A guided tour of time-dependent density functional theory

  • Kieron Burke
  • E. K. U. Gross
Chapter
Part of the Lecture Notes in Physics book series (LNP, volume 500)

Abstract

This chapter briefly reviews progress to date in the density functional theory of time-dependent phenomena. We discuss the fundamental theorems and their relation to other approaches. Several exact conditions are treated. We review the special case of the linear response to a weak external potential and look specifically at the linear response of the uniform electron gas, which is important for local density approximations. We discuss recent suggestions for functional approximations, including both the local current approximation and the local-with-memory density approximation. We review applications of the theory in three situations: Beyond linear response, linear response, and excitation energies, and conclude with a brief outlook.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    P. Hohenberg and W. Kohn, Phys. Rev. 136, B 864 (1964).Google Scholar
  2. 2.
    W. Kohn and L.J. Sham, Phys. Rev. 140, A 1133 (1965).Google Scholar
  3. 3.
    Modern Density Functional Theory: A Tool for Chemistry, edited by J. M. Seminario and P. Politzer (Elsevier, Amsterdam, 1995).Google Scholar
  4. 4.
    L.A. Curtiss, K. Raghavachari, P.C. Redfern, and J.A. Pople, J. Chem. Phys. 106, 1067 (1997), and references therein.ADSGoogle Scholar
  5. 5.
    W. Yang and Z. Zhou, in Density Functional Theory of Molecules, Clusters, and Solids, edited by D.E. Ellis (Kluwer Academic, Dordrecht, 1995).Google Scholar
  6. 6.
    K. Burke, J. P. Perdew, and M. Levy, in Modern Density Functional Theory: A Tool for Chemistry, edited by J. M. Seminario and P. Politzer (Elsevier, Amsterdam, 1995).Google Scholar
  7. 7.
    E.K.U. Gross, J.F. Dobson, M. Petersilka, in Topics in Current Chemistry 181, pg. 81 (Springer, 1996).Google Scholar
  8. 8.
    Y. Andersson, D.C. Langreth, and B.I. Lunqvist, Phys. Rev. Lett. 76, 102 (1996).ADSGoogle Scholar
  9. 9.
    Y. Zhang, W. Pan, and W. Yang, submitted to J. Chem. Phys., June 1997.Google Scholar
  10. 10.
    D.C. Patton and M.R. Pederson, submitted to Int. J. Quantum Chem. 1997.Google Scholar
  11. 11.
    W. Kohn, Y. Meir. and D.E. Makarov, Van der Waals energies in density functional theory, preprint, July, 1997.Google Scholar
  12. 12.
    Y. Wang and J.P. Perdew, Phys. Rev. B 44, 13298 (1991).ADSGoogle Scholar
  13. 13.
    R. Colle and O. Salvetti, Theoret. Chim. Acta 37, 329 (1975).Google Scholar
  14. 14.
    C. J. Umrigar and X. Gonze, in High Performance Computing and its Application to the Physical Sciences, Proceedings of the Mardi Gras 1993 Conference, edited by D. A. Browne et al. (World Scientific, Singapore, 1993).Google Scholar
  15. 15.
    Virial energy density in density functional theory, F.G. Cruz, K.C. Lam, and F.G. Cruz, to be submitted to J. Phys. Chem. A.Google Scholar
  16. 16.
    P. Mlynarski and D. R. Salahub, Phys. Rev. B 43, 1399 (1990).ADSGoogle Scholar
  17. 17.
    C.A. Ullrich, U.J. Gossman, and E.K.U. Gross, Ber. Bunsenges. Phys. Chem. 99, 488 (1995).Google Scholar
  18. 18.
    C.A. Ullrich, S. Erhard, and E.K.U. Gross, in Super Intense Laser Atom Physics IV, edited by H.G. Muller (Kluwer, Dordrecht, 1996).Google Scholar
  19. 19.
    S. Erhard and E.K.U. Gross, in Multiphoton Processes 1996, ed. P. Lambropoulos and H. Walther (IOP Publishing, London, 1997).Google Scholar
  20. 20.
    C.A. Ullrich and E.K.U. Gross, Comments At. Mol. Phys., 33, 211 (1997).Google Scholar
  21. 21.
    A. Zangwill and P Soven, Phys. Rev. A 21, 1561 (1980).ADSGoogle Scholar
  22. 22.
    M. Levy, in Density Matrices and Density Functionals, edited by R.M. Erdahl and V.H. Smith, Jr., (Reidel, Dordrecht, 1987), pg. 479.Google Scholar
  23. 23.
    J.F. Dobson and G.H. Harris, J. Phys. C 19, 3971 (1986).ADSGoogle Scholar
  24. 24.
    J.F. Dobson and G.H. Harris, J. Phys. C 20, 6127 (1987).ADSGoogle Scholar
  25. 25.
    J.F. Dobson and G.H. Harris, J. Phys. C 21, L729 (1988).Google Scholar
  26. 26.
    M. Petersilka, U.J. Gossmann, and E.K.U. Gross, Phys. Rev. Lett. 76, 1212 (1996).ADSGoogle Scholar
  27. 27.
    M. Petersilka, U.J. Gossmann, and E.K.U. Gross, in Electronic Density Functional Theory: Recent Progress and New Directions, eds. J.F. Dobson, G. Vignale, and M.P. Das (Plenum, NY, 1997).Google Scholar
  28. 28.
    M. Petersilka and E.K.U. Gross, Int. J. Quantum Chem. S 30, 1393 (1996).Google Scholar
  29. 29.
    C.J. Umrigar, A. Savin, and X. Gonze, in Electronic Density Functional Theory: Recent Progress and New Directions, eds. J.F. Dobson, G. Vignale, and M.P. Das (Plenum, NY, 1997).Google Scholar
  30. 30.
    M. Petersilka, private communication.Google Scholar
  31. 31.
    E. Runge and E.K.U. Gross, Phys. Rev. Lett. 52, 997 (1984).ADSGoogle Scholar
  32. 32.
    L. J. Sham and M. Schlüter, Phys. Rev. Lett. 51, 1888 (1983).ADSGoogle Scholar
  33. 33.
    R. van Leeuwen, Phys. Rev. Lett. 76, 3610 (1996).ADSGoogle Scholar
  34. 34.
    R.T. Sharp and G.K. Horton, Phys. Rev. 90, 317 (1953).ADSMathSciNetGoogle Scholar
  35. 35.
    J.D. Talman and W.F. Shadwick, Phys. Rev. A 14, 36 (1976).ADSGoogle Scholar
  36. 36.
    J. B. Krieger, Y. Li, and G. J. Iafrate, Phys. Rev. A 45, 101 (1992).ADSGoogle Scholar
  37. 37.
    G. Vignale, Phys. Rev. Lett. 74, 3233 (1995).ADSGoogle Scholar
  38. 38.
    G. Vignale, Phys. Lett. A 209, 206 (1995).ADSGoogle Scholar
  39. 39.
    J.F. Dobson, Phys. Rev. Lett. 73, 2244 (1994).ADSGoogle Scholar
  40. 40.
    G. Vignale and W. Kohn, Phys. Rev. Lett. 77, 2037 (1996).ADSGoogle Scholar
  41. 41.
    E.K.U. Gross and W. Kohn, Phys. Rev. Lett. 55, 2850 (1985).ADSGoogle Scholar
  42. 42.
    N. Iwamoto and E.K.U. Gross, Phys. Rev. B 35, 3003 (1987).ADSGoogle Scholar
  43. 43.
    J.F. Dobson, M. Bünner, and E.K.U. Gross, Phys. Rev. Lett. 79, Sept 1 (1997).Google Scholar
  44. 44.
    C.A. Ullrich, U.J. Gossman, and E.K.U. Gross, Phys. Rev. Lett. 74, 872 (1995).ADSGoogle Scholar
  45. 45.
    P. Mlynarski and D.R. Salahub, J. Chem. Phys. 95, 6050 (1991).ADSGoogle Scholar
  46. 46.
    D. Tiszauer and K.C. Kulander, Phys. Rev. A 29, 2909 (1984).ADSGoogle Scholar
  47. 47.
    L.F. Errea, L. Méndez, A. Riera, M. Yáñez, J. Hanssen, C. Harel, and A. Salin, J. Physique 46, 719 (1985).Google Scholar
  48. 48.
    I.L. Cooper, A.S. Dickinson, S.K. Sur, and C.T. Ta, J. Phys. B 20, 2005 (1987).ADSGoogle Scholar
  49. 49.
    A. Henne, H.J. Lüdde, A. Toepfer, and R.M. Dreizler, Phys. Lett. A 124, 508 (1987).ADSGoogle Scholar
  50. 50.
    W. Fritsch and C.D. Lin, Phys. Lett. A 123, 128 (1987).ADSGoogle Scholar
  51. 51.
