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Gradient expansion of the exchange energy from second-order density response theory

Svendsen, P.S. and von Barth, Ulf LU (1996) In Physical Review B 54.
Abstract
The basic idea behind the present work is that an atom is not a linear perturbation of the electron gas. We have thus analyzed the exchange energy of the inhomogeneous electron gas to third order in the deviation from a constant density. We give the symmetry properties obeyed by the corresponding second-order response function Lx, and demonstrate how Lx gives rise to gradient corrections to the exchange energy. The expansion, which is taken up to sixth order in the density gradient, also includes the Laplacian of the density. In the case of a statically screened Coulomb interaction, we have calculated the coefficients of second- and fourth-order gradient terms both analytically and numerically. In analogy with the corresponding results... (More)
The basic idea behind the present work is that an atom is not a linear perturbation of the electron gas. We have thus analyzed the exchange energy of the inhomogeneous electron gas to third order in the deviation from a constant density. We give the symmetry properties obeyed by the corresponding second-order response function Lx, and demonstrate how Lx gives rise to gradient corrections to the exchange energy. The expansion, which is taken up to sixth order in the density gradient, also includes the Laplacian of the density. In the case of a statically screened Coulomb interaction, we have calculated the coefficients of second- and fourth-order gradient terms both analytically and numerically. In analogy with the corresponding results from linear-response theory, the fourth-order coefficient is shown to diverge as the screening is made to vanish. For the bare Coulomb interaction we have not succeeded in obtaining analytical results, and, due to numerical problems at small-q vectors, our numerically obtained coefficients have an estimated uncertainty of 20%. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Physical Review B
volume
54
publisher
American Physical Society
external identifiers
  • Scopus:0001645305
ISSN
1550-235X
DOI
10.1103/PhysRevB.54.17402
language
English
LU publication?
yes
id
2dea5d38-ee04-4d87-b145-d354e25e2c23 (old id 952243)
date added to LUP
2008-01-24 16:21:47
date last changed
2016-10-16 04:16:40
@misc{2dea5d38-ee04-4d87-b145-d354e25e2c23,
  abstract     = {The basic idea behind the present work is that an atom is not a linear perturbation of the electron gas. We have thus analyzed the exchange energy of the inhomogeneous electron gas to third order in the deviation from a constant density. We give the symmetry properties obeyed by the corresponding second-order response function Lx, and demonstrate how Lx gives rise to gradient corrections to the exchange energy. The expansion, which is taken up to sixth order in the density gradient, also includes the Laplacian of the density. In the case of a statically screened Coulomb interaction, we have calculated the coefficients of second- and fourth-order gradient terms both analytically and numerically. In analogy with the corresponding results from linear-response theory, the fourth-order coefficient is shown to diverge as the screening is made to vanish. For the bare Coulomb interaction we have not succeeded in obtaining analytical results, and, due to numerical problems at small-q vectors, our numerically obtained coefficients have an estimated uncertainty of 20%.},
  author       = {Svendsen, P.S. and von Barth, Ulf},
  issn         = {1550-235X},
  language     = {eng},
  publisher    = {ARRAY(0xce1bf38)},
  series       = {Physical Review B},
  title        = {Gradient expansion of the exchange energy from second-order density response theory},
  url          = {http://dx.doi.org/10.1103/PhysRevB.54.17402},
  volume       = {54},
  year         = {1996},
}