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Modern Aspects of Electrochemistry No. 44 pp 341–408Cite as

Density-Functional Theory in External Electric and Magnetic Fields

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Part of the book series: Modern Aspects of Electrochemistry ((MAOE,volume 44))

Abstract

Density-functional theory (DFT) is one of the most widely used quantum mechanical approaches for calculating the structure and properties of matter on an atomic scale. It is nowadays routinely applied for calculating physical and chemical properties of molecules that are too large to be treatable by wave-function-based methods. The problem of determining the many-body wave function of a real system rapidly becomes prohibitively complex (1). Methods such as configuration interaction (CI) expansions, coupled cluster (CC) techniques or Møller–Plesset (MP) perturbation theory thus become harder and harder to apply. Computational complexity here is related to questions such as how many atoms there are in the molecule, how many electrons each atom contributes, how many basis functions are required to adequately describe these electrons, how many competing minima there are in the potential-energy surface determining the molecular geometry, and whether any additional external fields are present. The description of the many-body wave function in CI, CC and MP techniques depends sensitively on these questions, and becomes very difficult for systems with more than a few electrons.

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References

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

    CAS  Google Scholar 

  2. M. T. M. Koper, in Modern aspects of electrochemistry, edited by C. G. Vayenas, B. E. Conway, and R. E. White, vol. 36, chap. 2 (Kluwer/Plenum, New York, 2003).

    Google Scholar 

  3. G. Maroulis, ed., Atoms, Molecules and Clusters in Electric Fields: Theoretical Approaches to the Calculation of Electric Polarizability (Imperial College Press, London, 2006).

    Google Scholar 

  4. W. Schmickler, Annu. Rep. Prog. Chem., Sect. C 95, 117 (1999).

    CAS  Google Scholar 

  5. M. Jacoby, Chem. Eng. News 82, 25 (2004).

    Google Scholar 

  6. Z. Shia, J. Zhanga, Z.-S. Liua, H. Wanga, and D. P. Wilkinson, Electrochim. Acta 51, 1905 (2006).

    Google Scholar 

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

    Google Scholar 

  8. R. G. Parr and W. Yang, Density-Functional Theory of Atoms and Molecules (Oxford University Press, Oxford, 1989).

    Google Scholar 

  9. W. Koch and M. C. Holthausen, A Chemist’s Guide to Density Functional Theory (Wiley, New York, 2001).

    Google Scholar 

  10. R. O. Jones and O. Gunnarsson, Rev. Mod. Phys. 61, 689 (1989).

    CAS  Google Scholar 

  11. J. M. Seminario, ed., Recent Developments and Applications of Modern DFT (Elsevier, Amsterdam, 1996).

    Google Scholar 

  12. R. F. Nalewajski, ed., Density functional theory I–IV, Topics in Current Chemistry, vols. 180–183 (Springer, Berlin, 1996).

    Google Scholar 

  13. V. I. Anisimov, ed., Strong Coulomb Correlations in Electronic Structure Calculations: Beyond the Local Density Approximation (Gordon & Breach, Amsterdam, 1999).

    Google Scholar 

  14. N. H. March, Electron Density Theory of Atoms and Molecules (Academic, London, 1992).

    Google Scholar 

  15. B. B. Laird, R. B. Ross, and T. Ziegler, eds., Chemical Applications of Density Functional Theory (American Chemical Society, Washington, 1996).

    Google Scholar 

  16. D. P. Chong, ed., Recent Advances in Density Functional Methods (World Scientific, Singapore, 1995).

    Google Scholar 

  17. D. Joulbert, ed., Density functionals: theory and applications, Lecture Notes in Physics, vol. 500 (Springer, Berlin, 1998).

    Google Scholar 

  18. C. Fiolhais, F. Nogueira, and M. Marques, eds., A primer in density functional theory, Lecture Notes in Physics, vol. 620 (Springer, Berlin, 2003).

