Symmetry in clusters and molecules is an interesting field.
Al, Ti, Fe, Zr, Nb, Ta, Ga metal clusters have been observed in experiments. The magic these clusters are cuboctahedron or Icosahedron made of exactly 13 atoms. Pretty interesting.
Schriver et al, PRL 4, 2539 (1990)
Douglass et al, PRB 47, 12874, (1993)
Sakurai et al, JCP 111, 235, (1999)
Thomas et al, JCP, 114, 5514 (2001)
Also
Al13: icosahedron, decahedron
Nb13: relaxed icasohedron
Ni13: icasohedron
Rh13: icosahedron
Pd13: icosahderon
Pt13: cuboctahedron
Au13: cuboctahedron
Sn$_{12}^{2-}$: icosahedral (stannaspherene)
Pb$_{12}^{2-}$: nearly-spherical
(and many more).
The references are
Rao et al, PRB, 62, 4666 (2000)
Reddy et al, PRB, 59, 5214 (1999)
Kumar et al, PRB, 65, 125403 (2002)
Rothlisberger et al, JCP, 96, 1248 (1992)
Calleja et al, PRB, 60, 2020 (1990)
Zope et al, PRA, 64, 053202 (2001)
Reuse et al, CPL, 234, 77 (1995)
Moseler et al, PRL, 86, 2545 (2001)
Watari et al, PRB, 58, 1665 (1998)
Haberlen et al, JCP, 106 5189 (1997)
Cui et al, JPC A 110, 10169 (2006)
Cui et al, JACS 128, 8390 (2006)
Some atoms form Planar 13-atom magic clusters.
For example, Au$_{13}^{-}$, B$_{13}^{+}$
Hakkinen et al, PRL, 89, 033401 (2002)
Aihara, J. J. Phys. Chem. A 105, 5486 (2001)
Why these atoms form 13 atoms clusters?
Why not other atoms?
What causes these symmetry to be highly stable?
Click here to see the list of problems.
