Advertisement

Why do we Need Relativistic Computational Methods?

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

Abstract

Inclusion of relativistic effects is required for proper description of atomic and molecular properties, when electrons approach the region of space with high potential energy near the nuclei. The effects become particularly important for the systems with heavy and very heavy atoms leading to significant changes in the energetic structure of the molecule and in the values of spectroscopic molecular parameters, influencing the mechanism and character of the bonds. This chapter reviews the relativistic ab initio all electron four component calculations for molecular systems, whose results show that in many cases the nonrelativistic description is inadequate and cannot explain certain trends of properties observed and that the inclusion of relativistic effects is mandatory for correct predictions of molecular properties.

Keywords

Relativistic four component methods Dirac-Fock method relativistic corrections Electron correlation Correlation-relativistic cross terms Spectroscopic constants 

References

  1. 1.
    Swirles, B.: Proc. R. Soc. A 152, 625 (1935)CrossRefGoogle Scholar
  2. 2.
    Grant, I.P.: Adv. Phys. 19, 747 (1970)CrossRefGoogle Scholar
  3. 3.
    Desclaux, J.P.: Comput. Phys. Commun. 9, 31 (1975)CrossRefGoogle Scholar
  4. 4.
    Dyall, K.G., Grant, I.P., Johnson, C.T., Parpia, F.A., Plummer, E.P.: Comput. Phys. Commun. 55, 425 (1989)CrossRefGoogle Scholar
  5. 5.
    Malli, G.L., Oreg, J.: J. Chem. Phys. 63, 830 (1975)CrossRefGoogle Scholar
  6. 6.
    McLean, A.D., Lee, Y.S.: In: R. Carbo (ed.) Current Aspects of Quantum Chemistry. Elsevier, Amsterdam (1982)Google Scholar
  7. 7.
    Schwarz, W.H.E.: Chem. Phys. Lett. 85, 94 (1982)CrossRefGoogle Scholar
  8. 8.
    Mark, F., Schwarz, W.H.E.: Phys. Rev. Lett. 48, 673 (1982)CrossRefGoogle Scholar
  9. 9.
    Pestka, G., Bylicki, M., Karwowski, J.: In: S. Wilson, P.J. Grout, J. Maruani, G. Delgado-Barrio (eds.) Frontiers in Quantum Systems in Chemistry and Physics. Springer, The Netherlands (2008)Google Scholar
  10. 10.
    Visscher, L., Visser, O., Aerst, P.J.A, Merenga, H., Nieuwpoort, W.C.: Comput. Phys. Commun. 81, 120 (1994)CrossRefGoogle Scholar
  11. 11.
    Jensen, H.J.A., Saue, T., Visscher, L., Bakken, V., Eliav, E., Enevoldsen, T., Fleig, T., Fossgaard, O., Helgaker, T., Lærdahl, J., Larsen, C.V., Norman, P., Olsen, J., Pernpointner, M., Pedersen, J.K., Ruud, K., Salek, P., van Stralen, J.N.P., Thyssen, J., Visser, O., Winther, T.: Dirac, a Relativistic Ab initio Electronic Structure Program, Release DIRAC04.0 (2004)Google Scholar
  12. 12.
    Pyykko, P., Desclaux, J.P.: Acc. Chem. Res. 12, 276 (1979)CrossRefGoogle Scholar
  13. 13.
    Pyykko, P.: Chem. Rev. 88, 563 (1988)CrossRefGoogle Scholar
  14. 14.
    Dyall, K.G., Fægri, K.: Introduction to Relativistic Quantum Chemistry. Oxford University Press, New York (2007)Google Scholar
  15. 15.
    Lee, Y.S., McLean, A.D.: J. Chem. Phys. 76, 735 (1982)CrossRefGoogle Scholar