    J.F. Reading and A.L. Ford, Phys. Rev. Lett. 58, 543 (1987).ADSGoogle Scholar
  52. 52.
    J.F. Reading and A.L Ford, Phys. Rev. B, 20, 3747 (1987).Google Scholar
  53. 53.
    X. Tang, H. Rudolph, and P. Lambropoulos, Phys. Rev. A 44, R6994 (1991).Google Scholar
  54. 54.
    G.D. Mahan, Many-Particle Physics, 2nd ed. (Plenum Press, New York, 1990).Google Scholar
  55. 55.
    L.V. Keldysh, Sov. Phys. JETP 20, 1018 (1965).MathSciNetGoogle Scholar
  56. 56.
    R. van Leeuwen, Causality and symmetry in time-dependent density functional theory, preprint, September 7, 1997.Google Scholar
  57. 57.
    S. Erhard, Diplomarbeit, Universität Würzburg, 1996.Google Scholar
  58. 58.
    J.F. Dobson, in Density Functional Theory, Vol. 337 of NATO ASI Series B, edited by E.K.U. Gross and R.M. Dreizler (Plenum Press, New York, 1995), p. 393.Google Scholar
  59. 59.
    L. Brey, N.F. Johnson, and B.I. Halperin, Phys. Rev. B 40, 10647 (1989).ADSGoogle Scholar
  60. 60.
    T.K. Ng and K.S. Singwi, Phys. Rev. Lett. 59, 2627 (1987).ADSGoogle Scholar
  61. 61.
    W. Yang, Phys. Rev. A 38, 5512 (1988).ADSGoogle Scholar
  62. 62.
    N.W. Ashcroft, in Density Functional Theory, Vol. 337 of NATO ASI Series B, edited by E.K.U. Gross and R.M. Dreizler (Plenum Press, New York, 1995), p. 581.Google Scholar
  63. 63.
    A.A. Kugler, J. Stat. Phys. 12, 35 (1975).ADSGoogle Scholar
  64. 64.
    L.P Kadanoff and P.C. Martin, Ann. Phys. New York 24, 419 (1963).MATHADSMathSciNetGoogle Scholar
  65. 65.
    T.K. Ng, Phys. Rev. Lett. 62, 2417 (1989).ADSGoogle Scholar
  66. 66.
    S. Ichimaru, Rev. Mod. Phys. 54, 1017 (1982).ADSGoogle Scholar
  67. 67.
    V.D. Gorobchenko and E.G. Maksimov, Sov Phys. Usp. 23, 35 (1980).ADSGoogle Scholar
  68. 68.
    K.S. Singwi and M.P. Tosi, Solid State Physics 36, 177 (1981).Google Scholar
  69. 69.
    Y. Wang and J. P. Perdew, Phys. Rev. B 43, 8911 (1991).ADSGoogle Scholar
  70. 70.
    M.K. Harbola and V. Sahni, Phys. Rev. Lett. 62, 489 (1989).ADSGoogle Scholar
  71. 71.
    A.J. Glick and W.F. Long, Phys. Rev. B 4, 3455 (1971).ADSGoogle Scholar
  72. 72.
    D.F Dubois and M.G. Kivelson, Phys. Rev. 186, 409 (1969).ADSGoogle Scholar
  73. 73.
    M. Hasegawa and M. Watabe, J. Phys. Soc. Jap. 27, 1393 (1969).ADSGoogle Scholar
  74. 74.
    K. Sturm, Phys. Rev. B 52, 8028 (1995).ADSGoogle Scholar
  75. 75.
    B. Dabrowski, Phys. Rev. B 34, 4989 (1986).ADSGoogle Scholar
  76. 76.
    K.L. Liu, Can. J. Phys. 69, 573 (1991).ADSGoogle Scholar
  77. 77.
    H.M. Böhm. S. Conti, and M.P. Tosi, J. Phys. C 8, 781 (1996).Google Scholar
  78. 78.
    S. Conti, H.M. Böhm, and M.P. Tosi, Phys. Stat. Sol. B 193, K11 (1996).Google Scholar
  79. 79.
    S. Conti, R. Nifosi, and M.P. Tosi, Exchange-correlation potential for current density functional theory of frequency dependent response, preprint condmat/9707062, July 1997.Google Scholar
  80. 80.
    K. Burke, M. Ernzerhof, and J.P. Perdew, Why semi-local functionals work: Accuracy of the on-top hole density, work in progress.Google Scholar
  81. 81.
