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Introduction

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Brillouin-Wigner Methods for Many-Body Systems

Part of the book series: Progress in Theoretical Chemistry and Physics ((PTCP,volume 21))

Abstract

An overview of the many-body problem in atomic and molecular physics and in quantum chemistry is given. Some historical background on the Brillouin–Wigner methodology is presented together with basic derivations of the Rayleigh–Schrödinger and the Brillouin–Wigner perturbation theories. The elementary formulations of the two theories are compared. The recent resurgence of interest in Brillouin–Wigner methodology, particularly in studies of the multi-reference correlation problem, is explained.

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Notes

  1. 1.

    By Mr. Gordon Moore of Intel. This has been dubbed “Moore’s Law”.

  2. 2.

    The last paper in the series was coauthored by O. Goscinski.

  3. 3.

    Sir John Edward Lennard-Jones (1894–1954).

  4. 4.

    Léon Brillouin (1877–1972).

  5. 5.

    Eugene P. Wigner (1902–1995), Nobel Prize in Physics, 1963.

  6. 6.

    J.W.S. Rayleigh, The Theory of Sound, London and New York, 1894, vol. 1, p. 113; E. Schrödinger, Collected Papers on Wave Mechanics, London and Glasgow, 1928, p. 64.

  7. 7.

    L. Brillouin, Le Journal de Physique et le Radium Séries VII, Tome III, 373, 1932.

  8. 8.

    Per-Olov Löwdin (1916–2000).

  9. 9.

    We would prefer to avoid the use of the terms ‘size-consistency’ and ‘size-extensivity’ and simply describe a theory as exhibiting correct scaling with the number of particles considered. This point of view is also adopted by Nooijen, Shamasundar and Mukherjee [66] who write: “The notions of size-extensivity and size consistency are used very broadly in the literature and we prefer to speak more specifically of a physical quantity that is to scale properly in the context of a particular type of physical system or state (e.g. open or closed shell).”

  10. 10.

    We are not concerned here with questions of computational efficiency.

References

  1. R. McWeeny, in Handbook of Molecular Physics and Quantum Chemistry, Volume 2, Molecular Electronic Structure, edited by S. Wilson, P.F. Bernath and R. McWeeny, John Wiley & Sons, Chichester, 2003

    Google Scholar 

  2. J. Karwowski and I. Shavitt, in Handbook of Molecular Physics and Quantum Chemistry, Volume 2, Molecular Electronic Structure, edited by S. Wilson, P.F. Bernath and R. McWeeny, John Wiley & Sons, Chichester, 2003

    Google Scholar 

  3. J. Paldus, in Handbook of Molecular Physics and Quantum Chemistry, Volume 2, Molecular Electronic Structure, edited by S. Wilson, P.F. Bernath and R. McWeeny, John Wiley & Sons, Chichester, 2003

    Google Scholar 

  4. S. Wilson, in Handbook of Molecular Physics and Quantum Chemistry, Volume 2, Molecular Electronic Structure, edited by S. Wilson, P.F. Bernath and R. McWeeny, John Wiley & Sons, Chichester, 2003

