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Can Density Functional Theory Describe Strongly Correlated Electronic Systems?

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Abstract

Summarized here are the ideas of Kohn-Sham spin density functional theory for the many-electron ground state, the effects of exchange and correlation, and the limits of weak and strong correlation. In particular, the suppression of electron number fluctuations in one-electron regions due to correlation is discussed. While the standard local spin density and generalized gradient approximations (GGA’s) for the exchange-correlation energy can work for certain cases of strong correlation, they fail dramatically for others. It is suggested that the new self-correlation-free meta-GGA’s and self-interaction-free hyper-GGA’s might yield a more reliable description of strong correlation.

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References

  1. W. Kohn and L.J. Sham, Phys. Rev. 140, A1133 (1965).

    Article  MathSciNet  ADS  Google Scholar 

  2. W. Kohn, Rev. Mod. Phys. 71, 1253 (1999).

    Article  ADS  Google Scholar 

  3. D.R. Hartree, Proc. Camb. Phil. Soc. 24, 89, 111, 426 (1928).

    Google Scholar 

  4. D.C. Langreth and J.P. Perdew, Solid State Commun. 17, 1425 (1975).

    Article  ADS  Google Scholar 

  5. Gunnarsson and B.I. Lundqvist, Phys. Rev. B13, 4274 (1976).

    ADS  Google Scholar 

  6. H.T. Tran and J.P. Perdew, unpublished.

    Google Scholar 

  7. M. Levy and J.P. Perdew, Phys. Rev. A32, 2010 (1985).

    Google Scholar 

  8. T. Ziegler, A. Rauk, and E.J. Baerends, Theoret. Chim. Acta 43, 261 (1977).

    Article  Google Scholar 

  9. V.A. Rassolov, J.A. Pople, and M.A. Ratner, Phys. Rev. B62, 2232 (2000).

    ADS  Google Scholar 

  10. D. Pines and P. Nozieres, The Theory of Quantum Liquids ( Benjamin, NY, 1966 ).

    Google Scholar 

  11. M. Levy and J.P. Perdew, Phys. Rev. B48, 11638 (1993).

    Google Scholar 

  12. M. Seidl, J.P. Perdew, and M. Levy, Phys. Rev. A59, 51 (1999).

    Article  ADS  Google Scholar 

  13. J.P. Perdew, in Density Functional Methods in Physics, edited by R.M. Dreizler and J. da Providencia ( Plenum, NY, 1985 ).

    Google Scholar 

  14. P. Ziesche, J. Tao, M. Seidl, and J.P. Perdew, Int. J. Quantum Chem. 77, 819 (2000).

    Article  Google Scholar 

  15. P. Dufek, P. Blaha, V. Sliwko, and K. Schwarz, Phys. Rev. B49, 10170 (1994).

    Google Scholar 

  16. A. Svane and 0. Gunnarsson, Phys. Rev. Lett. 65, 1148 (1990).

    Article  ADS  Google Scholar 

  17. A. Svane, Phys. Rev. Lett. 68, 1900 (1992).

    Article  Google Scholar 

  18. A. Svane, Phys. Rev. Lett. 72, 1248 (1994).

    Article  Google Scholar 

  19. Z. Szotek, W.M. Temmerman, and H. Winter, Phys. Rev. B47, 4029 (1993).

    ADS  Google Scholar 

  20. P. Strange, A. Svane, W.M. Temmerman, Z. Szotek, and H. Winter, Nature 399, 756 (1999)

    Article  ADS  Google Scholar 

  21. W.M. Temmerman, H. Winter, Z. Szotek, and A. Svane, Phys. Rev. Lett. 86, 2435 (2001).

    Article  ADS  Google Scholar 

  22. J.-T. Hoeft, M. Kittel, M. Polcik, S. Bao, R.L. Toomes, J.-H. Kang, D.P. Woodruff, M. Pascal, and C.L.A. Lamont, Phys. Rev. Lett. 87, 86101 (2001).

