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Density Functional Approach to Time-Dependent and to Relativistic Systems

  • Eberhard K. U. Gross
  • Reiner M. Dreizler
Part of the NATO ASI Series book series (volume 123)

Abstract

Density functional methods, in general, can be discussed on three different levels. The first is the level of fundamental1,2 existence theorems such as those of Hohenberg, Kohn and Sham (HKS) and related mathematical topics. The second level consists of the various approaches 2–32 to a systematic construction of density functionals. Prominent among these are the different gradient expansion techniques. The approximations required on this level depend, of course, on the particular situation to be described. The third level consists of practical schemes and numerical solutions for real physical systems.

Keywords

Correlation Diagram Kinetic Energy Density Nonrelativistic Case Gradient Expansion Internuclear Separation 
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.
    P. Hohenberg and W. Kohn, Phys. Rev. 136: B864 (1964).MathSciNetADSCrossRefGoogle Scholar
  2. 2.
    W. Kohn and L.J. Sham, Phys. Rev. 140: A1133 (1965).MathSciNetADSCrossRefGoogle Scholar
  3. 3.
    L.J. Sham and W. Kohn, Phys. Rev. 145: 561 (1966).ADSCrossRefGoogle Scholar
  4. 4.
    G.A. Baraff and S. Borowitz, Phys. Rev. 121:1704 (1961).MathSciNetADSCrossRefGoogle Scholar
  5. 5.
    S.-K.Ma and K.A. Brueckner, Phys. Rev. 165:18 (1968).ADSCrossRefGoogle Scholar
  6. 6.
    L.J. Sham, in “Computational Methods in Band Structure,”p.458, P.M. Marcus, J.F. Janak, and A.R. Williams, eds., Plenum, New York (1971).Google Scholar
  7. 7.
    E.K.U. Gross and R.M. Dreizler, Z. Phys. A302: 103 (1981).ADSCrossRefGoogle Scholar
  8. 18.
    D.J.W. Geldart and M. Rasolt, Phys. Rev. B13:1477 (1976).ADSCrossRefGoogle Scholar
  9. 9.
    D.C. Langreth and J.P. Perdew, Phys. Rev. B21:5469 (1980).ADSCrossRefGoogle Scholar
  10. 10.
    V. Sahni, J. Gruenebaum, and J.P. Perdew, Phys. Rev. B26:4371 (1982).ADSCrossRefGoogle Scholar
  11. 11.
    J.C. Stoddart, A.M. Beattie, and N.H. March, Int. J. Quant.Chem. 4:35 (1971).Google Scholar
  12. 12.
    A.M. Beattie, J.C. Stoddart, and N.H. March, Proc. Roy. Soc. A326:97 (1971).ADSCrossRefGoogle Scholar
  13. 13.
    O. Gunnarsson and B.I. Lundqvist, Phys. Rev. B13:4274 (1975).ADSGoogle Scholar
  14. 14.
    O. Gunnarsson, M. Jonson and B.I. Lundqvist, Phys. Lett. 59A:177 (1976).ADSCrossRefGoogle Scholar
  15. 15.
    O. Gunnarsson, M. Jonson, and B.I. Lundqvist, Solid State Comm. 24:765 (1977).ADSCrossRefGoogle Scholar
  16. 16.
    D.A. Kirzhnits, “Field Theoretical Methods in Many-Body Systems,” Pergamon, Oxford (1967).Google Scholar
  17. 18.
