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
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J. C. Slater, Phys. Rev. 81, 385 (1951). (XS method)
W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965); and R. Gaspar, Acta Phys. Acad. Soc. Hung. 3, 263 (1954). (XKSG method)
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)
F. Herman and S. Skillman, Atomic Structure Calculations. ( Prentice Hall, Englewood Cliffs, NJ, 1963 ).
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 Also J. B. Mann, unpublished.
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).
B. Alder, S. Fernbach and M. Rotenberg, editors, Methods in Computational Physics. (Academic Press, New York, 1968 ), Vol. 8.
J. O. Dimmock, Solid State Phys. 26, 104 (1971).
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.
K. H. Johnson, J. Physique, 1972, in press (Menton Conference Proceedings).
K. H. Johnson, Advances in Quantum Chemistry, Vol. 7, edited by P.-O. Löwdin (Academic Press, New York) to be published.
K.-H. Schwarz and F. Herman, J. Physique, 1972,in press (Menton Conference Proceedings).
E. Kmetko, Phys. Rev. A1, 37 (1970).
J. H. Wood, Intern. J. Quantum Chem. 3S, 747 (1970).
K.-H. Schwarz, Phys. Rev., in press.
L. Hedin and S. Lundqvist, Solid State Phys. 24, 1 (1970).
L. Hedin and S. Lundqvist, J. Physique, 1972, in press (Menton Conference Proceedings).
B. I. Lundqvist and S. Lundqvist, this volume.
L. Hedin, this volume.
A. W. Overhauser, Phys. Rev. B2, 874 (1970).
F. Herman, J. P. van Dyke and I. B. Ortenburger, Phys. Rev. Letters 22, 807 (1969).
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).
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.
M. E. Boring, Phys. Rev. B2, 1506 (1970). Boring used the same convergence factors as we did in Ref. 21.
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).
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.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1972 Plenum Press, New York
About this paper
Cite this paper
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
Download citation
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