Skip to main content

Calculation of the Matrix Elements of the Hamiltonian; Nonorthogonal Spin Functions

  • Chapter
Book cover Spin Eigenfunctions
  • 344 Accesses

Abstract

The present chapter deals with the calculation of the matrix elements of the Hamiltonian for the case of projected spin function and spin-paired spin functions. The common property of these two bases is that the spin eigenfunctions form a nonorthogonal basis. In these cases it is not the representation matrices that are important for the energy but the matrix elements of the permutations operators. We shall give some examples of spatial functions for which these methods are most suitable.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 99.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 129.99
Price excludes VAT (USA)
  • Compact, lightweight 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. P. O. Lowdin, J. Appl. Phys. Suppl 33, 251 (1962).

    Article  CAS  Google Scholar 

  2. A. T. Amos and G. G. Hall, Proc. R. Soc. London Ser. A 263, 483 (1961).

    Article  Google Scholar 

  3. P. O. Löwdin, Symposium on Molecular Physics, Maruzen, Tokyo, (1953), p. 13;

    Google Scholar 

  4. P. O. Löwdin Phys. Rev. 97, 1509 (1955).

    Article  Google Scholar 

  5. R. Pauncz, J. de Heer and P. O. Lowdin, J. Chem. Phys. 36, 2247 (1962).

    Article  CAS  Google Scholar 

  6. J. de Heer, J. Phys. Chenu 66, 2288 (1962).

    Article  Google Scholar 

  7. R. Pauncz, J. Chem. Phys. 37, 2739 (1963).

    Article  Google Scholar 

  8. J. de Heer and R. Pauncz, J. Chem. Phys. 39, 2314 (1963).

    Article  CAS  Google Scholar 

  9. R. Pauncz, Alternant Molecular Orbital Method, W. B. Saunders, Philadelphia (1967).

    Google Scholar 

  10. F. E. Harris, J. Chem. Phys. 46, 2769 (1967).

    Article  CAS  Google Scholar 

  11. J. E. Harriman, J. Chem. Phys. 40, 2827 (1964).

    Article  CAS  Google Scholar 

  12. J. C. Slater, Phys. Rev. 38, 1109 (1931).

    Article  CAS  Google Scholar 

  13. L. Pauling, J. Chem. Phys. 1, 280 (1933).

    Article  CAS  Google Scholar 

  14. H. Eyring and G. E. Kimball, J. Chem. Phys. 1, 239, 626 (1933).

    Article  Google Scholar 

  15. J. Gerratt, Theoretical Chemistry, Vol. 1, Quantum Chemistry, The Chemical Society, London (1974), p. 60.

    Book  Google Scholar 

  16. R. McWeeny, Proc. R. Soc. London Ser. A 223, 63, 306 (1954);

    CAS  Google Scholar 

  17. R. McWeeny, Proc. R. Soc. London Ser. A 227, 288 (1955).

    Article  CAS  Google Scholar 

  18. C. Reeves, Thesis, University of Cambridge, England, 1957.

    Google Scholar 

  19. I. L. Cooper and R. McWeeny, J. Chem. Phys. 45, 226 (1966).

    Article  CAS  Google Scholar 

  20. B. T. Sutcliffe, J. Chem. Phys. 45, 235 (1966).

    Article  CAS  Google Scholar 

  21. C. M. Reeves, Commun. ACM 9, 276 (1966).

    Article  Google Scholar 

  22. R. McWeeny and B. T. Sutcliffe, Methods of Molecular Quantum Mechanics, Academic Press, London (1969), p. 163.

    Google Scholar 

  23. G. H. F. Diercksen and B. T. Sutcliffe, Theor. Chim. Acta 34, 105 (1974).

    Article  CAS  Google Scholar 

  24. B. Roos, in Computational Techniques in Quantum Chemistry and Molecular Physics, Eds. G. H. F. Diercksen, B. T. Sutcliffe and A. Veillard, D. Reidel, Dordrecht, Holland (1975), p. 251.

    Google Scholar 

  25. I. Shavitt, in Modern Theoretical Chemistry, Vol. 3, Ed. H. F. Schaefer III, Plenum Press, New York (1977), p. 189.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1979 Plenum Press, New York

About this chapter

Cite this chapter

Pauncz, R. (1979). Calculation of the Matrix Elements of the Hamiltonian; Nonorthogonal Spin Functions. In: Spin Eigenfunctions. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-8526-4_11

Download citation

  • DOI: https://doi.org/10.1007/978-1-4684-8526-4_11

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4684-8528-8

  • Online ISBN: 978-1-4684-8526-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics