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Kohn–Sham LCAO Method for Periodic Systems

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Quantum Chemistry of Solids

Part of the book series: Springer Series in Solid-State Sciences ((SSSOL,volume 153))

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Abstract

The progress in the electron-correlation study of solids is connected mainly with the density-functional theory (DFT), determining directly the various physical properties of a system without any knowledge of the many-electron wavefunction.

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References

  1. M. Springborg, Methods of Electronic Structure Calculations (Wiley, Chichester 2000)

    Google Scholar 

  2. R. Martin, Electronic Structure. Basic Theory and Practical Methods (Cambridge University Press, Cambridge, 2004)

    Google Scholar 

  3. L. Kantorovich, Quantum Theory of the Solid State (Kluwer Academic, Dordrecht, 2004)

    MATH  Google Scholar 

  4. V.R. Saunders, R. Dovesi, C. Roetti, R. Orlando, C.M. Zicovich-Wilson, N.M. Harrison, CRYSTAL-2003 Users Manual (University of Torino, Torino, 2003). http://www.crystal.unito.it

  5. P.P. Ewald, Ann. Phys. 64, 253 (1921)

    Article  MATH  Google Scholar 

  6. J. Moreno, J.M. Soler, Phys. Rev. B 46, 13891 (1992)

    Article  ADS  Google Scholar 

  7. C.J. Cramer, Essentials of Computational Chemistry, 2nd edn. (Wiley, New York, 2004)

    Google Scholar 

  8. Gaussian 03, Revision C.02, M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, J.A. Montgomery Jr., T. Vreven, K.N. Kudin, J.C. Burant, J.M. Millam, S.S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. Scalmani, N. Rega, G.A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, J.E. Knox, H.P. Hratchian, J.B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R.E. Stratmann, O. Yazyev, A.J. Austin, R. Cammi, C. Pomelli, J.W. Ochterski, P.Y. Ayala, K. Morokuma, G.A. Voth, P. Salvador, J.J. Dannenberg, V.G. Zakrzewski, S. Dapprich, A.D. Daniels, M.C. Strain, O. Farkas, D.K. Malick, A.D. Rabuck, K. Raghavachari, J.B. Foresman, J.V. Ortiz, Q. Cui, A.G. Baboul, S. Clifford, J. Cioslowski, B.B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R.L. Martin, D.J. Fox, T. Keith, M.A. Al-Laham, C.Y. Peng, A. Nanayakkara, M. Challacombe, P.M.W. Gill, B. Johnson, W. Chen, M.W. Wong, C. Gonzalez, J.A. Pople, Gaussian, Inc., Wallingford CT, 2004, http://www.gaussian.com/citation.htm

  9. Strong Coulomb Correlations in Electronic Structure Calculations. Beyond the Local Density Approximation, ed. by Vladimir I. Anisimov (Gordon and Breach, Amsterdam, 2000)

    Google Scholar 

  10. V.I. Anisimov, J. Zaanen, O.K. Andersen, Phys. Rev. B 44, 943 (1991)

    Article  ADS  Google Scholar 

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

    Article  ADS  MATH  Google Scholar 

  12. E. Fermi, Z. Phys. 48, 73 (1928)

    Article  ADS  MATH  Google Scholar 

  13. J.C. Slater, Phys. Rev. 91, 528 (1953)

    Article  ADS  MATH  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  15. N.C. Handy, Molec. Phys. 102, 2399 (2004)

    Article  ADS  Google Scholar 

  16. K. Capelle, A Birds-eye View of Density Functional Theory (2005), http://arXiv.org/archive/cond-mat/0211443v5

  17. W. Kohn, Rev. Mod. Phys. 71, 1253 (1998)

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

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

    Book  MATH  Google Scholar 

  20. W. Koch, M.C. Holthausen, A Chemist’s Guide to Density Functional Theory, 2nd edn. (Wiley, New York, 2002)

    Google Scholar 

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

    Article  ADS  Google Scholar 

  22. R. Neumann, Molec. Phys. 87, 1 (1996)

    Article  ADS  Google Scholar 

  23. J.P. Perdew, S. Kurth, Lect. Note Phys. 620, 1 (2003)

    Article  ADS  Google Scholar 

  24. K. Burke, J. Werschnik, E.K.U. Gross, J. Chem. Phys. 123, 062206 (2005)

    Google Scholar 

  25. I.G. Kaplan, Intermolecular Interactions. Physical Picture, Computational Methods and Model Potentials (Wiley, New York, 2006)

