Skip to main content
SpringerLink
Log in

Thomas-Fermi and Other Density-Functional Theories

  • Reference work entry
Springer Handbook of Atomic, Molecular, and Optical Physics

Part of the book series: Springer Handbooks ((SHB))

Abstract

The key idea in Thomas-Fermi theory and its generalizations is the replacement of complicated terms in the kinetic energy and electron-electron repulsion energy contributions to the total energy by relatively simple functionals of the electron density ρ. This chapter first describes Thomas-Fermi theory, and then its various generalizations which attempt to correct, with varying success, some of its deficiencies. It concludes with an overview of the Hohenberg-Kohn and Kohn-Sham density functional theories.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Abbreviations

DFT:

discrete Fourier transform

GGA:

generalized gradient approximation

LDA:

local density approximation

LYP:

Lee, Yang, and Parr

TF:

toroidal field

References

  1. L. H. Thomas: Proc. Camb. Philos. Soc. 23, 542 (1927)

    MATH  Google Scholar 

  2. E. Fermi: Rend. Accad. Naz. Lincei 6, 602 (1927)

    Google Scholar 

  3. E. Fermi: Rend. Accad. Naz. Lincei 7, 342 (1928)

    Google Scholar 

  4. E. Fermi: Z. Phys. 48, 73 (1928)

    ADS  Google Scholar 

  5. E. Fermi: Z. Phys. 49, 550 (1928)

    ADS  Google Scholar 

  6. W. Lenz: Z. Phys. 77, 713 (1932)

    MATH  ADS  Google Scholar 

  7. P. A. M. Dirac: Proc. Camb. Philos. Soc. 26, 376 (1930)

    MATH  Google Scholar 

  8. C. F. von Weizsäcker: Z. Phys. 96, 431 (1935)

    MATH  ADS  Google Scholar 

  9. E. H. Lieb, B. Simon: Phys. Rev. Lett. 31, 681 (1973)

    ADS  Google Scholar 

  10. E. H. Lieb, B. Simon: Adv. Math. 23, 22 (1977)

    MathSciNet  Google Scholar 

  11. J. W. Sheldon: Phys. Rev. 99, 1291 (1955)

    MATH  ADS  Google Scholar 

  12. E. Teller: Rev. Mod. Phys. 34, 627 (1962)

    MATH  ADS  Google Scholar 

  13. N. Balàzs: Phys. Rev. 156, 42 (1967)

    ADS  Google Scholar 

  14. E. H. Lieb, W. Thirring: Phys. Rev. Lett. 35, 687 (1975)

    ADS  Google Scholar 

  15. E. H. Lieb: Rev. Mod. Phys. 53, 603 (1981)

    MATH  ADS  MathSciNet  Google Scholar 

  16. E. H. Lieb: Rev. Mod. Phys., 54, 311(E) (1982)

    Google Scholar 

  17. L. Spruch: Rev. Mod. Phys. 63, 151 (1991)

    ADS  Google Scholar 

  18. P. Gombás: Die statistische Theorie des Atoms und ihre Anwendungen (Springer, Berlin, Heidelberg 1949)

    MATH  Google Scholar 

  19. P. Gombás: Statistische Behandlung des Atoms. In: Atome II, Handbuch der Physik, Vol. 36, ed. by S. Flügge (Springer, Berlin, Heidelberg 1956) pp. 109-231

    Google Scholar 

  20. N. H. March: The Thomas-Fermi approximation in quantum mechanics, Adv. Phys. 6, 1-98 (1957)

    ADS  Google Scholar 

  21. P. Hohenberg, W. Kohn: Phys. Rev. B 136, 864 (1964)

    ADS  MathSciNet  Google Scholar 

  22. W. Kohn, L. J. Sham: Phys. Rev. A 140, 1133 (1965)

    ADS  MathSciNet  Google Scholar 

  23. E. Fermi, E. Amaldi: Mem. Accad. d'Italia 6, 119 (1934)

    Google Scholar 

  24. E. A. Milne: Proc. Camb. Philos. Soc. 23, 794 (1927)

    MATH  Google Scholar 

  25. E. B. Baker: Phys. Rev. 36, 630 (1930)

    ADS  Google Scholar 

  26. Y. Tal, M. Levy: Phys. Rev. A 23, 408 (1981)

    ADS  MathSciNet  Google Scholar 

  27. C. H. Hodges: Can. J. Phys. 51, 1428 (1973)

    ADS  Google Scholar 

  28. R. Benguria, E. H. Lieb: J. Phys. B 18, 1045 (1985)

    ADS  MathSciNet  Google Scholar 

  29. R. Ahlrichs, T. Hoffmann-Ostenhof, M. Hoffmann-Ostenhof, J. D. Morgan III: Phys. Rev. A 23, 2107 (1981) and references therein

