Magic triangular and tetrahedral clusters

Physical Review B - Condensed Matter and Materials Physics

Volumn 56, Issue 19, 1997, Pages 12147-12150

  Reimann, S ^a   Koskinen, M ^b   Hakkinen H ^b  

^a UNIVERSITY OF COPENHAGEN   (Denmark)

^b UNIVERSITY OF JYVÄSKYLÄ   (Finland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000524214     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.56.12147     Document Type: Article

References (36)

1. 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).
2. W. Ekardt, Phys. Rev. B 29, 1558 (1984).
3. A. Hintermann and M. Manninen, Phys. Rev. B 27, 7262 (1983).
4. H. E. Jahn and E. Teller, Proc. R. Soc. London, Ser. A 161, 220 (1937).
5. M. Brack, Rev. Mod. Phys. 65, 677 (1993).
6. T. P. Martin, Phys. Rep. 273, 199 (1996).
7. S. N. Khanna and P. Jena, Chem. Phys. Lett. 218, 383 (1994).
8. S. Bjørnholm, J. Borggreen, O. Echt, K. Hansen, J. Pedersen, and H. D. Rasmussen, Phys. Rev. Lett. 65, 1627 (1990).
9. Z. Phys. D 19, 47 (1991).
10. S. M. Reimann, M. Brack, and K. Hansen, Z. Phys. D 28, 235 (1993).
11. W. A. de Heer, Rev. Mod. Phys. 65, 611 (1993).
12. I. Hamamoto, B. R. Mottelson, H. Xie, and X. Z. Zhang, Z. Phys. D 21, 163 (1991).
13. M. Koskinen, P. O. Lipas, and M. Manninen, Z. Phys. D 35, 285 (1995).
14. W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965).
15. F. E. Borgnis and C. H. Papas, in Encyclopaedia of Physics, edited by S. Flügge (Springer, Berlin, 1958), Vol. XVI, p. 285.
16. S. M. Reimann, M. Koskinen, P. E. Lindelof, and M. Manninen, Z. Phys. D 40, 310 (1997); S. H. Reimann, M. Koskinen, J. Helgesson, P. E. Lindelof, and M. Manninen (unpublished).
17. Note that for the quantization of the equilateral triangle, one uses the fact that one can tesselate the plane with such equilateral triangles. For a regular tetrahedron in 3D, however, this does not work, and its spectrum could not be given in a simple analytic form. To our knowledge, the only case where this is possible is the tetrahedron with corners (Formula presented) and (Formula presented) which is explicitly discussed in H. R. Krishnamurthy, H. S. Mani, and H. C. Verma, J. Phys. A 15, 2131 (1982).
18. B. Montag, Th. Hirschmann, J. Meyer, P.-G. Reinhard, and M. Brack, Phys. Rev. B 52, 4775 (1995).
19. S. Frauendorf and V. Pashkevich, Z. Phys. D 26, 98 (1993).
20. Ann. Phys. (Leipzig) 5, 43 (1996).
21. R. Poteau and F. Spiegelmann, Phys. Rev. B 45, 1878 (1992).
22. J. Chem. Phys. 98, 6540 (1993).
23. R. N. Barnett and U. Landman, Phys. Rev. B 48, 2081 (1993).
24. N. Troullier and J. L. Martins, Phys. Rev. B 43, 1993 (1991). The pseudopotentials were generated for (Formula presented) (nonlocal) and (Formula presented) (local) electrons, with core radii (Formula presented) and (Formula presented) respectively, common for Mg and Na. The single-electron wave functions were expanded on a plane-wave basis with a kinetic energy cutoff of 9.9 Ry.
25. S. H. Vosko, L. Wilks, and M. Nusair, Can. J. Phys. 58, 1200 (1980).
26. S. H. Vosko and L. Wilks, J. Phys. C 15, 2139 (1982).
27. V. Bonačić-Koutecký, P. Fantucci, and J. Koutecký, Chem. Rev. 91, 1035 (1991).
28. H. Häkkinen and M. Manninen, Phys. Rev. Lett. 76, 1599 (1996).
29. U. Röthlisberger and W. Andreoni, J. Chem. Phys. 94, 8129 (1991).
30. S. Pollack, C. Wang, and M. M. Kappes, J. Chem. Phys. 94, 2496 (1991).
31. H. Häkkinen and M. Manninen, Europhys. Lett. 34, 177 (1996).
32. J. Chem. Phys. 105, 10565 (1996).
33. J. Kolehmainen, H. Häkkinen, and M. Manninen, Z. Phys. D 40, 306 (1997).
34. C. Kohl and P.-G. Reinhard, Z. Phys. D 39, 225 (1997).
35. C. Kohl, B. Montag, and P.-G. Reinhard, Z. Phys. D 38, 81 (1996).
36. J. Jacobsen, K. W. Jacobsen, P. Stolze, and J. K. Nørskov, Phys. Rev. Lett. 74, 2295 (1995).