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The Pair Density in Approximate Density Functionals: The Hidden Agent

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Many-Electron Densities and Reduced Density Matrices

Part of the book series: Mathematical and Computational Chemistry ((MACC))

Abstract

In this chapter, we review the connection between density functional methods [1] and wave function methods [2]. Simple models of the pair density are shown to lead naturally to the local density approximation for exchange and correlation. The rigorous basis for this approach is exact density functional theory [1, 37]. We review recent advances from a pair density perspective.

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References

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

    Article  CAS  Google Scholar 

  2. J. A. Pople, Rev. Mod. Phys. 71, 1267 (1999).

    Article  CAS  Google Scholar 

  3. P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964).

    Article  Google Scholar 

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

    Article  Google Scholar 

  5. R. M. Dreizler and E. K. U. Gross, Density Functional Theory, Springer-Verlag, Berlin (1990).

    Book  Google Scholar 

  6. R. G. Parr and W. Yang, Density Functional Theory of Atoms and Molecules, Oxford, New York (1989).

    Google Scholar 

  7. J. P. Perdew and S. Kurth, in Density Functional: Theory and Applications, D. Joubert (ed.), Springer, Berlin (1998).

    Google Scholar 

  8. O. Gunnarsson and B. I. Lundqvist, Phys. Rev.B 13, 4274 (1976).

    Google Scholar 

  9. W. Kohn, Phys. Rev. Lett 76, 3168 (1996).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  11. D. C. Langreth and J.P. Perdew, Phys. Rev.B 15, 2884 (1977).

    Google Scholar 

  12. K. Burke, J.P. Perdew, and D.C. Langreth, Phys. Rev. Lett. 73, 1283 (1994).

    Article  CAS  Google Scholar 

  13. Y. Wang and J. P. Perdew, Phys. Rev.B 44, 13298 (1991).

    Google Scholar 

  14. D. J. W. Geldart, Can. J. Phys. 45, 3139 (1967).

    Article  CAS  Google Scholar 

  15. J. C. Slater, Phys. Rev. 81, 385 (1951); 82, 538 (1951); 91, 52 (1953).

    Article  CAS  Google Scholar 

  16. J. C. Kimball, Phys. Rev.A 7, 1648 (1973).

    Google Scholar 

  17. V.L. Klimov and D.W. McBranch, Phys. Rev. Lett 80, 4028 (1998).

    Article  CAS  Google Scholar 

  18. M. Levy, Phys. Rev.A 43, 4637 (1991).

    Google Scholar 

  19. E. H. Lieb and S. Oxford, Int. J. Quant. Chem. 19, 427 (1981).

    Article  CAS  Google Scholar 

  20. K. Burke and E. K. U. Gross, in Density Functional: Theory and Applications, D. Joubert (ed.), Springer, Berlin (1998).

    Google Scholar 

  21. J. Harris and R. O. Jones, J. Phys. F 4, 1170 (1974).

    Article  Google Scholar 

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

    Article  Google Scholar 

  23. K. Burke, M. Ernzerhof, and J. P. Perdew, Chem. Phys. Lett. 265, 115 (1997).

    Article  CAS  Google Scholar 

  24. M. Levy and J. P. Perdew, Phys. Rev.A 32, 2010 (1985).

    Google Scholar 

  25. J. P. Perdew, R. G. Parr, M. Levy, and J. L. Balduz, Jr., Phys. Rev. Lett. 49, 1691 (1982).

    Article  CAS  Google Scholar 

  26. J. P. Perdew and M. Levy, in Many-Body Phenomena at Surfaces, D. C. Langreth and H. Suhl (eds.), Academic, New York (1984).

    Google Scholar 

  27. J. P. Perdew and M. Ernzerhof, in Electronic Density Functional Theory: Recent Progress and New Directions, J.F. Dobson, G. Vignale, and M.P. Das (eds.), Plenum, NY (1998).

    Google Scholar 

  28. W. Yang, Phys. Rev.A 34 4575, (1986).

    Google Scholar 

  29. B. Grammaticos and A. Voros, Ann. Phys. 123, 359 (1979).

    Article  CAS  Google Scholar 

  30. M. Rasolt and H. L. Davis, Phys. Lett.A 86, 45 (1981).

    Google Scholar 

  31. M. Rasolt and D. J. W. Geldart, Phys. Rev.B 34, 1325 (1986).

    Google Scholar 

  32. J. P. Perdew, Phys. Rev.B 33, 8822 (1986); E 34, 7406 (1986).

    Google Scholar 

  33. S.-K. Ma and K. A. Brueckner, Phys. Rev. 165, 18 (1968).

    Article  Google Scholar 

  34. D. C. Langreth and M. J. Mehl, Phys. Rev.B 28, 1809 (1983).

    Google Scholar 

  35. D. C. Langreth and J. P. Perdew, Phys. Rev.B 21, 5469 (1980).

    Google Scholar 

  36. J. P. Perdew and Y. Wang, Phys. Rev.B 33, 8800 (1986); 40, 3399 (1989) (E).

    Google Scholar 

  37. J. P. Perdew, in Electronic Structure of Solids’ 91, P. Ziesche and H. Eschrig (eds.), Akademie Verlag, Berlin (1991).

