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Relativistic Density Functional Theory

  • Christoph van Wüllen
Chapter
Part of the Challenges and Advances in Computational Chemistry and Physics book series (COCH, volume 10)

Abstract

This review starts with the basics of nonrelativistic density functional theory, followed by the foundation of the relativistic variant. How to formulate a relativistic spin density functional theory is shown through the comparison of the non-collinear and collinear approximations. It is shown where relativistic corrections to the exchange-correlation functionals are important and that they have a sizeable influence on total energies but are not so important for valence properties. After discussing some four-component Dirac–Kohn–Sham implementations, quasirelativistic methods are reviewed with emphasis on the zeroth-order regular approximation and the Douglas–Kroll–Hess method. This review contains 163 references.

Relativistic Density functional theory Electron gas Collinear Four-current Dirac equation 

References

  1. 1.
    Hohenberg, P., Kohn, W.: Phys. Rev. 136, B864 (1964)CrossRefGoogle Scholar
  2. 2.
    Kohn, W., Sham, L.J.: Phys. Rev. 140, A1133 (1965)CrossRefGoogle Scholar
  3. 3.
    Jones, R.O., Gunnarsson, O.: Rev. Mod. Phys. 61, 689 (1989)CrossRefGoogle Scholar
  4. 4.
    Ceperley, D.M., Alder, B.J.: Phys. Rev. Lett. 45, 566 (1980)CrossRefGoogle Scholar
  5. 5.
    Vosko, S.H., Wilk, L., Nusair, M.: Can. J. Phys. 58, 1200 (1980)CrossRefGoogle Scholar
  6. 6.
    Perdew, J.P., Zunger, A.: Phys. Rev. B 23, 5048 (1981)CrossRefGoogle Scholar
  7. 7.
    Ma, S.K., Brueckner, K.A.: Phys. Rev. 165, 18 (1968)CrossRefGoogle Scholar
  8. 8.
    Levy, M., Perdew, J.P.: Int. J. Quantum Chem. 49, 539 (1994)CrossRefGoogle Scholar
  9. 9.
    Becke, A.D.: J. Comput. Chem. 20, 63 (1999)CrossRefGoogle Scholar
  10. 10.
    Langreth, D.C., Mehl, M.J.: Phys. Rev. B 28, 1809 (1983)CrossRefGoogle Scholar
  11. 11.
    Becke, A.D.: J. Chem. Phys. 98, 1372 (1993)CrossRefGoogle Scholar
  12. 12.
    Becke, A.D.: J. Chem. Phys. 98, 5648 (1993)CrossRefGoogle Scholar
  13. 13.
    Ghosh, S.K., Parr, R.G.: Phys. Rev. A 34, 785 (1986)CrossRefGoogle Scholar
  14. 14.
    Becke, A.D., Roussel, M.R.: Phys. Rev. A 39, 3761 (1989)CrossRefGoogle Scholar
  15. 15.
    Tao, J.M., Perdew, J.P., Staroverov, V.N., Scuseria, G.E.: Phys. Rev. Lett. 91, 146401 (2003)CrossRefGoogle Scholar
  16. 16.
    Engel, E., Dreizler, R.M.: J. Comput. Chem. 20, 31 (1999)CrossRefGoogle Scholar
  17. 17.
    Vignale, G., Rasolt, M.: Phys. Rev. Lett. 59, 2360 (1987)CrossRefGoogle Scholar
  18. 18.
    Vignale, G., Rasolt, M.: Phys. Rev. B 37, 10685 (1988)CrossRefGoogle Scholar
  19. 19.
    Gunnarsson, O., Lundqvist, B.I.: Phys. Rev. B 13, 4274 (1976)CrossRefGoogle Scholar
  20. 20.
    Rajagopal, A.K., Callaway, J.: Phys. Rev. B 7, 1912 (1973)CrossRefGoogle Scholar
  21. 21.
    Rajagopal, A.K.: J. Phys. C 11, L943 (1978)CrossRefGoogle Scholar
  22. 22.
