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New Horizons of Quantum Chemistry pp 15–29Cite as

Degenerate Perturbation Theory

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Part of the book series: International Academy of Quantum Molecular Science ((QUCH,volume 4))

Abstract

The algebraic structure of degenerate Rayleigh-Schroedinger perturbation theory is reviewed. There are a number of different but equivalent algorithms which generate this perturbation series; we argue that the frequent need to carry out infinite-order partial summations selects one of these algorithms as the most efficient. Recent developments include coupled-cluster formulations for open shells, a new diagrammatic representation, and the concept of incomplete model subspaces. These subjects are reviewed, as well as some applications.

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References

  1. B. H. Brandow, Int. J. Quantum Chem. 15, 207 (1979).

    Article  CAS  Google Scholar 

  2. P.-O. Löwdin, J. Chem. Phys. 19, 1396 (1951)

    Article  Google Scholar 

  3. P.-O. Löwdin, Int. J. Quantum. Chem. 2, 867 (1968) and references therein

    Article  Google Scholar 

  4. M. Lax, Phys. Rev. 79, 200A (1950).

    Google Scholar 

  5. B. H. Brandow, Rev. Mod. Phys. 39, 771 (1967).

    Article  CAS  Google Scholar 

  6. B. H. Brandow, Adv. Quantum Chem. 10, 187 (1977).

    Article  CAS  Google Scholar 

  7. P. J. Ellis and E. Osnes, Rev. Mod. Phys. 49, 111 (1977).

    Google Scholar 

  8. B. R. Barrett and M. W. Kirson, Adv. Nuc. Phys. 6, 219 (1973)

    CAS  Google Scholar 

  9. T. T. S. Kuo, Ann. Rev. Nucl. Sci. 24, 101 (1974)

    Article  CAS  Google Scholar 

  10. “Proceedings of the International Conference on Effective Interactions and Operators in Nuclei,” B. R. Barrett, ed., Lecture Notes in Physics, Vol. 40 (Springer-Verlag, Berlin, 1975)