  16. 16.
    Collins, C.L., Dyall, K.G., Schaefer, H.F.: J. Chem. Phys. 102, 2024 (1995)CrossRefGoogle Scholar
  17. 17.
    Saue, T., Visscher, L.: The Electronic Structure of Au, Au and AuH. http://rugch5.chem.-rug.nl:80/~luuk/AuH.html. Accessed 16 January 1996 (1996)Google Scholar
  18. 18.
    Mohanty, P.R.K., Parpia, F.A.: Phys. Rev. A 54, 2863 (1996)CrossRefGoogle Scholar
  19. 19.
    Huber, K., Herzberg, G.: Constants of Diatomic Molecules. Reinhold, New York (1979)Google Scholar
  20. 20.
    Lærdahl, J.K., Saue, T., Fægri, K.J.: Theor. Chem. Acc. 97, 177 (1997)CrossRefGoogle Scholar
  21. 21.
    Saue, T., Fægri, K., Helgaker, T., Gropen, O.: Mol. Phys. 91, 937 (1997)Google Scholar
  22. 22.
    Fossgaard, O., Gropen, O., Eliav, E., Saue, T.: J. Chem. Phys. 119, 9355 (2003)CrossRefGoogle Scholar
  23. 23.
    Busse, B., Weil, K.G.: Ber. Bunsen. Phys. Chem. 85, 309 (1981)CrossRefGoogle Scholar
  24. 24.
    Saue, T., Fægri, K., Gropen, O.: Chem. Phys. Lett. 263, 360 (1996)CrossRefGoogle Scholar
  25. 25.
    Visscher, L., Saue, T., Nieuwpoort, W.C., Fægri, K., Gropen, O.: J. Chem. Phys. 99, 6704 (1993)CrossRefGoogle Scholar
  26. 26.
    Mulliken, R.S.: Rev. Mod. Phys. 4, 1 (1932)CrossRefGoogle Scholar
  27. 27.
    Wang, S.G., Schwarz, W.H.E.: J. Chem. Phys. 109, 7252 (1998)CrossRefGoogle Scholar
  28. 28.
    Dyall, K.G.: J. Chem. Phys. 98, 9678 (1993)CrossRefGoogle Scholar
  29. 29.
    Scullman, R., Cederbalk, P.: J. Phys. B 10, 3659 (1977)CrossRefGoogle Scholar
  30. 30.
    Gustafsson, G., Scullman, R.: Mol. Phys. 67, 981 (1989)CrossRefGoogle Scholar
  31. 31.
    McCarthy, M.C., Field, R.W., Engelman, Jr. R., Bernath, P.F.: J. Mol. Spectrosc. 158, 208 (1993)CrossRefGoogle Scholar
  32. 32.
    Squires, R.R.: J. Am. Chem. Soc. 107, 4385 (1985)CrossRefGoogle Scholar
  33. 33.
    Sjowoll, M., Fægri, H., Gropen, O., Almlof, J., Saue, T., Olsen, J., Helgaker, T.: J. Chem. Phys. 107, 5496 (1997)CrossRefGoogle Scholar
  34. 34.
    Eliav, E., Kaldor, U., Hess, B.: J. Chem. Phys. 108, 3409 (1998)CrossRefGoogle Scholar
  35. 35.
    Visscher, L., Dyall, K.G.: J. Chem. Phys. 104, 9040 (1996)CrossRefGoogle Scholar
  36. 36.
    Visscher, L., Styszy\(\acute{\rm{ n}}\)ski, J., Nieuwpoort, W.C.: J. Chem. Phys. 105, 1987 (1996)Google Scholar
  37. 37.
    de Jong, W.A., Styszy\(\acute{\rm{ n}}\)ski, J., Visscher, L., Nieuwpoort, W.C.: J. Chem. Phys. 108, 5177 (1998)Google Scholar
  38. 38.
    Styszy\(\acute{\rm{ n}}\)ski, J.: Chem. Phys. Lett. 317, 351 (2000)Google Scholar
  39. 39.
    Styszy\(\acute{\rm{ n}}\)ski, J., Kobus, J.: Chem. Phys. Lett. 369, 441 (2003)Google Scholar
  40. 40.
    de Jong, W.A., Visscher, L., Nieuwpoort, W.C.: J. Chem. Phys. 107, 9046 (1997)CrossRefGoogle Scholar
  41. 41.
    Seth, M., Schwerdtfeger, P., Fægrii, K.: J. Chem. Phys. 111, 6422 (1999)CrossRefGoogle Scholar
  42. 42.
    Fægri, K., Saue, T.: J. Chem. Phys. 115, 2456 (2001)CrossRefGoogle Scholar
  43. 43.
    Heinemann, C., Schwarz, H., Koch, W., Dyall, K.G.: J. Chem. Phys. 104, 4642 (1996)CrossRefGoogle Scholar