    Macdonald, A.H., Vosko, S.H.: J. Phys. C 12, 2977 (1979)CrossRefGoogle Scholar
  23. 23.
    Ramana, M.V., Rajagopal, A.K.: Adv. Chem. Phys. 54, 231 (1983)CrossRefGoogle Scholar
  24. 24.
    Pyykkö, P., Tokman, M., Labzowsky, L.N.: Phys. Rev. A 57, R689 (1998)CrossRefGoogle Scholar
  25. 25.
    Labzowsky, L., Goidenko, I., Tokman, M., Pyykkö, P.: Phys. Rev. A 59, 2707 (1999)CrossRefGoogle Scholar
  26. 26.
    Dyall, K.G., Bauschlicher, C.W., Schwenke, D.W., Pyykkö, P.: Chem. Phys. Lett. 348, 497 (2001)CrossRefGoogle Scholar
  27. 27.
    Pyykkö, P., Dyall, K.G., Csazar, A.G., Tarczay, G., Polyansky, O.L., Tennyson, J.: Phys. Rev. A 6302, 024502 (2001)CrossRefGoogle Scholar
  28. 28.
    Colwell, S.M., Handy, N.C.: Chem. Phys. Lett. 217, 271 (1993)CrossRefGoogle Scholar
  29. 29.
    Lee, A.M., Colwell, S.M., Handy, N.C.: Chem. Phys. Lett. 229, 225 (1994)CrossRefGoogle Scholar
  30. 30.
    Lee, A.M., Handy, N.C., Colwell, S.M.: J. Chem. Phys. 103, 10095 (1995)CrossRefGoogle Scholar
  31. 31.
    Capelle, K., Gross, E.K.U.: Phys. Rev. Lett. 78, 1872 (1997)CrossRefGoogle Scholar
  32. 32.
    Eschrig, H., Servedio, V.D.P.: J. Comput. Chem. 20, 23 (1999)CrossRefGoogle Scholar
  33. 33.
    Eschrig, H.: The Fundamentals of Density Functional Theory. Teubner, Stuttgart (1996)CrossRefGoogle Scholar
  34. 34.
    van Wüllen, C.: J. Comput. Chem. 23, 779 (2002)CrossRefGoogle Scholar
  35. 35.
    Engel, E., Auth, T., Dreizler, R.M.: Phys. Rev. B 64, 235126 (2001)CrossRefGoogle Scholar
  36. 36.
    Jansen, H.J.F.: Phys. Rev. B 59, 4699 (1999)CrossRefGoogle Scholar
  37. 37.
    Fritsch, D., Koepernik, K., Richter, M., Eschrig, H.: J. Comput. Chem. 29, 2210 (2008)CrossRefGoogle Scholar
  38. 38.
    van Wüllen, C.: J. Chem. Phys. 139, 194109 (2009)CrossRefGoogle Scholar
  39. 39.
    Ellis, D.E., Goodman, G.L.: Int. J. Quantum Chem. 25, 185 (1984)CrossRefGoogle Scholar
  40. 40.
    Kübler, J., Hoeck, K.H., Sticht, J., Williams, A.R.: J. Appl. Phys. 63, 3482 (1988)CrossRefGoogle Scholar
  41. 41.
    Kübler, J., Hoeck, K.H., Sticht, J., Williams, A.R.: J. Phys. F 18, 469 (1988)CrossRefGoogle Scholar
  42. 42.
    Nordstrom, L., Singh, D.J.: Phys. Rev. Lett. 76, 4420 (1996)CrossRefGoogle Scholar
  43. 43.
    Sandratskii, L.M.: Adv. Phys. 47, 91 (1998)CrossRefGoogle Scholar
  44. 44.
    Ellis, D.E.: J. Phys. B-At. Mol. Opt. Phys. 10, 1 (1977)CrossRefGoogle Scholar
  45. 45.
    Engel, E., Keller, S., Bonetti, A.F., Müller, H., Dreizler, R.M.: Phys. Rev. A 52, 2750 (1995)CrossRefGoogle Scholar
  46. 46.