    Google Scholar 

  26. K. Capelle, V.L. Libero, Int. J. Quant. Chem. 105, 679 (2005)

    Article  ADS  Google Scholar 

  27. J.C. Slater, Phys. Rev. 81, 385 (1951)

    Article  ADS  MATH  Google Scholar 

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

    Article  ADS  MATH  Google Scholar 

  29. U. von Barth, L. Hedin, J. Phys. C Condens. Matter 5, 1629 (1972)

    Google Scholar 

  30. O. Gunnarsson, B.I. Lundqvist, Phys. Rev. B 13, 4274 (1976)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  32. S.J. Vosko, L. Wilk, M. Nussair, Can. J. Phys. 1980, 1200 (1980)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  34. J.P. Perdew, Y. Wang, Phys. Rev. B 40, 3389 (1989)

    Article  ADS  Google Scholar 

  35. J.P. Perdew, A. Zunger, Phys. Rev. B 45, 13244 (1992)

    Article  ADS  Google Scholar 

  36. J.P. Perdew, A. Zunger, Phys. Rev. B 33, 8800 (1986)

    Article  ADS  Google Scholar 

  37. J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996)

    Article  ADS  Google Scholar 

  38. J.P. Perdew, A. Ruzsinszky, J. Tao, V.N. Staroverov, G.E. Scuseria, G.I. Csonka, J. Chem. Phys. 123, 062201 (2005)

    Google Scholar 

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

    Article  ADS  Google Scholar 

  40. C. Lee, W. Wang, R.G. Parr, Phys. Rev. B 37, 785 (1988)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  42. Xin Xu, W.A. Goddard III, J. Chem. Phys. 121, 4068 (2004)

    Google Scholar 

  43. J. Tao, J.P. Perdew, V.N. Staroverov, G.E. Scuseria, Phys. Rev. B 69, 075102 (2004)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  45. J.P. Perdew, K. Burke, Y. Wang, Phys. Rev. B 54, 16533 (1996)

