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An RAPW Expanded Basis Set

  • G. Arbman
  • D. Koelling
Part of the The IBM Research Symposia Series book series (IRSS)

Abstract

The relativistic augmented plane wave (RAPW) method1 had been used extensively to perform energy band calculations for the heavier (higher atomic number) materials. Except for the use of the relativistic formalism, it is precisely the same method as the non-relativistic APW method2 which has done so well in the region of lower atomic numbers. Both are energy-variational based techniques3,4 using basis functions constructed by joining atomic-like functions near the nuclei onto plane waves in the outer regions. However, a new feature of an additional spin variable arises in the RAPW method because the spin-orbit coupling term has been included. This makes the RAPW method considerably more time consuming to apply because it doubles the size of the basis set in addition to making the matrix elements slightly more complicated.

Keywords

Basis Function Reciprocal Lattice Vector Large Matrice High Atomic Number Augmented Plane Wave 
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.

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References

  1. 1.
    T. Loucks, Augmented Plane Wave Method, W. A. Benjamin, New York (1967).Google Scholar
  2. 2.
    J. C. Slater, Phys. Rev. 51, 846 (1937).CrossRefGoogle Scholar
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    R. S. Leigh, Proc. Phys. Soc. (London) 69, 388 (1956); H. Schlosser and P. M. Marcus, Int. J. of Quantum Chem. 1, 567, 42, (1968)CrossRefGoogle Scholar
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    T. Loueks, Phys. Rev. 139, A1333 (1965)CrossRefGoogle Scholar
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    L. F. Mattheiss, J. H. Wood, and A. C. Switendick, Meth. in Comp. Phys. (vol. 8 ), Academic Press, New York (1968).Google Scholar
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    D. Koelling, Phys. Rev. 188, 1049 (1969).CrossRefGoogle Scholar
  7. 7.
    D. Koelling, “The relativistic APW Method and its Convergence in ℓ”, Quarterly Progress Report of the Solid State and Molecular Theory Group, MIT (unpublished) 68, 36 (1968). Also see ref. 6.Google Scholar
  8. 8.
    Some of the details are given in the refs. 6–7 and the use of the spherical harmonic sum rule is obvious. The rewriting of the spin-orbit term to actually look like a spin-orbit term by G.A.) will be presented in the forthcoming paper.Google Scholar
  9. 9.
    N. Parada, “Localized Defects in PbTe via a \(\overrightarrow K \cdot \overrightarrow \pi\) — APW Energy Band Calculation”, Tech. Rep. No. 8 of the Materials Theory Group, MIT (1968).Google Scholar
  10. 10.
    Our SRAPW tests indicate that there is still a bug in the construction of the RAPW matrix elements leading to small (.02 Ryd.) errors. Thus we can only discuss those features which are unaffected by these errors.Google Scholar

Copyright information

© Plenum Press, New York 1971

Authors and Affiliations

  • G. Arbman
    • 1
  • D. Koelling
    • 1
  1. 1.Magnetic Theory Group, Physics DepartmentNorthwestern UniversityEvanstonUSA

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