    Ramana, M.V., Rajagopal, A.K.: Phys. Rev. A 24, 1689 (1981)CrossRefGoogle Scholar
  47. 47.
    Bonetti, A.F., Engel, E., Dreizler, R.M., Andrejkovics, I., Müller, H.: Phys. Rev. A 58, 993 (1998)CrossRefGoogle Scholar
  48. 48.
    Ramana, M.V., Rajagopal, A.K.: J. Phys. C 12, L845 (1979)CrossRefGoogle Scholar
  49. 49.
    Ramana, M.V., Rajagopal, A.K.: J. Phys. C 14, 4291 (1981)CrossRefGoogle Scholar
  50. 50.
    Macdonald, A.H.: J. Phys. C 16, 3869 (1983)CrossRefGoogle Scholar
  51. 51.
    Xu, B.X., Rajagopal, A.K., Ramana, M.V.: J. Phys. C 17, 1339 (1984)CrossRefGoogle Scholar
  52. 52.
    Engel, E., Keller, S., Dreizler, R.M.: Phys. Rev. A 53, 1367 (1996)CrossRefGoogle Scholar
  53. 53.
    Mayer, M., Häberlen, O.D., Rösch, N.: Phys. Rev. A 54, 4775 (1996)CrossRefGoogle Scholar
  54. 54.
    Varga, S., Engel, E., Sepp, W.D., Fricke, B.: Phys. Rev. A 59, 4288 (1999)CrossRefGoogle Scholar
  55. 55.
    Schmid, R.N., Engel, E., Dreizler, R.M., Blaha, P., Schwarz, K.: Adv. Quantum Chem. 33, 209 (1998)CrossRefGoogle Scholar
  56. 56.
    Rosen, A., Ellis, D.E.: J. Chem. Phys. 62, 3039 (1975)CrossRefGoogle Scholar
  57. 57.
    Liberman, D., Waber, J.T., Cromer, D.T.: Phys. Rev. 137, A27 (1965)CrossRefGoogle Scholar
  58. 58.
    Liberman, D.A., Cromer, D.T., Waber, J.T.: Comput. Phys. Commun. 2, 107 (1971)CrossRefGoogle Scholar
  59. 59.
    Fricke, B., Sepp, W.D., Bastug, T., Varga, S., Schulze, K., Anton, J., Pershina, V.: Adv. Quantum Chem. 29, 109 (1997)CrossRefGoogle Scholar
  60. 60.
    Anton, J., Fricke, B., Engel, E.: Phys. Rev. A 69, 012505 (2004)CrossRefGoogle Scholar
  61. 61.
    Anton, J., Fricke, B., Schwerdtfeger, P.: Chem. Phys. 311, 97 (2005)CrossRefGoogle Scholar
  62. 62.
    Liu, W.J., Hong, G.Y., Dai, D.D., Li, L.M., Dolg, M.: Theor. Chem. Acc. 96, 75 (1997)CrossRefGoogle Scholar
  63. 63.
    Liu, W.J., Dolg, M.: Phys. Rev. A 57, 1721 (1998)CrossRefGoogle Scholar
  64. 64.
    Wang, F., Li, L.M.: J. Mol. Struct. (Theochem) 586, 193 (2002)Google Scholar
  65. 65.
    Liu, W.J., Wang, F., Li, L.M.: J. Theor. Comput. Chem. 2, 257 (2003)CrossRefGoogle Scholar
  66. 66.
    Liu, W., van Wüllen, C.: J. Chem. Phys. 113, 2506 (2000)CrossRefGoogle Scholar
  67. 67.
    Whitten, J.L.: J. Chem. Phys. 58, 4496 (1973)CrossRefGoogle Scholar
  68. 68.
    Baerends, E.J., Ellis, D.E., Ros, P.: Chem. Phys. 2, 41 (1973)CrossRefGoogle Scholar
  69. 69.
    Dunlap, B.I., Connolly, J.W.D., Sabin, J.R.: J. Chem. Phys. 71, 3396 (1979)CrossRefGoogle Scholar
  70. 70.
