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The Spherical-Wave Based Full-Potential ASW Method

  • Volker Eyert
Part of the Lecture Notes in Physics book series (LNP, volume 849)

Abstract

In contrast to the plane-wave based full-potential ASW method the scheme presented in this chapter aims at expressing the wave function, electron density, and effective potential throughout in terms of spherical waves, i.e. of atom-centered functions. Such an approach offers the distinct advantages of being applicable to both crystalline solids and finite systems as, e.g., molecules and clusters and at the same time allowing for very high computational efficiency due to the small basis sets needed. Again, the main steps are outlined in detail. This chapter concludes with two sections on local electronic correlations as covered by the LDA+U method as well as on the calculation of electric field gradients.

Keywords

Local Density Approximation Electric Field Gradient Envelope Function Interstitial Region Atomic 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.

References

  1. 1.
    V.I. Anisimov, F. Aryasetiawan, A.I. Liechtenstein, J. Phys.: Condens. Matter 9, 767 (1997) ADSCrossRefGoogle Scholar
  2. 2.
    V.I. Anisimov, O. Gunnarsson, Phys. Rev. B 43, 7570 (1991) ADSCrossRefGoogle Scholar
  3. 3.
    V.I. Anisimov, I.V. Solovyev, M.A. Korotin, M.T. Czyżyk, G.A. Sawatzky, Phys. Rev. B 48, 16929 (1993) ADSCrossRefGoogle Scholar
  4. 4.
    V.I. Anisimov, J. Zaanen, O.K. Andersen, Phys. Rev. B 44, 943 (1991) ADSCrossRefGoogle Scholar
  5. 5.
    K. Atkinson, J. Austral. Math. Soc. B 23, 332 (1982) zbMATHCrossRefGoogle Scholar
  6. 6.
    U. von Barth, Density functional theory for solids, in The Electronic Structure of Complex Systems, ed. by P. Phariseau, W. Temmerman (Plenum Press, New York, 1984), pp. 67–140 CrossRefGoogle Scholar
  7. 7.
    U. von Barth, An overview of density functional theory, in Many-Body Phenomena at Surfaces, ed. by D. Langreth, H. Suhl (Academic Press, Orlando, 1984), pp. 3–50 Google Scholar
  8. 8.
    Z.P. Bažant, B.H. Oh, Z. Angew. Math. Mech. 66, 37 (1986) MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    P.E. Blöchl, Gesamtenergien, Kräfte und Metall-Halbleiter Grenzflächen, PhD thesis, Universität Stuttgart, 1989 Google Scholar
  10. 10.
    M.T. Czyżyk, G.A. Sawatzky, Phys. Rev. B 49, 14211 (1995) ADSCrossRefGoogle Scholar
  11. 11.
    F.M.F. de Groot, J.C. Fuggle, B.T. Thole, G.A. Sawatzky, Phys. Rev. B 42, 5459 (1990) ADSCrossRefGoogle Scholar
  12. 12.
    V. Eyert, Entwicklung und Implementation eines Full-Potential-ASW-Verfahrens, PhD thesis, Technische Hochschule Darmstadt, 1991 Google Scholar
  13. 13.
    V. Eyert, Electronic Structure of Crystalline Materials, 2nd edn. (University of Augsburg, Augsburg, 2005) Google Scholar
  14. 14.
    J.D. Jackson, Classical Electrodynamics (Wiley, New York, 1975) zbMATHGoogle Scholar
  15. 15.
    P. Keast, J. Comput. Appl. Math. 17, 151 (1987) MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    P. Keast, J.C. Diaz, SIAM J. Numer. Anal. 20, 406 (1983) MathSciNetADSzbMATHCrossRefGoogle Scholar
  17. 17.
    J. Kübler, V. Eyert, Electronic structure calculations, in Electronic and Magnetic Properties of Metals and Ceramics, ed. by K.H.J. Buschow (VCH Verlagsgesellschaft, Weinheim, 1992), pp. 1–145; vol. 3A of Materials Science and Technology, ed. by R.W. Cahn, P. Haasen, E.J. Kramer (VCH Verlagsgesellschaft, Weinheim, 1991–1996) Google Scholar
  18. 18.
    F. Lechermann, Ab-initio Betrachtungen zur Elektronenstruktur und Statistischen Mechanik von mehrkomponentigen intermetallischen Systemen am Beispiel Ni-Fe-Al, PhD thesis, University of Stuttgart, 2003 Google Scholar
  19. 19.
    A.I. Liechtenstein, V.I. Anisimov, J. Zaanen, Phys. Rev. B 52, R5467 (1995) ADSCrossRefGoogle Scholar
  20. 20.
    A.D. McLaren, Math. Comput. 17, 361 (1963) MathSciNetzbMATHCrossRefGoogle Scholar
  21. 21.
    M.S. Methfessel, Phys. Rev. B 38, 1537 (1988) ADSCrossRefGoogle Scholar
  22. 22.
    M.S. Methfessel, M. van Schilfgaarde, R.A. Casali, A full-potential LMTO method based on smooth Hankel functions, in Electronic Structure and Physical Properties of Solids. The Uses of the LMTO Method, ed. by H. Dreyssé (Springer, Berlin, 2000), pp. 114–147 CrossRefGoogle Scholar
  23. 23.
    I.P. Mysovskih, Sov. Math. Dokl. 18, 925 (1977) Google Scholar
  24. 24.
    A.G. Petukhov, I.I. Mazin, L. Chioncel, A.I. Liechtenstein, Phys. Rev. B 67, 153106 (2003) ADSCrossRefGoogle Scholar
  25. 25.
    A.S. Popov, Comput. Math. Math. Phys. 35, 369 (1995) MathSciNetzbMATHGoogle Scholar
  26. 26.
    S.Y. Savrasov, D.Y. Savrasov, Phys. Rev. B 46, 12181 (1992) ADSCrossRefGoogle Scholar
  27. 27.
    A.B. Shick, A.I. Liechtenstein, W.E. Pickett, Phys. Rev. B 60, 10763 (1999) ADSCrossRefGoogle Scholar
  28. 28.
    I.V. Solovyev, P.H. Dederichs, V.I. Anisimov, Phys. Rev. B 50, 16861 (1994) ADSCrossRefGoogle Scholar
  29. 29.
    M. Springborg, O.K. Andersen, J. Chem. Phys. 87, 7125 (1987) ADSCrossRefGoogle Scholar
  30. 30.
    A.H. Stroud, Approximate Calculation of Multiple Integrals (Prentice-Hall, Englewood Cliffs, 1971) zbMATHGoogle Scholar
  31. 31.
    A.H. Stroud, SIAM J. Numer. Anal. 10, 559 (1973) MathSciNetADSzbMATHCrossRefGoogle Scholar
  32. 32.
    K.-H. Weyrich, Phys. Rev. B 37, 10269 (1988) ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Volker Eyert
    • 1
  1. 1.Materials Design SARLMontrougeFrance

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