    Google Scholar 

  11. J. Shurpin, D. Strottman, T. T. S. Kuo, M. Conze, and P. Manakos, Phys. Lett. 69B, 395 (1977); see also Ref. 22.

    CAS  Google Scholar 

  12. B. H. Brandow, in Barrett (1975), Ref. 6.

    Google Scholar 

  13. J. H. Van Vleck, Phys. Rev. 33, 467 (1929)

    Article  CAS  Google Scholar 

  14. O. M. Jordahl, Phys. Rev. 45, 87 (1934)

    Article  CAS  Google Scholar 

  15. E. C. Kemble, “The Fundamental Principles of Quantum Mechanics” ( McGraw-Hill, New York, 1937 ), p. 394.

    Google Scholar 

  16. D. J. Klein, J. Chem. Phys. 61, 786 (1974).

    Article  CAS  Google Scholar 

  17. H. Primas, Rev. Mod. Phys. 35, 710 (1963)

    Article  Google Scholar 

  18. R. A. Harris, J. Chem. Phys. 47, 3967 & 3972 (1967)

    Google Scholar 

  19. R. A. Harris, J. Chem. Phys. 48, 3600 (1968)

    Article  CAS  Google Scholar 

  20. S. Fischer, Int. J. Quantum Chem. Symp. 3, 651 (1970)

    Google Scholar 

  21. P. Westhaus, Int. J. Quantum Chem. Symp. 7, 463 (1973)

    Article  CAS  Google Scholar 

  22. P. Westhaus, E. G. Bradford, and D. Hall, J. Chem. Phys. 62, 1607 (1975)

    Article  CAS  Google Scholar 

  23. S. Iwata and K. F. Freed, J. Chem. Phys. 65, 1071 (1976)

    Article  CAS  Google Scholar 

  24. I. Shavitt and L. T. Redmon, J. Chem. Phys. 73, 5711 (1980)

    Article  CAS  Google Scholar 

  25. L. T. Redmon and R. J. Bartlett, J. Chem. Phys. 76, 1938 (1982); see also Ref. 10

    Article  CAS  Google Scholar 

  26. V. Kvasnicka and A. Holubec, Chem. Phys. Lett. 32, 489 (1975).

    Article  CAS  Google Scholar 

  27. J. O. Hirschfelder, Int. J. Quantum Chem. 3, 731 (1969)

    Article  CAS  Google Scholar 

  28. H. J. Silverstone, J. Chem. Phys. 54, 2325 (1971)

    Article  CAS  Google Scholar 

  29. J. O. Hirschfelder and P. R. Certain, J. Chem. Phys. 60, 1118 (1974)

    Article  CAS  Google Scholar 

  30. H. J. Silverstone and R. K. Moats, Phys. Rev. A 23, 1645 (1981).

    Article  CAS  Google Scholar 

  31. Z. Gershgorn and I. Shavitt, Int. J. Quantum Chem. 2, 751 (1968).

    Article  CAS  Google Scholar 

  32. B. Kirtman, J. Chem. Phys. 49, 3890 and 3895 (1968)

    Article  CAS  Google Scholar 

  33. P. R. Certain and J. O. Hirschfelder, Int. J. Quantum Chem. 52, 5977

    Google Scholar 

  34. P. R. Certain and J. O. Hirschfelder, Int. J. Quantum Chem. 53, 2992 (1970)

    Google Scholar 

  35. J. O. Hirschfelder, Chem. Phys. Lett. 54, 1 (1978); also Shavitt and Redmon, Ref. 11.

    Article  CAS  Google Scholar 

  36. B. Kirtman, J. Chem. Phys. 75,798 (1981); also comments in Redmon and Bartlett, Ref. 10.

    Article  CAS  Google Scholar 

  37. J. Hubbard, Proc. R. Soc. (London) A240, 539 (1957)

    Article  Google Scholar 

  38. N. M. Hugenholtz, Physica 23, 481 (1957).

    Article  CAS  Google Scholar 

  39. F. Coester, Nucl. Phys. 7, 421 (1958)

    Article  Google Scholar 

  40. F. Coester and H. Kümmel, Nucl. Phys. 17, 477 (1960).

    Article  CAS  Google Scholar 

  41. J. Paldus, J. Cizek, and I. Shavitt, Phys. Rev. A 5, 50 (1972)

    Article  Google Scholar 

  42. D. L. Freeman, Phys. Rev. B 15, 5512 (1977).

    Article  Google Scholar 

  43. The first such attempt was by F. Coester, in “Lectures in Theoretical Physics,” Vol. 11B, K. T. Mahanthappa and W. E. Brittin, eds. (Gordon and Breach, New York, 1969), p. 157. See also Ref. 22, and further references in Ref. 24.

    Google Scholar 

  44. K. Emrich, J. G. Zabolitzky, and K. H. Lührmann, Phys. Rev. C 16, 1650 (1977)

    Article  CAS  Google Scholar 

  45. J. Zabolitzky and W. Ey, Nucl. Phys. A238, 507 (1979).

    Google Scholar 

  46. I. Lindgren, Int. J. Quantum Chem. Symp. 12, 33 (1978).

    CAS  Google Scholar 

  47. R. Offerman, W. Ey, and H. Kümmel, Nucl. Phys. A273, 349 (1976)

    Article  Google Scholar 

  48. R. Offerman, Nucl. Phys. A273, 368 (1976)

    Article  Google Scholar 

  49. W. Ey, Nucl. Phys. A296, 189 (1978).

    CAS  Google Scholar 

  50. G. Hose and U. Kaldor, J. Phys. B 12, 3827 (1979)

    Article  CAS  Google Scholar 

  51. G. Hose and U. Kaldor, Phys. Scripta 21, 357 (1980)

    Article  CAS  Google Scholar 

  52. G. Hose and U. Kaldor, J. Chem. Phys. 62, 469 (1981).

    CAS  Google Scholar 

  53. B. Jeziorski and H. Monkhorst, Phys. Rev. A 24, 1668 (1981).

    Article  CAS  Google Scholar 

  54. L. M. Frantz and R. L. Mills, Nucl. Phys. 15, 16 (1960).

    Article  Google Scholar 

  55. The diagrams included in various RPA extensions have been carefully analyzed by J. Oddershede and P. Jørgensen, J. Chem. Phys. 66, 1541 (1977)