    ADS  MathSciNet  Google Scholar 

  30. T. Kato: Commun. Pure Appl. Math. 10, 151 (1957)

    MATH  Google Scholar 

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

    ADS  Google Scholar 

  32. M. Levy, J. P. Perdew: In: Density Functional Methods in Physics, NATO ASI Series B, Vol. 123, ed. by R. M. Dreizler, J. da Providência (Plenum, New York 1985) pp. 11-30

    Google Scholar 

  33. E. H. Lieb: In: Density Functional Methods in Physics, NATO ASI Series B, Vol. 123, ed. by R. M. Dreizler, J. da Providência (Plenum, New York 1985) pp. 31-80

    Google Scholar 

  34. J. A. Goldstein, G. R. Rieder: J. Math. Phys. 32, 2907 (1991)

    ADS  MathSciNet  Google Scholar 

  35. J. A. Goldstein, G. R. Rieder: J. Math. Phys. 29, 709 (1988)

    MATH  ADS  MathSciNet  Google Scholar 

  36. J. M. C. Scott: Philos. Mag. 43, 859 (1952)

    Google Scholar 

  37. E. H. Lieb: Rev. Mod. Phys. 48, 553 (1976)

    ADS  MathSciNet  Google Scholar 

  38. J. Schwinger: Phys. Rev. A 22, 1827 (1980)

    ADS  MathSciNet  Google Scholar 

  39. H. Siedentop, R. Weikard: Commun. Math. Phys. 112, 471 (1987)

    MATH  ADS  MathSciNet  Google Scholar 

  40. H. Siedentop, R. Weikard: Invent. Math. 97, 159 (1989)

    MATH  ADS  MathSciNet  Google Scholar 

  41. W. Hughes: Adv. Math. 79, 213 (1990)

    MATH  MathSciNet  Google Scholar 

  42. V. Bach: Rep. Math. Phys. 28, 213 (1989)

    MATH  ADS  MathSciNet  Google Scholar 

  43. V. J. Ivrii, I. M. Sigal: Annals of Math. 138, 243 (1993)

    MATH  MathSciNet  Google Scholar 

  44. J. Schwinger: Phys. Rev. A 24, 2353 (1981)

    ADS  MathSciNet  Google Scholar 

  45. N. H. March, J. S. Plaskett: Proc. Roy. Soc. Lond. A 235, 419 (1956)

    MATH  ADS  MathSciNet  Google Scholar 

  46. R. Shakeshaft, L. Spruch, J. Mann: J. Phys. B 14, L121 (1981)

    ADS  Google Scholar 

  47. R. Shakeshaft, L. Spruch: Phys. Rev. A 23, 2118 (1981)

    ADS  Google Scholar 

  48. B.-G. Englert, J. Schwinger: Phys. Rev. A 26, 2322 (1982)

    ADS  Google Scholar 

  49. B.-G. Englert, J. Schwinger: Phys. Rev. A 29, 2331, 2339, 2353 (1984)

    ADS  MathSciNet  Google Scholar 

  50. B.-G. Englert, J. Schwinger: Phys. Rev. A 32, 28, 36, 47 (1985)

    ADS  Google Scholar 

  51. A. Iantchenko, E. H. Lieb, H. Siedentop: J. Reine Angew. Math. 472, 177 (1996)

    MATH  MathSciNet  Google Scholar 

  52. O. J. Heilman, E. H. Lieb: Phys. Rev. A 52, 3628 (1995)

    ADS  Google Scholar 

  53. C. L. Fefferman, L. A. Seco: Bull. Amer. Math. Soc. 23, 525 (1990)

    MATH  MathSciNet  Google Scholar 

  54. C. Fefferman, L. A. Seco: Adv. Math. 107, 1 (1994)

    MATH  MathSciNet  Google Scholar 

  55. C. Fefferman, L. Seco: Adv. Math. 95, 145 (1992)

    MATH  MathSciNet  Google Scholar 

  56. C. Fefferman, L. A. Seco: Revista Matemática Iberoamericana 9, 409 (1993)

    MATH  MathSciNet  Google Scholar 

  57. C. Fefferman, L. Seco: Adv. Math. 107, 187 (1994)

    MATH  MathSciNet  Google Scholar 

  58. C. Fefferman, L. Seco: Adv. Math. 108, 263 (1994)

    MATH  MathSciNet  Google Scholar 