    Google Scholar 

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

    Google Scholar 

  20. H. Eschrig, The Fundamentals of Density Functional Theory (Teubner, Leipzig, 1996).

    Google Scholar 

  21. E. K. U. Gross and R. M. Dreizler, eds., Density Functional Theory (Plenum, New York, 1995).

    Google Scholar 

  22. N. Argaman and G. Makov, Am. J. Phys. 68, 69 (2000).

    CAS  Google Scholar 

  23. K. Capelle, Braz. J. Phys. 36, 1318 (2006), also available from arXiv:cond-mat/0211443.

    Google Scholar 

  24. T. Kreibich and E. K. U. Gross, Phys. Rev. Lett. 86, 2984 (2001).

    CAS  Google Scholar 

  25. A. K. Rajagopal and J. Callaway, Phys. Rev. B 7, 1912 (1973).

    CAS  Google Scholar 

  26. A. H. MacDonald and S. H. Vosko, J. Phys. C 12, 2977 (1979).

    CAS  Google Scholar 

  27. P. Strange, Relativistic Quantum Mechanics with Applications in Condensed Matter and Atomic Physics (Cambridge University Press, Cambridge, 1998).

    Google Scholar 

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

    CAS  Google Scholar 

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

    Google Scholar 

  30. E. Runge and E. K. U. Gross, Phys. Rev. Lett. 52, 997 (1984).

    CAS  Google Scholar 

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

    CAS  Google Scholar 

  32. E. H. Lieb, in Density functional methods in physics, edited by R. M. Dreizler and J. da Providencia (Plenum, New York, 1985).

    Google Scholar 

  33. E. Schrödinger, Ann. Phys. 79, 361, 489, 734 (1926); 80, 437 (1926); 81, 109 (1926).

    Google Scholar 

  34. K. Capelle, C. A. Ullrich, and G. Vignale, Phys. Rev. A 76, 012508 (2007).

    Google Scholar 

  35. H. Eschrig and W. E. Pickett, Solid State Commun. 118, 123 (2001).

    CAS  Google Scholar 

  36. K. Capelle and G. Vignale, Phys. Rev. Lett. 86, 5546 (2001).

    CAS  Google Scholar 

  37. K. Capelle and G. Vignale, Phys. Rev. B 65, 113106 (2002).

    Google Scholar 

  38. O. Gritsenko and E. J. Baerends, J. Chem. Phys. 120, 8364 (2004).

    CAS  Google Scholar 

  39. N. Argaman and G. Makov, Phys. Rev. B 66, 052413 (2002).

    Google Scholar 

  40. N. Gidopolous, in The fundamentals of density matrix and density functional theory in atoms, molecules and solids, edited by N. Gidopoulos and S. Wilson (Kluwer, Boston, 2003), Progress in Theoretical Chemistry and Physics.

    Google Scholar 

  41. W. Kohn, A. Savin, and C. A. Ullrich, Int. J. Quantum Chem. 100, 20 (2004).

    CAS  Google Scholar 

  42. C. A. Ullrich, Phys. Rev. B 72, 073102 (2005).

    Google Scholar 

  43. T. Gál, Phys. Rev. B 75, 235119 (2007).

    Google Scholar 

  44. N. I. Gidopoulos, Phys. Rev. B 75, 134408 (2007).

    Google Scholar 

  45. W. E. Pickett and H. Eschrig, J. Phys. Condens. Matter 19, 315203 (2007).

    Google Scholar 

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

    Google Scholar 

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

    CAS  Google Scholar 

  48. J. T. Chayes, L. Chayes, and M. B. Ruskai, J. Stat. Phys. 38, 497 (1985).

    Google Scholar 

  49. C. A. Ullrich and W. Kohn, Phys. Rev. Lett. 89, 156401 (2002); 87, 093001 (2001).

    Google Scholar 

  50. P. E. Lammert, J. Chem. Phys. 125, 074114 (2006).

    Google Scholar 

  51. A. P. Favaro, J. V. B. Ferreira, and K. Capelle, Phys. Rev. B 73, 045133 (2006).

    Google Scholar 

  52. N. H. March, Self-consistent Fields in Atoms (Pergamon, Oxford, 1975).

    Google Scholar 

  53. L. W. Wang and M. P. Teter, Phys. Rev. B 45, 13196 (1992).

    CAS  Google Scholar 

  54. M. Foley and P. A. Madden, Phys. Rev. B 53, 10589 (1996).

    CAS  Google Scholar 

  55. B. J. Zhou, V. L. Ligneres, and E. A. Carter, J. Chem. Phys. 122, 044103 (2005).

    Google Scholar 

  56. E. K. U. Gross, E. Runge, and O. Heinonen, Many Particle Theory (Adam Hilger, Bristol, 1991).

    Google Scholar 

  57. A. Szabo and N. S. Ostlund, Modern Quantum Chemistry (McGraw-Hill, New York, 1989).

    Google Scholar 

  58. E. K. U. Gross, M. Petersilka, and T. Grabo, in Chemical applications of density-functional theory, edited by B. B. Laird, R. B. Ross, and T. Ziegler (American Chemical Society, Washington, 1996a), ACS Symposium Series.