    Google Scholar 

  5. P.A.M. Dirac, The Principles of Quantum Mechanics, 1st edition, Clarendon Press, Oxford, 1930.

    Google Scholar 

  6. G.G. Hall, Proc. Roy. Soc. (London) A205, 541, 1951

    Google Scholar 

  7. C.C.J. Roothaan, Rev. Mod. Phys. 23, 69, 1951

    Article  CAS  Google Scholar 

  8. R. McWeeny, Nature 166, 21, 1950

    Google Scholar 

  9. S.F. Boys, Proc. Roy. Soc. (London) A200, 542, 1950

    Google Scholar 

  10. I. Shavitt, Israel J. Chem. 34, 357, 1993

    Google Scholar 

  11. J. Goldstone, Proc. Roy. Soc. (London) A 239, 267, 1957

    Google Scholar 

  12. R.P. Feynman, Phys. Rev. 76, 749, 1949

    Article  CAS  Google Scholar 

  13. R.P. Feynman, Phys. Rev. 76, 769, 1949

    Article  Google Scholar 

  14. F. Dyson, Phys. Rev. 75, 486, 1949

    Article  Google Scholar 

  15. F. Dyson, Phys. Rev. 75, 1736, 1949

    Article  Google Scholar 

  16. K.A. Brueckner, Phys. Rev. 100, 36, 1955

    Article  CAS  Google Scholar 

  17. N. Hugenholtz, Physica 23, 481, 1957

    Google Scholar 

  18. J. Hubbard, Proc. Roy. Soc. (London) A240, 539, 1957

    Google Scholar 

  19. F. Coester, Nucl. Phys. 7, 421, 1958

    Google Scholar 

  20. F. Coester and H. Kümmel, Nucl. Phys. 17. 4777, 1960

    Google Scholar 

  21. J. Paldus, in Methods in Computational Molecular Physics, NATO ASI Series, edited by S. Wilson and G.H.F. Diercksen, p. 99ff , Plenum Press, New York, 1992

    Google Scholar 

  22. H.P. Kelly, Phys. Rev. 131, 684, 1963

    Article  Google Scholar 

  23. H.P. Kelly, Phys. Rev. A134, 1450, 1964

    Article  Google Scholar 

  24. H.P. Kelly, Phys. Rev. B136, 896, 1964

    Article  Google Scholar 

  25. H.P. Kelly, Phys. Rev. 144, 39, 1966

    Article  CAS  Google Scholar 

  26. H.P. Kelly, Adv. Theor. Phys. 2, 75, 1968

    Google Scholar 

  27. H.P. Kelly, Adv. Chem. Phys. 14, 129, 1969

    CAS  Google Scholar 

  28. H.P. Kelly, Phys. Rev. Lett. 23, 255, 1969

    Article  Google Scholar 

  29. H.P. Kelly, Intern. J. Quantum Chem. Symp. 3, 349, 1970

    Google Scholar 

  30. H.P. Kelly, Phys. Rev. A1, 274, 1970

    Google Scholar 

  31. H.P. Kelly and A. Ron, Phys. Rev. A4, 11, 1971

    Google Scholar 

  32. J. Čížek, J. Chem. Phys. 45, 4256, 1966

    Article  Google Scholar 

  33. J. Paldus, J. Čížek and I. Shavitt, Phys. Rev. A 5, 50, 1972

    Article  Google Scholar 

  34. U. Kaldor, Phys. Rev. A 7, 427 (1973)

    Article  Google Scholar 

  35. S. Wilson and D.M. Silver, Phys. Rev. A 14, 1949, 1976

    Article  CAS  Google Scholar 

  36. J.M. Roberts, Twentieth Century: The History of the World - 1901 to present, Allen Lane, The Penguin Press, London, 1999

    Google Scholar 

  37. J.E. Lennard-Jones, Proc. Roy. Soc. (London) A 129, 598, 1930

    Google Scholar 

  38. A. Dalgarno, in Quantum Theory. I. Elements, edited by D.R. Bates, Vol. 1, Chap. 5, Academic Press, New York, 1961

    Google Scholar 

  39. S. Wilson, Electron correlation in molecules, Clarendon Press, Oxford, 1984; reprinted, Dover Publications, New York 2007