  59. A. Cordoba, C. Fefferman, L. Seco: Proc. Natl. Acad. Sci. 91, 5776 (1994)

    MATH  ADS  MathSciNet  Google Scholar 

  60. A. Cordoba, C. Fefferman, L. A. Seco: Revista Matématica Iberoamericana 11, 165 (1995)

    MATH  MathSciNet  Google Scholar 

  61. C. Fefferman, L. Seco: Adv. Math. 111, 88 (1995)

    MATH  MathSciNet  Google Scholar 

  62. C. Fefferman, L. Seco: Adv. Math. 119, 26 (1996)

    MATH  MathSciNet  Google Scholar 

  63. C. Fefferman: Adv. Math. 124, 100 (1996)

    MATH  MathSciNet  Google Scholar 

  64. V. Heine: Solid State Phys. 24, 1 (1970)

    Google Scholar 

  65. M. L. Cohen, V. Heine: Solid State Phys. 24, 37 (1970)

    Google Scholar 

  66. V. Heine, D. Weaire: Solid State Phys. 24, 249 (1970)

    Google Scholar 

  67. M. C. Payne, M. P. Teter, D. C. Allan, T. A. Arias, J. D. Joannopoulos: Rev. Mod. Phys. 64, 1045 (1992)

    ADS  Google Scholar 

  68. A. K. Rajagopal: Adv. Chem. Phys. 41, 59 (1980)

    Google Scholar 

  69. A. S. Bamzai, B. M. Deb: Rev. Mod. Phys. 53, 95, 593(E) (1981)

    ADS  Google Scholar 

  70. R. G. Parr: Ann. Rev. Phys. Chem. 34, 631 (1983)

    ADS  Google Scholar 

  71. J. Callaway, N. H. March: Solid State Phys. 38, 135 (1984)

    Google Scholar 

  72. R. O. Jones, O. Gunnarsson: Rev. Mod. Phys. 61, 689 (1989)

    ADS  Google Scholar 

  73. S. B. Trickey: In: Conceptual trends in quantum chemistry, Vol. 1, ed. by E. S. Kryachko, J. L. Calais (Kluwer, Amsterdam 1994) pp. 87-100

    Google Scholar 

  74. S. Lundqvist, N. H. March (Eds.): Theory of the Inhomogeneous Electron Gas (Plenum, New York 1983)

    Google Scholar 

  75. N. H. March, B. M. Deb (Eds.): The Single-Particle Density in Physics and Chemistry (Academic, New York 1987)

    Google Scholar 

  76. S. B. Trickey (Ed.): Density Functional Theory of Many-Fermion Systems, Advances in Quantum Chemistry, Vol. 21 (Academic, New York 1990)

    Google Scholar 

  77. J. Keller, J. L. Gázquez: In: Density Functional Theory, Lecture Notes in Physics, Vol. 187 (Springer, Berlin, Heidelberg 1983)

    Google Scholar 

  78. D. Langreth, H. Suhl (Eds.): Many-Body Phenomena at Surfaces (Academic, New York 1984)

    Google Scholar 

  79. J. P. Dahl, J. Avery (Eds.): Local Density Approximations in Quantum Chemistry and Solid State Physics (Plenum, New York 1984)

    Google Scholar 

  80. P. Phariseau, W. M. Temmermann (Eds.): The Electronic Structure of Complex Systems, NATO ASI Series B, Vol. 113 (Plenum, New York 1984)

    Google Scholar 

  81. R. M. Dreizler, J. da Providência (Eds.): Density Functional Methods in Physics, NATO ASI Series B, Vol. 123 (Plenum, New York 1985)

    Google Scholar 

  82. R. Erdahl, V. H. Smith Jr. (Eds.): Density Matrices and Density Functionals (Reidel, Dordrecht 1987)

    Google Scholar 

  83. J. K. Labanowski, J. W. Andzelm (Eds.): Density Functional Methods in Chemistry (Springer, New York 1991)

    Google Scholar 

  84. P. J. Grout, A. B. Lidiard (Eds.): Density Functional Theory and its Applications. To celebrate the 65th Birthday of Norman H. March, Philos. Mag. B 69, 725-1074 (1994)