    Google Scholar 

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

    CAS  Google Scholar 

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

    CAS  Google Scholar 

  61. G. K.-L. Chan and N. C. Handy, Phys. Rev. A 59, 3075 (1999).

    Google Scholar 

  62. M. M. Odashima, K. Capelle, and S. B. Trickey, J. Chem. Theory Comput. 5, 798 (2009).

    CAS  Google Scholar 

  63. J. P. Perdew and Y. Wang, Phys. Rev. B 45, 13244 (1992).

    Google Scholar 

  64. S. H. Vosko, L. Wilk, and M. Nusair, Can. J. Phys. 58, 1200 (1980).

    CAS  Google Scholar 

  65. J. P. Perdew, J. A. Chevary, S. H. Vosko, K. A. Jackson, M. R. Pederson, D. J. Singh, and C. Fiolhais, Phys. Rev. B 46, 6671 (1992).

    CAS  Google Scholar 

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

    Google Scholar 

  67. J. Tao, J. P. Perdew, V. N. Staroverov, and G. E. Scuseria, Phys. Rev. Lett. 91, 146401 (2003).

    Google Scholar 

  68. J. P. Perdew and Y. Wang, Phys. Rev. B 33, 8800 (1986).

    Google Scholar 

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

    CAS  Google Scholar 

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

    CAS  Google Scholar 

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

    CAS  Google Scholar 

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

    CAS  Google Scholar 

  73. A. D. Becke and E. R. Johnson, J. Chem. Phys. 127, 124108 (2007).

    Google Scholar 

  74. L. J. Sham and M. Schlüter, Phys. Rev. Lett. 51, 1888 (1983).

    Google Scholar 

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

    CAS  Google Scholar 

  76. J. P. Perdew and M. Levy, Phys. Rev. Lett. 51, 1884 (1983).

    CAS  Google Scholar 

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

    Google Scholar 

  78. W. Kohn, A. D. Becke, and R. G. Parr, J. Phys. Chem. 100, 12974 (1996).

    CAS  Google Scholar 

  79. C. O. Almbladh and U. von Barth, Phys. Rev. B 31, 3231 (1985).

    CAS  Google Scholar 

  80. M. Levy, J. P. Perdew, and V. Sahni, Phys. Rev. A 30, 2745 (1984).

    Google Scholar 

  81. J. Chen, J. B. Krieger, Y. Li, and G. J. Iafrate, Phys. Rev. A 54, 3939 (1996).

    CAS  Google Scholar 

  82. M. Lüders, A. Ernst, W. M. Temmerman, Z. Szotek, and P. J. Durham, J. Phys. Condens. Matter 13, 8587 (2001).

    Google Scholar 

  83. J. Muskat, A. Wander, and N. M. Harrison, Chem. Phys. Lett. 342, 397 (2001).

    Google Scholar 

  84. A. Savin, C. J. Umrigar, and X. Gonze, Chem. Phys. Lett. 288, 391 (1998).

    CAS  Google Scholar 

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

    CAS  Google Scholar 

  86. U. von Barth, Phys. Rev. A 20, 1693 (1979).

    Google Scholar 

  87. A. Görling, Phys. Rev. Lett. 85, 4229 (2000).

    Google Scholar 

  88. J. P. Perdew and M. Levy, Phys. Rev. B 31, 6264 (1985).

    CAS  Google Scholar 

  89. H. J. P. Freire and J. C. Egues, Phys. Rev. Lett. 99, 026801 (2007).

    Google Scholar 

  90. A. Görling, Phys. Rev. A 54, 3912 (1996); 59, 3359 (1999).

    Google Scholar 

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

    CAS  Google Scholar 

  92. P. Samal and M. K. Harbola, J. Phys. B 39, 4065 (2006).

    CAS  Google Scholar 

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

    CAS  Google Scholar 

  94. E. K. U. Gross, L. N. Oliveira, and W. Kohn, Phys. Rev. A 37, 2805 (1988); 37, 2809 (1988); 37, 2821 (1988).

    Google Scholar 

  95. Á. Nagy, Phys. Rev. A 49, 3074 (1994); 42, 4388 (1990).

    Google Scholar 

  96. N. I. Gidopoulos, P. G. Papaconstantinou, and E. K. U. Gross, Phys. Rev. Lett. 88, 033003 (2002).

    CAS  Google Scholar 

  97. R. van Leeuwen, Phys. Rev. Lett. 82, 3863 (1999).

    Google Scholar 

  98. E. K. U. Gross, J. F. Dobson, and M. Petersilka in Ref. [(12)]; K. Burke and E. K. U. Gross in Ref. [(17)]

    Google Scholar 

  99. M. Petersilka, U. J. Gossmann, and E. K. U. Gross, Phys. Rev. Lett. 76, 1212 (1996). See also T. Grabo, M. Petersilka, and E. K. U. Gross, J. Mol. Struct. (Theochem) 501, 353 (2000).

    Google Scholar 

  100. M. E. Casida, in Ref. [(16)]; J. Jamorski, M. E. Casida, and D. R. Salahub, J. Chem. Phys. 104, 5134 (1996).

    Google Scholar 

  101. S. J. A. van Gisbergen, J. G. Snijders, and E. J. Baerends, Comput. Phys. Commun. 118, 119 (1999).

    Google Scholar 

  102. R. E. Stratmann, G. E. Scuseria, and M. J. Frisch, J. Chem. Phys. 109, 8218 (1998).

    CAS  Google Scholar 

  103. G. Onida, L. Reining, and A. Rubio, Rev. Mod. Phys. 74, 601 (2002).

    CAS  Google Scholar 

  104. W. G. Aulbur, L. Jönsson, and J. W. Wilkins, Solid State Phys. 54, 1 (1999).

    Google Scholar 

  105. F. Aryasetiawan and O. Gunnarsson, Rep. Prog. Phys. 61, 237 (1998).

    CAS  Google Scholar 

  106. A. Svane and O. Gunnarsson, Phys. Rev. Lett. 65, 1148 (1990); 72, 1248 (1994).

    Google Scholar 

  107. Z. Szotek, W. M. Temmermann, and H. Winter, Phys. Rev. Lett. 72, 1244 (1994).

    CAS  Google Scholar 

  108. P. Strange, A. Svane, W. M. Temmermann, Z. Szotek, and H. Winter, Nature 399, 756 (1999).

    CAS  Google Scholar 

  109. U. von Barth and L. Hedin, J. Phys. C 5, 1629 (1972).

    Google Scholar 

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

    CAS  Google Scholar 

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

    CAS  Google Scholar 

  112. C. Filippi, C. J. Umrigar, and M. Taut, J. Chem. Phys. 100, 1290 (1994).

    CAS  Google Scholar 

  113. P. Ziesche, S. Kurth, and J. P. Perdew, Comp. Mat. Sci. 11, 122 (1998).

    Google Scholar 

  114. P. J. Stephens, F. Devlin, C. Chabalowski, and M. Frisch, J. Phys. Chem 98, 11623 (1994).

    CAS  Google Scholar 

  115. A. D. Becke, J. Chem. Phys. 107, 8554 (1997). See also A. D. Becke, J. Comp. Chem. 20, 63 (1999).

    Google Scholar 

  116. D. J. Tozer and N. C. Handy, J. Chem. Phys. 108, 2545 (1998).

    CAS  Google Scholar 

  117. T. van Voorhis and G. E. Scuseria, J. Chem. Phys. 109, 400 (1998).

    Google Scholar 

  118. J. Tao, J. P. Perdew, V. N. Staroverov, and G. E. Scuseria, Phys. Rev. Lett. 120, 6898 (2004); Phys. Rev. B 69, 075102 (2004).

