Skip to main content
SpringerLink
Log in

On the Construction of Size Extensive Effective Hamiltonians in General Model Spaces Using Quasi-Hilbert and Quasi-Fock Strategies

  • Chapter
Applied Many-Body Methods in Spectroscopy and Electronic Structure

  • 234 Accesses

Abstract

There has been an ever-growing interest over the last two decades towards developing and implementing the formalism of effective hamiltonians [1] in the framework of many-body perturbation theory (MBPT) and coupled cluster (CC) theory [2, 3]. One major thrust in all these developments has been the desire to obtain size-extensive effective hamiltonians Heff which give size-extensive energies upon diagonalization within the model space. The traditional formulations of both MBPT [4] and CC theory [5–9] for the open-shells were built upon complete model spaces (CMS), and a connected Heff could be obtained in all these formalisms. The energies obtained on diagonalization were automatically size-extensive owing to the completeness of the model space.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. See, e.g. P. Durand and J.P. Malrieu, Adv Chem Phys 57, 321 (1987) for a general Survey of the effective hamiltonian formalisms.

    Google Scholar 

  2. See, e.g. D. Mukherjee and S. Pal, Adv Quantum Chem, 20, 291, (1989) for an extensive and critical survey of both MBPT and CC theory, both for complete and incomplete model spaces.

    Google Scholar 

  3. For an earlier exposition, see, e.g. I. Lindgren and D. Mukherjee, Phys Rep., 151, 93 (1987)

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

  5. I. Lindgren, J. Phys 5 7, 2441 (1974)

    Google Scholar 

  6. D. Mukherjee, R.K. Moitra and A. Mukhopadhyay, Mol Phys. 33, 955 (1977).

    Article  CAS  Google Scholar 

  7. D. Mukherjee, Pramana, 12, 203 (1979)

    Article  CAS  Google Scholar 

  8. A. Hague and D. Mukherjee, J Chem Phys. 80, 5058 (1984)

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  11. W. Ey, Nucl Phys., 296, 189 (1978)

    Article  Google Scholar 

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

    CAS  Google Scholar 

  13. A. Hague and U. Kaldor, Chem. Phys. Lett. 117, 347 (1985)

    Article  Google Scholar 

  14. A. Hague and U. Kaldor, Chem. Phys. Lett. 120, 261 (1985).

    Article  Google Scholar 

  15. U. Kaldor, Int. J. Quantum Chem. Symp. 20, 445 (1986)

    Article  CAS  Google Scholar 

  16. B. Jeziorski and H.J. Monkhorst, Phys Rev. A24, 1668 (1981).

    Article  CAS  Google Scholar 

  17. G. Hose and U. Kaldor, J Phys B12, 3827 (1979)

    CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  20. G. Hose and U. Kaldor, J. Phys. Chem. 86, 2133 (1982)

    Article  CAS  Google Scholar 

  21. H.G. Sheppard, J. Chem Phys. 80, 1225 (1984)

    Article  CAS  Google Scholar 

  22. L. Meissner, K. Jankowski and J. Wasilewski, Int. J. Quantum Chem. 34, 535 (1988)

    Article  CAS  Google Scholar 

  23. L. Meissner and R.J. Bartlett, J. Chem. Phys. 91, 4800 (1989)

    Article  CAS  Google Scholar 

  24. R. Chaudhuri, D. Sinha and D. Mukherjee, Chem. Phys Lett. 163,“165 (1989)

    Google Scholar 

  25. D. Mukherjee, Proc. Ind. Acad. Sci. 96, 145 (1986)

    Google Scholar 

  26. D. Mukherjee, Chem Phys Lett. 125, 207 (1986)

    Article  CAS  Google Scholar 

  27. D. Mukherjee, Int J Quantum Chem Symp. 20, 409 (1986)

    Article  CAS  Google Scholar 

  28. D. Sinha, S.K. Mukhopadhyay and D. Mukherjee, Chem Phys Lett. 129, 369 (1986)

    Article  CAS  Google Scholar 

  29. W. Kutzelnigg, D. Mukherjee and S. Koch, J. Chem Phys. 87, 5902 (1987).

    Article  CAS  Google Scholar 

  30. D. Mukherjee, W. Kutzelnigg and S. Koch, J. Chem Phys. 87, 5911 (1987)

    Article  CAS  Google Scholar 

  31. R. Chaudhuri, D. Mukhopadhyay and D. Mukherjee, in Lecture Notes in Chemistry, Vol 50 (Ed. D. Mukherjee, Springer Verlag, Heidelberg, 1989 )