    Article  ADS  Google Scholar 

  46. P. Ziesche, S. Kurth, J.P. Perdew, Comput. Mater. Sci. 11, 122 (1998)

    Article  Google Scholar 

  47. E.H. Lieb, S. Oxford, Int. J. Quant. Chem. 19, 427 (1981)

    Article  Google Scholar 

  48. E.J. Baerends, O.V. Gritsenko, J. Chem. Phys. 123, 062202 (2005)

    Google Scholar 

  49. M. Gruning, O.V. Gritsenko, E.J. Baerends, J. Chem. Phys. 118, 7183 (2003)

    Google Scholar 

  50. M.A. Buijse, E.J. Baerends, Molec. Phys. 100, 401 (2002)

    Article  ADS  Google Scholar 

  51. F. Cora, M. Alfredsson, G. Mallia, D. Midlemiss, W.C. Mackrodt, R. Dovesi, R. Orlando, Struct. Bond. 113, 171 (2004)

    Article  Google Scholar 

  52. A.D. Becke, J. Chem. Phys. 112, 4020 (2000)

    Google Scholar 

  53. A.D. Becke, J. Chem. Phys. 98, 1372, 5468 (1993)

    Google Scholar 

  54. O.V. Gritsenko, P.R. T.Schipper, E.J. Baerends, Int. J. Quant. Chem. Symp. 30, 1375 (1996)

    Article  Google Scholar 

  55. J.P. Perdew, M. Ernzerhof, K. Burke, J. Chem. Phys. 105, 9982 (1996)

    Google Scholar 

  56. J.E. Jaffe, A.C. Hess, J. Chem. Phys. 105, 10983 (1996)

    Google Scholar 

  57. M.C. Payne, M.P. Teller, D.C. Allan, J.A. Arias, J.D. Joannopoulos, Rev. Mod. Phys. 64, 1045 (1992)

    Article  ADS  Google Scholar 

  58. K.N. Kudin, G.E. Scuseria, Phys. Rev. B 61, 16440 (2000)

    Article  ADS  Google Scholar 

  59. V.N. Staroverov, G.E. Scuseria, J. Tao, J.P. Perdew, Phys. Rev. B 69, 075102 (2004)

    Article  ADS  Google Scholar 

  60. L. Greengard, V. Rokhlin, J. Comput. Phys. 73, 325 (1987)

    MATH  Google Scholar 

  61. K.N. Kudin, G.E. Scuseria, Chem. Phys. Lett. 289, 611 (1998)

    Article  ADS  Google Scholar 

  62. E. Artacho, D. Sanchez-Portal, P. Ordejon, A. Garcia, J.M. Soler, Phys. Stat. Sol. (b) 215, 809 (1999)

    Article  ADS  Google Scholar 

  63. P. Ordejon, E. Artacho, J.M. Soler, Phys. Rev. B 53, R10441 (1996)

    Article  ADS  Google Scholar 

  64. J.R. Chelikowsky, S.G. Loucie, Phys. Rev. B 29, 3470 (1987)

    Article  ADS  Google Scholar 

  65. M. Towler, A. Zupan, M. Causa, Comput. Phys. Commun. 98, 181 (1996)

    Article  ADS  Google Scholar 

  66. A. Lichanot, M. Merawa, M. Causa, Chem. Phys. Lett. 246, 263 (1995)

    Article  ADS  Google Scholar 

  67. A. Zupan, M. Causa, Int. J. Quant. Chem. 56, 337 (1995)

    Article  Google Scholar 

  68. A. Savin, Int. J. Quant. Chem. S22, 457 (1988)

    Google Scholar 

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

    Google Scholar 

  70. M. Causa, Lecture Notes in Chem. 48, 91 (1996)

    Article  Google Scholar 

  71. F. Figueirido, R.M. Levy, R. Zhou, B. Berne, J. Chem. Phys. 106, 9835 (1997)

    Google Scholar 

  72. M. Challacombe, C. White, M. Head-Gordon, J. Chem. Phys. 107, 1013 (1997)

    Google Scholar 

  73. K.N. Kudin, G.E. Scuseria, J. Chem. Phys. 121, 2886 (2004)

    Google Scholar 

  74. K.N. Kudin, G.E. Scuseria, Phys. Rev. B 61, 5141 (2000)

    Article  ADS  Google Scholar 

  75. D.L. Strout, G.E. Scuseria, J. Chem. Phys. 102, 8448 (1995)

    Google Scholar 

  76. J.M. Soler, E. Artacho, J.D. Gale, A. Garcia, J. Junquera, P. Ordejon, D. Sanchez-Portal, J. Phys. Condens. Matter 14, 2745 (2002)