    Google Scholar 

  119. V. N. Staroverov, G. E. Scuseria, J. Tao, and J. P. Perdew, J. Chem. Phys. 119, 12129 (2003).

    CAS  Google Scholar 

  120. A. D. Becke, J. Chem. Phys. 104, 1040 (1996).

    CAS  Google Scholar 

  121. J. Tao and J. P. Perdew, J. Chem. Phys. 122, 114102 (2005).

    Google Scholar 

  122. Y.-H. Kim, I.-H. Lee, S. Nagaraja, J.-P. Leburton, R. Q. Hood, and R. M. Martin, Phys. Rev. B 61, 5202 (2000).

    CAS  Google Scholar 

  123. S. Kurth, J. P. Perdew, and P. Blaha, Int. J. Quantum Chem. 75, 889 (1999).

    CAS  Google Scholar 

  124. C. Adamo, M. Ernzerhof, and G. E. Scuseria, J. Chem. Phys. 112, 2643 (2000).

    CAS  Google Scholar 

  125. O. A. Vydrow and G. E. Scuseria, J. Chem. Phys. 121, 8187 (2004).

    Google Scholar 

  126. J. Gräfenstein, E. Kraka, and D. Cremer, J. Chem. Phys. 120, 524 (2004).

    Google Scholar 

  127. S. Patchkovskii and T. Ziegler, J. Chem. Phys. 116, 7806 (2002).

    CAS  Google Scholar 

  128. S. Goedecker and C. J. Umrigar, Phys. Rev. A 55, 1765 (1997).

    CAS  Google Scholar 

  129. B. G. Johnson, C. A. Gonzales, P. M. W. Gill, and J. A. Pople, Chem. Phys. Lett. 221, 100 (1994).

    CAS  Google Scholar 

  130. G. I. Csonka and B. G. Johnson, Theor. Chem. Acc. 99, 158 (1998).

    CAS  Google Scholar 

  131. U. Lundin and O. Eriksson, Int. J. Quantum Chem. 81, 247 (2001).

    CAS  Google Scholar 

  132. C. Legrand, E. Suraud, and P.-G. Reinhard, J. Phys. B 35, 1115 (2002).

    CAS  Google Scholar 

  133. J. B. Krieger, Y. Li, and G. J. Iafrate, Phys. Rev. A 45, 101 (1992); 46, 5453 (1992); 47, 165 (1993).

    Google Scholar 

  134. E. Engel and S. H. Vosko, Phys. Rev. A 47, 2800 (1993).

    CAS  Google Scholar 

  135. T. Grabo, T. Kreibich, S. Kurth, and E. K. U. Gross, in Ref. [(13)]

    Google Scholar 

  136. T. Grabo and E. K. U. Gross, Int. J. Quantum Chem. 64, 95 (1997); Chem. Phys. Lett. 240, 141 (1995).

    Google Scholar 

  137. T. Kotani, Phys. Rev. Lett. 74, 2989 (1995).

    CAS  Google Scholar 

  138. M. Stadele, J. A. Majewski, P. Vogl, and A. Görling, Phys. Rev. Lett. 79, 2089 (1997); M. Stadele, M. Moukara, J. A. Majewski, P. Vogl, and A. Görling, Phys. Rev. B 59, 10031 (1999); Y.-H. Kim, M. Stadele, and R. M. Martin, Phys. Rev. A 60, 3633 (1999).

    Google Scholar 

  139. S. Kümmel and J. P. Perdew, Phys. Rev. B 68, 035103 (2003).

    Google Scholar 

  140. W. Yang and Q. Qu, Phys. Rev. Lett. 89, 143002 (2002).

    Google Scholar 

  141. V. N. Staroverov, G. E. Scuseria, and E. R. Davidson, J. Chem. Phys. 125, 081104 (2006).

    Google Scholar 

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

    CAS  Google Scholar 

  143. M. Cafiero and C. Gonzalez, Phys. Rev. A 71, 042505 (2005).

    Google Scholar 

  144. M. P. Lima, L. S. Pedroza, A. J. R. da Silva, A. Fazzio, D. Vieira, H. J. P. Freire, and K. Capelle, J. Chem. Phys. 126, 144107 (2007).

