Gradient expansion of the exchange energy from second-order density response theory
(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:
https://lup.lub.lu.se/record/952243
- author
- Svendsen, P.S. and von Barth, Ulf LU
- organization
- publishing date
- 1996
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Physical Review B
- volume
- 54
- article number
- 17402
- 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
- 2016-04-04 10:49:39
- date last changed
- 2022-02-21 03:44:30
@article{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 = {{American Physical Society}},
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}},
doi = {{10.1103/PhysRevB.54.17402}},
volume = {{54}},
year = {{1996}},
}