Carbon clusters, magic numbers

Mass spectra from a carbon cluster ion source show strong magic numbers at C, and C d[136]. This led to the... 

A striking observation that lacks a satisfactory explanation is the existence of magic numbers, i.e. the fact that in a distribution of clusters some species with a certain number of carbon atoms are much more abundant than others. The exact clustering mechanisms are not completely understood, and, as noted by Rohifing et al.(IO), the origin of the observed distribution of clusters may depend upon instrumental factors. Accounting for this fact, however, there still seems to be a preference for clusters with certain numbers of atoms which cannot be explained solely as due to the experimental conditions. 

FIGURE 1 Laser-vaporization supersonic cluster-beam time-of-flight mass spectrum of various lanthanum-carbon clusters. LaCeo is seen as an enhanced (magic number) peak. 

It had been expected, before the first macroscopic production and extraction of La Cs2 (Chai et al., 1991), that metallofullerenes based on the Cgo cage would be the most abundant metallofullerenes that were prepared in macroscopic amoimts, as was the case in empty fullerenes. This is simply because that Ceo is the most abundant fullerene which can be easily produced by either the arc-discharge or the laser furnace method (cf. Section 2.1). In fact, an earlier gas phase experiment on the production of carbon clusters containing La via the laser-vaporization cluster-beam technique (Heath et al., 1985) indicated that La Cgo is a prominent "magic number" species among various La C (44 < n < 80) clusters (Figure 1). 

Figure 2 Time-of-flight mass spectrum of carbon clusters produced by laser vaporization of graphite (September 4, 1985) imder conditions which first exhibited the dominance of the Cgo cluster and led to the recognition that 60 might be a magic number. (Reprinted with permission from Ref 2a. 1991 American Chemical Society)...

The fullerenes were first discovered by laser ablation cluster ion formation in a mass spectrometer.89 Soon after the identification of C60 as a magic number cluster, [LaC60]+ was also identified.90 Later, macroscopic quantities of fullerenes were produced by the carbon arc method91 soon followed by the macroscopic production of the lanthanum endohedral fullerenes.92 Fullerene chemistry has developed rapidly since the preparation of macroscopic quantities of these compounds. The development of the metallofullerenes has been hampered by the low yield... 

The case of carbon clusters is quite different. A model suitable for metals will not work. Instead, a definite structure must exist using ordinary covalent bonds. For A < 30 the clusters exist in linear, cyclic and bicyclic forms. For A > 30 the structures are three-dimensional (3D) and evolve into the cage or soccer-ball structure characterisic of Ceo and C70. For A < 30, the magic numbers are given by A = 4 -t- 2, where n is an integer. This suggests an aromatic type of stabilization. 

A more detailed analysis of these fluctuations shows, however, that there often exist some periodicities in this behaviour which in some cases can be understood as shell closings, geometric [63] or electronic [64], with the appearance of so-called magic numbers . Studies of clusters composed of a few hundred or up to thousands of atoms [65,66] also showed that the periodicity could be extended with the existence of a new type of shells known as supershells representing a transition from pure quantum phenomena towards the limit of large quantum numbers, where a correspondence should exist between classical and quantum motion [71,72]. We will also see how there will be connections to powder technology [50,57,58] and to the mesoscopic world of nanotechnology with a two-dimensioned electron gas [73-75]. In addition to these clusters characterized by shell structure also very unique species of carbon have been... 

Magic Number Carbon Clusters Ionization Potentials and Selective Reactivity. D. L. Lichtenberger, K. W. Nebesny, C. D. Ray, D. R. Huffman, and L. D. Lamb, Chem. Phys. Lett., 176, 203 (1991). Valence and Core Photoelectron Spectroscopy of C o, Buckrainsterfullerene. 

Recent theoretical calculations on hypothetical Si fullerene-like clusters with N > 28 showed that they would be unstable. However, the addition of Si atoms inside the cluster (stuffed fullerenes) make them more stable, giving rise to some magic numbers of N, such as 33, 36, 39, 45, 50 [68, 69]. According to Li et al. [70], the most probable structure of Siso would be a distorted truncated icosahedron with Th symmetry instead of L. On the other hand, the existence of clathrate forms of carbon seems possible [71-73]. 

Novoselov, K. S.,Geim, A. K., Morozov, S.V., Jiang, D., Zhang, Y., Dubonos, S. V., Grigorieva, I. V., Firsov, A. A. (2004). Electric field effect in atomically thin carbon films. Science, 306, 666. Noya, E. G., Doye, J. P. K. (2006), Structural transitions in the 309-atom magic number Lennard-Jones cluster. Journal of Physical Chemistry, 124, 104503. 

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