    Google Scholar 

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

    CAS  Google Scholar 

  146. A. Cancio, M. Y. Chou, and R. O. Hood, Phys. Rev. B 64, 115112 (2002).

    Google Scholar 

  147. P. García-González, Phys. Rev. B 62, 2321 (2000).

    Google Scholar 

  148. N. Rösch and S. B. Trickey, J. Chem. Phys. 106, 8940 (1997).

    Google Scholar 

  149. P. Schwerdtfeger, in Ref. [(3)]

    Google Scholar 

  150. P. Fuentealba, in Ref. [(3)]

    Google Scholar 

  151. C. Pouchana, D. Y. Zhang, and D. Begue, in Ref. [(3)]

    Google Scholar 

  152. D. C. Patton and M. R. Pederson, Phys. Rev. A 56, 2495 (1997).

    Google Scholar 

  153. W. Kohn, Y. Meir, and D. E. Makarov, Phys. Rev. Lett. 80, 4153 (1998).

    CAS  Google Scholar 

  154. M. Lein, J. F. Dobson, and E. K. U. Gross, J. Comp. Chem. 20, 12 (1999).

    CAS  Google Scholar 

  155. J. F. Dobson and B. P. Dinte, Phys. Rev. Lett. 76, 1780 (1996).

    CAS  Google Scholar 

  156. Y. Andersson, D. C. Langreth, and B. I. Lundqvist, Phys. Rev. Lett. 76, 102 (1996).

    CAS  Google Scholar 

  157. E. R. Johnson and A. D. Becke, J. Chem. Phys. 123, 024101 (2005).

    Google Scholar 

  158. A. D. Becke and E. R. Johnson, J. Chem. Phys. 123, 154101 (2005).

    Google Scholar 

  159. A. D. Becke and E. R. Johnson, J. Chem. Phys. 127, 154108 (2007).

    Google Scholar 

  160. M. J. Frisch et al., Gaussian 03, Revision C.02, Gaussian, Inc., Wallingford, CT, 2004.

    Google Scholar 

  161. J. Olsen, P. Jørgensen, H. Koch, A. Balkova, and R. J. Bartlett, J. Chem. Phys. 104, 8007 (1996).

    CAS  Google Scholar 

  162. F. D. Giacomo, F. A. Gianturco, F. Raganelli, and F. Schneider, J. Chem. Phys. 101, 3952 (1994).

    Google Scholar 

  163. J. M. L. Martin, Spectrochim. Acta A 57, 875 (2001).

    CAS  Google Scholar 

  164. E. K. U. Gross, J. F. Dobson, and M. Petersilka, in Density functional theory I–IV, edited by R. F. Nalewajski, Topics in Current Chemistry, vols. 180–183 (Springer, Berlin, 1996).

    Google Scholar 

  165. K. Burke and E. K. U. Gross, in Density functionals: theory and applications, edited by D. Joulbert, Lecture Notes in Physics, vol. 500 (Springer, Berlin, 1998).

    Google Scholar 

  166. M. A. L. Marques, C. A. Ullrich, F. Nogueira, A. Rubio, K. Burke, and E. K. U. Gross, eds., Time-dependent density functional theory, Lecture Notes in Physics, vol. 706 (Springer, Berlin, 2006).

    Google Scholar 

  167. G. L. Oliver and J. P. Perdew, Phys. Rev. A 20, 397 (1979).

    CAS  Google Scholar 

  168. K. Capelle and V. L. Libero, Int. J. Quantum Chem. 105, 679 (2005).

    CAS  Google Scholar 

  169. L. M. Sandratskii, Adv. Phys. 47, 91 (1998).

    CAS  Google Scholar 

  170. L. Nordström and D. Singh, Phys. Rev. Lett. 76, 4420 (1996).

    Google Scholar 

  171. K. Capelle and L. N. Oliveira, Phys. Rev. B 61, 15228 (2000).

    CAS  Google Scholar 

  172. E. Engel, T. Auth, and R. M. Dreizler, Phys. Rev. B 64, 235126 (2001).

    Google Scholar 

  173. A. Trellakis, Phys. Rev. Lett. 91, 056405 (2003).

    CAS  Google Scholar 

  174. W. Cai and G. Galli, Phys. Rev. Lett. 92, 186402 (2004).

    Google Scholar 

  175. R. M. Dickson and T. Ziegler, J. Phys. Chem. 100, 5286 (1996).

    CAS  Google Scholar 

  176. G. Schreckenbach and T. Ziegler, J. Phys. Chem. 99, 606 (1995).

    CAS  Google Scholar 

  177. G. Magyarfalvi and P. Pulay, J. Chem. Phys. 119, 1350 (2003).

    CAS  Google Scholar 

  178. S. N. Maximoff and G. E. Scuseria, Chem. Phys. Lett. 390, 408 (2004).

    CAS  Google Scholar 

  179. V. G. Malkin, O. L. Malkina, and D. R. Salahub, Chem. Phys. Lett. 204, 80 (1993).

    CAS  Google Scholar 

  180. P. Pyykkö, Adv. Quantum Chem. 11, 353 (1978).

    Google Scholar 

  181. O. Eriksson and J. Wills, in The augmented spherical wave method: a comprehensive treatment, edited by H. Dreyssé, Lecture Notes in Physics, vol. 535, pp. 247–285 (Springer, Berlin/Heidelberg, 1999).

