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Small can be different

  • R. N. Barnett
  • C. Yannouleas
  • Uzi Landman
Article

Abstract

Theoretical investigations of size evolutionary patterns for multiply charged anionic metal clusters and solvation of sodium in water clusters are discussed. For Na N Z- clusters, energetic stability and electron decay channels are determined. Formation of a “surface Rydberg-like state” in Na(H2O) N , correlating with calculated and measured ionization potentials, is analyzed.

PACS

36.40.+d 31.20.Sy 32.80.Dz 71.10.+x 

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References

  1. [1]
    See articles in (a)Elemental and Molecular Clusters, edited by G. Benedek and M. Pacchioni (Springer, Berlin, 1988); (b)Physics and Chemistry of Small Clusters, edited by P. Jena, S.N. Khanna, and B.K. Rao (Plenum, New York, 1987); (c)Physics and Chemistry of Finite Systems: From Clusters to Crystals, edited by P. Jena, S.N. Khanna, and B.K. Rao (Kluwer, Dordrecht, 1992).Google Scholar
  2. [2]
    H.-P. Kaukonen, U. Landman, and C.L. Cleveland, J. Chem. Phys.95, 4997 (1991).Google Scholar
  3. [3]
    See articles inNuclear Physics Concepts in Atomic Cluster Physics, edited by R. Schmidtet al. (Springer, Berlin, 1992).Google Scholar
  4. [4]
    C. L. Cleveland and U. Landman, Science257, 355 (1992).Google Scholar
  5. [5]
    C. Yannouleas and U. Landman, submitted to Phys. Rev. Lett. (1992).Google Scholar
  6. [6]
    R.N. Barnett and U. Landman, submitted to Phys. Rev. Lett. (1992).Google Scholar
  7. [7]
    C. Coulomb,Mémoires de l' Académie, (1786) p. 67ff;ibid. (1787) p. 452; M. Faraday,Experimental research in electricity, (1839) (Dover, New York, 1965), Vol. I, p. 360ff.Google Scholar
  8. [8]
    W. A. de Heer, W. D. Knight, M. Y. Chou, and M. L. Cohen, Solid State Phys.40, 93 (1987).Google Scholar
  9. [9]
    Fifth International Symposium on Small Particles and Inorganic Clusters, Konstanz, 1990, Z. Phys. D19 (1991);ibid. 20 (1991).Google Scholar
  10. [10]
    For a study of highly charged cationic clusters, see T.P. Martinet al. Chem. Phys. Lett.196, 113 (1992), and references therein.Google Scholar
  11. [11]
    We are not aware of any studies ofmultiply negatively charged metal clusters. For a recent review of singly charged anionic metal clusters, see J. G. Eatonet al. inLecture Notes in Physics 404 (Springer, Berlin, 1992) p. 291.Google Scholar
  12. [12]
    W. Ekardt, Phys. Rev. B29, 1558 (1984).Google Scholar
  13. [13]
    U. Röthlisberger and W. Andreoni, J. Chem. Phys.94, 8129 (1991).Google Scholar
  14. [14]
    R. N. Barnett, U. Landman, and G. Rajagopal, Phys. Rev. Lett.67, 3058 (1991).Google Scholar
  15. [15]
    El. Serra, F. Garcías, M. Barranco, J. Navarro, L. C. Balbás, and A. Mañanes, Phys. Rev. B39, 8247 (1989).Google Scholar
  16. [16]
    M. Brack, Phys. Rev. B39, 3533 (1989).Google Scholar
  17. [17]
    C. Yannouleas and R. A. Broglia, Phys. Rev. A44, 5793 (1991); C. Yannouleas, Chem. Phys. Lett.193, 587 (1992).Google Scholar
  18. [18]
    Å. Bohr. and B. R. Mottelson,Nuclear Structure, (Benjamin, Reading, Massachusetts, 1975), Vol. II.Google Scholar
  19. [19]
    V. M. Strutinsky, Nucl. Phys.A95, 420 (1967);A122, 1 (1968).Google Scholar
  20. [20]
    Ph. J. Siemens and A. S. Jensen,Elements of nuclei, (Addison-Wesley, New York, 1987).Google Scholar
  21. [21]
    J. Harris, Phys. Rev. B31, 1770 (1985).Google Scholar
  22. [22]
    L. C. Balbás, A. Rubio, and J. A. Alonso, Chemical Phys.120, 239 (1988).Google Scholar
  23. [23]
    M. Y. Chou, A. Cleland, and M. L. Cohen, Solid State Commun.52, 645 (1984).Google Scholar
  24. [24]
    D. M. Wood, Phys. Rev. Lett.46, 749 (1981).Google Scholar
  25. [25]
    M. P. J. van Staveren, H. B. Brom, L. J. de Jongh, and Y. Ishii, Phys. Rev. B35, 7749 (1987).Google Scholar
  26. [26]
    J. P. Perdew and Y. Wang, Phys. Rev. B38, 12 228 (1988).Google Scholar
  27. [27]
    J. P. Perdew and A. Zunger, Phys. Rev. B23, 5048 (1981).Google Scholar
  28. [28]
    We emphasize that while the effective potentials are significantly different when SIC is used, other quantities, such as the total energy, IP's, and EA's are only slightly altered by SIC as shown in Ref. [27], and by our own calculations.Google Scholar
  29. [29]
    S. Hofmann,Proton radioactivity, eds. D.N. Poenaru and M.S. Ivascu (CRC Press, Boca Raton, Florida, 1989), Vol. II, p. 25.Google Scholar
  30. [30]
