlation energy for one-electron systems where local and semi-local approximations often fail badly. Other proposed approximations generalize existing global hybrids by using a fraction of the exchange-correlation energy in the strong-correlation limit to replace an equal fraction of the semi-local approximation to the exchange-correlation energy in the strong-correlation limit. The performance of the proposed approximations is evaluated for molecular atomization energies, total atomic energies, and ionization potentials.},
doi = {10.1063/1.4931160},
journal = {Journal of Chemical Physics},
number = 12,
volume = 143,
place = {United States},
year = 2015,
month = 9
}
  • The correlation factor model is developed in which the spherically averaged exchange-correlation hole of Kohn-Sham theory is factorized into an exchange hole model and a correlation factor. The exchange hole model reproduces the exact exchange energy per particle. The correlation factor is constructed in such a manner that the exchange-correlation energy correctly reduces to exact exchange in the high density and rapidly varying limits. Four different correlation factor models are presented which satisfy varying sets of physical constraints. Three models are free from empirical adjustments to experimental data, while one correlation factor model draws on one empirical parameter. The correlationmore » factor models are derived in detail and the resulting exchange-correlation holes are analyzed. Furthermore, the exchange-correlation energies obtained from the correlation factor models are employed to calculate total energies, atomization energies, and barrier heights. It is shown that accurate, non-empirical functionals can be constructed building on exact exchange. Avenues for further improvements are outlined as well.« less
  • The phase diagram of a two-dimensional N-site N-electron system (N>>1) with site-diagonal electron-phonon (e-ph) coupling is studied in the context of polaron theory, so as to clarify the competition between the superconducting (SC) state and the charge-density wave (CDW) state. The Fermi surface of noninteracting electrons is assumed to be a complete circle with no nesting-type instability in the case of weak e-ph coupling, so as to focus on such a strong coupling that even the standard ''strong-coupling theory'' for superconductivity breaks down. Phonon clouds moving with electrons as well as a frozen phonon are taken into account by amore » variational method, combined with a mean-field theory. It covers the whole region of three basic parameters characterizing the system: the intersite transfer energy of electron T, the e-ph coupling energy S, and the phonon energy ..omega... The resultant phase diagram is given in a triangular coordinate space spanned by T, S, and ..omega... In the adiabatic region ..omega..<<(T,S) near the T-S line of the triangle, each electron becomes a large polaron with a thin phonon cloud, and the system changes discontinuously from the SC state to the CDW state with a frozen phonon as S/T increases. In the inverse-adiabatic limit ..omega..>>(T,S) near the ..omega.. vertex of the triangle, on the other hand, each electron becomes a small polaron, and the SC state is always more stable than the CDW state, because the retardation effect is absent.« less
  • No abstract prepared.
  • Anions and radicals are important for many applications including environmental chemistry, semiconductors, and charge transfer, but are poorly described by the available approximate energy density functionals. Here we test an approximate exchange-correlation functional based on the exact strong-coupling limit of the Hohenberg-Kohn functional on the prototypical case of the He isoelectronic series with varying nuclear charge Z < 2, which includes weakly bound negative ions and a quantum phase transition at a critical value of Z, representing a big challenge for density functional theory. We use accurate wavefunction calculations to validate our results, comparing energies and Kohn-Sham potentials, thus alsomore » providing useful reference data close to and at the quantum phase transition. We show that our functional is able to bind H{sup −} and to capture in general the physics of loosely bound anions, with a tendency to strongly overbind that can be proven mathematically. We also include corrections based on the uniform electron gas which improve the results.« less
  • A strong correlation is observed between the formation of electromagnetic solitons, generated during the interaction of a short intense laser pulse (30 fs, {approx}10{sup 18} W/cm{sup 2}) with a rarefied (<0.1n{sub c}) plasma, and pulse self-focusing. Pulse defocusing, which occurs after soliton generation, results in laser-pulse energy depletion. The role of stimulated Raman scattering in soliton generation is analyzed from 2D particle-in-cell simulations. An observed relationship between initial plasma density and soliton generation is presented that might have relevance to wake-field accelerators.