A Full-Potential LMTO Method Based on Smooth Hankel Functions

  • M. Methfessel
  • M. van Schilfgaarde
  • R. A. Casali
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 535)


The paper presents a recently developed full-potential linear muffin-tin orbital (FP-LMTO) method which does not require empty spheres and can calculate the forces accurately. Similar to previous approaches, this method uses numerical integration to calculate the matrix elements for the interstitial potential, which is the limiting step for any FP-LMTO approach. However, in order to reduce the numerical e.ort as far as possible, we use a newly introduced basis consisting of “augmented smooth Hankel functions” which play the role of the LMTO envelope functions. After presenting the basics of the approach, we report the results of numerical test for typical condensed-matter systems. The calculations show that good accuracy can be reached with an almost minimal basis set. These features of the method open the way to efficient molecular dynamics studies and simulated-annealing calculations to optimize structures while retaining the advantages of the LMTO method.


Envelope Function Hankel Function Multipole Moment 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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    O.K. Andersen, Phys. Rev. B 12, 3060 (1975).CrossRefADSGoogle Scholar
  2. 2.
    P. Hohenberg and W. Kohn, Phys. Rev. 136, B6864 (1964); W. Kohn and L.J. Sham, Phys. Rev. 140, A1133 (1965); R.O. Jones and O. Gunnarsson, Rev. Mod. Phys. 61, 689 (1989).CrossRefMathSciNetGoogle Scholar
  3. 3.
    D. Glötzel, B. Segall, and O.K. Andersen, Solid State Commun. 36, 403 (1980); A.K. McMahan, Phys. Rev. B 30, 5835 (1984).CrossRefADSGoogle Scholar
  4. 4.
    R. Car and M. Parrinello, Phys. Rev. Lett. 55, 2471 (1985).CrossRefADSGoogle Scholar
  5. 5.
    P.E. Blöchl, Phys. Rev. B 50, 17953 (1994).CrossRefADSGoogle Scholar
  6. 6.
    D. Vanderbilt, Phys. Rev. B 41, 7892 (1990).CrossRefADSGoogle Scholar
  7. 7.
    K.H. Weyrich, Phys. Rev. B 37, 10269 (1988).CrossRefADSGoogle Scholar
  8. 9.
    S.Y. Savrasov, Phys. Rev. B 54, 16470 (1996).CrossRefADSGoogle Scholar
  9. 10.
    M. Methfessel, Phys. Rev. B 38, 1537 (1988); M. Methfessel, C.O. Rodriguez, and O.K. Andersen, Phys. Rev. B 40, 2009 (1989).CrossRefADSGoogle Scholar
  10. 11.
    M. Methfessel and M. van Schilfgaarde, Phys. Rev. B 48, 4937 (1993).CrossRefADSGoogle Scholar
  11. 12.
    M. Springborg and O.K. Andersen, J. Chem. Phys. 87, 7125 (1987).CrossRefADSGoogle Scholar
  12. 14.
    E. Bott, Diplomarbeit, Technical University Darmstadt (1997); E. Bott, M. Methfessel, W. Krabs, and P.C. Schmidt, J. Math. Phys. 39, 3393 (1998).Google Scholar
  13. 15.
    G.B. Bachelet, D.R. Haman, and M. Schlüter, Phys. Rev. B 26, 4199 (1982).CrossRefADSGoogle Scholar
  14. 16.
    M. Methfessel, NFP Manual (Institute for Semiconductor Physics, Frankfurt (Oder), 1997).Google Scholar
  15. 17.
