Advertisement

Simple Views of Metallic Clusters

  • John P. Perdew
Part of the NATO ASI Series book series (NSSB, volume 337)

Abstract

The intent of this article is to show what can be understood of the properties of metallic clusters from a simple perspective. The jellium, stabilized jellium, and liquid drop (volume + surface + curvature) models are presented to explain the size-dependences of the total and ionization energies, as well as the electronic structures, shapes, and sizes of clusters. The high-and low-density limits for the surface energy and work function are derived in an Appendix.

Keywords

Work Function Liquid Drop Electron Density Profile Simple Analytic Model Spherical Cluster 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    W.A. de Heer, Rev. Mod. Phys. 65, 611 (1993).ADSCrossRefGoogle Scholar
  2. P. Jena, C. Yannouleas, S.N. Khanna, and B.K. Rao, in Recent Progress in Many-Body Theories, Vol. 3 (Plenum, New York, 1992).Google Scholar
  3. [2]
    M. Brack, Rev. Mod. Phys. 65, 677 (1993).ADSCrossRefGoogle Scholar
  4. [3]
    R.M. Dreizler and E.K.U. Gross, Density Functional Theory, (Springer-Verlag, Berlin, 1990).zbMATHCrossRefGoogle Scholar
  5. N.H. March, Electron Density Theory of Atoms and Molecules (Academic, New York, 1992).Google Scholar
  6. [4]
    R.G. Parr and W. Yang, Density Functional Theory of Atoms and Molecules (Oxford, New York, 1989).Google Scholar
  7. [5]
    R.O. Jones and O. Gunnarsson, Rev. Mod. Phys. 61, 689 (1989).ADSCrossRefGoogle Scholar
  8. [6]
    W.A. Harrison, Pseudopotentials in the Theory of Metals (W.A. Benjamin, New York, 1966).Google Scholar
  9. [7]
    W.E. Pickett, Computer Phys. Rep. 9, 117 (1989).ADSCrossRefGoogle Scholar
  10. [8]
    R.O. Jones, this volume.Google Scholar
  11. [9]
    W. Kohn and L.J. Sham, Phys. Rev. 140, A1133 (1965).MathSciNetADSCrossRefGoogle Scholar
  12. [10]
    J.P. Perdew, in Electronic Structure of Solids ‘91, edited by P. Ziesche and H. Eschrig (Akademie Verlag, Berlin, 1991); J.P. Perdew and Y. Wang, unpublished.Google Scholar
  13. [11]
    J.P. Perdew, J.A. Chevary, S.H. Vosko, K.A. Jackson, M.R. Pederson, D.J. Singh, and C. Fiolhais, Phys. Rev. B46, 6671 (1992).ADSGoogle Scholar
  14. J.P. Perdew, J.A. Chevary, S.H. Vosko, K.A. Jackson, M.R. Pederson, D.J. Singh, and C. Fiolhais, Phys. Rev. 48 4978 (1993) (E).ADSGoogle Scholar
  15. [12]
    N.W. Ashcroft, Phys. Lett. 23, 48 (1966).ADSCrossRefGoogle Scholar
  16. [13]
    C. Fiolhais and J.P. Perdew, unpublished.Google Scholar
  17. [14]
    N.D. Lang and W. Kohn, Phys. Rev. B1, 4555 (1970).ADSGoogle Scholar
  18. N.D. Lang and W. Kohn, Phys. Rev. 3, 1215 (1971).ADSCrossRefGoogle Scholar
  19. [15]
    W. Ekardt, Phys. Rev. B31, 6360 (1985).ADSGoogle Scholar
  20. W. Ekardt, Phys. Rev. 32, 1961 (1985).ADSCrossRefGoogle Scholar
  21. [16]
    K. Clemenger, Phys. Rev.B. 32, 1359 (1985).ADSCrossRefGoogle Scholar
  22. [17]
    W.D. Knight, K. Clemenger, W.A. de Heer, W.A. Saunders, M.Y. Chou, and M.L. Cohen, Phys. Rev. Lett. 52, 2141 (1984).ADSCrossRefGoogle Scholar
  23. W.D. Knight, K. Clemenger, W.A. de Heer, and W.A. Saunders, Phys. Rev. B 31, 2539 (1985).ADSCrossRefGoogle Scholar
  24. [18]
    J.P. Perdew, in Condensed Matter Theories, Vol. IV, edited by J. Keller (Plenum, New York, 1989).Google Scholar
  25. [19]
    J.L. Martins, R. Car, and J. Buttet, Surf. Sci. 106, 265 (1981).ADSCrossRefGoogle Scholar
  26. J.L. Martins, J. Buttet, and R. Car, Phys. Rev. B31, 1804 (1985).ADSGoogle Scholar
  27. [20]
    E. Engel, U.R. Schmitt, H.-J. Lüdde, A. Toepfer, E. Wüst, and R.M. Dreizler, Phys. Rev. B48, 1862 (1993).ADSGoogle Scholar
  28. [21]
