Skip to main content
SpringerLink
Log in

Reduced Hamiltonians. I: Spin-adapted and spin-nonadapted reduced Hamiltonians

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

Abstract

Closed formulae are derived for matrix elements of spin-nonadapted reduced Hamiltonians in a finite-dimensional, antisymmetric Hilbert space. The role of the spin-adaptation is discussed. Some numerical results confirm that this role is not critical for approaches based upon the eigenvectors of these Hamiltonians.

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. P.A.M. Dirac, Proc. Camb. Phil. Soc. 26 (1930) 376.

    Google Scholar 

  2. J. von Neumann,Mathematische Grundlagen der Quantenmechanik (Springer, Berlin, 1932) chap. 4.

    Google Scholar 

  3. K. Husimi, Proc. Phys. Math. Soc. Jpn. 22 (1940) 264.

    Google Scholar 

  4. P.O. Löwdin, Phys. Rev. 97 (1955) 1474.

    Google Scholar 

  5. P.O. Löwdin, Phys. Rev. 97 (1955) 1490.

    Google Scholar 

  6. P.O. Löwdin, Phys. Rev. 97 (1955) 1512.

    Google Scholar 

  7. R. McWeeny, Rev. Mod. Phys. 32 (1960) 355.

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  10. A.J. Coleman, Rep. Math. Phys. 4 (1973) 113.

    Google Scholar 

  11. D. Ter Haar, Physica 26 (1960) 1041.

    Google Scholar 

  12. D. Ter Haar, Rep. Progr. Phys. 24 (1961) 804.

    Google Scholar 

  13. M. Rosina and R.M. Erdahl, Queen's Papers Pure Appl. Math. 40 (1974) 36.

    Google Scholar 

  14. H. Kummer, J. Math. Phys. 8 (1967) 2063.

    Google Scholar 

  15. E.R. Davidson,Reduced Density Matrices in Quantum Chemistry (Academic, New York, 1959).

    Google Scholar 

  16. F. Bopp, Z. Phys. 156 (1959) 348.

    Google Scholar 

  17. T.B. Grimley, Proc. R. Soc. London 84 (1964) 178.

    Google Scholar 

  18. T.B. Grimley and F.D. Peat, Proc. Phys. Soc. London 86 (1965) 249.

    Google Scholar 

  19. I. Absar and A.J. Coleman, Chem. Phys. Lett. 39 (1976) 609.

    Google Scholar 

  20. I. Absar and A.J. Coleman, Int. J. Quant. Chem., Quant. Chem. Symp. 10 (1976) 319.

    Google Scholar 

  21. A.J. Coleman, Int. J. Quant. Chem. 13 (1978) 67.

    Google Scholar 

  22. I. Absar, Int. J. Quant. Chem. 13 (1978) 777.

    Google Scholar 

  23. A.J. Coleman and I. Absar, Int. J. Quant. Chem. 18 (1980) 1279.

    Google Scholar 

  24. C. Valdemoro, Ann. R. Soc. Fis. 79 (1983) 106.

    Google Scholar 

  25. C. Valdemoro, Phys. Rev. A31 (1985) 2114.

    Google Scholar 

  26. C. Valdemoro, Phys. Rev. A31 (1985) 2123.

    Google Scholar 

  27. J. Karwowski, W. Duch and C. Valdemoro, Phys. Rev. A33 (1986) 2254.

    Google Scholar 

  28. J. Planelles, C. Valdemoro and J. Karwowski, Phys. Rev. A43 (1991) 3392.

    Google Scholar 

  29. R. Erdahl and V. Smith (eds.),Density Matrices and Density Funcionals, Proc. A.J. Coleman Symp., Kingston, Ontario, 1985 (Reidel, Dordrecht, 1987).

    Google Scholar 

  30. W. Duch and J. Karwowski, Comp. Phys. Rep. 2 (1985) 95.

    Google Scholar 

  31. J. Planelles and J. Karwowski, Theor. Chim. Acta 82 (1992) 239.

    Google Scholar 

  32. J. Planelles, C. Valdemoro and J. Karwowski, Phys. Rev. A41 (1990) 2391.

    Google Scholar 

  33. C. Valdemoro, in:Nuevas Tendencias en Qufmica Teórica, ed. S. Fraga (CSIC, Madrid, 1987) p. 95.

    Google Scholar 

  34. L. Lain, A. Torre and C. Valdemoro, Phys. Rev. A37 (1988) 2868.

    Google Scholar 

  35. J. Karwowski, C. Valdemoro and L. Lain, Phys. Rev. A39 (1989) 4967.

    Google Scholar 

  36. J. Paldus, J. Chem. Phys. 61 (1974) 5521.

    Google Scholar 

  37. E. Clementi and C. Roetti, At. Data Nucl. Data Tables 14 (1974) 428.

    Google Scholar 

  38. P. Viciano, Master's Thesis, Valencia (1992) p. 88.

Download references

Author information

Author notes

  1. Josep Planelles

    Present address: Departament de Ciències Experimentals, Universitat Jaune I, Apartat 224, 12080, Castelló, Spain

Authors and Affiliations

  1. Department of Applied Mathematics, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    Josep Planelles & Pascual Viciano

Authors
  1. Josep Planelles
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Pascual Viciano
    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

Planelles, J., Viciano, P. Reduced Hamiltonians. I: Spin-adapted and spin-nonadapted reduced Hamiltonians. J Math Chem 16, 137–148 (1994). https://doi.org/10.1007/BF01169202

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01169202

Keywords

Search

Navigation