    J. Harris, Phys. Rev. B 31, 1770 (1985); W.M.C. Foulkes and R. Haydock, Phys. Rev. B 39, 12 520 (1989).CrossRefADSGoogle Scholar
  16. 18.
    P. Pulay, Mol. Phys. 17, 197 (1969).CrossRefADSGoogle Scholar
  17. 19.
    A. Dal Corso and R. Resta, Phys. Rev. B 50, 4327 (1994).CrossRefADSGoogle Scholar
  18. 20.
    C.-Y. Yeh, Z. W. Lu, S. Froyen and A. Zunger, Phys. Rev. B 46, 10086 (1992).CrossRefADSGoogle Scholar
  19. 21.
    K. Osamura, S. Naka and Y. Murakami, J. Appl. Phys. 46, 3432 (1975).CrossRefADSGoogle Scholar
  20. 22.
    S. Strite, D. Chandrasekhar, D. J. Smith, J. Sariel, N. Teraguchi and H. Morkoç, J. Crys. Growth 127, 204 (1993).CrossRefADSGoogle Scholar
  21. 23.
    H. Morkoç, S. Strite, G. B. Gao, M. E. Lin, B. Sverdlov and M. Burns, J. Appl. Phys. 76, 1363 (1994).CrossRefADSGoogle Scholar
  22. 24.
    P. Petrov, E. Mojab, R. C. Powell and J. E. Greene Appl. Phys. Lett. 60 2491(1992).CrossRefADSGoogle Scholar
  23. 25.
    M. J. Paisley, Z. Sitar, J. B. Posthill and R. F. Davis, J. Vac. Sci. Technol. A7 1701 (1989).Google Scholar
  24. 26.
    S. Strite, J. Ruan, Z. Li, A. Salvador, H. Chen D. J. Smith, W. Y. Choyke and H. Morkoç, J. Vac. Sci. Technol. B 9, 1924 (1991).CrossRefGoogle Scholar
  25. 27.
    R. C. Powell, G. A. Tomasch, Y.-W. Kim, J. A. Thornton and J. E. Green, Mater. Res. Soc. Symp. Proc. 162, 525 (1990).Google Scholar
  26. 28.
    T. Lei, M. Fanciulli, R. J. Molnar, T. D. Moustakas, R. J. Graham and J. Scanlon, Appl. Phys. Lett. 59, 944 (1991).CrossRefADSGoogle Scholar
  27. 29.
    M. Mizuta, S. Fujieda, Y. Matsumoto and T. Kawamura, Jpn. J. Appl. Phys. 25, L945 (1986).CrossRefADSGoogle Scholar
  28. 30.
    H. Schulz and K. H. Thiemann, Sol. State Commun. 23, 815 (1977).CrossRefADSGoogle Scholar
  29. 31.
    M. van Schilfgaarde, A. Sher and A.-B. Chen “Theory of AlN, GaN, InN and Their Alloys,” J. Crystal Growth 178, 8 (1997).CrossRefADSGoogle Scholar
  30. 32.
    S.-H.-Wei, private communication.Google Scholar
  31. 33.
    A. F. Wright and J. S. Nelson, Phys. Rev. B51, 7866 (1995); A. F. Wright and J. S. Nelson, Phys. Rev. B50, 2159 (1994).CrossRefADSGoogle Scholar
  32. 34.
    U. von Barth and L. Hedin, J. Phys. C 5, 1629 (1972).CrossRefADSGoogle Scholar
  33. 35.
    J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996).CrossRefADSGoogle Scholar
  34. 36.
    G. Kresse and J. Hafner, Phys. Rev. B 47, 558 (1993); G. Kresse, Thesis, Technische Universität Wien 1993; G. Kresse and J. Furthmüller, Comput. Mat. Sci. 6, 15-50 (1996); G. Kresse and J. Furthmüller, Phys. Rev. B54, 11169 (1996).CrossRefADSGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • M. Methfessel
    • 1
  • M. van Schilfgaarde
    • 2
    • 3
  • R. A. Casali
    • 4
  1. 1.Institute for Semiconductor PhysicsFrankfurt(Oder)Germany
  2. 2.SRI InternationalCalifornia
  3. 3.Sandia National LaboratoriesLivermore
  4. 4.Department of PhysicsUniversidad Nacional del NordesteCorrientesArgentina

Personalised recommendations