    Google Scholar 

  40. L. Brillouin, J. Physique 7, 373, 1932

    Google Scholar 

  41. E.P. Wigner, Math. naturw. Anz. ungar. Akad. Wiss. 53, 475, 1935

    Google Scholar 

  42. P.-O. Löwdin, J. Molec. Spectros. 10, 12, 1963

    Article  Google Scholar 

  43. P.-O. Löwdin, J. Molec. Spectros. 13, 326, 1964

    Article  Google Scholar 

  44. P.-O. Löwdin, J. Math. Phys. 3, 969, 1962

    Article  Google Scholar 

  45. P.-O. Löwdin, J. Math. Phys. 3, 1171, 1962

    Article  Google Scholar 

  46. P.-O. Löwdin, J. Molec. Spectros. 14, 112, 1964

    Article  Google Scholar 

  47. P.-O. Löwdin, J. Molec. Spectros. 14, 119, 1964

    Article  Google Scholar 

  48. P.-O. Löwdin, J. Molec. Spectros. 14, 131, 1964

    Article  Google Scholar 

  49. P.-O. Löwdin, J. Math. Phys. 6, 1341, 1965

    Article  Google Scholar 

  50. P.-O. Löwdin, Phys. Rev. A 139, 357, 1965

    Google Scholar 

  51. P.-O. Löwdin, in Perturbation Theory and its Application to Quantum Mechanics, ed. C.H. Wilcox, John Wiley and Sons, New York, 1966

    Google Scholar 

  52. P.-O. Löwdin, Intern. J. Quantum Chem. 2, 867, 1968

    Article  Google Scholar 

  53. P.-O. Löwdin, and O. Goscinski, Intern. J. Quantum Chem. 5, 685, 1971

    Article  Google Scholar 

  54. S. Wilson, in Methods in Computational Molecular Physics, NATO ASI Series B, Vol. 293, p. 203, Plenum Press, New York, 1992

    Google Scholar 

  55. N.H. March, W.H. Young and S. Sampanthar, The many-body problem in quantum mechanics, Cambridge University Press, 1967; Reprinted by Dover Publications, New York

    Google Scholar 

  56. C. Møller and M.S. Plesset, Phys. Rev., 46, 618, 1934

    Google Scholar 

  57. S. Wilson, in Theoretical Chemistry, Senior Reporter: C. Thomson, Specialist Periodical Reports 4, 1, The Royal Society of Chemistry, London, 1981

    Google Scholar 

  58. S. Wilson, in Chemical Modelling: Applications and Theory, Senior Reporter: A. Hinchliffe, Specialist Periodical Reports 1, 364, The Royal Society of Chemistry, London, 2000

    Google Scholar 

  59. S. Wilson, in Chemical Modelling: Applications and Theory, Senior Reporter: A. Hinchliffe, Specialist Periodical Reports 2, 329, The Royal Society of Chemistry, London, 2002

    Google Scholar 

  60. S. Wilson, in Chemical Modelling: Applications and Theory, Senior Reporter: A. Hinchliffe, Specialist Periodical Reports 3, 379, The Royal Society of Chemistry, London, 2004

    Google Scholar 

  61. S. Wilson, in Chemical Modelling: Applications and Theory, ed. A. Hinchliffe, Specialist Periodical Reports 4, 470, The Royal Society of Chemistry, London, 2006

    Google Scholar 

  62. S. Wilson, in Chemical Modelling: Applications and Theory, ed. A. Hinchliffe, Specialist Periodical Reports 5, 208, The Royal Society of Chemistry, London, 2008

    Google Scholar 

  63. I. Lindgren and J. Morrison, Atomic Many-Body Theory, Springer-Verlag, Berlin, 1982; 2nd edition, 1986

    Google Scholar 

  64. F.E. Harris, H.J. Monkhorst and D.L. Freeman, Algebraic and Diagrammatic Methods in Many-Fermion Theory, Oxford University Press, 1992

    Google Scholar 

  65. E.R. Davidson, in The world of quantum chemistry, Proceedings of the First International Congress on Quantum Chemistry, ed. R. Daudel and B. Pullman, Reidel, Dordrecht, 1974