    Google Scholar 

  32. S. Pal, M. Rittby, R.J. Bartlett, D. Sinha and D. Mukherjee, Chem Phys. Lett. 137, 273 (1987)

    Article  CAS  Google Scholar 

  33. S. Pal, M. Rittby, R.J. Bartlett, D. Sinha and D. Mukherjee, J. Chem. Phys. 88, 4357 (1988)

    Article  CAS  Google Scholar 

  34. M. Rittby, S. Pal and R.J Bartlett, J. Chem Phys. 90, 3214 (1989)

    Article  CAS  Google Scholar 

  35. R. Mattie, M. Rittby, R.J. Bartlett and S. Pal, in Lecture Notes in Chemistry, Vol 50 (Ed: D. Mukherjee, Springer Verlag, Heidelberg, 1989 )

    Google Scholar 

  36. D. Mukhopadhyay and D. Mukherjee, Chem Phys Lett. 163, 171 (1989)

    Article  CAS  Google Scholar 

  37. D. Mukhopadhyay, R. Chaudhuri, S.K. Mukhopadhyay and D. Mukherjee, Theoretica Chimica Acta (Special Issue on CC Theory, in press)

    Google Scholar 

  38. D. Mukhopadhyay and D. Mukherjee, Chem Phys Lett. 177, 441 (1991)

    Article  CAS  Google Scholar 

  39. D. Mukhopadhyay and D. Mukherjee, to be published

    Google Scholar 

  40. L. Meissner, S.A. Kucharski and R.J. Bartlett, J. Chem. Phys. 91, 6187 (1989)

    Article  CAS  Google Scholar 

  41. L. Meissner and R.J. Bartlett, J. Chem Phys. 92, 561 (1990)

    Article  CAS  Google Scholar 

  42. D. Mukherjee, in Condensed Matter Theories, Vol 3 ( Ed: J. Arponen, R.F. Bishop and M. Manninen, Plenum Press, N.Y., 1988 )

    Google Scholar 

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

    Article  Google Scholar 

  44. I. Lindgren, Phys. Scripta. 32, 291, 611 (1985)

    Article  Google Scholar 

  45. J.P. Malrieu, P. Durand and J.P. Daudey, J. Phys. A18, 809 (1985)

    CAS  Google Scholar 

  46. J.L. Heully and J.P. Daudey, J. Chem. Phys. 88, 1048 (1988)

    Article  Google Scholar 

  47. A. V. Zaitsevski and A.I. Dement’ev, J. Phys. B23, L517 (1990)

    Google Scholar 

  48. S. Koch, submitted to Theoretica Chim. Acta

    Google Scholar 

  49. U. Kaldor, Chem. Phys. 140, 1 (1990)

    Article  CAS  Google Scholar 

  50. The last entry of ref. [15], and D. Mukhopadhyay and D. Mukherjee, to be published.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Theory Group, Department of Physical Chemistry, Indian Association for the Cultivation of Science, Calcutta, 700-032, India

    Debasis Mukhopadhyay Jr. & Debashis Mukherjee

Authors
  1. Debasis Mukhopadhyay Jr.
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Debashis Mukherjee
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Indian Association for the Cultivation of Science, Calcutta, India

    Debashis Mukherjee

Rights and permissions

Reprints and permissions

Copyright information

© 1992 Springer Science+Business Media New York

About this chapter

Cite this chapter

Mukhopadhyay, D., Mukherjee, D. (1992). On the Construction of Size Extensive Effective Hamiltonians in General Model Spaces Using Quasi-Hilbert and Quasi-Fock Strategies. In: Mukherjee, D. (eds) Applied Many-Body Methods in Spectroscopy and Electronic Structure. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-9256-0_10

Download citation

  • DOI: https://doi.org/10.1007/978-1-4757-9256-0_10

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4757-9258-4

  • Online ISBN: 978-1-4757-9256-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation