Skip to main content
SpringerLink
Log in

On geminals and symplectic bases in quantum chemistry

  • Published:
Journal of Mathematical Chemistry Aims and scope Submit manuscript

Abstract

The construction of a symplectic basis set with >N electrons is exhibited by means of three kinds of units, the first kind geminal, the second kind geminal and the one‐particle operators. The optimization procedure of the variation method is extended to the coefficients in the linear sum of the symplectic bases, the parameters in the geminals, and the orbitals. For practical use, these bases are expanded explicitly as a linear sum of the Slater determinants. For illustration, the LiH molecule, which is taken as an example, is calculated by using some symplectic bases.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J.M. Blatt, Prog. Theor. Phys. 23 (1960) 447.

    Article  CAS  Google Scholar 

  2. A.J. Coleman, Rev. Mod. Phys. 35 (1963) 668.

    Article  Google Scholar 

  3. A.J. Coleman, J. Math. Phys. 6 (1965) 1425.

    Article  Google Scholar 

  4. A.J. Coleman, J. Math. Phys. 13 (1972) 214.

    Article  Google Scholar 

  5. N. Elander, E. Sangfelt, H.A. Kurtz and O. Goscinski, Int. J. Quantum Chem. 23 (1983) 1047.

    Article  CAS  Google Scholar 

  6. R. Fletcher, Practical Methods of Optimization (New York, 1980).

  7. B.H. Flowers, Proc. Roy. Soc. A212 (1952) 248.

    CAS  Google Scholar 

  8. O. Goscinski, Int. J. Quantum Chem. Symp. 16 (1982) 591.

    CAS  Google Scholar 

  9. K. Helmers, Nuc. Phys. 23 (1961) 594.

    Article  CAS  Google Scholar 

  10. H.J.Aa. Jensen, B. Weiner and Y. Öhrn, Int. J. Quantum Chem. 23 (1983) 65.

    Article  CAS  Google Scholar 

  11. H.J.Aa. Jensen, B. Weiner, J.V. Ortiz and Y. Öhrn, Int. J. Quantum Chem. Symp. 16 (1982) 615.

    CAS  Google Scholar 

  12. H.A. Kurtz, N. Elander, Int. J. Quantum Chem. Symp. 16 (1982) 605.

    CAS  Google Scholar 

  13. H.A. Kurtz, N. Elander, O. Goscinski and E. Sangfelt, Int. J. Quantum Chem. Symp. 15 (1981) 143.

    CAS  Google Scholar 

  14. B. Lorazo, Nucl. Phys. A397 (1983) 225.

    CAS  Google Scholar 

  15. B. Lorazo and C. Quesne, Nucl. Phys. A403 (1983) 327.

    CAS  Google Scholar 

  16. E. Sangfelt and O. Goscinski, J. Chem. Phys. 82 (1985) 4187.

    Article  CAS  Google Scholar 

  17. E. Sangfelt, O. Goscinski, N. Elander and H.A. Kurtz, Int. J. Quantum Chem. Symp. 15 (1981) 133.

    CAS  Google Scholar 

  18. E. Sangfelt, H.A. Kurtz, N. Elander and O. Goscinski, J. Chem. Phys. 81 (1984) 3976.

    Article  CAS  Google Scholar 

  19. A.K.Q. Siu and E.R. Davidson, Int. J. Quantum Chem. 4 (1970) 223.

    Article  CAS  Google Scholar 

  20. C.C. Sun, B.F. Li, Z.H. Zeng and C.B. Liu, Chem. J. Chinese Univ. 5 (1989) 344.

    Google Scholar 

  21. J. Vortiz, B. Weiner and Y. Öhrn, Int. J. Quantum Chem. Symp. 15 (1981) 113.

    Google Scholar 

  22. B. Weiner and O. Goscinski, Phys. Rev. 22 (1980) 2374.

    Article  CAS  Google Scholar 

  23. B. Weiner and O. Goscinski, Phys. Rev. A27 (1983) 58.

    Google Scholar 

  24. B. Weiner, H.J.Aa. Jensen and Y. Öhrn, J. Chem. Phys. 80 (1984) 2009.

    Article  CAS  Google Scholar 

  25. B. Weiner and Y. Öhrn, J. Chem. Phys. 83 (1985) 15.

    Article  Google Scholar 

  26. H.J. Werner and P.J. Knowles, J. Chem. Phys. 82 (11) (1985) 5053.

    Article  CAS  Google Scholar 

  27. L.G. Yaffe and W.A. Goddard, III, Phys. Rev. A13 (1976) 1682.

    Google Scholar 

  28. Z.H. Zeng, C.C. Sun and A.J. Coleman, in: Density Matrices and Density Functionals, eds. R. Erdahl and V.H. Smith, Jr. (D. Reidel, 1987) p. 141.

Download references

Author information

Authors and Affiliations

  1. Institute of Theoretical Chemistry, Jilin University, Changchun, 130023, P.R. China

    Jing‐Yao Liu, Chia‐Chung Sun, Xu‐Ri Huang & Ze‐Sheng Li

Authors
  1. Jing‐Yao Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chia‐Chung Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xu‐Ri Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ze‐Sheng Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Liu, J., Sun, C., Huang, X. et al. On geminals and symplectic bases in quantum chemistry. Journal of Mathematical Chemistry 21, 159–182 (1997). https://doi.org/10.1023/A:1019118318475

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1019118318475

Keywords

Search

Navigation