    C.H. Hodges, Can. J. Phys. 51:1428 (1973).ADSCrossRefGoogle Scholar
  18. 18.
    D.R. Murphy, Phys. Rev. 24:1682 (1981).ADSCrossRefGoogle Scholar
  19. 19.
    B. Grammaticos and A. Voros, Ann. Phys. 123: 359 (1979).MathSciNetADSCrossRefGoogle Scholar
  20. 20.
    S.F.J. Wilk, Y. Fujiwara, and T.A. Osborn, Phys. Rev. A24:2187 (1981).MathSciNetADSGoogle Scholar
  21. 21.
    Y. Fujiwara, T.A. Osborn, and S.F.J. Wilk, Phys. Rev. A25: 14 (1982).Google Scholar
  22. 22.
    E. Tirapegui, F. Langouche, and D. Roekaerts, Phys. Rev. A27:2649 (1982).MathSciNetADSGoogle Scholar
  23. 23.
    V. Peuckert, J. Phys. C7: 2221 (1974).ADSGoogle Scholar
  24. 24.
    V. Peuckert, J. Phys. C9: 809 (1976).ADSGoogle Scholar
  25. 25.
    V. Peuckert, J. Phys. C9: 4173 (1976).ADSGoogle Scholar
  26. 26.
    C.Q. Ma and V. Sahni, Phys. Rev. B16: 4249 (1977).ADSCrossRefGoogle Scholar
  27. 27.
    U. von Barth and L. Hedin, J. Phys. C5: 1629 (1972).Google Scholar
  28. 28.
    G.L. Oliver and J.P. Perdew, Phys. Rev. A20:397 (1979).ADSCrossRefGoogle Scholar
  29. 29.
    L. Fritsche and H. Gollisch, in: “Local Density Approximations in Quantum Chemistry and Solid State Physics,” J.P. Dahl and J. Avery, eds., Plenum, New York (1984).Google Scholar
  30. 30.
    G.E.W. Bauer, Phys. Rev. B27: 5912 (1983).ADSCrossRefGoogle Scholar
  31. 31.
    K.F. Freed and M. Levy, J. Chem. Phys. 77:396 (1982).ADSCrossRefGoogle Scholar
  32. 32.
    G. Zumbach and K. Maschke, Phys. Rev. A28:544 (1983).MathSciNetADSGoogle Scholar
  33. 33.
    E. Runge and E.K.U. Gross, Phys. Rev. Lett. 52:997 (1984).ADSCrossRefGoogle Scholar
  34. 34.
    E.K.U. Gross and R.M. Dreizler, Phys. Rev. A20:1798 (1979).Google Scholar
  35. 35.
    W. Stich, E.K.U. Gross, P. Malzacher, and R.M. Dreizler, Z. Phys. A309: 5 (1982).ADSCrossRefGoogle Scholar
  36. 36.
    E.K.U. Gross, A. Toepfer, B. Jacob, and R.M. Dreizier, in: “Proceedings of the XVII International Winter Meeting on Nuclear Physics in Bormio 1979,” p. 68–94, I. Iori, ed., Instituto Nazionale di Fisica Nucleare, Milano (1979)Google Scholar
  37. 37.
    R.M. Dreizier, E.K.U. Gross, and A. Toepfer, Phys. Lett. 71A: 49 (1979).ADSCrossRefGoogle Scholar
  38. 38.
    A. Toepfer, E.K.U. Gross, and R.M. Dreizier, Phys. Rev. A20: 1808 (1979).ADSCrossRefGoogle Scholar
  39. 39.
    A. Toepfer, E.K.U. Gross, and R.M. Dreizler, Z. Phys. A298: 167 (1980).ADSCrossRefGoogle Scholar
  40. 40.
    E.K.U. Gross and J. Rafeiski, Phys. Rev. A20:44 (1979).ADSCrossRefGoogle Scholar
  41. 41.
    R.M. Dreizler, E.K.U. Gross, M. Horbatsch, B. Jacob, H.J. Lüdde, and A. Toepfer, in:“ Proceedings of the XVIII International Winter Meeting on Nuclear Physics in Bormio 1980,” p.764–794, RicercaScientifica ed Educazione Permanente, supplemento n.13, Milano (1980).Google Scholar
