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

Dahlen, Nils-Erik LU ; van Leeuwen, R and von Barth, Ulf LU (2006) In Physical Review A (Atomic, Molecular and Optical Physics) 73(1).
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... (More)
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. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Physical Review A (Atomic, Molecular and Optical Physics)
volume
73
issue
1
publisher
American Physical Society
external identifiers
  • wos:000235008900085
  • scopus:33144466655
ISSN
1050-2947
DOI
10.1103/PhysRevA.73.012511
language
English
LU publication?
yes
id
9f274c6c-e6e8-4508-a8c4-ca11993b42bd (old id 417674)
date added to LUP
2016-04-01 12:32:13
date last changed
2019-11-13 02:12:27
@article{9f274c6c-e6e8-4508-a8c4-ca11993b42bd,
  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 efficient method for studying the merits of various self-energy approximations while avoiding the computationally demanding task of solving the Dyson equation self-consistently.},
  author       = {Dahlen, Nils-Erik and van Leeuwen, R and von Barth, Ulf},
  issn         = {1050-2947},
  language     = {eng},
  number       = {1},
  publisher    = {American Physical Society},
  series       = {Physical Review A (Atomic, Molecular and Optical Physics)},
  title        = {Variational energy functionals of the Green function and of the density tested on molecules},
  url          = {http://dx.doi.org/10.1103/PhysRevA.73.012511},
  doi          = {10.1103/PhysRevA.73.012511},
  volume       = {73},
  year         = {2006},
}