Real Space Full Potential Multiple Scattering Theory

  • Keisuke Hatada
  • Calogero R. Natoli
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 204)


We show how to implement a Full Potential Multiple Scattering (fpms) code based on a real-space FPMS theory valid for both continuum and bound states, under conditions for space partitioning that are less restrictive than those applied so far. This theory is free from the need to expand cell shape functions in spherical harmonics or to use rectangular matrices. Tests of the program show that it is able to reproduce with very good accuracy known solutions of the Schrödinger equation. Applications to the spectroscopy of low dimensional systems, such as one-dimensional (1D) chain like systems, 2D layered systems and 3D diamond structure systems, where the Muffin-Tin approximation is known to give very poor results, show a remarkable improvement toward the agreement with experiments. The default mode of the code uses superimposed atomic charge densities, which works satisfactorily in most of the applications, but with help of the es2ms interface, incorporated in the program, one can also use self-consistent charge densities derived from the vasp program. The program is also incorporated in the photoelectron diffraction code msspec and parallelized for energy point.


  1. 1.
    J. Korringa, Physica 13, 392–400 (1947)Google Scholar
  2. 2.
    W. Kohn, N. Rostoker, Phys. Rev. 94, 1111–1120 (1954)Google Scholar
  3. 3.
    J.C. Slater, K.H. Johnson, Phys. Rev. B 5, 844–853 (1972)Google Scholar
  4. 4.
    D. Dill, J.L. Dehmer, J. Chem. Phys. 61, 692–699 (1974)Google Scholar
  5. 5.
    K. Hatada, K. Hayakawa, M. Benfatto, C.R. Natoli, Phys. Rev. B 76, 060102R1–4 (2007)Google Scholar
  6. 6.
    K. Hatada, K. Hayakawa, M. Benfatto, C.R. Natoli, J. Phys.: Condens. Matter 21, 104206 (2009)Google Scholar
  7. 7.
    K. Hatada, K. Hayakawa, M. Benfatto, C.R. Natoli, J. Phys.: Condens. Matter 22, 185501 (2010)Google Scholar
  8. 8.
    J. Xu, P. Krüger, C.R. Natoli, K. Hayakawa, Z. Wu, K. Hatada, Phys. Rev. B 92, 125408–1–11 (2015)Google Scholar
  9. 9.
    O.K. Andersen, Phys. Rev. B 12, 3060–3083 (1975)Google Scholar
  10. 10.
    A.R. Williams, J.W. van Morgan, J. Phys. C: Solid State Phys. 7, 37–60 (1974)Google Scholar
  11. 11.
    N. Papanikolau, R. Zeller, P.H. Dederich, J. Phys.: Condens. Matter 14, 2799–2823 (2002)Google Scholar
  12. 12.
    A. Gonis, W.H. Butler, Multiple Scattering in Solids (Springer Science & Business Media, New York, 2012)Google Scholar
  13. 13.
    G. Breit, H.A. Bethe, Phys. Rev. 93, 888–890 (1954)Google Scholar
  14. 14.
    L.F. Canto, M.S. Hussein, Scattering Theory of Molecules, Atoms and Nuclei (World Scientific, Singapore, 2013)Google Scholar
  15. 15.
    W.H. Butler, A. Gonis, X.G. Zhang, Phys. Rev. B 45, 11527–11541 (1992)Google Scholar
  16. 16.
    D. Sebilleau, R. Gunnella, Z.-Y. Wu, S. Di Matteo, C.R. Natoli, J. Phys.: Condens. Matter 18, R175–R230 (2006)Google Scholar
  17. 17.
    V.I. Lebedev, Comput. Math. Math. Phys. 15, 44–51 (1975)Google Scholar
  18. 18.
    X.G. Wang, T. Carrington Jr., J. Theor. Comput. Chem. 4, 599–608 (2003)Google Scholar
  19. 19.
