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An Improved Statistical Exchange Approximation

  • Conference paper
Computational Solid State Physics

Part of the book series: The IBM Research Symposia 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

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References

  1. J. C. Slater, Phys. Rev. 81, 385 (1951). (XS method)

    Article  ADS  MATH  Google Scholar 

  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. 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. F. Herman and S. Skillman, Atomic Structure Calculations. ( Prentice Hall, Englewood Cliffs, NJ, 1963 ).

    Google Scholar 

  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 Also J. B. Mann, unpublished.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. 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. B. Alder, S. Fernbach and M. Rotenberg, editors, Methods in Computational Physics. (Academic Press, New York, 1968 ), Vol. 8.

    Google Scholar 

  8. J. O. Dimmock, Solid State Phys. 26, 104 (1971).

    Google Scholar 

  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. K. H. Johnson, J. Physique, 1972, in press (Menton Conference Proceedings).

    Google Scholar 

  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. K.-H. Schwarz and F. Herman, J. Physique, 1972,in press (Menton Conference Proceedings).

    Google Scholar 

  13. E. Kmetko, Phys. Rev. A1, 37 (1970).

    Article  ADS  Google Scholar 

  14. J. H. Wood, Intern. J. Quantum Chem. 3S, 747 (1970).

    Google Scholar 

  15. K.-H. Schwarz, Phys. Rev., in press.

    Google Scholar 

  16. L. Hedin and S. Lundqvist, Solid State Phys. 24, 1 (1970).

    Article  Google Scholar 

  17. L. Hedin and S. Lundqvist, J. Physique, 1972, in press (Menton Conference Proceedings).

    Google Scholar 

  18. B. I. Lundqvist and S. Lundqvist, this volume.

    Google Scholar 

  19. L. Hedin, this volume.

    Google Scholar 

  20. A. W. Overhauser, Phys. Rev. B2, 874 (1970).

    Article  ADS  Google Scholar 

  21. F. Herman, J. P. van Dyke and I. B. Ortenburger, Phys. Rev. Letters 22, 807 (1969).

    Article  ADS  Google Scholar 

  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. 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. M. E. Boring, Phys. Rev. B2, 1506 (1970). Boring used the same convergence factors as we did in Ref. 21.

    ADS  Google Scholar 

  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. 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 

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© 1972 Plenum Press, New York

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Herman, F., Schwarz, K. (1972). An Improved Statistical Exchange Approximation. In: Herman, F., Dalton, N.W., Koehler, T.R. (eds) Computational Solid State Physics. The IBM Research Symposia Series. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-1977-1_20

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  • DOI: https://doi.org/10.1007/978-1-4684-1977-1_20

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4684-1979-5

  • Online ISBN: 978-1-4684-1977-1

  • eBook Packages: Springer Book Archive

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