    M. Rasolt and D.J.W. Geldart, Phys. Rev. B 34, 1325 (1986).ADSGoogle Scholar
  82. 82.
    G. Vignale, C.A. Ullrich, and S. Conti, Time-dependent density functional theory beyond the ALDA, preprint, July 1997.Google Scholar
  83. 83.
    K.C. Kulander and B.W. Shore, J. Opt. Soc. Am. B 7, 502 (1990).ADSGoogle Scholar
  84. 84.
    S.K. Ghosh and B.M. Deb, Chem. Phys. 71, 295 (1982).ADSGoogle Scholar
  85. 85.
    S.K. Ghosh and B.M. Deb, Theoret. Chim. Acta 62, 209 (1983).Google Scholar
  86. 86.
    S.K. Ghosh and B.M. Deb, J. Mol. Struct. 103, 163 (1983).Google Scholar
  87. 87.
    A. Zangwill and P Soven, Phys. Rev. Lett. 45, 204 (1980).ADSGoogle Scholar
  88. 88.
    A. Zangwill and P Soven, Phys. Rev. B 24, 4121 (1981).ADSGoogle Scholar
  89. 89.
    Z.H. Levine and P. Soven, Phys. Rev. Lett. 50, 2074 (1983).ADSGoogle Scholar
  90. 90.
    Z.H. Levine and P. Soven, Phys. Rev. A 29, 625 (1984).ADSGoogle Scholar
  91. 91.
    W. Ekardt, Phys. Rev. Lett. 52, 1925 (1984).ADSGoogle Scholar
  92. 92.
    M.J. Puska, R.M. Nieminen, and M. Manninen, Phys. Rev. B 31, 3486 (1985).ADSGoogle Scholar
  93. 93.
    W. Ekardt, Phys. Rev. B 31, 6360 (1985).ADSGoogle Scholar
  94. 94.
    D.E. Beck, Phys. Rev. B 35, 7352 (1987).Google Scholar
  95. 95.
    A. Rubio, L.C. Balbás, and J.A. Alonso, Phys. Rev. B 46, 4891 (1992).ADSGoogle Scholar
  96. 96.
    W. Ekardt, Phys. Rev. B 32, 1961 (1985).ADSGoogle Scholar
  97. 97.
    W. Ekardt and Z. Penzar, Phys. Rev. B 43, 1322 (1991).ADSGoogle Scholar
  98. 98.
    J.A. Alonso, A. Rubio, and L.C. Balbás, Phil. Mag. B 69, 1037 (1994).Google Scholar
  99. 99.
    J.M. Pacheco and W. Ekardt, Z. Phys. D 24, 65 (1992).ADSGoogle Scholar
  100. 100.
    J.M. Pacheco and W. Ekardt, Ann. Physik 1, 254 (1992).ADSGoogle Scholar
  101. 101.
    J.M. Pacheco and W. Ekardt, Phys. Rev. B 47, 6667 (1993).ADSGoogle Scholar
  102. 102.
    P. Gies and R.R. Gerhardts, Phys. Rev. B 36, 4422 (1987).ADSGoogle Scholar
  103. 103.
    P Gies and R.R. Gerhardts, Phys. Rev. B 37, 10020 (1988).ADSGoogle Scholar
  104. 104.
    K. Kempa and W.L. Schaich, Phys. Rev. B 37, 6711 (1988).ADSGoogle Scholar
  105. 105.
    T. Ando, Z. Phys. B. 26, 263 (1977).ADSGoogle Scholar
  106. 106.
    T. Ando, Solid State Commun. 21, 133 (1977).MathSciNetADSGoogle Scholar
  107. 107.
    K.S. Yi and J.J. Quinn, Phys. Rev. B 27, 2396 (1983).ADSGoogle Scholar
  108. 108.
    L. Wendler and V.G. Grigoryan, Solid State Commun. 71, 527 (1989).ADSGoogle Scholar
  109. 109.
    J. M. Seminario, Chem. Phys. Lett. 206, 547 (1993).ADSGoogle Scholar
  110. 110.
    Z.H. Levine and D.C. Allan, Phys. Rev. Lett. 63, 1719 (1989).ADSGoogle Scholar
  111. 111.
    See, e.g., Studies of Electron Distributions in Molecules and Crystals, Transactions of the American Crystallographic Association, ed. R. Blessing (Polycrystal Book Service, Dayton, OH, 1990), Vol. 26.Google Scholar
  112. 112.