    See J. V. Coe et al., J. Chem. Phys.92, 3980 (1990), and references therein.Google Scholar
  31. [31]
    See reviews, and references therein, by (a) U. Landman et al., inRadiation Research, edited by W. C. Dewey et al. (Academic Press, San Diego, 1992), Vol. II, p. 43;Google Scholar
  32. [31] (b)
    R. N. Barnett, et al., Isr. J. Chem.30, 85 (1990);Google Scholar
  33. [31] (d)
    H.-P. Kaukonen, R. N. Barnett and U. Landman, J. Chem. Phys.97, 1365 (1992).Google Scholar
  34. [32] (a)
    C. P. Schulz et al., Z. Phys. D10, 279 (1988);Google Scholar
  35. [32] (b)
    I. V. Hertel et al., Phys. Rev. Lett.67, 1767 (1991).Google Scholar
  36. [33]
    K. Fuke et al., inPhysics and Chemistry of Finite Systems, Vol. II, eds. P. Jena, S. N. Khana and B. K. Rao, (Kluwer, Dordrecht, 1992), p. 925.Google Scholar
  37. [34]
    For earlier studies of Na(H2O)N, 1≤N≤4, see: S. Dhar and N. R. Kestner, Radiat. Phys. Chem.32, 355 (1988), and references therein.Google Scholar
  38. [35]
    N. Troullier and J. L. Martins, Phys. Rev. B43, 1993 (1991).Google Scholar
  39. [36]
    R. N. Barnett and U. Landman (to be published); For an earlier account of the method, see Ref. [14].Google Scholar
  40. [37]
    D. M. Ceperley and B. J. Alder, Phys. Rev. Lett.45, 566 (1980). We use the parametrization given by S. H. Vosko, L. Wilks and M. Nusair, Can. J. Phys.58, 1200 (1980).Google Scholar
  41. [38]
    A. D. Becke, Phys. Rev. A38, 3098 (1988); J. Chem. Phys.96, 2155 (1992).Google Scholar
  42. [39]
    J. P. Perdew, Phys. Rev. B33, 8822 (1986).Google Scholar
  43. [40]
    L. Fan and T. Ziegler, J. Chem. Phys.94, 6057 (1991); G. Ortiz and P. Ballone, Phys. Rev. B43, 6376 (1991).Google Scholar
  44. [41]
    In addition to the optimized structures of the neutral and ionized Na(H2O)N clusters other isomeric structures are possible. From our results, and comparisons to experimental data, we may conclude that our optimized structures are among the lowest energy ones. Structures forN=1 and 2 are evident from Fig. 4. ForN=3 and 4, results (shown in Fig. 4) correspond to a trigonal pyramid (the Na at the apex above the oxygen plane with the H2O molecules hydrogen bonded), and a tetrahedral structure around the sodium, respectively. ForN=5 the lowest energy structure is based on a tetrahedral arranment and an H2O molecule outside it. ForN>3 other, higher-energy, structures were found: ForN=3 a planar structure of the ionized cluster (with the 3 oxygens and sodium at the corners of an approximate rhombus) is degenerate in energy with the trigonal pyramidal one, and for the neutral this structure is slightly higher in energy (by 0.05 eV) and its IP=3.75 eV; forN=4 a square-based pyramidal structure (with the oxygens forming the base, and the H2O molecules hydrogen bonded) of the ionized and neutral clusters is higher in energy (by 0.34 eV and 0.1 respectively) than the tetrahedral ones, and its IP=3.59 eV; ForN=5, a pentagonal pyramidal structure (with the oxygens at the base) is higher in energy than the optimized one by 0.28 eV for the ionized cluster and 0.04 eV for the neutral one, and its IP=3.37 eV. For Na(H2O)6 results for three structures are shown. The first two [denoted as 6(4+2) and 6] which for the neutral cluster have the same energy, but the first is more stable for the ionized one (by 0.18 eV), correspond to 4 and 6 molecules in the first hydration shell, respectively. The structure marked 6b, which is the highest in energy, is like 6(4+2) but with the two H2O molecules outside the first shell hydrogen-bonded to each other. Structures such as 6b, which possesses a dipole moment associated with the two outer molecules resulting in enhanced partial localization of the electron, may be involved in the eventual formation of a separated ion-solvated electron pair.Google Scholar
  45. [42]
    R. N. Barnett et al., J. Chem. Phys.88, 6670 (1988); See also G. J. Martyna and M. L. Klein, J. Chem. Phys.96, 7662 (1992).Google Scholar
  46. [43]
    H. Haberland, H. G. Schindler, and D. R. Worsnop, Ber. Bunsenges. Phys. Chem.88, 270 (1984).Google Scholar
  47. [44]
    R. N. Barnett et al., J. Chem. Phys.88, 4421 (1988); R. N. Barnett, U. Landman and J. Jortner, Chem. Phys. Lett.145, 382 (1988).Google Scholar

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • R. N. Barnett
    • 1
  • C. Yannouleas
    • 1
  • Uzi Landman
    • 1
  1. 1.School of PhysicsGeorgia Institute of TechnologyAtlanta

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