  44. 44.
    Irikura, K.K., Beauchamp, J.L.: J. Am. Chem. Soc. 113, 2769 (1991)CrossRefGoogle Scholar
  45. 45.
    de Jong, W.A., Nieuwpoort, W.C.: Int. J. Quantum Chem. 58, 203 (1996)CrossRefGoogle Scholar
  46. 46.
    Fægri, Jr. K.: Theor. Chem. Acc. 105, 252 (2001)CrossRefGoogle Scholar
  47. 47.
    Malli, G.L., Styszy\(\acute{\rm{ n}}\)ski, J.: J. Chem. Phys. 104, 1012 (1996)Google Scholar
  48. 48.
    Compton, R.N.: J. Chem. Phys. 66, 4478 (1977)CrossRefGoogle Scholar
  49. 49.
    Andrews, L., Liang, B.Y., Li, J., Bursten, B.E.: J. Am. Chem. Soc. 125, 3126 (2003)CrossRefGoogle Scholar
  50. 50.
    Andrews, L., Liang, B.Y., Li, J., Bursten, B.E.: New J. Chem. 28, 289 (2004)CrossRefGoogle Scholar
  51. 51.
    Infante, I., Visscher, L.: J. Chem. Phys. 121, 5783 (2004)CrossRefGoogle Scholar
  52. 52.
    de Jong, W.A., Visscher, L., Nieuwpoort, W.C.: J. Mol. Struct.: Theochem 458, 41 (1999)CrossRefGoogle Scholar
  53. 53.
    Fægri, K.: (2009)Google Scholar
  54. 54.
    Roos, B.O., Widmark, P.O., Gagliardi, L.: Faraday Discuss. 124, 57 (2003)CrossRefGoogle Scholar
  55. 55.
    Visscher, L., Saue, T., Oddershede, J.: Chem. Phys. Lett. 274, 181 (1997)CrossRefGoogle Scholar
  56. 56.
    Davis, R.E., Muenter, J.S.: J. Chem. Phys. 57, 2836 (1972)CrossRefGoogle Scholar
  57. 57.
    Ewing, R.E., Tigelaar, H.L., Flygare, W.H.: J. Chem. Phys. 56, 1957 (1972)CrossRefGoogle Scholar
  58. 58.
    Nair, K.P.R., Hoeft, J., Tiemann, E.: J. Mol. Spectrosc. 78, 506 (1979)CrossRefGoogle Scholar
  59. 59.
    Nair, K.P.R., Hoeft, J., Tiemann, E.: Chem. Phys. Lett. 58, 153 (1978)CrossRefGoogle Scholar
  60. 60.
    Nair, K.P.R., Hoeft, J., Tiemann, E.: Chem. Phys. Lett. 60, 253 (1979)CrossRefGoogle Scholar
  61. 61.
    Herbst, E., Steinmetz, W.: J. Chem. Phys. 56, 5342 (1972)CrossRefGoogle Scholar
  62. 62.
    Durand, A., Loison, J.C., Vigue, J.: J. Chem. Phys. 106, 477 (1997)CrossRefGoogle Scholar
  63. 63.
    Tiemann, E., Dreyer, A.: Chem. Phys. 23, 231 (1977)CrossRefGoogle Scholar
  64. 64.
    Nair, K.P.R., Hoeft, J.: J. Mol. Struct. 79, 227 (1982)CrossRefGoogle Scholar
  65. 65.
    van Stralen, J.N.P., Visscher, L.: J. Chem. Phys. 117, 3103 (2002)CrossRefGoogle Scholar
  66. 66.
    van Stralen, J.N.P., Visscher, L.: Mol. Phys. 101, 2115 (2003)CrossRefGoogle Scholar
  67. 67.
    Belpassi, L., Tarantelli, F., Sgamellotti, A., Quiney, H.M., van Stralen, J.N.P., Visscher, L.: J. Chem. Phys. 126, 064314 (2007)CrossRefGoogle Scholar
  68. 68.
    Pernpointner, M., Visscher, L.: J. Chem. Phys. 114, 10389 (2001)CrossRefGoogle Scholar
  69. 69.
    Styszy\(\acute{\rm{ n}}\)ski, J.: Badanie efektów relatywistycznych w molekułach. Metody czteroskładnikowe. Wydawnictwo Naukowe Uniwersytetu Szczeciskiego, Szczecin (2007)Google Scholar
  70. 70.
    Pisani, L., Clementi, E.: J. Chem. Phys. 103, 9321 (1995)CrossRefGoogle Scholar
  71. 71.
    Dyall, K.G.: Chem. Phys. Lett. 196, 178 (1992)CrossRefGoogle Scholar
  72. 72.
    Dyall, K.G.: J. Chem. Phys. 98, 2191 (1993)CrossRefGoogle Scholar
  73. 73.
