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Part of the book series: Physics of Solids and Liquids ((PSLI))

Abstract

Over the course of the last 15 years density functional theory (DFT)* has evolved as a conceptually and practically useful method for studying the electronic properties of many-electron systems. In this chapter we present a critical review of the general theory together with some illustrative examples.† More complete discussions of several important areas of application may be found in other chapters of this book.

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References

  1. A. K. Rajagopal, in Advances in Chemical Physics, I. Prigogine and S. A. Rice, editors, Vol. 41, pp. 59–193 (Wiley, New York, 1980).

    Google Scholar 

  2. L. H. Thomas, Proc. Camb. Phil Soc. 23, 542–547 (1927).

    ADS  MATH  Google Scholar 

  3. E. Fermi, Rend. Acad. Naz. Lincei 6, 602–607 (1927).

    Google Scholar 

  4. N. H. March, Self-Consistent Fields in Atoms (Pergamon Press, New York, 1975).

    Google Scholar 

  5. P. Hohenberg and W. Kohn, Phys. Rev. 136, B864–871 (1964).

    MathSciNet  ADS  Google Scholar 

  6. W. Kohn and L. J. Sham, Phys. Rev. A 140, 1133–1138 (1965).

    MathSciNet  ADS  Google Scholar 

  7. E. P. Wigner, Trans. Faraday Soc. 34, 678–685 (1938).

    Google Scholar 

  8. M. Gell-Mann and K. A. Brueckner, Phys. Rev. 106, 364–368 (1957).

    MathSciNet  ADS  MATH  Google Scholar 

  9. L. Onsager, L. Mittag, and M. J. Stephen, Ann. Phys. (Leipzig) 18, 71–77 (1966).

    ADS  Google Scholar 

  10. P. Nozieres and D. Pines, Phys. Rev. 111, 442–454 (1958).

    ADS  MATH  Google Scholar 

  11. T. Gaskell, Proc. Phys. Soc. 77, 1182–1192 (1961).

    MathSciNet  ADS  MATH  Google Scholar 

  12. P. Vashishta and K. S. Singwi, Phys. Rev. B 6, 875–887 (1972).

    ADS  Google Scholar 

  13. P. Vashishta and K. S. Singwi, Phys. Rev. B 6, 4883–4883 (1972).

    ADS  Google Scholar 

  14. K. S. Singwi, A. Sjölander, M. P. Tosi, and R. H. Land, Phys. Rev. B 1, 1044–1053 (1970).

    ADS  Google Scholar 

  15. K. S. Singwi, M. P. Tosi, R. H. Land, and A. Sjölander, Phys. Rev. 176, 589–599 (1968).

    ADS  Google Scholar 

  16. L. Kleinman, Phys. Rev. B 10, 2221–2225 (1974)(E).

    ADS  Google Scholar 

  17. L. Kleinman, Phys. Rev. B 12, 3512 (1975).

    ADS  Google Scholar 

  18. C. F. von Weizsäcker, Z. Phys. 96, 431–458 (1935).

    ADS  MATH  Google Scholar 

  19. D. A. Kirzhnits, Zh. Eksp. Teor. Fiz. 32, 115–123 (1957) English Transl.

    Google Scholar 

  20. D. A. Kirzhnits, Sov. Phys.—JETP 5, 64–71 (1957).

    MathSciNet  MATH  Google Scholar 

  21. L. J. Sham and W. Kohn, Phys. Rev. 145, 561–567 (1966).