    Google Scholar 

  66. M. Nooijen, K.R. Shamasundar and D. Mukherjee, Molec. Phys. 103, 2277, 2005

    CAS  Google Scholar 

  67. B.H. Brandow, Rev. Mod. Phys. 39, 771, 1967

    Article  CAS  Google Scholar 

  68. I. Hubač and P. Neogrády, Phys. Rev. A50, 4558, 1994

    Google Scholar 

  69. I. Hubač, in New Methods in Quantum Theory, NATO ASI Series, ed. C.A. Tsipis, V.S. Popov, D.R. Herschbach and J.S. Avery, pp. 183, Kluwer, Dordrecht, 1996

    Google Scholar 

  70. J. Mášik and I. Hubač, Coll. Czech. Chem. Commun. 62, 829, 1997

    Article  Google Scholar 

  71. J. Mášik and I. Hubač, in Quantum Systems in Chemistry and Physics: Trends in Methods and Applications, ed. R. McWeeny, J. Maruani, Y.G. Smeyers and S. Wilson, pp. 283, Kluwer Academic Publishers, Dordrecht, 1997

    Google Scholar 

  72. J. Mášik and I. Hubač, Adv. Quantum Chem. 31, 75, 1998

    Article  Google Scholar 

  73. J. Mášik, P. Mach and I. Hubač, J. Chem. Phys. 108, 6571, 1998

    Article  Google Scholar 

  74. P. Mach, J. Mášik, J. Urban and I. Hubač, Molec. Phys. 94, 173, 1998

    CAS  Google Scholar 

  75. J. Mášik, P. Mach, J. Urban, M. Polasek, P. Babinec and I. Hubač, Collect. Czech. Chem. Comm. 63, 1213, 1998

    Article  Google Scholar 

  76. P. Čársky, V. Hrouda, V. Sychrovsky, I. Hubač, P. Babinec, P. Mach, J. Urban and J. Mášik, Collect. Czech. Chem. Comm. 60, 1419, 1995

