Brief Introduction to Density Functional Theory

  • John F. Dobson
  • Mukunda P. Das
Chapter

Abstract

The physics of many interacting particles is notoriously difficult. The attraction of density functional theory is that it facilitates approximate calculations on many-body systems without requiring the construction of many-body wavefunctions or their equivalent. Instead one extracts the needed information from a one-body quantity, the number density. While density functional methods can be applied to many systems such as classical fluids, nuclei and thermal ensembles, this book is principally devoted to quantum states of many-electron systems. All of the articles are relevant to quantum chemistry and/or condensed matter physics.

Keywords

Density Functional Theory Correlation Energy Thomas Fermi Pair Density Electronic Density Functional Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References

  1. 1.
    L. H. Thomas, Proc. Cambridge Phil. Soc. 23, 542 (1927).ADSMATHCrossRefGoogle Scholar
  2. 2.
    E. Fermi, Z. Phys. 48, 73 (1928).ADSMATHCrossRefGoogle Scholar
  3. 3.
    P. A. M. Dirac, Proc. Cambridge Phil. Soc. 26, 376 (1930).ADSMATHCrossRefGoogle Scholar
  4. 4.
    J. C. Slater, The Self-Consistent Field for Molecules and Solids (McGraw-Hill, New York, 1974), Vol. IV.Google Scholar
  5. 5.
    P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964).MathSciNetADSCrossRefGoogle Scholar
  6. 6.
    M. Levy, Proc. Natl. Acad. Sci. USA 76, 6062 (1979).ADSCrossRefGoogle Scholar
  7. 7.
    R. G. Parr and W. Yang, Density Functional Theory of Atoms and Molecules (Clarendon Press, Oxford, 1989).Google Scholar
  8. 8.
    W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965).MathSciNetADSCrossRefGoogle Scholar
  9. 9.
    R. M. Dreizler and E. K. U. Gross, Density Functional Theory (Springer Verlag, Berlin, 1990).MATHCrossRefGoogle Scholar
  10. 10.
    A. S. Davydov, Quantum Mechanics (Pergamon Press, Oxford, 1965).Google Scholar
  11. 11.
    G. D. Mahan, Many-Particle Physics (Plenum, New York, 1981).Google Scholar
  12. 12.
    E. Wigner, Phys. Rev. 46, 1002 (1934).ADSCrossRefGoogle Scholar
  13. 13.
    D. M. Ceperley and B. J. Alder, Phys. Rev. Lett. 45, 566 (1980).ADSCrossRefGoogle Scholar
  14. 14.
    S. Vosko, Wilk, and Nusair, Can. J. Phys. 58, 1200 (1980).ADSCrossRefGoogle Scholar
  15. 15.
    R. O. Jones and O. Gunnarsson, Rev. Mod. Phys. 61, 689 (1989).ADSCrossRefGoogle Scholar
  16. 16.
    U. V. Barth and L. Hedin, J. Phys. C 5, 1629 (1972).ADSCrossRefGoogle Scholar
  17. 17.
    M. M. Pant and A. K. Rajagopal, Sol. State Commun. 10, 1157 (1972).ADSCrossRefGoogle Scholar
  18. 18.
    J. F. Janak, Phys. Rev. B 18, 7165 (1978).ADSCrossRefGoogle Scholar
  19. see also J. Callaway and N. H. March, Solid State Physics 38, 135 (1984), especially p. 169-170.CrossRefGoogle Scholar
  20. 19.
    J. P. Perdew, R. G. Parr, M. Levy, and J. L. Balduz, Phys. Rev. Lett. 49, 1691 (1982).ADSCrossRefGoogle Scholar
  21. 20.
