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Title: Variational energy functionals of the Green function and of the density tested on molecules

Abstract

We have calculated total energies of atoms and diatomic molecules from the Luttinger-Ward functional, using self-energy approximations to second order as well as the GW approximation. In order to assess the variational quality of this functional, we have also solved the Dyson equation self-consistently. The Luttinger-Ward functional is compared to the variational functional due to Klein, and we demonstrate that the variational property of the latter functional is inferior to that of the Luttinger-Ward functional. We also show how to obtain variational density functionals from the functionals of the Green function. These orbital functional schemes are important for systems where density-functional theory using local functionals of the density necessarily fails. We derive an optimized effective potential (OEP) scheme that is based on the Luttinger-Ward functional and, unlike the conventional OEP schemes, produces energies in good agreement with the values obtained from the self-consistent Green function. Our calculations show that, when applied to molecules, the Luttinger-Ward functional is more sensitive to the quality of the input Green function than when applied to atoms, but the energies are remarkably close to the self-consistent values when the Hartree-Fock Green function is used as input. This Luttinger-Ward functional is therefore a simple and efficientmore » method for studying the merits of various self-energy approximations while avoiding the computationally demanding task of solving the Dyson equation self-consistently.« less

Authors:
; ;  [1];  [2]
  1. Theoretical Chemistry, Materials Science Centre, Rijksuniversiteit Groningen, Nijenborgh 4, 9747 AG Groningen (Netherlands)
  2. (Sweden)
Publication Date:
OSTI Identifier:
20786701
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 73; Journal Issue: 1; Other Information: DOI: 10.1103/PhysRevA.73.012511; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; ATOMS; DENSITY; DENSITY FUNCTIONAL METHOD; ENERGY DENSITY; GREEN FUNCTION; HARTREE-FOCK METHOD; MOLECULES; POTENTIALS; SELF-ENERGY

Citation Formats

Dahlen, Nils Erik, Leeuwen, Robert van, Barth, Ulf von, and Department of Physics, Lund University, Soelvegatan 14 A, SE-22362 Lund. Variational energy functionals of the Green function and of the density tested on molecules. United States: N. p., 2006. Web. doi:10.1103/PHYSREVA.73.0.
Dahlen, Nils Erik, Leeuwen, Robert van, Barth, Ulf von, & Department of Physics, Lund University, Soelvegatan 14 A, SE-22362 Lund. Variational energy functionals of the Green function and of the density tested on molecules. United States. doi:10.1103/PHYSREVA.73.0.
Dahlen, Nils Erik, Leeuwen, Robert van, Barth, Ulf von, and Department of Physics, Lund University, Soelvegatan 14 A, SE-22362 Lund. Sun . "Variational energy functionals of the Green function and of the density tested on molecules". United States. doi:10.1103/PHYSREVA.73.0.
@article{osti_20786701,
title = {Variational energy functionals of the Green function and of the density tested on molecules},
author = {Dahlen, Nils Erik and Leeuwen, Robert van and Barth, Ulf von and Department of Physics, Lund University, Soelvegatan 14 A, SE-22362 Lund},
abstractNote = {We have calculated total energies of atoms and diatomic molecules from the Luttinger-Ward functional, using self-energy approximations to second order as well as the GW approximation. In order to assess the variational quality of this functional, we have also solved the Dyson equation self-consistently. The Luttinger-Ward functional is compared to the variational functional due to Klein, and we demonstrate that the variational property of the latter functional is inferior to that of the Luttinger-Ward functional. We also show how to obtain variational density functionals from the functionals of the Green function. These orbital functional schemes are important for systems where density-functional theory using local functionals of the density necessarily fails. We derive an optimized effective potential (OEP) scheme that is based on the Luttinger-Ward functional and, unlike the conventional OEP schemes, produces energies in good agreement with the values obtained from the self-consistent Green function. Our calculations show that, when applied to molecules, the Luttinger-Ward functional is more sensitive to the quality of the input Green function than when applied to atoms, but the energies are remarkably close to the self-consistent values when the Hartree-Fock Green function is used as input. This Luttinger-Ward functional is therefore a simple and efficient method for studying the merits of various self-energy approximations while avoiding the computationally demanding task of solving the Dyson equation self-consistently.},
doi = {10.1103/PHYSREVA.73.0},
journal = {Physical Review. A},
number = 1,
volume = 73,
place = {United States},
year = {Sun Jan 15 00:00:00 EST 2006},
month = {Sun Jan 15 00:00:00 EST 2006}
}