    Article  CAS  Google Scholar 

  56. E. S. Nielsen, P. Jørgensen, and J. Oddershede, ibid. 73, 6238 (1980).

    Google Scholar 

  57. U. Kaldor, Phys. Rev. Lett. 31, 1338 (1973)

    Article  CAS  Google Scholar 

  58. U. Kaldor, J. Chem. Phys. 62, 4634 (1975)

    Article  CAS  Google Scholar 

  59. U. Kaldor, J. Chem. Phys. 63, 2199 (1975)

    Article  CAS  Google Scholar 

  60. P. S. Stern and U. Kaldor, J. Chem. Phys. 64, 2002 (1976)

    Article  CAS  Google Scholar 

  61. U. Kaldor, J. Comput. Phys. 20, 432 (1976).

    Article  Google Scholar 

  62. K. Tanaka, Int. J. Quantum Chem. 6, 1087 (1972)

    CAS  Google Scholar 

  63. S. Iwata and K. F. Freed, J. Chem. Phys. 61, 1500 (1974)

    Article  CAS  Google Scholar 

  64. S. Iwata and K. F. Freed, Chem. Phys. Lett. 28, 176 (1974)

    Article  CAS  Google Scholar 

  65. P. Westhaus and M. Moghtaderi, J. Chem. Phys. 72, 4174 (1980).

    Article  CAS  Google Scholar 

  66. H. Baker, D. Hegarty, and M. A. Robb, Mol. Phys. 41, 653 (1980).

    Article  CAS  Google Scholar 

  67. D. Hegarty and M. A. Robb, Mol. Phys. 37, 1455 (1979)

    Article  CAS  Google Scholar 

  68. H. Baker, M. A. Robb, and Z. Slattery, Mol. Phys. 44, 1035 (1981). (Compare with Shurpin et al., Ref. 6.)

    Article  CAS  Google Scholar 

  69. D. L. Yeager, H. Sun, K. F. Freed, and M. F. Herman, Chem. Phys. Lett. 57, 490 (1978)

    Article  CAS  Google Scholar 

  70. H. Sun, K. F. Freed, J. Chem. Phys. 72, 4158 (1980)

    Article  CAS  Google Scholar 

  71. M. G. Sheppard and K. F. Freed, J. Chem. Phys. 75, 4525 (1981)

    Article  CAS  Google Scholar 

  72. M. G. Sheppard and K. F. Freed, Int. J. Quantum Chem. Symp. 15, 21 (1981)

    CAS  Google Scholar 

  73. M. G. Sheppard and K. F. Freed, Chem. Phys. Lett. 82, 235 (1981).

    Article  CAS  Google Scholar 

  74. Y. S. Lee, H. Sun, M. G. Sheppard, and K. F. Freed, J. Chem. Phys. 73, 1472 (1980).

    Article  CAS  Google Scholar 

  75. K. F. Freed and H. Sun, Israel J. Chem. 19, 99 (1980)

    CAS  Google Scholar 

  76. H. Sun, M. G. Sheppard, K. F. Freed, and M. F. Herman, Chem. Phys. Lett. 77, 555 (1981)

    Article  CAS  Google Scholar 

  77. S. Iwata and K. F. Freed, Chem. Phys. Lett. 38, 425 (1976).

    Article  CAS  Google Scholar 

  78. H. Sun and K. F. Freed, Chem. Phys. Lett. 78, 531 (1981).

    Article  CAS  Google Scholar 

  79. D. W. Davies and G. J. R. Jones, Chem. Phys. Lett. 81, 279 (1981).

    Article  CAS  Google Scholar 

  80. S. Salomonson, I. Lindgren, and A.M. Martensson, Phys. Scripta 21, 351 (1980).

    Article  CAS  Google Scholar 

  81. I. Hubac, V. Kvasnicka, and A.Holubec, Chem. Phys. Lett. 23, 381 (1973)

    Article  CAS  Google Scholar 

  82. I. Hubac and M. Urban, Theoret. Chim. Acta 45, 185 (1977)

    CAS  Google Scholar 

  83. S. Prime and M. A. Robb, Chem. Phys. Lett. 47, 527 (1977)

    Article  CAS  Google Scholar 

  84. S. Yamamoto and A. Saika, Chem. Phys. Lett. 78, 316 (1981).

    Article  CAS  Google Scholar 

  85. B. H. Brandow, Ann. Phys. (NY) 64, 21 (1971); see Appendix C.

    Article  CAS  Google Scholar 

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Author information

Authors and Affiliations

  1. Los Alamos National Laboratory, University of California, Los Alamos, New Mexico, 87545, USA

    Baird Brandow

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  1. Baird Brandow
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Editor information

Editors and Affiliations

  1. Department of Quantum Chemistry, Uppsala University, Uppsala, Sweden

    Per-Olov Löwdin

  2. Institut de Biologie Physico-Chimique, Paris, France

    Bernard Pullman

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© 1983 D. Reidel Publishing Company

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Brandow, B. (1983). Degenerate Perturbation Theory. In: Löwdin, PO., Pullman, B. (eds) New Horizons of Quantum Chemistry. International Academy of Quantum Molecular Science, vol 4. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-7950-5_4

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  • DOI: https://doi.org/10.1007/978-94-009-7950-5_4

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-009-7952-9

  • Online ISBN: 978-94-009-7950-5

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