    A.A. Quong and A.G. Eguiluz, Phys. Rev. Lett. 70, 3955 (1993).ADSGoogle Scholar
  113. 113.
    N.E. Maddocks, R.W. Godby, and R.J. Needs, Europhys. Lett. 27, 681 (1994).ADSGoogle Scholar
  114. 114.
    A. Fleszar, A.A. Quong, and A.G. Eguiluz, Phys. Rev. Lett. 74, 590 (1995).ADSGoogle Scholar
  115. 115.
    P.J. Feibelman, Prog. Surf. Sci. 12, 287 (1982).ADSGoogle Scholar
  116. 116.
    J.F. Dobson and B.P. Dinte, Phys. Rev. Lett., in press.Google Scholar
  117. 117.
    Y. Andersson, B.I. Lunqvist, and D.C. Langreth, Phys. Rev. Lett. 77, 2029 (1996).ADSGoogle Scholar
  118. 118.
    Y. Andersson, E. Hult, H. Rydberg, P. Apell, B.I. Lundqvist, and D.C. Langreth, Van der Waals interactions in density functional theory in Electronic Density Functional Theory: Recent Progress and New Directions, eds. J.F. Dobson, G. Vignale, and M.P. Das (Plenum, NY, 1997).Google Scholar
  119. 119.
    G. Senatore and K.R. Subbaswamy, Phys. Rev. A 35, 2440 (1987).ADSGoogle Scholar
  120. 120.
    X. Gonze and J.P. Vigneron, Phys. Rev. B 39, 13120 (1989).ADSGoogle Scholar
  121. 121.
    A. Theophilou, J. Phys. C 12, 5419 (1979).ADSGoogle Scholar
  122. 122.
    N. Hadjisavvas and A. Theophilou, Phys. Rev. A 32, 720 (1985).ADSGoogle Scholar
  123. 123.
    W. Kohn, Phys. Rev. A 34, 5419 (1986).Google Scholar
  124. 124.
    E.K.U. Gross, L.N. Oliveira, and W. Kohn, Phys. Rev. A 37, 2809 (1988).ADSMathSciNetGoogle Scholar
  125. 125.
    E.K.U. Gross, L.N. Oliveira, and W. Kohn, Phys. Rev. A 37, 2805 (1988).ADSMathSciNetGoogle Scholar
  126. 126.
    L.N. Oliveira, E.K.U. Gross and W. Kohn, Phys. Rev. A 37, 2821 (1988).ADSMathSciNetGoogle Scholar
  127. 127.
    A. Nagy, Phys. Rev. A 42, 4388 (1990).ADSGoogle Scholar
  128. 128.
    A. Nagy, Phys. Rev. A 49, 3074 (1994).ADSGoogle Scholar
  129. 129.
    A. Nagy, Int. J. Quantum Chem. Symp. 29, (1995).Google Scholar
  130. 130.
    M. Levy, in Density Functional Theory, eds. R. Dreizler and E. K. U. Gross, NATO ASI Series (Plenum, New York, 1995).Google Scholar
  131. 131.
    P.K. Chattaraj, S.K. Ghosh, S. Liu, and R.G. Parr, Int. J. Quant. Chem, in press.Google Scholar
  132. 132.
    O. Gunnarsson and B.I. Lundqvist, Phys. Rev. B 13, 4274 (1976).ADSGoogle Scholar
  133. 133.
    T. Ziegler, A. Rauk, and E. J. Baerends, Theoret. Chim. Acta 43, 261 (1977).Google Scholar
  134. 134.
    U. von Barth, Phys. Rev. A 20, 1693 (1979).ADSGoogle Scholar
  135. 135.
    A. Görling, Phys. Rev. A 54, 3912 (1996).ADSGoogle Scholar
  136. 136.
    C. Filippi, C.J. Umrigar, and X. Gonze, Excitation energies from density functional perturbation theory, submitted to J. Chem. Phys., July 1997.Google Scholar
  137. 137.
    Femtosecond Chemistry, ed. by J. Manz and L. Wöste (VCH, Weinheim, 1995).Google Scholar
  138. 138.
    F. Zimmermann and W. Ho, Surf. Sci. Reps. 22, 127 (1995).ADSGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Kieron Burke
    • 1
  • E. K. U. Gross
    • 2
  1. 1.Department of ChemistryRutgers UniversityCamden
  2. 2.Institut für Theoretische PhysikUniversität WürzburgWürzburgGermany

Personalised recommendations