Physics of Metal Clusters

Physics of Metal Clusters

Brief introduction

Atomic clusters, covering the size range from a few to several hundred thousand atoms, represent an intermediate stage in the transition from small molecules to solids (for an overview see [1]). For the theoretical description of clusters a variety of concepts, reflecting the interdisciplinary nature of this research area, has been introduced. In microscopic approaches to small clusters the atoms are usually decomposed into ionic cores, represented by suitable pseudo-potentials, and the chemically active valence electrons. The structure of the cluster is determined by searching for the ionic configuration, which minimizes the total energy. The absolute energy minimum corresponds to the ground state configuration, local minima represent isomers of the cluster. The search for energy minima is combined with the solution of the electronic many-particle problem via density functional methods in a particularly efficient way by the Car-Parrinello technique [2,3] (also called quantum molecular dynamics). Based on the structures obtained in this way, the dynamical properties of clusters can be investigated by means of linear response and/or time-dependent density functional theory. In our group the structure of small phosphorus clusters and the fusion of two Na_8 clusters [4] have been studied on the basis of this microscopic approach (see also [5]).

With increasing cluster size, however, the Car-Parrinello scheme sooner or later becomes intractable with the available computational resources, the critical size depending on the system under consideration and the computer technology at hand. In order to calculate properties of larger clusters additional approximations are necessary. A prominent approach to medium size and large metal clusters is the so-called jellium model . Here the ionic structure is smeared out to a uniform positive background of bulk density, which binds a delocalized valence electron cloud. The jellium model thus emphasizes collective electronic effects over the detailed ionic structure, which is only reflected by the shape of the jellium background. This approach is thus particularly suitable for systems with rather delocalized valence electrons. A large variety of properties of metal clusters, such as static polarizabilities, collective electronic excitations, ionization potentials as well as the so-called 'magic numbers' [6-10], can be explained in terms of the jellium model.

Our research aims at a deeper understanding of the role of collective electronic effects in the fission and fusion of metal clusters [11,12], their magnetic [13] and optical [14] properties as well as cluster-cluster collisions [15] (utilizing density functional methods). In addition, a liquid drop model has been developed for the description of very large metal clusters [16,17].

Topics which have been investigated are:


  1. H. Haberland (ed.), Clusters of Atoms and Molecules, Vol. I + II, Springer Series of Chemical Physics, Vol. 52 and 56 (1994).
  2. R. Car and M. Parrinello, Phys. Rev. Lett. 55, 2471 (1985).
  3. M. C. Payne, M. P. Teter, D. C. Allan, T. A. Arias, and J. D. Joannopoulos, Rev. Mod. Phys. 64, 1045 (1992).
  4. L. Jung, Diploma thesis, Univ. of Frankfurt (1995).
  5. F. S. Zhang, E. Suraud, F. Spiegelmann, V. Fraysse, F. Chatelin, and R. Glowinski, Z. Phys. D 35, 131 (1995).
  6. 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).
  7. W. Ekardt, Phys. Rev. B 29, 1558 (1984).
  8. D. E. Beck, Solid State Commun. 49, 381 (1984).
  9. M. Y. Chou, A. Cleland, and M. L. Cohen, Solid State Commun. 52, 645 (1984).
  10. W. A. de Heer, W. D. Knight, M. Y. Chou, and M. L. Cohen, Solid State Phys. 40, 93 (1987).
  11. E. Engel, U. R. Schmitt, H.-J. Lüdde, A. Toepfer, E. Wüst, R. M. Dreizler, O. Knospe, R. Schmidt, and P. Chattopadhyay, Phys. Rev. B 48, 1862 (1993).
  12. U. R. Schmitt, E. Engel, and R. M. Dreizler, Phys. Rev. B 50, 14674 (1994).
  13. U. R. Schmitt, PhD thesis, University of Frankfurt (1995).
  14. Th. Maier, PhD thesis, University of Frankfurt (1997).
  15. O. Knospe, R. Schmidt, E. Engel, U. R. Schmitt, R. M. Dreizler, and H. O. Lutz, Phys. Lett. A 183, 332 (1993).
  16. J. P. Perdew, Y. Wang, and E. Engel, Phys. Rev. Lett. 66, 508 (1991).
  17. E. Engel and J. P. Perdew, Phys. Rev. B 43, 1331 (1991).

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Last modified: Mar 30, 2004