    Dunlap, B.I.: Phys. Chem. Chem. Phys. 2, 2113 (2000)CrossRefGoogle Scholar
  71. 71.
    Dunlap, B.I.: J. Mol. Struct. (Theochem) 529, 37 (2000)Google Scholar
  72. 72.
    Stephens, P.J., Devlin, F.J., Chabalowski, C.F., Frisch, M.J.: J. Phys. Chem. 98, 11623 (1994)CrossRefGoogle Scholar
  73. 73.
    Becke, A.D.: J. Chem. Phys. 98, 5648 (1993)CrossRefGoogle Scholar
  74. 74.
    Becke, A.D.: Phys. Rev. A 38, 3098 (1988)CrossRefGoogle Scholar
  75. 75.
    Lee, C., Yang, W., Parr, R.G.: Phys. Rev. B 37, 785 (1988)CrossRefGoogle Scholar
  76. 76.
    Saue, T., Helgaker, T.: J. Comput. Chem. 23, 814 (2002)CrossRefGoogle Scholar
  77. 77.
    Henriksson, J., Saue, T., Norman, P.: J. Chem. Phys. 128, 024105 (2008)CrossRefGoogle Scholar
  78. 78.
    Salek, P., Helgaker, T., Saue, T.: Chem. Phys. 311, 187 (2005)CrossRefGoogle Scholar
  79. 79.
    Gaston, N., Schwerdtfeger, P., Saue, T., Greif, J.: J. Chem. Phys. 124, 044304 (2006)CrossRefGoogle Scholar
  80. 80.
    Fossgaard, O., Gropen, O., Valero, M.C., Saue, T.: J. Chem. Phys. 118, 10418 (2003)CrossRefGoogle Scholar
  81. 81.
    Fossgaard, O., Gropen, O., Eliav, E., Saue, T.: J. Chem. Phys. 119, 9355 (2003)CrossRefGoogle Scholar
  82. 82.
    Gourlaouen, C., Piquemal, J.P., Saue, T., Parisel, O.: J. Comput. Chem. 27, 142 (2006)CrossRefGoogle Scholar
  83. 83.
    Thierfelder, C., Schwerdtfeger, P., Saue, T.: Phys. Rev. A 76, 034501 (2007)CrossRefGoogle Scholar
  84. 84.
    Bast, R., Hesselmann, A., Salek, P., Helgaker, T., Saue, T.: Chem. Phys. Chem. 9, 445 (2008)CrossRefGoogle Scholar
  85. 85.
    Nakajima, T., Suzumura, T., Hirao, K.: Chem. Phys. Lett. 304, 271 (1999)CrossRefGoogle Scholar
  86. 86.
    Yanai, T., Iikura, H., Nakajima, T., Ishikawa, Y., Hirao, K.: J. Chem. Phys. 115, 8267 (2001)CrossRefGoogle Scholar
  87. 87.
    Nakajima, T., Yanai, T., Hirao, K.: J. Comput. Chem. 23, 847 (2002)CrossRefGoogle Scholar
  88. 88.
    Yanai, T., Nakajima, T., Ishikawa, Y., Hirao, K.: J. Chem. Phys. 114, 6526 (2001)CrossRefGoogle Scholar
  89. 89.
    Yanai, T., Harrison, R.J., Nakajima, T., Ishikawa, Y., Hira, K.: Int. J. Quantum Chem. 107, 1382 (2007)CrossRefGoogle Scholar
  90. 90.
    Yanai, T., Nakajima, T., Ishikawa, Y., Hirao, K.: J. Chem. Phys. 116, 10122 (2002)CrossRefGoogle Scholar
  91. 91.
    Friesner, R.A.: Chem. Phys. Lett. 116, 39 (1985)CrossRefGoogle Scholar
  92. 92.
    Friesner, R.A.: J. Chem. Phys. 85, 1462 (1986)CrossRefGoogle Scholar
  93. 93.
    Nakajima, T., Hirao, K.: J. Chem. Phys. 121, 3438 (2004)CrossRefGoogle Scholar
  94. 94.