    Article  ADS  Google Scholar 

  77. E. Anglada, J.M. Soler, J. Junquera, E. Artacho, Phys. Rev. B 66, 205101 (2002)

    Article  ADS  Google Scholar 

  78. M.C. Strain, G.E. Scuseria, M.J. Frisch, Science 271, 51 (1996)

    Article  ADS  Google Scholar 

  79. J.C. Burant, M.C. Strain, G.E. Scuseria, M.J. Frisch, Chem. Phys. Lett. 258, 45 (1998)

    Article  Google Scholar 

  80. P. Pulay, J. Comput. Chem. 3, 556 (1982)

    Google Scholar 

  81. R.E. Stratmann, G.E. Scuseria, M.J. Frisch, Chem. Phys. Lett. 257, 213 (1996)

    Article  ADS  Google Scholar 

  82. C. Adamo, V. Barone, J. Chem. Phys. 110, 6158 (1999)

    Google Scholar 

  83. J. Heyd, G.E. Scuseria, M. Ernzerhof, J. Chem. Phys. 118, 8207 (2003)

    Google Scholar 

  84. J. Heyd, G.E. Scuseria, J. Chem. Phys. 120, 7274 (2004)

    Google Scholar 

  85. W. Kohn, Int. J. Quant. Chem. 56, 229 (1995)

    Article  Google Scholar 

  86. J.P. Perdew, M. Ernzerhof, K. Burke, J. Chem. Phys. 105, 9982 (1996)

    Google Scholar 

  87. M. Ernzerhof, G.E. Scuseria, J. Chem. Phys. 110, 5029 (1999)

    Google Scholar 

  88. J.C. Burant, G.E. Scuseria, M.J. Frisch, J. Chem. Phys. 105, 8969 (1996)

    Google Scholar 

  89. C. Ochsenfeld, C.A. White, M. Head-Gordon, J. Chem. Phys. 109, 1163 (1998)

    Google Scholar 

  90. M.W. Gill, J.A. Pople, Int. J. Quant. Chem. 40, 753 (1991)

    Article  Google Scholar 

  91. M. Ernzerhof, J.P. Perdew, J. Chem. Phys. 109, 3313 (1998)

    Google Scholar 

  92. GAUSSIAN Development Version, Revision B.07, M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, J.A. Montgomery Jr., T. Vreven, K.N. Kudin, J.C. Burant, J.M. Millam, S.S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. Scalmani, N. Rega, G.A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, J.E. Knox, H.P. Hratchian, J.B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R.E. Stratmann, O. Yazyev, A.J. Austin, R. Cammi, C. Pomelli, J.W. Ochterski, P.Y. Ayala, K. Morokuma, G.A. Voth, P. Salvador, J.J. Dannenberg, V.G. Zakrzewski, S. Dapprich, A.D. Daniels, M.C. Strain, O. Farkas, D.K. Malick, A.D. Rabuck, K. Raghavachari, J.B. Foresman, J.V. Ortiz, Q. Cui, A.G. Baboul, S. Clifford, J. Cioslowski, B.B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R.L. Martin, D.J. Fox, T. Keith, M.A. Al-Laham, C.Y. Peng, A. Nanayakkara, M. Challacombe, P.M.W. Gill, B. Johnson, W. Chen, M.W. Wong, C. Gonzalez, J.A. Pople (Gaussian Inc., Pittsburg, PA, 2003)

    Google Scholar 

  93. J. Heyd, J.E. Peralta, G.E. Scuseria, R.L. Martin, J. Chem. Phys. 123, 174101 (2005)

    Google Scholar 

  94. J. Uddin, G.E. Scuseria, Phys. Rev. B 72, 035101 (2005)

    Article  ADS  Google Scholar 

  95. J. Uddin, J.E. Peralta, G.E. Scuseria, Phys. Rev. B 71, 155112 (2005)

    Article  ADS  Google Scholar 

  96. I.D. Prodan, G.E. Scuseria, J.A. Sordo, K.N. Kudin, R.L. Martin, J. Chem. Phys. 123, 014703 (2005)

    Google Scholar 

  97. V. Barone, J.E. Peralta, J. Uddin, G.E. Scuseria, J. Chem. Phys. 124, 024709 (2006)

    Google Scholar 

  98. I.D. Prodan, G.E. Scuseria, R.L. Martin, Phys. Rev. B 73, 045104 (2006)

    Article  ADS  Google Scholar 

  99. J. Paier, R. Hirschl, M. Marsman, G. Kresse, J. Chem. Phys. 122, 234102 (2005)

    Google Scholar 

  100. V.R. Saunders, R. Dovesi, C. Roetti, M. Causa, N.M. Harrison, R. Orlando, C.M. Zicovich-Wilson, Crystal98 User’s Manual (University of Torino, Torino, 1998)

    Google Scholar 

  101. M.S. Hybertsen, S.G. Louie, Phys. Rev. Lett. 55, 1418 (1985)

    Article  ADS  Google Scholar 

  102. M.C. Foulkes, L. Mitas, R. Needs, G. Rajagopal, Rev. Mod. Phys. 73, 33 (2001)

    Article  ADS  Google Scholar 

  103. T. Bredow, A.R. Gerson, Phys. Rev. B 61, 5194 (2000)

    Article  ADS  Google Scholar 

  104. F. Illas, R.L. Martin, J. Chem. Phys. 108, 2519 (1998)

    Google Scholar 

  105. J. Muscat, A. Wander, N.M. Harrison, Chem. Phys. Lett. 342, 397 (2001)

    Article  ADS  Google Scholar 

  106. W.G. Aulbur, L. Johnsson, J.W. Wilkins, Solid State Phys. 54, 1 (2000)

    Article  Google Scholar 

  107. F. Aryasetiawan, in Strong Coulomb Correlations in Electronic Structure Calculations, ed. by V.I. Anisimov (Gordon and Breach, Singapore, 2000), p. 1