    Google Scholar 

  85. E. S. Kryachko, E. V. Ludeña: Energy Density Functional Theory of Many-Electron Systems (Kluwer, Dordrecht 1990)

    Google Scholar 

  86. E. K. U. Gross, R. M. Dreizler (Eds.): Density Functional Theory, NATO ASI Series B, Vol. 337 (Plenum, New York 1995)

    Google Scholar 

  87. A. Goursot, C. Mijoule, N. Russo (Eds.): CECAM Workshop, Theoret. Chim. Acta 91, 111-266 (1995)

    Google Scholar 

  88. R. G. Parr, W. Yang: Density-Functional Theory of Atoms and Molecules (Clarendon, Oxford 1989)

    Google Scholar 

  89. R. M. Dreizler, E. K. U. Gross: Density Functional Theory: An Approach to the Quantum Many-Body Problem (Springer, Berlin, Heidelberg 1990)

    MATH  Google Scholar 

  90. T. L. Gilbert: Phys. Rev. B 12, 2111 (1975)

    ADS  Google Scholar 

  91. J. E. Harriman: Phys. Rev. A 24, 680 (1981)

    ADS  Google Scholar 

  92. E. H. Lieb: In: Physics as Natural Philosophy: Essays in Honor of Laszlo Tisza on his 75th Birthday, ed. by H. Feshbach, A. Shimony (MIT, Cambridge 1982) pp. 111-149; reprinted in [20.173]

    Google Scholar 

  93. M. Levy: Phys. Rev. A 26, 1200 (1982)

    ADS  Google Scholar 

  94. J. K. Percus: Intern. J. Quantum Chem. 13, 89 (1978)

    Google Scholar 

  95. M. Levy: Proc. Natl. Acad. Sci. USA 76, 6062 (1979)

    ADS  Google Scholar 

  96. D. M. Ceperley, B. J. Alder: Phys. Rev. Lett. 45, 566 (1980)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  98. A. D. Becke: Intern. J. Quantum Chem. Symp. 23, 599 (1989)

    Google Scholar 

  99. A. D. Becke: J. Chem. Phys. 96, 2155 (1992)

    ADS  Google Scholar 

  100. A. D. Becke: J. Chem. Phys. 97, 9173 (1992)

    ADS  Google Scholar 

  101. A. D. Becke: J. Chem. Phys. 98, 5648 (1993)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  103. R. M. Dickson, A. D. Becke: J. Chem. Phys. 99, 3898 (1993)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    Google Scholar 

  106. R. Colle, O. Salvetti: Theoret. Chim. Acta 53, 55 (1979)

    Google Scholar 

  107. R. Colle, O. Salvetti: J. Chem. Phys. 79, 1404 (1983)

    ADS  Google Scholar 

  108. B. G. Johnson, P. M. W. Gill, J. A. Pople: J. Chem. Phys. 98, 5612 (1993)

    ADS  Google Scholar 

  109. C. W. Murray, N. C. Handy, R. D. Amos: J. Chem. Phys. 98, 7145 (1993)

    ADS  Google Scholar 

  110. G. J. Laming, V. Termath, N. C. Handy: J. Chem. Phys. 99, 8765 (1993)

    ADS  Google Scholar 

  111. G. Ortiz, P. Ballone: Phys. Rev. B 43, 6376 (1991)

    ADS  Google Scholar 

  112. C. Lee, Z. Zhou: Phys. Rev. A 44, 1536 (1991)

    ADS  Google Scholar 

  113. E. Engel, J. A. Chevary, L. D. Macdonald, S. H. Vosko: Z. Phys. D 23, 7 (1992)

    ADS  Google Scholar 

  114. S. H. Vosko, L. Wilk, M. Nusair: Can. J. Phys. 1200 (1980)

    Google Scholar 

  115. D. C. Langreth, M. J. Mehl: Phys. Rev. Lett. 47, 446 (1981)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  117. D. C. Langreth, M. J. Mehl: Phys. Rev. B 29, 2310(E) (1984)