    Matsuoka, O., Pisani, L., Clementi, E.: Chem. Phys. Lett. 202, 13 (1993)CrossRefGoogle Scholar
  74. 74.
    Watanabe, Y., Matsuoka, O.: J. Chem. Phys. 107, 3738 (1997)CrossRefGoogle Scholar
  75. 75.
    Abe, M., Mori, S., Nakajima, T., Hirao, K.: Chem. Phys. 311, 129 (2005)CrossRefGoogle Scholar
  76. 76.
    Sousa, C., de Jong, W.A., Broer, R., Nieuwpoort, W.C.: J. Chem. Phys. 106, 7162 (1997)CrossRefGoogle Scholar
  77. 77.
    Sousa, C., de Jong, W.A., Broer, R., Nieuwpoort, W.C.: Mol. Phys. 92, 677 (1997)CrossRefGoogle Scholar
  78. 78.
    Dyall, K.G., Partridge, H.: Chem. Phys. Lett. 206, 565 (1993)CrossRefGoogle Scholar
  79. 79.
    Tatewaki, H., Matsuoka, O.: J. Chem. Phys. 106, 4558 (1997)CrossRefGoogle Scholar
  80. 80.
    Tatewaki, H., Matsuoka, O.: Chem. Phys. Lett. 283, 161 (1998)CrossRefGoogle Scholar
  81. 81.
    Visscher, L., Lee, T.J., Dyall, K.G.: J. Chem. Phys. 105, 8769 (1996)CrossRefGoogle Scholar
  82. 82.
    Visscher, L.: Theor. Chem. Acc. 98, 68 (1997)CrossRefGoogle Scholar
  83. 83.
    Matsuoka, O.: J. Chem. Phys. 97, 2271 (1992)CrossRefGoogle Scholar
  84. 84.
    Pisani, L., Clementi, E.: J. Comput. Chem. 15, 466 (1994)CrossRefGoogle Scholar
  85. 85.
    Pisani, L., Clementi, E.: J. Chem. Phys. 101, 3079 (1994)CrossRefGoogle Scholar
  86. 86.
    Quiney, H.M., Skaane, H., Grant, I.P.: Chem. Phys. Lett. 290, 473 (1998)CrossRefGoogle Scholar
  87. 87.
    Visscher, L., Dyall, K.G., Lee, T.J.: Int. J. Quantum Chem.: Quantum Chem. Symp. 29, 411 (1995)CrossRefGoogle Scholar
  88. 88.
    Dyall, K.G., Taylor, P.R., Fægri, K., Partridge, H.: J. Chem. Phys. 95, 2583 (1991)CrossRefGoogle Scholar
  89. 89.
    Visser, O., Visscher, L., Aerts, P.J.C., Nieuwpoort, W.C.: Theor. Chim. Acta 81, 405 (1992)CrossRefGoogle Scholar
  90. 90.
    Styszy\(\acute{\rm{ n}}\)ski, J., Cao, X., Malli, G.L., Visscher, L.: J. Comput. Chem. 18, 601 (1997)Google Scholar
  91. 91.
    Malli, G.L., Styszy\(\acute{\rm{ n}}\)ski, J., da Silva, A.B.F.: Int. J. Quantum Chem. 55, 213 (1995)Google Scholar
  92. 92.
    Haiduke, R.L.A., Filho, H.P.M., da Silva, A.B.F.: Chem. Phys. 348, 89 (2008)CrossRefGoogle Scholar
  93. 93.
    Styszy\(\acute{\rm{ n}}\)ski, J., Malli, G.L.: Int. J. Quantum Chem. 55, 227 (1995)Google Scholar
  94. 94.
    Malli, G.L., Styszy\(\acute{\rm{ n}}\)ski, J.: J. Chem. Phys. 101, 10736 (1994)Google Scholar
  95. 95.
    Malli, G.L., Styszy\(\acute{\rm{ n}}\)ski, J.: J. Chem. Phys. 109, 4448 (1998)Google Scholar
  96. 96.
    Visser, O., Visscher, L., Aerts, P.J.C., Nieuwpoort, W.C.: J. Chem. Phys. 96, 2910 (1992)CrossRefGoogle Scholar
  97. 97.
    Dijkstra, F., de Jong, W.A., Nieuwpoort, W.C.: Int. J. Quantum Chem.: Quantum Chem. Symp. 29, 609 (1995)CrossRefGoogle Scholar
  98. 98.
    Visscher, L., Nieuwpoort, W.C.: Theor. Chim. Acta 88, 447 (1994)CrossRefGoogle Scholar
  99. 99.
    de Macedo, L.G.M., Sambrano, J.R., de Souza, A.R., Borin, A.C.: Chem. Phys. Lett. 440, 367 (2007)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Instytut Fizyki, Uniwersytet SzczecińskiSzczecinPoland

Personalised recommendations