    Google Scholar 

  108. J.P. Perdew, S. Kurth, A. Zupan, P. Blaha, Phys. Rev. Lett. 82, 544 (1999)

    Article  Google Scholar 

  109. L. Petit, A. Svane, Z. Szotek, W.M. Temmerman, Phys. Rev. B 72, 205118 (2005)

    Article  ADS  Google Scholar 

  110. T. Fujiwara, M. Arai, Y. Ishii, in Strong Coulomb Correlations in Electronic Structure Calculations, ed. by V.I. Anisimov (Gordon and Breach, Singapore, 2000), p. 167

    Google Scholar 

  111. V.I. Anisimov, A.I. Lichtenstein, in Strong Coulomb Correlations in Electronic Structure Calculations, ed. by V.I. Anisimov, (Gordon and Breach, Singapore, 2000), p. 97

    Google Scholar 

  112. V. Polo, E. Kraka, D. Cremer, Molec. Phys. 100, 1771 (2002)

    Article  ADS  Google Scholar 

  113. D. Cremer, Molec. Phys. 99, 1899 (2001)

    Article  ADS  Google Scholar 

  114. G.I. Csonka, B.J. Johnson, Theor. Chem. Acc. 99, 158 (1998)

    Article  Google Scholar 

  115. O.A. Vydrov, G.E. Scuseria, J. Chem. Phys. 121, 8187 (2004)

    Google Scholar 

  116. O.A. Vydrov, G.E. Scuseria, J. Chem. Phys. 122, 184107 (2005)

    Google Scholar 

  117. A. Svane, W.M. Temmerman, Z. Szotek, J. Laegsgaard, H. Winter, Int. J. Quant. Chem. 77, 799 (2000)

    Article  Google Scholar 

  118. A. Flipetti, N.A. Spaldin, Phys. Rev. B 67, 125109 (2003)

    Article  ADS  Google Scholar 

  119. M. Arai, T. Fujiwara, Phys. Rev. B 51, 1477 (1995)

    Article  ADS  Google Scholar 

  120. O.K. Anderson, Phys. Rev. B 12, 3060 (1975)

    Article  ADS  Google Scholar 

  121. M. Imada, A. Fujimori, Y. Tokura, Rev. Mod. Phys. 70, 1040 (1998)

    Article  ADS  Google Scholar 

  122. A. Rohrbach, J. Hafner, G. Kresse, J. Phys. C Condens. Matter 15, 979 (2003)

    Article  ADS  Google Scholar 

  123. G. Kresse, J. Furthmuller, Comput. Mater. Sci. 6, 15 (1996)

    Article  Google Scholar 

  124. G. Ricardo, F. Cora, A.A. Sokol, N.H. de Leeuw, C.R.A. Catlow, Phys. Rev. B 73, 035116 (2006)

    Article  ADS  Google Scholar 

  125. S.ZN. Karazhanov, P. Ravindran, A. Kjekhus, H. Fjellvag, U. Grossner, B.G. Svensson, J. Cryst. Growth 287, 162 (2006)

    Google Scholar 

  126. A.G. Eguiluz, O.D. Restrepo, B.C. Larson, J.Z. Tischler, P. Zschack, G.E. Jellison, J. Phys. Chem. Solids 66, 2281 (2005)

    Article  ADS  Google Scholar 

  127. R. Laskowskii, P. Blaha, K. Schwarz, Phys. Rev. B 67, 075102 (2003)

    Article  ADS  Google Scholar 

  128. A.L. Ivanovskii, T.I. Chupakhina, V.G. Zubkov, A.P. Tyutyunnik, V.N. Krasilnikov, G.V. Bazuev, S.V. Okatov, A.I. Lichtenstein, Phys. Lett. A 348, 66 (2005)

    Article  ADS  Google Scholar 

  129. Y. Wang, D.J. Doren, Solid State Commun. 136, 142 (2005)

    Article  ADS  Google Scholar 

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Evarestov, R.A. (2012). Kohn–Sham LCAO Method for Periodic Systems. In: Quantum Chemistry of Solids. Springer Series in Solid-State Sciences, vol 153. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30356-2_7

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