    O. Knospe, R. Schmidt, E. Engel, U.R. Schmitt, R.M. Dreizler, and H.O. Lutz, Phys. Lett. A183, 332 (1993).ADSGoogle Scholar
  29. [22]
    J.P. Perdew and Y. Wang, Phys. Rev. B45, 13244 (1992).ADSGoogle Scholar
  30. [23]
    N.W. Ashroft and D.C. Langreth, Phys. Rev. 155, 682 (1967).ADSCrossRefGoogle Scholar
  31. [24]
    J.H. Rose and J.F. Dobson, Solid State Commun. 37, 91 (1981).ADSCrossRefGoogle Scholar
  32. [25]
    R. Monnier and J.P. Perdew, Phys. Rev. B17, 2595 (1978).ADSGoogle Scholar
  33. R. Monnier and J.P. Perdew, Phys. Rev. 22, 1124 (1980) (E).ADSGoogle Scholar
  34. R. Monnier, J.P. Perdew, D.C. Langreth, and J.W. Wilkins, Phys. Rev. B18, 656 (1978).ADSGoogle Scholar
  35. [26]
    J.P. Perdew, H.Q. Tran, and E.D. Smith, Phys. Rev. B42, 11627 (1990). Antecedents are Refs. [23] and [25]. See also Ref. [30].ADSGoogle Scholar
  36. [27]
    H.B. Shore and J.H. Rose, Phys. Rev. Lett. 66, 2519 (1991). This “ideal metal” has the same surface properties as the “stabilized jellium” of Ref. [26], but different bulk properties.ADSCrossRefGoogle Scholar
  37. J.M. Soler, Phys. Rev. Lett. 67, 3044 (1991).ADSCrossRefGoogle Scholar
  38. [28]
    M. Brajczewska, C. Fiolhais, and J.P. Perdew, Int. J. Quantum Chem. S27, 249 (1993).CrossRefGoogle Scholar
  39. [29]
    M. Brack, C. Guet, and H.-B. Hakansson, Phys. Rep. 123, 275 (1985).ADSCrossRefGoogle Scholar
  40. [30]
    C. Fiolhais and J.P. Perdew, Phys. Rev. B45, 6207(1992).ADSGoogle Scholar
  41. A. Kiejna, Phys. Rev. B47, 7361 (1993).ADSGoogle Scholar
  42. [31]
    J.P. Perdew, Y. Wang, and E. Engel, Phys. Rev. Lett. 66, 508 (1991). M. Seidl, this volume.ADSCrossRefGoogle Scholar
  43. [32]
    G. Makov and A. Nitzan, Phys. Rev. B47, 2301 (1993).ADSGoogle Scholar
  44. [33]
    P. Ziesche, M.J. Puska, T. Korhonen, and R.M. Nieminen, J. Phys.: Condens. Matter. 5, 9049 (1993).ADSCrossRefGoogle Scholar
  45. [34]
    J.P. Perdew, P. Ziesche, and C. Fiolhais, Phys. Rev. B47, 16460 (1993).ADSGoogle Scholar
  46. P. Ziesche, J.P. Perdew, and C. Fiolhais, Phys. Rev. B 49, February 15 (1994). P. Ziesche, this volume.Google Scholar
  47. [35]
    J.P. Perdew, M. Brajczewska, and C. Fiolhais, Solid State Commun. 88 795 (1993).ADSCrossRefGoogle Scholar
  48. [36]
    Some numerical tests are reported in Ref. [31]. Quantitative verification is not found in the muffin-tinned calculations of H.L. Skriver and N.M. Rosengaard, Phys. Rev. B43, 9538 (1991), but might be found when full-potential results for the surface energies of the simple metals become available.ADSGoogle Scholar
  49. [37]
    J.P. Perdew, R.G. Parr, M. Levy, and J.L. Balduz, Phys. Rev. Lett. 49, 1691 (1982). J.P. Perdew, in Density Functional Methods in Physics. edited by R.M. Dreizler and J. da Providencia (Plenum, 1985).ADSCrossRefGoogle Scholar
  50. [38]
    J.P. Perdew, Phys. Rev. B37, 6175 (1988).ADSGoogle Scholar
  51. [39]
    G. Makov, A. Nitzan, and L.E. Brus, J. Chem. Phys. 88, 5076 (1988).ADSCrossRefGoogle Scholar
  52. [40]
    J.M. Smith, Am. Inst. Aeronaut. Astronaut. J. 3, 648 (1965).CrossRefGoogle Scholar
  53. [41]
    D.M. Wood, Phys. Rev. Lett. 46, 749 (1981).ADSCrossRefGoogle Scholar
  54. [42]
    M. Seidl and J.P. Perdew, unpublished.Google Scholar
  55. [43]
    E. Engel and J.P. Perdew, Phys. Rev. B43, 1331 (1991).ADSGoogle Scholar
  56. [44]
    M. Seidl and M. Brack, unpublished.Google Scholar
  57. [45]
    J.P. Perdew and Y. Wang, Phys. Rev. B38, 12228 (1988).ADSGoogle Scholar
  58. [46]
    N.D. Lang, Solid State Physics. 28, 225 (1973).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • John P. Perdew
    • 1
  1. 1.Department of Physics and Quantum Theory GroupTulane UniversityNew OrleansUSA

Personalised recommendations