    Google Scholar 

  182. M. Eisenbach, B. L. Györffy, G. M. Stocks, and B. Újfalussy, Phys. Rev. B 65, 144424 (2002).

    Google Scholar 

  183. H. Ebert, Rep. Prog. Phys. 59, 1665 (1996).

    CAS  Google Scholar 

  184. K. Capelle, E. K. U. Gross, and B. L. Györffy, Phys. Rev. Lett. 78, 3753 (1997).

    CAS  Google Scholar 

  185. G. Vignale and M. Rasolt, Phys. Rev. B 37, 10685 (1988).

    Google Scholar 

  186. M. Rasolt and F. Perrot, Phys. Rev. Lett. 69, 2563 (1992).

    Google Scholar 

  187. G. Vignale and M. Rasolt, Phys. Rev. Lett. 59, 2360 (1987).

    CAS  Google Scholar 

  188. E. Orestes, T. Marcasso, and K. Capelle, Phys. Rev. A 68, 022105 (2003).

    Google Scholar 

  189. E. Orestes, A. B. F. da Silva, and K. Capelle, Int. J. Quantum Chem. 103, 516 (2005).

    CAS  Google Scholar 

  190. J. Tao and J. P. Perdew, Phys. Rev. Lett. 95, 196403 (2005).

    Google Scholar 

  191. M. Ferconi and G. Vignale, Phys. Rev. B 50, 14722 (1994).

    CAS  Google Scholar 

  192. O. Steffens, U. Rössler, and M. Suhrke, Europhys. Lett. 42, 529 (1998).

    CAS  Google Scholar 

  193. M. Pi, M. Barranco, A. Emperador, E. Lipparini, and L. Serra, Phys. Rev. B 57, 14783 (1998).

    CAS  Google Scholar 

  194. S. M. Colwell and N. C. Handy, Chem. Phys. Lett. 217, 271 (1994).

    Google Scholar 

  195. A. M. Lee, S. M. Colwell, and N. C. Handy, Chem. Phys. Lett. 229, 225 (1994).

    CAS  Google Scholar 

  196. H. Ebert, M. Battocletti, and E. K. U. Gross, Europhys. Lett. 40, 545 (1997).

    CAS  Google Scholar 

  197. G. Vignale, Phys. Rev. B 47, 10105 (1993).

    Google Scholar 

  198. S. Sharma, S. Pittalis, S. Kurth, S. Shallcross, J. K. Dewhurst, and E. K. U. Gross, Phys. Rev. B 76, 100401 (2007).