    J. P. Perdew and M. Levy, Phys. Rev. Lett. 51, 1884 (1983).ADSCrossRefGoogle Scholar
  22. 21.
    L. J. Sham and M. Schluter, Phys. Rev. Lett. 51, 1888 (1983).ADSCrossRefGoogle Scholar
  23. 22.
    W. Kohn, Phys. Rev. B 33, 4331 (1986ADSCrossRefGoogle Scholar
  24. 23.
    M. S. Hybertson and S. G. Louie, Phys. Rev. B 34, 5390 (1986).ADSCrossRefGoogle Scholar
  25. 24.
    G. Vignale and M. Rasolt, Phys. Rev. B 37, 10658 (1988).CrossRefGoogle Scholar
  26. 25.
    D. C. Langreth and J. P. Perdew, Sol. State Commun. 17, 1425 (1975).ADSCrossRefGoogle Scholar
  27. 26.
    O. unnarsson and B. I. Lundqvist, Phys. Rev. B 13, 4274 (1976).ADSCrossRefGoogle Scholar
  28. 27.
    K. Burke, J. P. Perdew, and D. C. Langreth, Phys. Rev. Lett. 73, 1283 (1994).ADSCrossRefGoogle Scholar
  29. 28.
    J. P. Perdew, M. Ernzerhof, K. Burke, and A. Savin, Int. J. Quantum Chem. 61, 197 (1997).CrossRefGoogle Scholar
  30. 29.
    M. Rasolt and D. J. W. Geldart, Phys. Rev. B 34, 1325 (1986).ADSCrossRefGoogle Scholar
  31. 30.
    D. Langreth and J. Perdew, Solid State Commun. 31, 567 (1979).ADSCrossRefGoogle Scholar
  32. 31.
    J. Perdew, Phys. Rev. Lett. 55, 1665 (1985).ADSCrossRefGoogle Scholar
  33. 32.
    J. P. Perdew, Phys. Rev. Lett. 55, 2370 (E) (1995).ADSCrossRefGoogle Scholar
  34. 33.
    J. Perdew and Y. Wang, Phys. Rev. B 33, 8800 (1986).ADSCrossRefGoogle Scholar
  35. 34.
    J. P. Perdew et al. Phys. Rev. B 46, 6671 (1992).ADSCrossRefGoogle Scholar
  36. 35.
    J. P. Perdew, in Electronic Structure of Solids’ 91, edited by P. Ziesche and H. Eschrig (Akademie Verlag, Berlin, 1991).Google Scholar
  37. 36.
    J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996).ADSCrossRefGoogle Scholar
  38. 37.
    A. D. Becke, Phys. Rev. A 38, 3098 (1988).ADSCrossRefGoogle Scholar
  39. 38.
    A. D. Becke and M. R. Roussel, Phys. Rev. A 39, 3761 (1989).ADSCrossRefGoogle Scholar
  40. 39.
    A. D. Becke, J. Chem. Phys. 88, 1053 (1987).ADSCrossRefGoogle Scholar
  41. 40.
    R. Colle and O. Salvetti, Theor. Chim. Acta 37, 329 (1975).CrossRefGoogle Scholar
  42. 41.
    R. Colle and O. Salvetti, Theor. Chim. Acta 53, 55 (1979).CrossRefGoogle Scholar
  43. 42.
    C. Lee, W. Yang, and R. G. Parr, Phys. Rev. B 37, 785 (1988).ADSCrossRefGoogle Scholar
  44. 43.
    A. D. Becke, J. Chem. Phys. 98, 5648 (1993).ADSCrossRefGoogle Scholar
  45. 44.
    W. Kohn and W. Hanke, private communication.Google Scholar
  46. 45.
    M. Levy, Adv. Quantum Chem. 21, 69 (1990).ADSCrossRefGoogle Scholar
  47. 46.
    M. Levy and J. Perdew, Int. J. Quantum. Chem. 49, 539 (1994).CrossRefGoogle Scholar
  48. 47.
    A. Görling and M. Levy, Phys. Rev. B 47, 13105 (1993).ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • John F. Dobson
    • 1
  • Mukunda P. Das
    • 2
  1. 1.School of ScienceGriffith UniversityNathanAustralia
  2. 2.Department of Theoretical PhysicsAustralian National UniversityCanberraAustralia

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