    ADS  Google Scholar 

  118. J. P. Perdew, Y. Wang: Phys. Rev. B 33, 8800 (1986)

    ADS  Google Scholar 

  119. J. P. Perdew: Phys. Rev. B 33, 8822 (1986)

    ADS  Google Scholar 

  120. J. P. Perdew: Phys. Rev. B 34, 7406(E) (1986)

    ADS  Google Scholar 

  121. A. E. DePristo, J. D. Kress: J. Chem. Phys. 86, 1425 (1987)

    ADS  Google Scholar 

  122. L. C. Wilson, M. Levy: Phys. Rev. B 41, 12930 (1990)

    ADS  Google Scholar 

  123. J. P. Perdew: Physica B 172, 1 (1991)

    ADS  Google Scholar 

  124. J. P. Perdew, Y. Wang: Phys. Rev. B 45, 13244 (1992)

    ADS  Google Scholar 

  125. D. J. Lacks, R. G. Gordon: Phys. Rev. A 47, 4681 (1993)

    ADS  Google Scholar 

  126. J. P. Perdew: Int. J. Quantum Chem. Symp. 27, 93 (1993)

    Google Scholar 

  127. C. Filippi, C. J. Umrigar, M. Taut: J. Chem. Phys. 100, 1290 (1994)

    ADS  Google Scholar 

  128. C. J. Umrigar, X. Gonze: Phys. Rev. A 50, 3827 (1994)

    ADS  Google Scholar 

  129. C. J. Umrigar: High Performance Computing and its Application to the Physical Sciences. In: Proc. of the Mardi Gras '93 Conference, ed. by D. A. Browne, J. Callaway, J. P. Drayer, R. W. Haymaker, R. K. Kalia, J. E. Tohline, P. Vashishta (World Scientific, Singapore 1993) pp. 43-59

    Google Scholar 

  130. M. Levy, J. P. Perdew: Phys. Rev. A 32, 2010 (1985)

    ADS  Google Scholar 

  131. M. Levy, H. Ou-Yang: Phys. Rev. A 38, 625 (1988)

    ADS  Google Scholar 

  132. M. Levy: In: Density Functional Theory of Many-Fermion Systems, Advances in Quantum Chemistry, Vol. 21, ed. by S. B. Trickey (Academic, New York 1990) pp. 69-95

    Google Scholar 

  133. M. Levy: In: Density Functional Methods in Chemistry, ed. by J. K. Labanowski, J. W. Andzelm (Springer, New York 1991) pp. 175-193

    Google Scholar 

  134. A. Görling, M. Levy: Phys. Rev. A 45, 1509 (1992)

    ADS  Google Scholar 

  135. Q. Zhao, M. Levy, R. G. Parr: Phys. Rev. A 47, 918 (1993)

    ADS  Google Scholar 

  136. A. Görling, M. Levy: Phys. Rev. B 47, 13105 (1993)

    ADS  Google Scholar 

  137. M. Levy, J. P. Perdew: Phys. Rev. B 48, 11638 (1993)

    ADS  Google Scholar 

  138. A. Görling, M. Levy: Phys. Rev. A 50, 196 (1994)

    ADS  Google Scholar 

  139. M. Levy, A. Görling: Philos. Mag. B 69, 763 (1994)

    Google Scholar 

  140. O. Gunnarson, B. J. Lundqvist: Phys. Rev. B 13, 4274 (1976)

    ADS  Google Scholar 

  141. A. K. Theophilou: J. Phys. C 12, 5419 (1979)

    ADS  Google Scholar 

  142. N. Hadjisavvas, A. Theophilou: Phys. Rev. A 30, 2183 (1984)

    ADS  MathSciNet  Google Scholar 

  143. N. Hadjisavvas, A. K. Theophilou: Philos. Mag. B 69, 771 (1994)

    Google Scholar 

  144. J. Katriel: J. Phys. C 13, L375 (1980)

    ADS  Google Scholar 

  145. A. Theophilou: Phys. Rev. A 32, 720 (1985)

    ADS  Google Scholar 

  146. W. Kohn: Phys. Rev. A 34, 737 (1986)

    ADS  Google Scholar 

  147. E. K. U. Gross, L. N. Oliveira, W. Kohn: Phys. Rev. A 37, 2805, 2809 (1988)

    ADS  MathSciNet  Google Scholar 

  148. L. N. Oliveira, E. K. U. Gross, W. Kohn: Phys. Rev. A 37, 2821 (1988) and earlier references therein

    ADS  MathSciNet  Google Scholar 

  149. H. Englisch, H. Fieseler, A. Haufe: Phys. Rev. A 37, 4570 (1988)

    ADS  Google Scholar 

  150. L. N. Oliveira: In: Density Functional Theory of Many-Fermion Systems, Advances in Quantum Chemistry, Vol. 21, ed. by S. B. Trickey (Academic, New York 1990) pp. 135-154