    ADS  Google Scholar 

  22. T. C. Koopmans, Physica 1, 104–113 (1933).

    ADS  MATH  Google Scholar 

  23. V. von Barth and L. Hedin, J. Phys. C 5, 1629–1642 (1972).

    ADS  Google Scholar 

  24. O. Gunnarsson and B. I. Lundqvist, Phys. Rev. B 13, 4274–4298 (1976).

    ADS  Google Scholar 

  25. S. K. Ma and K. Brueckner, Phys. Rev. 165, 18–31 (1968).

    ADS  Google Scholar 

  26. D. J. W. Geldart and M. Rasolt, Phys. Rev. B 13, 1477–1488 (1976).

    ADS  Google Scholar 

  27. A. K. Gupta and K. S. Singwi, Phys. Rev. B 15, 1801–1810 (1977).

    ADS  Google Scholar 

  28. K. H. Lau and W. Kohn, J. Phys. Chem. Solids 37, 99–104 (1976).

    ADS  Google Scholar 

  29. J. P. Perdew, D. C. Langreth, and V. Sahni, Phys. Rev. Lett. 38, 1030–1033 (1977).

    ADS  Google Scholar 

  30. J. Harris and R. O. Jones, J. Phys. F 4, 1170–1186 (1974).

    ADS  Google Scholar 

  31. D. C. Langreth and J. P. Perdew, Phys. Rev. B 15, 2884–2901 (1977).

    ADS  Google Scholar 

  32. O. Gunnarsson, in Electrons in Disordered Metals and at Metallic Surfaces, P. Phariseau, B. L. Gyorffy, and L. Schiene, editors, pp. 1–53 (Plenum Press, New York, 1979).

    Google Scholar 

  33. O. Gunnarsson, M. Jonson, and B. I. Lundquist, Solid State Commun. 24, 765–768 (1977).

    ADS  Google Scholar 

  34. A. J. Coleman, Rev. Mod. Phys. 35, 668–687 (1963).

    ADS  Google Scholar 

  35. M. Levy, Proc. Natl. Acad. Sci. USA 76, 6062–6065 (1979).

    ADS  Google Scholar 

  36. L. D. Landau, Sov. Phys. JETP 3, 920–925 (1956).

    Google Scholar 

  37. S. Chakravarty, M. Fogel, and W. Kohn, Phys. Rev. Lett. 43, 775–778 (1979).

    ADS  Google Scholar 

  38. B. Y. Tong and L. J. Sham, Phys. Rev. 144, 1–4 (1966).

    ADS  Google Scholar 

  39. J. C. Slater, Phys. Rev. 81, 385–390 (1951).

    ADS  MATH  Google Scholar 

  40. J. C. Slater in Advances in Quantum Chemistry, P. O. Lowdin, ed., Vol. 6, pp. 1–92, (Academic Press, New York, 1972).

    Google Scholar 

  41. J. C. Slater, Int. J. Qu. Chem. Symp. 9, 7–21 (1975).

    Google Scholar 

  42. J. C. Slater, The S elf-Consistent Field for Molecules and Solids, Vol. 4 (McGraw-Hill Co., New York, 1974).

    Google Scholar 

  43. J. C. Slater, The Calculations of Molecular Orbitals, Vol. 5 (McGraw-Hill Co., New York, 1979).

    Google Scholar 

  44. D. C. Langreth and J. P. Perdew, Phys. Rev. B 15, 2884–2901 (1977).

    ADS  Google Scholar 

  45. O. Gunnarsson, J. Harris, and R. O. Jones, J. Chem. Phys. 67, 3970–3979 (1977).

    ADS  Google Scholar 

  46. V. L. Morruzzi, J. F. Janak, and A. R. Williams, Calculated Electronic Properties of Metals (Pergamon Press, New York, 1978).

