Advertisement

An Improved Statistical Exchange Approximation

  • Frank Herman
  • Karlheinz Schwarz
Part of the The IBM Research Symposia Series book series (IRSS)

Abstract

Various forms of the statistical exchange approximation1–3 (abbreviated XA) have been used in atomic structure4–6 and energy band7, 8 calculations over the past 20 years. In view of the continuing importance of the XA in atomic and solid state investigations and its increasing prominence in molecular studies,9–11 it would be desirable to have a version of the XA which (a) is simple to deal with in a wide variety of applications, (b) is at least as satisfactory from a physical point of view as existing versions, and (c) is universal in character, in the sense that its key parameters are all independent of atomic number. The object of this short note is to propose such a form of the XA. For additional details and supporting information, the reader is referred to a recent paper.12

Keywords

Virial Coefficient Solid State Phys Virial Theorem Convergence Factor Inscribe Sphere 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    J. C. Slater, Phys. Rev. 81, 385 (1951). (XS method)ADSMATHCrossRefGoogle Scholar
  2. 2.
    W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965); and R. Gaspar, Acta Phys. Acad. Soc. Hung. 3, 263 (1954). (XKSG method)Google Scholar
  3. 3.
    J. C. Slater, T. M. Wilson and J. H. Wood, Phys. Rev. 179, 28 (1969); J. C. Slater and J. H. Wood, Intern. J. Quantum Chem. 4S, 3 (1971); and J. C. Slater, Advances in Quantum Chemistry, Vol. 6. P.-O. Löwdin, editor (Academic Press, New York), to be published. (Xα method)Google Scholar
  4. 4.
    F. Herman and S. Skillman, Atomic Structure Calculations. ( Prentice Hall, Englewood Cliffs, NJ, 1963 ).Google Scholar
  5. 5.
    D. Liberman, J. T. Waber and D. Cromer, Phys. Rev. 137, A27 (1965); and D. Liberman, D. Cromer and J. T. Waber, Computer Phys. Commun. 2, 107 (1971). Also J. B. Mann, unpublished.Google Scholar
  6. 6.
    J. P. Desclaux, Computer Phys. Commun. 1, 216 (1970); and C. C. Lu, T.A. Carlson, F. B. Malik, T. C. Tucker and C. W. Nestor, Jr., Atomic Data 3, 1 (1971).Google Scholar
  7. 7.
    B. Alder, S. Fernbach and M. Rotenberg, editors, Methods in Computational Physics. (Academic Press, New York, 1968 ), Vol. 8.Google Scholar
  8. 8.
    J. O. Dimmock, Solid State Phys. 26, 104 (1971).Google Scholar
  9. 9.
    K. H. Johnson and F. C. Smith, Computational Methods in Band Theory, edited by P. M. Marcus, J. F. Janak, and A. R. Williams ( Plenum Press, New York, 1971 ), p. 377.Google Scholar
  10. 10.
    K. H. Johnson, J. Physique, 1972, in press (Menton Conference Proceedings).Google Scholar
  11. 11.
    K. H. Johnson, Advances in Quantum Chemistry, Vol. 7, edited by P.-O. Löwdin (Academic Press, New York) to be published.Google Scholar
  12. 12.
    K.-H. Schwarz and F. Herman, J. Physique, 1972,in press (Menton Conference Proceedings).Google Scholar
  13. 13.
    E. Kmetko, Phys. Rev. A1, 37 (1970).ADSCrossRefGoogle Scholar
  14. 14.
    J. H. Wood, Intern. J. Quantum Chem. 3S, 747 (1970).Google Scholar
  15. 15.
    K.-H. Schwarz, Phys. Rev., in press.Google Scholar
  16. 16.
    L. Hedin and S. Lundqvist, Solid State Phys. 24, 1 (1970).CrossRefGoogle Scholar
  17. 17.
    L. Hedin and S. Lundqvist, J. Physique, 1972, in press (Menton Conference Proceedings).Google Scholar
  18. 18.
    B. I. Lundqvist and S. Lundqvist, this volume.Google Scholar
  19. 19.
    L. Hedin, this volume.Google Scholar
  20. 20.
    A. W. Overhauser, Phys. Rev. B2, 874 (1970).ADSCrossRefGoogle Scholar
  21. 21.
    F. Herman, J. P. van Dyke and I. B. Ortenburger, Phys. Rev. Letters 22, 807 (1969).ADSCrossRefGoogle Scholar
  22. 22.
    F. Herman, I. B. Ortenburger and J. P. van Dyke, Intern. J. Quantum Chem. 3S, 827 (1970). See also N. O. Folland, Phys. Rev. A3, 1535 (1971); and J. C. Stoddart, A. M. Beattie, and N. H. March, Intern. J. Quantum Chem. 4S, 35 (1971).Google Scholar
  23. 23.
    I. B. Ortenburger and F. Herman, Computational Methods in Band Theory, edited by P. M. Marcus, J. F. Janak and A. R. Williams, ( Plenum Press, New York, 1971 ) p. 469.Google Scholar
  24. 24.
    M. E. Boring, Phys. Rev. B2, 1506 (1970). Boring used the same convergence factors as we did in Ref. 21.ADSGoogle Scholar
  25. 25.
    M. Berrondo and O. Goscinski, Phys. Rev. 184, 10 (1969); and D. J. McNaughton and V. H. Smith, Jr., Intern. J. Quantum Chem. 3S, 775 (1970).Google Scholar
  26. 26.
    J. B. Mann, “Atomic Structure Calculations. I. Hartree-Fock Energy Results for the Elements Hydrogen to Lawrencium,” Los Alamos Scientific Laboratory Report LA-3690 (1967), unpublished.Google Scholar

Copyright information

© Plenum Press, New York 1972

Authors and Affiliations

  • Frank Herman
    • 1
  • Karlheinz Schwarz
    • 1
    • 2
  1. 1.IBM Research LaboratorySan JoseUSA
  2. 2.Institute for Physical ChemistryUniversity of ViennaViennaAustria

Personalised recommendations