Digging into the Exchange-Correlation Energy: The Exchange-Correlation Hole

  • Kieron Burke


In this chapter, I summarize much of what is known about the exchange-correlation hole in density functional theory. The aim of this summary is to introduce the non-expert to key concepts in electronic density functional theory. For a much broader introduction, see the book by Parr and Yang [1]. For more detail, see the book by Dreizler and Gross [2], and other chapters in the current volume. Most of the references in this chapter are either classic papers in which a fundamental result has been established (and so are well worth reading), or are references to illustrative figures in my own work. I conclude with some simple exercises. Solutions are provided to the odd-numbered problems, while true experts will make short work of the even-numbered ones.


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  1. 1.
    R.G. Parr and W. Yang, Density Functional Theory of Atoms and Molecules (Oxford, New York, 1989).Google Scholar
  2. 2.
    R.M. Dreizler and E.K.U. Gross, Density Functional Theory (Springer-Verlag, Berlin, 1990).MATHCrossRefGoogle Scholar
  3. 3.
    M. Levy, Proc. Natl. Acad. Sci. (U.S.A.) 76, 6062 (1979).ADSCrossRefGoogle Scholar
  4. 4.
    E. H. Lieb, Int. J. Quantum Chem. 24, 224 (1983).CrossRefGoogle Scholar
  5. 5.
    P. Hohenberg and W. Kohn, Phys. Rev. 136, B 864 (1964).MathSciNetADSCrossRefGoogle Scholar
  6. 6.
    M. Levy and J.P. Perdew, Phys. Rev. A 32, 2010 (1985).ADSCrossRefGoogle Scholar
  7. 7.
    M. Levy, Int. J. Quantum Chem. S23, 617 (1989).Google Scholar
  8. 8.
    D.C. Langreth and J.P. Perdew, Solid State Commun. 17, 1425 (1975).ADSCrossRefGoogle Scholar
  9. 9.
    J. P. Perdew and Y. Wang, Phys. Rev. B 46, 12947 (1992).ADSCrossRefGoogle Scholar
  10. 10.
    G.D. Mahan, Many-Particle Physics, 2nd ed. (Plenum Press, New York, 1990).CrossRefGoogle Scholar
  11. 11.
    J. C. Kimball, Phys. Rev. A 7, 1648 (1973).ADSGoogle Scholar
  12. 12.
    D. Vanderbilt and D.C. Langreth, unpublished.Google Scholar
  13. 13.
    R.O. Jones and O. Gunnarsson, Rev. Mod. Phys. 61, 689 (1989).ADSCrossRefGoogle Scholar
  14. 14.
    K. Burke and J. P. Perdew, Int. J. Quantum Chem. 56, 199 (1995).CrossRefGoogle Scholar
  15. 15.
    M. Ernzerhof, J.P. Perdew, and K. Burke, in Density Functional Theory, edited by R. Nalewajski (Springer, Berlin, 1996).Google Scholar
  16. 16.
    W. Kohn and L.J. Sham, Phys. Rev. 140, A 1133 (1965).MathSciNetADSCrossRefGoogle Scholar
  17. 17.
    D. M. Ceperley and B. J. Alder, Phys. Rev. Lett. 45, 566 (1980).ADSCrossRefGoogle Scholar
  18. 18.
    Peter Fulde, Electron Correlations in Molecules and Solids (Springer-Verlag, Berlin, 1991).CrossRefGoogle Scholar
  19. 19.
    M. Rasolt and D.J.W. Geldart, Phys. Rev. B 34, 1325 (1986).ADSCrossRefGoogle Scholar
  20. 20.
    K. Burke, J. P. Perdew, and M. Levy, in Modern Density Functional Theory: A Tool for Chemistry, Springer-Verlag, Berlin edited by J. M. Seminario and P. Politzer (Elsevier, Amsterdam, 1995).Google Scholar
  21. 21.
    O. Gunnarsson and B.I. Lundqvist, Phys. Rev. B 13, 4274 (1976).ADSCrossRefGoogle Scholar
  22. 22.
    O. Gunnarsson, M. Jonson, and B. I. Lundqvist, Solid State Commun. 24, 765 (1977).ADSCrossRefGoogle Scholar
  23. 23.
    J.P. Perdew, Phys. Rev. B 33, 8822 (1986).; 34, 7406 (1986) (E).ADSCrossRefGoogle Scholar
  24. 24.
    A.D. Becke, Phys. Rev. A 38, 3098 (1988).ADSCrossRefGoogle Scholar
  25. 25.
    C. Lee, W. Yang, and R.G. Parr, Phys. Rev. B 37, 785 (1988).ADSCrossRefGoogle Scholar
  26. 26.
    J.P. Perdew, in Electronic Structure of Solids’ 91, edited by P. Ziesche and H. Eschrig (Akademie Verlag, Berlin, 1991), page 11.Google Scholar
  27. 27.
    J. P. Perdew, J. A. Chevary, S. H. Vosko, K. A. Jackson, M. R. Pederson, D.J. Singh, and C. Fiolhais, Phys. Rev. B 46, 6671 (1992).; 48, 4978 (1993) (E).ADSCrossRefGoogle Scholar
  28. 28.
    J.P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996); 78, 1396 (1997) (E).ADSCrossRefGoogle Scholar
  29. 29.
    D.C. Langreth and M.J. Mehl, Phys. Rev. B 28, 1809 (1983).ADSCrossRefGoogle Scholar
  30. 30.
    J.P. Perdew, K. Burke, and Y. Wang, Phys. Rev. B 54, 16533 (1996).ADSCrossRefGoogle Scholar
  31. 31.
    M. Ernzerhof, K. Burke, and J.P. Perdew, in Recent developments and applications in density functional theory,11 edited by J.M. Seminario (Elsevier, Amsterdam, 1996).Google Scholar
  32. 32.
    J. B. Krieger, Y. Li, and G. J. Iafrate, Phys. Rev. A 45, 101 (1992).ADSCrossRefGoogle Scholar
  33. 33.
    K. Burke, J.P. Perdew, and M. Ernzerhof, Int. J. Quantum Chem. 61, 287 (1997).CrossRefGoogle Scholar
  34. 34.
    J. P. Perdew and A. Zunger, Phys. Rev. B 23, 5048 (1981).ADSCrossRefGoogle Scholar
  35. 35.
    A. Görling and M. Levy, Phys. Rev. B 47, 13105 (1993).ADSCrossRefGoogle Scholar
  36. 36.
    M. Levy, Phys. Rev. A 43, 4637 (1991).ADSCrossRefGoogle Scholar
  37. 37.
    A. Görling and M. Levy, Phys. Rev. A 45, 1509 (1992).ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Kieron Burke
    • 1
  1. 1.Department of ChemistryRutgers University-CamdenCamdenUSA

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