    Google Scholar 

  199. C. J. Grayce and R. A. Harris, Phys. Rev. A 50, 3089 (1994).

    CAS  Google Scholar 

  200. F. R. Salsbury, Jr and R. A. Harris, J. Chem. Phys. 108, 6102 (1998).

    CAS  Google Scholar 

  201. K. Capelle, Phys. Rev. A 60, R733 (1999).

    CAS  Google Scholar 

  202. R. W. Danz and M. L. Glasser, Phys. Rev. B 4, 94 (1971).

    Google Scholar 

  203. P. Skudlarski and G. Vignale, Phys. Rev. B 48, 8547 (1993).

    CAS  Google Scholar 

  204. Y. Takada and H. Goto, J. Phys. Condens. Matter 10, 11315 (1998).

    CAS  Google Scholar 

  205. G. Vignale, M. Rasolt, and D. J. W. Geldart, Phys. Rev. B 37, 2502 (1988).

    Google Scholar 

  206. G. Vignale, C. A. Ullrich, and S. Conti, Phys. Rev. Lett. 79, 4878 (1997).

    CAS  Google Scholar 

  207. R. Resta, Rev. Mod. Phys. 66, 899 (1994).

    CAS  Google Scholar 

  208. G. Nenciu, Rev. Mod. Phys. 63, 91 (1991).

    Google Scholar 

  209. R. W. Nunes and D. Vanderbilt, Phys. Rev. Lett. 73, 712 (1994).

    CAS  Google Scholar 

  210. X. Gonze, P. Ghosez, and R. W. Godby, Phys. Rev. Lett. 74, 4035 (1995).

    CAS  Google Scholar 

  211. P. Umari and A. Pasquarello, Int. J. Quantum Chem. 101, 666 (2005).

    CAS  Google Scholar 

  212. D. Vanderbilt, Phys. Rev. Lett. 79, 3966 (1997).

    CAS  Google Scholar 

  213. R. Resta, Phys. Rev. Lett. 77, 2265 (1996).

    CAS  Google Scholar 

  214. X. Gonze, P. Ghosez, and R. W. Godby, Phys. Rev. Lett. 78, 294 (1997).

    CAS  Google Scholar 

  215. R. M. Martin and G. Ortiz, Phys. Rev. B 56, 1124 (1997).

    CAS  Google Scholar 

  216. F. Kootstra, P. L. de Boeij, and J. G. Snijders, J. Chem. Phys. 112, 6517 (2000).

    CAS  Google Scholar 

  217. G. F. Bertsch, J.-I. Iwata, A. Rubio, and K. Yabana, Phys. Rev. B 62, 7998 (2000).

    CAS  Google Scholar 

  218. M. van Faassen, P. L. de Boeij, R. van Leeuwen, J. A. Berger, and J. G. Snijders, J. Chem. Phys. 118, 1044 (2003).

    Google Scholar 

  219. D. Xiao, J. Shi, and Q. Niu, Phys. Rev. Lett. 95, 137204 (2005).

    Google Scholar 

  220. J. Shi, G. Vignale, D. Xiao, and Q. Niu, Phys. Rev. Lett. 99, 197202 (2007).

    Google Scholar 

  221. T. Thonhauser, D. Ceresoli, D. Vanderbilt, and R. Resta, Phys. Rev. Lett. 95, 137205 (2005).

    CAS  Google Scholar 

  222. D. Ceresoli, T. Thonhauser, D. Vanderbilt, and R. Resta, Phys. Rev. B 74, 024408 (2006).

    Google Scholar 

  223. A. M. Lee, N. C. Handy, and S. M. Colwell, J. Chem. Phys. 103, 10095 (1995).

    CAS  Google Scholar 

  224. O. Gunnarsson and K. Schönhammer, Phys. Rev. Lett. 56, 1968 (1986).

    CAS  Google Scholar 

  225. N. A. Lima, M. F. Silva, L. N. Oliveira, and K. Capelle, Phys. Rev. Lett. 90, 146402 (2003). N. A. Lima, L. N. Oliveira, and K. Capelle, Europhys. Lett. 60, 601 (2002). M. F. Silva, N. A. Lima, A. L. Malvezzi, and K. Capelle, Phys. Rev. B 71, 125130 (2005).

    Google Scholar 

  226. R. J. Magyar and K. Burke, Phys. Rev. A 70, 032508 (2004).

    Google Scholar 

  227. V. L. Líbero and K. Capelle, Phys. Rev. B 68, 024423 (2003). P. E. G. Assis, V. L. Libero, and K. Capelle, Phys. Rev. B 71, 052402 (2005). See also Ref. [(168)]

    Google Scholar 

  228. V. L. Libero and K. Capelle, cond-mat/0506206.

    Google Scholar 

  229. H. Chermette, J. Comp. Chem. 20, 129 (1999).

    CAS  Google Scholar 

  230. F. D. Proft and P. Geerlings, Chem. Rev. 101, 1451 (2001).

    Google Scholar 

  231. Veillard and Clementi, J. Chem. Phys. 49, 2415 (1968).

    CAS  Google Scholar 

  232. E. Orestes, A. B. F. da Silva, and K. Capelle, Physical Chemistry – Chemical Physics, accepted (2009). Available in electronic form as arXiv:0712.1586.

    Google Scholar 

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Acknowledgements

This work was supported financially by FAPESP and CNPq. We thank Daniel Vieira for providing the original version of Fig. 1 and the Brazilian Journal of Physics for permission to use Fig. 1 and Table 1, which were originally published in Ref. [23].

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  1. Departamento de Química e Física Molecular, Instituto de Química de São Carlos, Universidade de São Paulo, Caixa Postal 780, 13560-970, São Carlos, São Paulo, Brazil

    Ednilsom Orestes

  2. Departamento de Física e Informática, Instituto de Física de São Carlos, Universidade de São Paulo, Caixa Postal 369, 13560-970, São Carlos, São Paulo, Brazil

    Ednilsom Orestes, Henrique J. P. Freire & Klaus Capelle

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  1. Dept. Physics, University of Windsor, Windsor, N9B 3P4, Canada

    Mordechay Schlesinger

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Orestes, E., Freire, H.J.P., Capelle, K. (2009). Density-Functional Theory in External Electric and Magnetic Fields. In: Schlesinger, M. (eds) Modern Aspects of Electrochemistry No. 44. Modern Aspects of Electrochemistry, vol 44. Springer, New York, NY. https://doi.org/10.1007/978-0-387-49586-6_8

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