    Google Scholar 

  38. J. P. Perdew, K. Burke, and Y. Wang, Phys. Rev.B 54, 16533 (1996); E 57, 14999 (1998).

    Google Scholar 

  39. J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett 77, 3865 (1996); E 78, 1396 (1997).

    Article  CAS  Google Scholar 

  40. A. D. Becke, Phys. Rev.A 38, 3098 (1988).

    Google Scholar 

  41. C. Lee, W. Yang, and R. G. Parr, Phys. Rev.B 37, 785 (1988).

    Google Scholar 

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

    Article  CAS  Google Scholar 

  43. B. Miehlich, A. Savin, H. Stoll, and H. Preuss, Chem. Phys. Lett 157, 200 (1989).

    Article  CAS  Google Scholar 

  44. M. Ernzerhof, J. P. Perdew, and K. Burke, in Density Functional Theory, R. Nalewajski (ed.), Springer-Verlag, Berlin (1996).

    Google Scholar 

  45. R. Singh, L. Massa, and V. Sahni, Phys. Rev.A 60, 4135 (1999).

    Google Scholar 

  46. Y. Zhang and W. Yang, Phys. Rev. Lett 80, 890 (1998).

    Article  CAS  Google Scholar 

  47. J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 80, 891 (1998).

    Article  CAS  Google Scholar 

  48. M. Ernzerhof, J. P. Perdew, and K. Burke, Int. J. Quant. Chem. 64, 285 (1997).

    Article  CAS  Google Scholar 

  49. A. D. Becke, J. Chem. Phys. 98, 1372 (1993).

    Article  CAS  Google Scholar 

  50. J. P. Perdew, M. Ernzerhof, and K. Burke, J. Chem. Phys. 105, 9982 (1996).

    Article  CAS  Google Scholar 

  51. M. Seidl, and J. P. Perdew, and S. Kurth (to be published).

    Google Scholar 

  52. O. Gunnarsson, M. Jonson, and B. I. Lundqvist, Phys. Rev.B 20, 3136 (1979).

    Google Scholar 

  53. J. A. Alonso and L. C. Balbâs, Phys. Lett A 81, 467 (1981).

    Google Scholar 

  54. A. Görling, Phys. Rev. A 47, 2783 (1993).

    Google Scholar 

  55. J. P. Perdew and A. Zunger, Phys. Rev.B 23, 5048 (1981).

    Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  58. R. T. Sharp and G. K. Horton, Phys. Rev. 90, 317 (1953).

    Article  Google Scholar 

  59. J. B. Krieger, Y. Li, and G. J. Iafrate, Phys. Lett.A 146, 256 (1990).

    Google Scholar 

  60. J. B. Krieger, Y. Li, and G. J. Iafrate, Phys. Rev.A 45, 101 (1992).

    Google Scholar 

  61. T. Grabo, T. Kreibich, S. Kurth, and E. K. U. Gross, in Strong Coulomb Correlations in Electronic Structure: Beyond the Local Density Approximation, V.L. Anisimov (ed.), Gordon and Breach, Tokyo (1998).

    Google Scholar 

  62. M. Städele, J. A. Majewski, P. Vogl, and A. Görling, Phys. Rev. Lett. 79, 2089 (1997).

    Article  Google Scholar 

  63. A. Görling, Phys. Rev. Lett. 83, 5459 (1999).

    Article  Google Scholar 

  64. S. Ivanov, S. Hirata, and R. J. Bartlett, Phys. Rev. Lett. 83, 5455 (1999).

    Article  CAS  Google Scholar 

  65. M. Levy and A. Nagy, Phys. Rev. Lett. 83, 4361 (1999).

    Article  CAS  Google Scholar 

  66. Y. Andersson, E. Hult, H. Rydberg, P. Apell, B. I. Lundqvist, and D. C. Lan-greth, in Electronic Density Functional Theory: Recent Progress and New Directions, J.F. Dobson, G. Vignale, and M.P. Das (eds.), Plenum, NY (1997).

    Google Scholar 

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Maitra, N.T., Burke, K. (2000). The Pair Density in Approximate Density Functionals: The Hidden Agent. In: Cioslowski, J. (eds) Many-Electron Densities and Reduced Density Matrices. Mathematical and Computational Chemistry. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-4211-7_9

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  • DOI: https://doi.org/10.1007/978-1-4615-4211-7_9

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-6890-8

  • Online ISBN: 978-1-4615-4211-7

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