  42. 42.
    E.K.U. Gross and R.M. Dreizler, Phys. Lett. 81A:447 (1981).Google Scholar
  43. 43.
    R.M. Dreizier and E.K.U. Gross, in:“ Quantum Electrodynamics of Strong Fields,” p. 383–412, W. Greiner, ed., Plenum, New York (1983).Google Scholar
  44. 44.
    E.K.U. Gross and R.M. Dreizler, in:“ Local Density Approxi- mations in Quantum Chemistry and Solid State Physics,” p. 353–380, J.P. Dahl and J. Avery, eds., Plenum, New York (1984).Google Scholar
  45. 45.
    M. Horbatsch and R.M. Dreizler, Z. Phys.A300:119 (1981).Google Scholar
  46. 46.
    M. Horbatsch and R.M. Dreizier, Z.Phys. A308:329 (1982).ADSCrossRefGoogle Scholar
  47. 47.
    H.J. Lüdde, M. Horbatsch, E.K.U. Gross, and R.M. Dreizler, in: “Proceedings of the XVII International Winter Meeting on Nuclear Physics in Bormio 1979,” p. 120–136, I. Iori, ed., Instituto Nazionale di Fisica Nucleare, Milano (1979).Google Scholar
  48. 48.
    M. Horbatsch, H.J. Lüdde, A. Henne, E.K.U. Gross, and R.M. Dreizler, in:“ XII International Conference on the Physics of Electronic and Atomic Collisions (Gatlinburg, Tennessee, 1981), Abstracts of Contributed Papers I,” p. 545–546, S. Datz, ed., Oak Ridge (1981).Google Scholar
  49. 49.
    G. Holzwarth, Phys. Lett. B66:29 (1977).ADSCrossRefGoogle Scholar
  50. 50.
    G. Holzwarth, Phys. Rev. C16: 885 (1977).ADSGoogle Scholar
  51. 51.
    For a similar treatment of nuclear giant resonances, see G. Holzwarth, this volume.Google Scholar
  52. 52.
    P. Malzacher and R.M. Dreizler, Z. Phys. A307: 211 (1982).ADSCrossRefGoogle Scholar
  53. 53.
    S.C. Ying, Nuovo Cim. 23B: 270 (1974).ADSCrossRefGoogle Scholar
  54. 54.
    G. Mukhopadhyay and S. Lundqvist, Nuovo Cim. 27B: 1 (1975).ADSCrossRefGoogle Scholar
  55. 55.
    L.J. Bartolotti, Phys. Rev.A24:1661 (1981); ibid. A26: 2243 (1982).Google Scholar
  56. 56.
    M. Levy, Proc. Natl. Acad. Sci. USA 76: 6062 (1979).ADSCrossRefGoogle Scholar
  57. 57.
    V. Peuckert, J. Phys. C11: 4945 (1978).ADSGoogle Scholar
  58. 58.
    L.H. Thomas, Proc. Camb. Phil. Soc. 23:542 (1926).ADSCrossRefGoogle Scholar
  59. 59.
    E. Fermi, Rend. Acad. Naz. Linzei 6:602 (1927).Google Scholar
  60. 60.
    P.A.M. Dirac, Proc. Camb. Phil. Soc. 26:376 (1930).ADSMATHCrossRefGoogle Scholar
  61. 61.
    C.F.v.Weizsäcker,Z. Phys. 96: 431 (1935).CrossRefGoogle Scholar
  62. 62.
    C. Schweitzer, R.M. Dreizler, and E.K.U. Gross, to be published.Google Scholar
  63. 63.
    F. Herman, J.P. Van Dyke, and I.B. Ortenburger, Phys. Rev. Lett. 22:807 (1969).ADSCrossRefGoogle Scholar
  64. 64.
    L. Kleinman, Phys. Rev. B10: 2221 (1974).ADSCrossRefGoogle Scholar
  65. 65.