    M. Abramowitz, I.N. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (U.S. Goverment Printing Office, Washington, 1972)zbMATHGoogle Scholar
  20. 20.
    A.D. Becke, J. Chem. Phys. 88, 2547–2553 (1988)Google Scholar
  21. 21.
    V.F. Brastev, Atomic Wavefunctions (Nauka, Moscow, 1966)Google Scholar
  22. 22.
    S. Flügge, Practical Quantum Mechanics, Springer study edn. (Springer, Berlin, 1974), problem 22, p. 42Google Scholar
  23. 23.
    M. Benfatto, C.R. Natoli, A. Bianconi, J. Garcia, A. Marcelli, M. Fanfoni, I. Davoli, Phys. Rev. B 34, 5774–5781 (1986)Google Scholar
  24. 24.
    F.G. Tricomi, Integral Equations (Courier Dover Publications, New York, 1985)Google Scholar
  25. 25.
    R.G. Newton, Scattering Theory of Waves and Particles, 2nd edn. (Courier Dover Publications, New York, 2002)zbMATHGoogle Scholar
  26. 26.
    A. Gonis, W.H. Butler, Multiple Scattering in Solids (Springer, New York, 2000), and references thereinGoogle Scholar
  27. 27.
    E.T. Whittaker, G.N. Watson, A Course of Modern Analysis (Cambridge University Press, Cambridge, 1965)zbMATHGoogle Scholar
  28. 28.
    R.V. Vedrinskii, A.A. Novakovich, Phys. Met. Metallogr. 39, 7–15 (1975)Google Scholar
  29. 29.
    D. Pacilé, M. Papagno, A.F. Rodríguez, M. Grioni, L. Papagno, Ç.Ö. Girit, J.C. Meyer, G.E. Begtrup, A. Zettl, Phys. Rev. Lett. 101, 066806 (2008)Google Scholar
  30. 30.
    K. Hatada, J. Xu, K. Hayakawa, C.R. Natoli (2005),
  31. 31.
    G. Subías, J. Herrero-Martín, J. García, J. Blasco, C. Mazzoli, K. Hatada, S. Di Matteo, C.R. Natoli, Phys. Rev. B 75, 235101 (2007)Google Scholar
  32. 32.
    X. Junqing, C.R. Natoli, P. Krüger, K. Hayakawa, D. Sébilleau, L. Song, K. Hatada, Comput. Phys. Commun. 203, 331–338 (2016)Google Scholar
  33. 33.
    G. Kresse, D. Joubert, Phys. Rev. B 59, 1758–1775 (1999)Google Scholar
  34. 34.
    K. Hayakawa, K. Hatada, S. Della Longa, P. D’Angelo, M. Benfatto, AIP Conf. Proc. 882, 111–113 (2007)Google Scholar
  35. 35.
    K. Hatada, K. Hayakawa, unpublished 2011Google Scholar
  36. 36.
    D. Sébilleau, C. Natoli, G.M. Gavaza, H. Zhao, F. Da Pieve, K. Hatada, Comput. Phys. Commun. 182, 2567–2579 (2011)Google Scholar
  37. 37.
    OpenGL, Opengl 4.0 specification (2013),
  38. 38.
    Message P Forum, Mpi: a message-passing interface standard, Technical report, Knoxville, TN, USA (1994)Google Scholar
  39. 39.
    E. Anderson, Z. Bai, J. Dongarra, A. Greenbaum, A. McKenney, J. Du Croz, S. Hammerling, J. Demmel, C. Bischof, D. Sorensen, in Proceedings of the 1990 ACM/IEEE Conference on Supercomputing, Supercomputing’90, Los Alamitos, CA, USA (IEEE Computer Society Press, 1990), pp. 2–11Google Scholar
  40. 40.
    L.S. Blackford, J. Demmel, J. Dongarra, I. Duff, S. Hammarling, G. Henry, M. Heroux, L. Kaufman, A. Lumsdaine, A. Petitet, R. Pozo, K. Remington, R.C. Whaley, ACM Trans. Math. Softw. 28, 135–151 (2002)Google Scholar
  41. 41.
    G. Rossi, M. Calizzi, V. Di Cintio, S. Magkos, L. Amidani, L. Pasquini, F. Boscherini, J. Phys. Chem. C 120, 7457–7466 (2016)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department ChemieLudwig-Maximilians-Universität MünchenMunich, BavariaGermany
  2. 2.LNF-INFNFrascatiItaly

Personalised recommendations