    Google Scholar 

  47. F. Stern, CRC Crit. Rev. Solid State Sci. 4, 499–514 (1974).

    Google Scholar 

  48. T. Ando, Phys. Rev. B 13, 3468–3477 (1976).

    ADS  Google Scholar 

  49. T. Ando, Z. Phys. B 26, 263–272 (1977).

    ADS  Google Scholar 

  50. P. Kneschaurek, A. Kamgar, and J. F. Koch, Phys. Rev. B 14, 1610–1612 (1976).

    ADS  Google Scholar 

  51. R. Gordon and Y. S. Kim, J. Chem. Phys. 56, 3122–3133 (1972).

    ADS  Google Scholar 

  52. J. R. Smith, Phys. Rev. 181, 522–529 (1969).

    ADS  Google Scholar 

  53. P. Vashishta and W. Kohn, Bull. Am. Phys. Soc. 24, 439 (1979).

    Google Scholar 

  54. M. M. Pant and A. K. Rajagopal, Solid State Commun. 10, 1157–1160 (1972).

    ADS  Google Scholar 

  55. A. K. Rajagopal and J. Calloway, Phys. Rev. B 7, 1912–1919 (1973).

    ADS  Google Scholar 

  56. G. Pizzimenti, M. P. Tosi, and A. Villari, Lett. Nuovo Cimento Serie 2 2, 81–84 (1971).

    Google Scholar 

  57. R. Dupree and D. J. W. Geldart, Solid State Commun. 9, 145–149 (1971).

    ADS  Google Scholar 

  58. P. Vashishta and K. S. Singwi, Solid State Commun. 13, 901–904 (1973).

    ADS  Google Scholar 

  59. O. K. Anderson and R. G. Wesley, Mol. Phys. 26, 905–927 (1973).

    ADS  Google Scholar 

  60. S. H. Vosko and J. P. Perdew, Can. J. Phys. 53, 1385–1397 (1975).

    ADS  Google Scholar 

  61. S. H. Vosko, J. P. Perdew, and A. H. MacDonald, Phys. Rev. Lett. 35, 1725–1728 (1975).

    ADS  Google Scholar 

  62. A. H. MacDonald, J. P. Perdew, and S. H. Vosko, Solid State Commun. 18, 85–91 (1976).

    ADS  Google Scholar 

  63. A. H. MacDonald and S. H. Vosko, J. Low Temp. Phys. 25, 27–41 (1976).

    ADS  Google Scholar 

  64. J. F. Janak, Phys. Rev. B 16, 255–262 (1977).

    ADS  Google Scholar 

  65. K. L. Liu and S. H. Vosko, J. Phys. F 8, 1539–1556 (1978).

    ADS  Google Scholar 

  66. C. S. Wang and J. Callaway, Solid State Commun. 20, 255–256 (1976).

    ADS  Google Scholar 

  67. L. M. Sander, H. B. Shore, and L. J. Sham, Phys. Rev. Lett. 31, 533–536 (1973).

    ADS  Google Scholar 

  68. H. Bütner and E. Gerlach, J. Phys. C 6, L433–L436 (1973).

    Google Scholar 

  69. T. M. Rice, Phys. Rev. B 9, 1540–1546 (1974).

    ADS  Google Scholar 

  70. T. L. Reinecke and S. C. Ying, Solid State Commun. 14, 381–385 (1974).

    ADS  Google Scholar 

  71. T. L. Reinecke, F. Crowne, and S. C. Ying, in Proceedings of 12th International Conference on the Physics of Semiconductors, Stuttgart, Germany, 1974, pp. 61–65, M. H. Pilkuhn, ed. (Teubner, Stuttgart, 1975).

    Google Scholar 

  72. P. Vashishta, R. K. Kalia, and K. S. Singwi, Solid State Commun. 19, 935–938 (1976).

    ADS  Google Scholar 

  73. M. Morimoto, K. Shindo, and A. Morita, in Proceedings of the Oji Seminar on the Physics of Highly Excited States in Solids, Vol. 57, pp. 230–236, M. Ueta and Y. Nishina, eds. (Springer-Verlag, Berlin, 1976).

    Google Scholar 

  74. T. M. Rice, in Solid State Physics, H. Ehrenreich, F. Seitz, and D. Turnbull, eds., Vol. 32, pp. 1–86 (Academic Press, New York, 1977).

    Google Scholar 

  75. R. K. Kalia and P. Vashishta, Solid State Commun. 24, 171–174 (1977).

    ADS  Google Scholar 

  76. M. Rasolt and D. J. W. Geldart, Phys. Rev. B 15, 979–988 (1977).

    ADS  Google Scholar 

  77. M. Rasolt and D. J. W. Geldart, Phys. Rev. B 15, 4804–4816 (1977).

    ADS  Google Scholar 

  78. J. H. Rose and H. B. Shore, Phys. Rev. B 17, 1884–1892 (1978).

    ADS  Google Scholar 

  79. R. K. Kalia and P. Vashishta, Phys. Rev. B 17, 2655–2672 (1978).

    ADS  Google Scholar 

  80. K. A. Brueckner, J. R. Buchler, R. C. Clark, and R. J. Lombard, Phys. Rev. 181, 1543–1551 (1969).

    ADS  Google Scholar 

  81. G. Baym, H. A. Bethe, and C. J. Pethick, Nucl. Phys. A 175, 225–271 (1971).

    ADS  Google Scholar 

  82. K. A. Brueckner, J. H. Chirico, and H. W. Meldner, Phys. Rev.C 4, 732–740 (1971).

    ADS  Google Scholar 

  83. L. V. Keldysh, in Proceedings of the 9th International Conference on Physics of Semiconductors, Moscow 1968, pp. 1303–1312, S. M. Ryvkin and V. V. Shmastsev, eds. (Nauka, Leningrad, 1968).