    Nakajima, T., Hirao, K.: Mon. Chem. 136, 965 (2005)CrossRefGoogle Scholar
  95. 95.
    Quiney, H.M., Belanzoni, P.: J. Chem. Phys. 117, 5550 (2002)CrossRefGoogle Scholar
  96. 96.
    Belpassi, L., Tarantelli, F., Sgamellotti, A., Quiney, H.M.: J. Chem. Phys. 122, 184109 (2005)CrossRefGoogle Scholar
  97. 97.
    Quiney, H.M., Belanzoni, P., Sgamellotti, A.: Theor. Chem. Acc. 108, 113 (2002)CrossRefGoogle Scholar
  98. 98.
    Belpassi, L., Tarantelli, F., Sgamellotti, A., Quiney, H.M.: J. Chem. Phys. 128, 124108 (2008)CrossRefGoogle Scholar
  99. 99.
    Belpassi, L., Tarantelli, F., Sgamellotti, A., Quiney, H.M.: J. Chem. Phys. 124, 124104 (2006)CrossRefGoogle Scholar
  100. 100.
    Belpassi, L., Tarantelli, F., Sgamellotti, A., Quiney, H.M.: Phys. Rev. B 77, 233403 (2008)CrossRefGoogle Scholar
  101. 101.
    Belpassi, L., Infante, I., Tarantelli, F., Visscher, L.: J. Am. Chem. Soc. 130, 1048 (2008)CrossRefGoogle Scholar
  102. 102.
    Belpassi, L., Tarantelli, F., Sgamellotti, A., Gotz, A.W., Visscher, L.: Chem. Phys. Lett. 442, 233 (2007)CrossRefGoogle Scholar
  103. 103.
    Belpassi, L., Tarantelli, F., Sgamellotti, A., Quiney, H.M.: J. Phys. Chem. A 110, 4543 (2006)CrossRefGoogle Scholar
  104. 104.
    Belpassi, L., Tarantelli, F., Sgamellotti, A., Quiney, H.M., van Stralen, J.N.P., Visscher, L.: J. Chem. Phys. 126, 064314 (2007)CrossRefGoogle Scholar
  105. 105.
    Kutzelnigg, W.: Chem. Phys. 225, 203 (1997)CrossRefGoogle Scholar
  106. 106.
    Liu, W., van Wüllen, C., Han, Y.K., Choi, Y.J., Lee, Y.S.: Adv. Quantum Chem. 39, 325 (2001)CrossRefGoogle Scholar
  107. 107.
    Lee, Y.S.: In: P. Schwerdtfeger Relativistic Electronic Structure Theory: Part 2. Applications, p. 352. Elsevier, Amsterdam (2004)Google Scholar
  108. 108.
    Pitzer, R.M., Winter, N.W.: Int. J. Quantum Chem. 40, 773 (1991)CrossRefGoogle Scholar
  109. 109.
    Mitin, A.V., van Wüllen, C.: J. Chem. Phys. 124, 064305 (2006)CrossRefGoogle Scholar
  110. 110.
    Armbruster, M.K., Weigend, F., van Wüllen, C., Klopper, W.: Phys. Chem. Chem. Phys. 10, 1748 (2008)CrossRefGoogle Scholar
  111. 111.
    Chang, C., Pelissier, M., Durand, P.: Phys. Scr. 34, 394 (1986)CrossRefGoogle Scholar
  112. 112.
    van Lenthe, E., Baerends, E.J., Snijders, J.G.: J. Chem. Phys. 99, 4597 (1993)CrossRefGoogle Scholar
  113. 113.
    Hess, B.A.: Phys. Rev. A 33, 3742 (1986)CrossRefGoogle Scholar
  114. 114.
    Knappe, P., Rösch, N.: J. Chem. Phys. 92, 1153 (1990)CrossRefGoogle Scholar
  115. 115.
    Rösch, N., Häberlen, O.D.: J. Chem. Phys. 96, 6322 (1992)CrossRefGoogle Scholar
  116. 116.
    Häberlen, O.D., Rösch, N.: Chem. Phys. Lett. 199, 491 (1992)CrossRefGoogle Scholar
  117. 117.
