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On the gradient expansion of the exchange energy within linear-response theory and beyond

Svendsen, Per-Sverre and von Barth, Ulf LU (1995) In International Journal of Quantum Chemistry 56(4). p.351-361
Abstract
In the present work, we reexamined the gradient expansion of the exchange energy of an electron gas with a slowly varying charge density. We stay within the exchange-only approximation of Sharp, Horton, Talman, and Shadwick but go to second order in the deviation from the homogeneous limit. The coefficient of the lowest-order gradient correction is obtained analytically both for a bare and a screened Coulomb interaction-the former yielding the value previously obtained by Kleinman numerically and by Engel and Vosko analytically. A screened Coulomb interaction gives Sham's coefficient in the limit of infinite screening length. The cause of the difference between the coefficients of Kleinman and Sham is clearly exhibited. The coefficients of... (More)
In the present work, we reexamined the gradient expansion of the exchange energy of an electron gas with a slowly varying charge density. We stay within the exchange-only approximation of Sharp, Horton, Talman, and Shadwick but go to second order in the deviation from the homogeneous limit. The coefficient of the lowest-order gradient correction is obtained analytically both for a bare and a screened Coulomb interaction-the former yielding the value previously obtained by Kleinman numerically and by Engel and Vosko analytically. A screened Coulomb interaction gives Sham's coefficient in the limit of infinite screening length. The cause of the difference between the coefficients of Kleinman and Sham is clearly exhibited. The coefficients of the two next highest-order gradient corrections, one of which originates in second-order response theory, is shown to diverge as the screening length becomes large. The bare Coulomb interaction gives finite coefficients of which the one originating from linear response is obtained analytically and differs from the presumably correct result obtained by Engel and Vosko. This discrepancy demonstrates the extreme sensitivity of the analytical expressions to different regularization procedures. We suggest that coefficients should rather be chosen according to the performance of the resulting gradient approximations in weakly perturbed electron gases. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
International Journal of Quantum Chemistry
volume
56
issue
4
pages
351 - 361
publisher
John Wiley & Sons
external identifiers
  • scopus:84981578070
ISSN
0020-7608
DOI
10.1002/qua.560560421
language
English
LU publication?
yes
id
57fc84dd-e2da-4c13-92ad-47caf77e4ca4 (old id 31358)
date added to LUP
2007-06-19 14:35:14
date last changed
2017-07-30 03:47:16
@article{57fc84dd-e2da-4c13-92ad-47caf77e4ca4,
  abstract     = {In the present work, we reexamined the gradient expansion of the exchange energy of an electron gas with a slowly varying charge density. We stay within the exchange-only approximation of Sharp, Horton, Talman, and Shadwick but go to second order in the deviation from the homogeneous limit. The coefficient of the lowest-order gradient correction is obtained analytically both for a bare and a screened Coulomb interaction-the former yielding the value previously obtained by Kleinman numerically and by Engel and Vosko analytically. A screened Coulomb interaction gives Sham's coefficient in the limit of infinite screening length. The cause of the difference between the coefficients of Kleinman and Sham is clearly exhibited. The coefficients of the two next highest-order gradient corrections, one of which originates in second-order response theory, is shown to diverge as the screening length becomes large. The bare Coulomb interaction gives finite coefficients of which the one originating from linear response is obtained analytically and differs from the presumably correct result obtained by Engel and Vosko. This discrepancy demonstrates the extreme sensitivity of the analytical expressions to different regularization procedures. We suggest that coefficients should rather be chosen according to the performance of the resulting gradient approximations in weakly perturbed electron gases.},
  author       = {Svendsen, Per-Sverre and von Barth, Ulf},
  issn         = {0020-7608},
  language     = {eng},
  number       = {4},
  pages        = {351--361},
  publisher    = {John Wiley & Sons},
  series       = {International Journal of Quantum Chemistry},
  title        = {On the gradient expansion of the exchange energy within linear-response theory and beyond},
  url          = {http://dx.doi.org/10.1002/qua.560560421},
  volume       = {56},
  year         = {1995},
}