    Article  Google Scholar 

  77. W. Wenzel and M.M. Steiner, J. Chem. Phys. 108, 4714, 1998

    Article  CAS  Google Scholar 

  78. W. Wenzel, Intern. J. Quantum Chem. 70, 613, 1998

    Article  CAS  Google Scholar 

  79. J. Pittner, P. Nechtigall, P. Čársky, J. Mášik and I. Hubač, J. Chem. Phys. 110, 10275 1999

    Article  CAS  Google Scholar 

  80. I. Hubač and S. Wilson, J. Phys. B: At. Mol. Opt. Phys. 33, 365, 2000

    Article  Google Scholar 

  81. I. Hubač, J. Pittner, and P. Čársky, J. Chem. Phys. 112, 8779 2000

    Article  Google Scholar 

  82. J. Sancho-García, J. Pittner, P. Čársky, and I. Hubač, J. Chem. Phys. 112, 8785, 2000

    Article  Google Scholar 

  83. I. Hubač, P. Mach and S. Wilson, J. Phys. B: At. Mol. Opt. Phys. 33, 4735, 2000

    Article  Google Scholar 

  84. I. Hubač, P. Mach and S. Wilson, Adv. Quantum Chem. 39, 225, 2001

    Article  Google Scholar 

  85. I. Hubač and S. Wilson, Adv. Quantum Chem. 39, 209, 2001

    Article  Google Scholar 

  86. I. Hubač and S. Wilson, J. Phys. B: At. Mol. Opt. Phys. 34, 4259, 2001

    Article  Google Scholar 

  87. H.M. Quiney, I. Hubač and S. Wilson, J. Phys. B: At. Mol. Opt. Phys. 34, 4323, 2001

    Article  CAS  Google Scholar 

  88. S. Wilson and I. Hubač, Molec. Phys. 99, 1813, 2001

    CAS  Google Scholar 

  89. I. Hubač and S. Wilson, J. Phys. B: At. Mol. Opt. Phys. 34, 4259, 2001

    Article  Google Scholar 

  90. I. Hubač, P. Mach and S. Wilson, Molec. Phys. 100, 859, 2002

    Google Scholar 

  91. I. Hubač and S. Wilson, Int. J. Molec. Science 3, 570, 2002

    Article  Google Scholar 

  92. I. Hubač, P. Mach and S. Wilson, Int. J. Quantum Chem. 89, 198, 2002

    Article  Google Scholar 

  93. I. Hubač and S. Wilson, in Fundamental World of Quantum Chemistry - A Tribute to the Memory of Per-Olov Löwdin, volume 1, edited by E.J. Brändas and E.S. Kryachko, p. 407, Kluwer Academic Publisher, Dordrecht, 2003

    Google Scholar 

  94. I. Hubač, P. Mach and S. Wilson, Molec. Phys. 101, 3493, 2003

    Google Scholar 

  95. S. Wilson, I. Hubač, P. Mach, J. Pittner and P. Čársky, in Advanced Topics in Theoretical Chemical Physics, Progress in Theoretical Chemistry and Physics, edited by J. Maruani, R. Lefebvre and E. Brändas, p. 71, Kluwer Academic Publishers, Dordrecht, 2003

    Google Scholar 

  96. I. Hubač and S. Wilson, in Encyclopedia of Computational Chemistry - electronic edition, 2004 DOI: 10.1002/0470845015.cu0032

    Google Scholar 

  97. I. Hubač, P. Mach, P. Papp and S. Wilson, Molec. Phys. 102, 701, 2004

    Google Scholar 

  98. I. Hubač, P. Mach and S. Wilson, Intern. J. Quantum Chem. 104, 387, 2005

    Article  Google Scholar 

  99. P.Papp, P. Mach, J. Pittner, I. Hubač and S. Wilson, Molec. Phys. 104, 2367, 2006

    CAS  Google Scholar 

  100. P. Papp, P. Mach, I. Hubač and S. Wilson, Intern. J. Quantum Chem. 107, 2622, 2007

    Article  CAS  Google Scholar 

  101. P. Papp, P. Neogrády, P. Mach, J. Pittner, I. Hubač and S. Wilson, Molec. Phys. 106, 57, 2008

    CAS  Google Scholar 

  102. S. Wilson, in Methods in Computational Molecular Physics, NATO ASI Series B, Vol. 293, p. 99, Plenum Press, New York, 1992

    Google Scholar 

  103. J. Paldus, in Relativistic and Correlation Effects in Molecules and Solids, NATO ASI Series, edited by G.L. Malli, p. 207, Plenum Press, New York (1994)

    Google Scholar 

  104. Recent Advances in Coupled Cluster Methods, Recent Advances in Computational Chemistry, Vol. 3, edited by R.J. Bartlett, World Scientific, Singapore (1997)

    Google Scholar 

  105. J. Paldus, in Handbook of Molecular Physics and Quantum Chemistry, 2, ed. S. Wilson, P.F. Bernath and R. McWeeny, John Wiley, Chichester, 2002

    Google Scholar 

  106. B.P. Lippmann and J. Schwinger, Phys. Rev. 79, 469, 1950

    Article  Google Scholar 

  107. S. Wilson, in Methods in Computational Molecular Physics, NATO ASI Series B, Vol. 293, p. 222, Plenum Press, New York, 1992

    Google Scholar 

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Authors and Affiliations

  1. Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynska Dolina F 1, 842 48, Bratislava, Solvakia

    Ivan Hubač

  2. Institute of Physics, Silesian University, 74601, Opava, Czech Republic

    Ivan Hubač

  3. Theoretical Chemistry Group Physical & Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford, OX1 3QZ, United Kingdom

    Stephen Wilson

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  1. Ivan Hubač
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Hubač, I., Wilson, S. (2010). Introduction. In: Brillouin-Wigner Methods for Many-Body Systems. Progress in Theoretical Chemistry and Physics, vol 21. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3373-4_1

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