    Mayer, M., Krüger, S., Rösch, N.: J. Chem. Phys. 115, 4411 (2001)CrossRefGoogle Scholar
  118. 118.
    Garcia-Hernandez, M., Lauterbach, C., Krüger, S., Matveev, A., Rösch, N.: J. Comput. Chem. 23, 834 (2002)CrossRefGoogle Scholar
  119. 119.
    Majumder, S., Matveev, A.V., Rösch, N.: Chem. Phys. Lett. 382, 186 (2003)CrossRefGoogle Scholar
  120. 120.
    Matveev, A.V., Mayer, M., Rösch, N.: Comput. Phys. Commun. 160, 91 (2004)CrossRefGoogle Scholar
  121. 121.
    Boettger, J.C.: Int. J. Quantum Chem. 65, 565 (1997)CrossRefGoogle Scholar
  122. 122.
    Boettger, J.C.: Phys. Rev. B 57, 8743 (1998)CrossRefGoogle Scholar
  123. 123.
    Boettger, J.C.: Phys. Rev. B 62, 7809 (2000)CrossRefGoogle Scholar
  124. 124.
    van Wüllen, C., Michauk, C.: J. Chem. Phys. 123, 204113 (2005)CrossRefGoogle Scholar
  125. 125.
    Peralta, J.E., Scuseria, G.E.: J. Chem. Phys. 120, 5875 (2004)CrossRefGoogle Scholar
  126. 126.
    Batista, E.R., Martin, R.L., Hay, P.J., Peralta, J.E., Scuseria, G.E.: J. Chem. Phys. 121, 2144 (2004)CrossRefGoogle Scholar
  127. 127.
    Melo, J.I., de Azua, M.C.R., Peralta, J.E., Scuseria, G.E.: J. Chem. Phys. 123, 204112 (2005)CrossRefGoogle Scholar
  128. 128.
    Peralta, J.E., Batista, E.R., Scuseria, G.E., Martin, R.L.: J. Chem. Theory Comput. 1, 612 (2005)CrossRefGoogle Scholar
  129. 129.
    Thaller, B.: The Dirac Equation. Springer, Heidelberg (1992)Google Scholar
  130. 130.
    Baerends, E.J., Schwarz, W.H.E., Schwerdtfeger, P., Snijders, J.G.: J. Phys. B-At. Mol. Opt. Phys. 23, 3225 (1990)CrossRefGoogle Scholar
  131. 131.
    Kellö, V., Sadlej, A.J.: Int. J. Quantum Chem. 68, 159 (1998)CrossRefGoogle Scholar
  132. 132.
    Matveev, A., Rösch, N.: J. Chem. Phys. 118, 3997 (2003)CrossRefGoogle Scholar
  133. 133.
    van Lenthe, E., Baerends, E.J., Snijders, J.G.: J. Chem. Phys. 101, 9783 (1994)CrossRefGoogle Scholar
  134. 134.
    van Leeuwen, R., van Lenthe, E., Baerends, E.J., Snijders, J.G.: J. Chem. Phys. 101, 1272 (1994)CrossRefGoogle Scholar
  135. 135.
    van Lenthe, E., van Leeuwen, R., Baerends, E.J., Snijders, J.G.: Int. J. Quantum Chem. 57, 281 (1996)CrossRefGoogle Scholar
  136. 136.
    Sadlej, A.J., Snijders, J.G., van Lenthe, E., Baerends, E.J.: J. Chem. Phys. 102, 1758 (1995)CrossRefGoogle Scholar
  137. 137.
    van Lenthe, E., Snijders, J.G., Baerends, E.J.: J. Chem. Phys. 105, 6505 (1996)CrossRefGoogle Scholar
  138. 138.
