Gradient expansion of the exchange energy from secondorder 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 secondorder 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 fourthorder 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 secondorder 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 fourthorder gradient terms both analytically and numerically. In analogy with the corresponding results from linearresponse theory, the fourthorder 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 smallq 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
 1550235X
 DOI
 10.1103/PhysRevB.54.17402
 language
 English
 LU publication?
 yes
 id
 2dea5d38ee044d87b145d354e25e2c23 (old id 952243)
 date added to LUP
 20160404 10:49:39
 date last changed
 20220221 03:44:30
@article{2dea5d38ee044d87b145d354e25e2c23, 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 secondorder 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 fourthorder gradient terms both analytically and numerically. In analogy with the corresponding results from linearresponse theory, the fourthorder 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 smallq vectors, our numerically obtained coefficients have an estimated uncertainty of 20%.}}, author = {{Svendsen, P.S. and von Barth, Ulf}}, issn = {{1550235X}}, language = {{eng}}, publisher = {{American Physical Society}}, series = {{Physical Review B}}, title = {{Gradient expansion of the exchange energy from secondorder density response theory}}, url = {{http://dx.doi.org/10.1103/PhysRevB.54.17402}}, doi = {{10.1103/PhysRevB.54.17402}}, volume = {{54}}, year = {{1996}}, }