    Google Scholar 

  23. V.I. Anisimov, F. Aryasetiawan, and A.I. Lichtenstein, J. Phys.: Con-dens. Matter 9, 767 (1997).

    Article  ADS  Google Scholar 

  24. V.I. Anisimov, I.V. Solovyev, M.A. Korotin, M.T. Czyzyk, and G.A. Sawatzky, Phys. Rev. B48, 16929 (1993).

    Google Scholar 

  25. A. Georges, G. Kotliar, W. Krauth, and M.J. Rozenberg, Rev. Mod. Phys. 68, 13 (1996).

    Article  MathSciNet  ADS  Google Scholar 

  26. J.P. Perdew and K. Schmidt, in Density Functional Theory and Its Application to Materials, edited by V. E. Van Doren, K. Van Alsenoy, and P. Geerlings (American Institute of Physics, 2001 ).

    Google Scholar 

  27. U. von Barth and L. Hedin, J. Phys. C: Solid State Phys. 5, 1629 (1972).

    Article  ADS  Google Scholar 

  28. J.P. Perdew and Y. Wang, Phys. Rev. B45, 13244 (1992).

    Google Scholar 

  29. K. Burke, J.P. Perdew, and M. Ernzerhof, J. Chem. Phys. 109, 3760 (1998).

    Article  ADS  Google Scholar 

  30. J.P. Perdew and A. Zunger, Phys. Rev. B23, 5048 (1981).

    ADS  Google Scholar 

  31. D.C. Langreth and M.J. Mehl, Phys. Rev B28, 1809 (1983).

    MathSciNet  ADS  Google Scholar 

  32. J.P. Perdew and Y. Wang, Phys. Rev. B33, 8800 (1986).

    ADS  Google Scholar 

  33. A.D. Becke, Phys. Rev. A38, 3098 (1988).

    Article  ADS  Google Scholar 

  34. J.P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996).

    Article  ADS  Google Scholar 

  35. J.P. Perdew, K. Burke, and Y. Wang, Phys. Rev. B54, 16533 (1996).

    Google Scholar 

  36. S. Kurth, J.P. Perdew, and P. Blaha, Int. J. Quantum Chem. 75, 889 (1999).

    Article  Google Scholar 

  37. R. Colle and O. Salvetti, Theoret. Chim. Acta 37, 329 (1975).

    Article  Google Scholar 

  38. J.P. Perdew, Phys. Rev. Lett. 55, 1665 (1985).

    Article  Google Scholar 

  39. A.D. Becke and M.R. Roussel, Phys. Rev. A 39, 3761 (1989).

    Article  ADS  Google Scholar 

  40. E.I. Proynov, S. Sirois, and D.R. Salahub, Int. J. Quantum Chem. 64, 427 (1998).

    Article  Google Scholar 

  41. T. Van Voorhis and G.E. Scuseria, J. Chem. Phys. 109, 400 (1998).

    Article  ADS  Google Scholar 

  42. A.D. Becke, J. Chem. Phys. 109, 2092 (1998).

    Article  ADS  Google Scholar 

  43. J.P. Perdew, S. Kurth, A. Zupan, and P. Blaha, Phys. Rev. Lett. 82, 2544 (1999).

    Article  ADS  Google Scholar 

  44. A. Goerling and M. Levy, Phys. Rev. B47, 13105 (1993)

    Google Scholar 

  45. A. Goerling and M. Levy, Phys. Rev. A52, 4493 (1995).

    Article  ADS  Google Scholar 

  46. M. Seidl, J.P. Perdew, and S. Kurth, Phys. Rev. A62, 12502 (2000).

    Article  ADS  Google Scholar 

  47. J.P. Perdew, A. Savin, and K. Burke, Phys. Rev. A51, 4531 (1995).

    Article  ADS  Google Scholar 

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Perdew, J.P. (2002). Can Density Functional Theory Describe Strongly Correlated Electronic Systems?. In: Gonis, A., Kioussis, N., Ciftan, M. (eds) Electron Correlations and Materials Properties 2. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3760-8_13

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  • DOI: https://doi.org/10.1007/978-1-4757-3760-8_13

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-3392-8

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