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Hard Sphere Packing Model 
Structural transitions in metaldoped noble gas clusters Using timeofflight (TOF) mass spectrometry, the stability and the structure of metal iondoped noble gas clusters M^{+}X_{n} (M=metal atom and X=noble gas atom) is studied. The observed change in magic number series is explained by a simple hard sphere packing model, showing that the observed new magic numbers are consistent with a cluster growth sequence based on a capped square antiprism (CSA) 11atomic cluster. Additionally, molecular dynamics simulations using pairwise additive LennardJones potentials are performed. The results of these calculations verify the structural results from the hard sphere model and furthermore explain the structural transition as a function of cluster size.

Typical TOF spectra of metal iondoped noble gas clusters of the type M^{+}X_{n}. The most stable clusters are indicated by the total number of atoms N=n+1. 
Highsymmetry Polyhedra formed from two twisted polygons each of them shaped from n/2 atoms

R^{*}=R_{M}/R_{X}=

0.225

Tetrahedron n=4

0.414

Octahedron antiprism n=8

n+1 = 
5 
7 
0.645

Square antiprism n=8 Capped Square antiprism n=8+2 
11 
Pentagonal antiprism n=10 Icosahedron (closed) n=10+2 
0.902

13 
Hexagonal antiprism n=12 Capped Hexagonal antiprism n=12+2 
1.17 
15 
Schlegel Diagrams explaining cluster growth sequences and magic numbers

ICOSAHEDRON

CSA
