Skip to main content
banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
The full text of this article is not currently available.
/content/aip/journal/jcp/141/24/10.1063/1.4904448
1.
1.E. H. Lieb and S. Oxford, “Improved lower bound on the indirect Coulomb energy,” Int. J. Quantum Chem. 19, 427439 (1981).
http://dx.doi.org/10.1002/qua.560190306
2.
2.C. Fiolhais, F. Nogueira, and M. Marques, A Primer in Density Functional Theory (Springer-Verlag, New York, 2003).
3.
3.J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized gradient approximation made simple,” Phys. Rev. Lett. 77, 38653868 (1996);
http://dx.doi.org/10.1103/PhysRevLett.77.3865
3. J. P. Perdew, K. Burke, and M. Ernzerhof, ibid 78 , 1396(E) (1997).
http://dx.doi.org/10.1103/PhysRevLett.78.1396
4.
4.A. D. Becke, “Perspective: Fifty years of density-functional theory in chemical physics,” J. Chem. Phys. 140, 18A30 (2014).
http://dx.doi.org/10.1063/1.4869598
5.
5.M. M. Odashima and K. Capelle, “How tight is the lieb-oxford bound?,” J. Chem. Phys. 127, 054106 (2007).
http://dx.doi.org/10.1063/1.2759202
6.
6.M. Lewin and E. H. Lieb, “Improved lieb-oxford exchange-correlation inequality with gradient correction,” preprint arXiv:1408.3358v3 (2014).
7.
7.G.-L. Chan and N. Handy, “Optimized lieb-oxford bound for the exchange-correlation energy,” Phys. Rev. A 59, 3075 (1999).
http://dx.doi.org/10.1103/PhysRevA.59.3075
8.
8.D. Langreth and J. Perdew, “The exchange-correlation energy of a metallic surface,” Solid State Commun. 17, 1425 (1975).
http://dx.doi.org/10.1016/0038-1098(75)90618-3
9.
9.O. Gunnarsson and B. Lundqvist, “Exchange and correlation in atoms, molecules, and solids by the spin-density-functional formalism,” Phys. Rev. B 13, 4274 (1976).
http://dx.doi.org/10.1103/PhysRevB.13.4274
10.
10.M. Levy and J. Perdew, “Hellmann-feynman, virial, and scaling requisites for the exact universal density functionals. Shape of the correlation potential and diamagnetic susceptibility for atoms,” Phys. Rev. A 32, 2010 (1985).
http://dx.doi.org/10.1103/PhysRevA.32.2010
11.
11.M. Levy, “Density-functional exchange-correlation through coordinate scaling in adiabatic connection and correlation hole,” Phys. Rev. A 43, 4637 (1991).
http://dx.doi.org/10.1103/PhysRevA.43.4637
12.
12.E. Engel and R. M. Dreizler, “From explicit to implicit density functionals,” J. Comput. Chem. 20, 3150 (1999).
http://dx.doi.org/10.1002/(SICI)1096-987X(19990115)20:1%3C31::AID-JCC6%3E3.0.CO;2-P
13.
13.S. P. McCarthy and A. J. Thakkar, “Accurate all-electron correlation energies for the closed-shell atoms from ar to rn and their relationship to the corresponding mp2 correlation energies,” J. Chem. Phys. 134, 044102 (2011).
http://dx.doi.org/10.1063/1.3547262
14.
14.K. Burke, A. Cancio, T. Gould, and S. Pittalis, “Atomic correlation energies and the generalized gradient approximation,” preprint arXiv:1409.4834v1  (2014).
15.
15.E. Lieb and B. Simon, “Thomas-fermi theory revisited,” Phys. Rev. Lett. 31, 681 (1973).
http://dx.doi.org/10.1103/PhysRevLett.31.681
16.
16.D. Lee, L. A. Constantin, J. P. Perdew, and K. Burke, “Condition on the kohn–sham kinetic energy and modern parametrization of the thomas–fermi density,” J. Chem. Phys. 130, 034107 (2009).
http://dx.doi.org/10.1063/1.3059783
17.
17.J. Schwinger, “Thomas-fermi model: The second correction,” Phys. Rev. A 24, 23532361 (1981).
http://dx.doi.org/10.1103/PhysRevA.24.2353
18.
18. .
19.
19.M. Taut, “Two electrons in an external oscillator potential: Particular analytic solutions of a coulomb correlation problem,” Phys. Rev. A 48, 3561 (1993).
http://dx.doi.org/10.1103/PhysRevA.48.3561
20.
20.J. G. Vilhena, E. Räsänen, L. Lehtovaara, and M. A. L. Marques, “Violation of a local form of the lieb-oxford bound,” Phys. Rev. A 85, 052514 (2012).
http://dx.doi.org/10.1103/PhysRevA.85.052514
21.
21.K. Burke, J. P. Perdew, and Y. Wang, “Derivation of a generalized gradient approximation: The pw91 density functional,” in Electronic Density Functional Theory: Recent Progress and New Directions, edited by J. F. Dobson, G. Vignale, and M. P. Das (Plenum, NY, 1997), p. 81.
22.
22.J. P. Perdew, A. Ruzsinszky, J. Sun, and K. Burke, “Gedanken densities and exact constraints in density functional theory,” J. Chem. Phys. 140, 18 (2014).
http://dx.doi.org/10.1063/1.4870763
23.
23.K. C. E. Rasanen, S. Pittalis, and C. R. Proetto, “Lower bounds on the exchange-correlation energy in reduced dimensions,” Phys. Rev. Lett. 102, 206406 (2009).
http://dx.doi.org/10.1103/PhysRevLett.102.206406
24.
24.L. A. Constantin and A. Terentjevs, “Gradient-dependent upper bound for the exchange-correlation energy and application to density functional theory,” preprint arXiv:1411.1579 (2014).
http://aip.metastore.ingenta.com/content/aip/journal/jcp/141/24/10.1063/1.4904448
Loading
/content/aip/journal/jcp/141/24/10.1063/1.4904448
Loading

Data & Media loading...

Loading

Article metrics loading...

/content/aip/journal/jcp/141/24/10.1063/1.4904448
2014-12-23
2016-09-30

Abstract

Lewin and Lieb have recently proven several new bounds on the exchange-correlation energy that complement the Lieb-Oxford bound. We test these bounds for atoms, for slowly-varying gases, and for Hooke’s atom, finding them usually less strict than the Lieb-Oxford bound. However, we also show that, if a generalized gradient approximation is to guarantee satisfaction of the new bounds for all densities, new restrictions on the exchange-correlation enhancement factor are implied.

Loading

Full text loading...

/deliver/fulltext/aip/journal/jcp/141/24/1.4904448.html;jsessionid=aKo1eteJsW_ylv8cmgXyVF6L.x-aip-live-06?itemId=/content/aip/journal/jcp/141/24/10.1063/1.4904448&mimeType=html&fmt=ahah&containerItemId=content/aip/journal/jcp
true
true

Access Key

  • FFree Content
  • OAOpen Access Content
  • SSubscribed Content
  • TFree Trial Content
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
/content/realmedia?fmt=ahah&adPositionList=
&advertTargetUrl=//oascentral.aip.org/RealMedia/ads/&sitePageValue=jcp.aip.org/141/24/10.1063/1.4904448&pageURL=http://scitation.aip.org/content/aip/journal/jcp/141/24/10.1063/1.4904448'
Right1,Right2,Right3,