    Google Scholar 

  151. L. N. Oliveira, E. K. U. Gross, W. Kohn: Int. J. Quantum Chem. Symp. 24, 707 (1990)

    Google Scholar 

  152. R. M. Dreizler: Phys. Scr. T46, 167 (1993)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  155. R. F. Nalewajski (Ed.): Functionals and Effective Potentials I; Relativistic and Time Dependent Extensions II; Interpretation, Atoms, Molecules and Clusters III; Theory of Chemical Reactivity IV, Topics in Current Chemistry, Vol. 180-183 (Springer, New York 1996)

    Google Scholar 

  156. J. M. Seminario (Ed.): Density Functional Theory, Advances in Quantum Chemistry, Vol. 33 (Academic, New York 1999)

    Google Scholar 

  157. B. B. Laird, R. B. Ross, T. Ziegler: Chemical Applications of Density-Functional Theory, ACS Symposium Series, Vol. 629 (American Chemical Society, Washington 1996)

    Google Scholar 

  158. J. F. Dobson, G. Vignale, M. P. Das (Eds.): Electronic Density Functional Theory: Recent Progress and New Directions (Plenum, New York 1998)

    Google Scholar 

  159. D. Joubert (Ed.): Density Functionals: Theory and Applications (Springer, New York 1998)

    MATH  Google Scholar 

  160. W. Koch, M. C. Holthausen: A Chemist's Guide to Density Functional Theory (Wiley, New York 2001)

    Google Scholar 

  161. C. Fiolhais, F. Nogueira, M. Marques: A Primer in Density Functional Theory, Lecture Notes in Physics, Vol. 620 (Springer, New York 2003)

    MATH  Google Scholar 

  162. M. A. L. Marques, E. K. U. Gross: Annu. Rev. Phys. Chem. 55, 427 (2004)

    ADS  Google Scholar 

  163. F. Furche, K. Burke: Ann. Rep. Comput. Chem. 1, 19 (2004)

    Google Scholar 

  164. H. Englisch, R. Englisch: Phys. Status Solidi B 123, 711 (1984)

    ADS  Google Scholar 

  165. H. Englisch, R. Englisch: Phys. Status Solidi B 124, 373 (1984)

    ADS  Google Scholar 

  166. R. van Leeuwen: Adv. Quantum Chem. 43, 25 (2003)

    ADS  Google Scholar 

  167. R. K. Nesbet: Phys. Rev. A 58, R12 (1998)

    ADS  Google Scholar 

  168. R. K. Nesbet: Phys. Rev. A 65, 010502(R) (2001)

    Google Scholar 

  169. R. K. Nesbet: Adv. Quantum Chem. 43, 1 (2003)

    ADS  Google Scholar 

  170. R. K. Nesbet: e-print physics/0309120.

    Google Scholar 

  171. R. K. Nesbet: e-print physics/0309121.

    Google Scholar 

  172. I. Lindgren, S. Salomonson: Phys. Rev. A 70, 032509 (2004)

    ADS  Google Scholar 

  173. E. H. Lieb: Intern. J. Quantum Chem. 24, 243 (1983)

    Google Scholar 

Download references

Acknowledgements

I am grateful to Cyrus Umrigar and Michael P. Teter of Cornell University for generously providing sabbatical support in the spring of 1995. I should also like to thank them, as well as Elliott Lieb and Mel Levy, for helpful discussions. This work was supported by my National Science Foundation grant PHY-9215442.

Author information

Authors and Affiliations

  1. Department of Physics and Astronomy, University of Delaware, 19716, Newark, DE, USA

    John Morgan III

Authors
  1. John Morgan III
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to John Morgan III .

Editor information

Editors and Affiliations

  1. Department of Physics, University of Windsor, 401 Sunset St., N9B 3P4, Windsor, ON, Canada

    Gordon Drake Prof.

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag

About this entry

Cite this entry

Morgan III, J. (2006). Thomas-Fermi and Other Density-Functional Theories. In: Drake, G. (eds) Springer Handbook of Atomic, Molecular, and Optical Physics. Springer Handbooks. Springer, New York, NY. https://doi.org/10.1007/978-0-387-26308-3_20

Download citation

Publish with us

Policies and ethics

Search

Navigation