    Philipsen, P.H.T., van Lenthe, E., Snijders, J.G., Baerends, E.J.: Phys. Rev. B 56, 13556 (1997)CrossRefGoogle Scholar
  139. 139.
    van Wüllen, C.: J. Chem. Phys. 109, 392 (1998)CrossRefGoogle Scholar
  140. 140.
    van Wüllen, C.: J. Comput. Chem. 20, 51 (1999)CrossRefGoogle Scholar
  141. 141.
    van Lenthe, E., Ehlers, A., Baerends, E.J.: J. Chem. Phys. 110, 8943 (1999)CrossRefGoogle Scholar
  142. 142.
    Filatov, M.: Chem. Phys. Lett. 365, 222 (2002)CrossRefGoogle Scholar
  143. 143.
    Fedorov, D.G., Nakajima, T., Hirao, K.: Chem. Phys. Lett. 335, 183 (2001)CrossRefGoogle Scholar
  144. 144.
    Barysz, M., Sadlej, A.J., Snijders, J.G.: Int. J. Quantum Chem. 65, 225 (1997)CrossRefGoogle Scholar
  145. 145.
    Barysz, M., Sadlej, A.J.: J. Mol. Struct. (Theochem) 573, 181 (2001)Google Scholar
  146. 146.
    Barysz, M., Sadlej, A.J.: J. Chem. Phys. 116, 2696 (2002)CrossRefGoogle Scholar
  147. 147.
    Kedziera, D., Barysz, M.: J. Chem. Phys. 121, 6719 (2004)CrossRefGoogle Scholar
  148. 148.
    Kutzelnigg, W., Liu, W.J.: Mol. Phys. 104, 2225 (2006)CrossRefGoogle Scholar
  149. 149.
    Kutzelnigg, W., Liu, W.J.: J. Chem. Phys. 123, 241102 (2005)CrossRefGoogle Scholar
  150. 150.
    Liu, W.J., Peng, D.L.: J. Chem. Phys. 125, 044102 (2006)CrossRefGoogle Scholar
  151. 151.
    Liu, W.J., Kutzelnigg, W.: J. Chem. Phys. 126, 114107 (2007)CrossRefGoogle Scholar
  152. 152.
    Dyall, K.G.: J. Chem. Phys. 106, 9618 (1997)CrossRefGoogle Scholar
  153. 153.
    Filatov, M.: J. Chem. Phys. 125, 107101 (2006)CrossRefGoogle Scholar
  154. 154.
    Ilias, M., Saue, T.: J. Chem. Phys. 126, 064102 (2007)CrossRefGoogle Scholar
  155. 155.
    Peng, D.L., Liu, W.J., Xiao, Y.L., Cheng, L.: J. Chem. Phys. 127, 104106 (2007)CrossRefGoogle Scholar
  156. 156.
    Komorovsky, S., Repisky, M., Malkina, O.L., Malkin, V.G., Malkin, I., Kaupp, M.: J. Chem. Phys. 124, 084108 (2006)CrossRefGoogle Scholar
  157. 157.
    Komorovsky, S., Repisky, M., Malkina, O.L., Malkin, V.G., Ondik, I.M., Kaupp, M.: J. Chem. Phys. 128, 104101 (2008)CrossRefGoogle Scholar
  158. 158.
    van Wüllen, C., Langermann, N.: J. Chem. Phys. 126, 114106 (2007)CrossRefGoogle Scholar
  159. 159.
    Quiney, H.M., Skaane, H., Grant, I.P.: Adv. Quantum Chem. 32, 1 (1999)CrossRefGoogle Scholar
  160. 160.
    Dyall, K.G.: J. Chem. Phys. 100, 2118 (1994)CrossRefGoogle Scholar
  161. 161.
    Sadlej, A.J., Snijders, J.G.: Chem. Phys. Lett. 229, 435 (1994)CrossRefGoogle Scholar
  162. 162.
    Visscher, L., van Lenthe, E.: Chem. Phys. Lett. 306, 357 (1999)CrossRefGoogle Scholar
  163. 163.
    Faas, S., Snijders, J.G., van Lenthe, J.H., van Lenthe, E., Baerends, E.J.: Chem. Phys. Lett. 246, 632 (1995)CrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.Fachbereich Chemie and Forschungszentrum OPTIMAS, Technische Universität KaiserslauternKaiserslauternGermany

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