    Google Scholar 

  84. Y. E. Pokrovsky, Phys. Stat. Sol. A11, 385–410 (1972).

    ADS  Google Scholar 

  85. V. S. Bagaev, Springer Tracts Mod. Phys. 73, 72–90 (1951).

    ADS  Google Scholar 

  86. C. D. Jeffries, Science 189, 955–964 (1975).

    ADS  Google Scholar 

  87. M. Voos and C. Benoit a la Guillaume, in Optical Properties of Solids: New Developments, B. O. Seraphin, ed., pp. 143–186 (American Elsevier, New York, 1976).

    Google Scholar 

  88. J. C. Hensel, T. G. Phillips, and G. A. Thomas, in Solid State Physics, H. Ehrenreich, F. Seitz, and D. Turnbull, eds., Vol. 32, pp. 88–314 (Academic Press, New York, 1977).

    Google Scholar 

  89. L. J. Sham and T. M. Rice, Phys. Rev. 144, 708–714 (1966).

    ADS  Google Scholar 

  90. E. Hanamura, in Proceedings of the 10th International Conference on the Physics of Semiconductors, Cambridge, Massachusetts, 1970.

    Google Scholar 

  91. S. P. Keller, J. C. Hensel, and F. Stern, eds., pp. 487–493, CONF-700801 (U. S. AEC Div. Tech. Information, Springfield, Virginia 1970).

    Google Scholar 

  92. M. Combescot and P. Nozieres, J. Phys. C 5, 2369–2391 (1972).

    ADS  Google Scholar 

  93. W. F. Brinkman, T. M. Rice, P. W. Anderson, and S. T. Chui, Phys. Rev. Lett. 28, 961–964 (1972).

    ADS  Google Scholar 

  94. W. F. Brinkman and T. M. Rice, Phys. Rev. B 7, 1508–1523 (1973).

    ADS  Google Scholar 

  95. P. Vashishta, S. G. Das, and K. S. Singwi, Phys. Rev. Lett. 33, 911–914 (1974).

    ADS  Google Scholar 

  96. P. Vashishta, P. Bhattacharyya, and K. S. Singwi, Phys. Rev. B 10, 5108–5126 (1974).

    ADS  Google Scholar 

  97. B. Etienne, L. M. Sander, G. Benoit a la Guillaume, M. Voos, and J. Y. Prieur, Phys. Rev. Lett. 37, 1299–1302 (1976).

    ADS  Google Scholar 

  98. Y. E. Pokrovsky and K. I. Svistunova, in Proceedings of the Twelfth International Conference on the Physics of Semiconductors, Stuttgart, Germany, 1974, pp. 71–75, M. H. Pilkuhn, ed. (Teubner, Stuttgart, 1975).

    Google Scholar 

  99. T. Ugumori, K. Morigaki, and C. Magashima J. Phys. Soc.Jpn 46, 536–541 (1979).

    ADS  Google Scholar 

  100. N. D. Mermin, Phys. Rev. 137A, 1441–1443 (1965).

    MathSciNet  ADS  Google Scholar 

  101. J. M. Luttinger, Phys. Rev. 119, 1153–1163 (1960).

    MathSciNet  ADS  MATH  Google Scholar 

  102. A. Ghazali and P. Leroux Hugon, Phys. Rev. Lett. 41, 1569–1572 (1978).

    ADS  Google Scholar 

  103. A. A. Abrikosov, L. P. Gorkov, and I. E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics (Prentice-Hall, Englewood Cliffs, New Jersey, 1963).

    MATH  Google Scholar 

  104. R. Kubo, J. Phys. Soc.Jpn Vol. 12, 570 (1957).

    MathSciNet  ADS  Google Scholar 

  105. P. B. Roulet and P. Nozieres, J. Phys. (Paris) 29, 167–180 (1968).

    Google Scholar 

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Kohn, W., Vashishta, P. (1983). General Density Functional Theory. In: Lundqvist, S., March, N.H. (eds) Theory of the Inhomogeneous Electron Gas. Physics of Solids and Liquids. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-0415-7_2

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