    D.J.W. Geldart, M. Rasolt, and C.O. Almbladh, Solid State Comm. 16: 243 (1975).ADSCrossRefGoogle Scholar
  66. 66.
    R. Latter, Phys. Rev. 99:510 (1955).ADSCrossRefGoogle Scholar
  67. 67.
    S.B. Schneiderman and A. Russek, Phys. Rev. 181:311 (1969).ADSCrossRefGoogle Scholar
  68. 68.
    K. Taulbjerg, J. Vaaben, and B. Fastrup, Phys. Rev. Al2:2325 (1975).ADSCrossRefGoogle Scholar
  69. 69.
    R.M. Dreizler, in:“ Critical Phenomena in Heavy Ion Physics (Brasov International School 1980),” p.205–257, A.A. Raduta and G. Stratan,eds., Central Institute of Physics, Bucharest (1980).Google Scholar
  70. 70.
    E. Clementi and C. Roetti, At. Data Nucl. Data Tab. 14:177 (1974).Google Scholar
  71. 71.
    J. Scott, Phil. Mag. 43: 859 (1952).Google Scholar
  72. 72.
    J. Schwinger, Phys. Rev. A22:1827 (1980).MathSciNetADSCrossRefGoogle Scholar
  73. 73.
    E. Lieb, Rev. Mod. Phys. 53:603 (1981).MathSciNetADSMATHCrossRefGoogle Scholar
  74. 74.
    J.P. Desclaux, At. Data Nucl. Data Tab. 12:311 (1973).ADSCrossRefGoogle Scholar
  75. 75.
    W.C. Ermler, R.S. Mulliken, and A.C. Wahl, J. Chem. Phys. 66:30–31 (1977).Google Scholar
  76. 76.
    J. Eichler and U. Wille, Phys. Rev. A11: 1973 (1975).ADSCrossRefGoogle Scholar
  77. 77.
    A. Toepfer, B. Jacob, H.J. Lüdde, and R.M. Dreizier, Phys. Lett. 93A:18 (1982).Google Scholar
  78. 78.
    A. Toepfer, B. Jacob, H.J. Lüdde, and R.M. Dreizier, Z. Phys.Google Scholar
  79. 79.
    T. Andersen, E. Beaving, P. Hedegard, and 0.J. Ostgard, J. Phys. B11: 1449 (1978).ADSGoogle Scholar
  80. 80.
    R. Hippler and K.-H. Schartner, J. Phys. B8:25–28 (1975).Google Scholar
  81. 81.
    For a broad review, see M.V. Ramana and A.K. Rajagopal, Adv. Chem. Phys. 54:231 (1983).Google Scholar
  82. 82.
    A.K. Rajagopal, this volume.Google Scholar
  83. 83.
    M.S. Vallarta and N. Rosen, Phys. Rev. 41: 708 (1932).ADSMATHCrossRefGoogle Scholar
  84. 84.
    H. Jensen, Z. Phys. 82: 794 (1933).ADSCrossRefGoogle Scholar
  85. 85.
    N. Ashby and M.A. Holzman, Phys. Rev. A1:764 (1970).Google Scholar
  86. 86.
    M. Rudkjqcbing, Kgl. Danske Videnskab Selskab, Mat.-Fys. Med. 27, No. 5 (1952).Google Scholar
  87. 87.
    B. Jancovici, Nuovo Cim. 25: 428 (1962).MATHCrossRefGoogle Scholar
  88. 88.
    E.E. Salpeter, Astrophys. J. 134:669 (1961).ADSGoogle Scholar
  89. 89.
    F. Constantinescu, “ Distributionen und ihre Anwendungen in der Physik,” p. 59 ff, Teubner, Stuttgart (1974).CrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1985

Authors and Affiliations

  • Eberhard K. U. Gross
    • 1
  • Reiner M. Dreizler
    • 1
  1. 1.Institut für Theoretische PhysikUniversität FrankfurtFrankfurt am MainFederal Republic of Germany

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