Magic number species

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). 

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 22. Series of mass spectra showing progression of the etching reaction of aluminum anions with oxygen. Note that magic number clusters corresponding to electron shell closings for 40 and 70 electrons (AI13 and AI23) appear as the terminal product species of reactions with oxygen at flow rates of (a) 0.0, (b) 7.5, and (c) 100.0 standard cubic centimeters per minute (seem). Taken with permission from ref. 92.

As a result of this electron-filling scheme for jellium clusters, the magic numbers for closed shell configurations in a jellium cluster are very different from those in free atoms. The first magic number of chemical significance in a jellium sphere is the 20 valence electron configuration of white phosphorus P4 and other isoelectronic species of the type E4 (E = As, Sb, Bi) and E4" (E = Si, Ge, Sn, Pb), which are shown by the NICS method to be highly aromatic systems [39, 79]. 

The next magic number for jellium clusters is 40. This is a particularly important magic number in cluster chemistry, since numerous 40 valence electron bare clusters with 9 to 11 vertices of the post-transition elements in Groups 13 to 15 are known as isolable species in intermetallics or salts with suitable counterions. Examples of such species include lun, Geg", and Big, all of which have been isolated in intermetallics (for Inn ) or as stable salts with suitable counterions (Geg" and Big ) and characterized by X-ray crystallography. 

Fig. 33. Electrospray ionization mass spectrum of a Starburst PAMAM (generation = 4). Note the last significant peak M = 10632 daltons (degree of polymerization = 93), corresponding to the magic number for ideal structure. The remaining labeled species correspond to M — x(l 14) (defects due to missing monomer units) and the unlabeled species which correspond to M — x(60) (defects due to macrocycle formation)...

Re/ro-Michael reactions produce mutant species at [5154 — n (114)] (e.g., 5040, 4925 and 4812 daltons), whereas macrocycle formation gives mutant products at [5154 — n (60)] (e.g., 5094, 4980 and 4865 daltons). Note the perfect structure at 5154 daltons is the predicted magic number for generation = 3. In some cases a mutant defect (i.e., a retro-Michael reaction site) may be repaired in subsequent iteration sequence to give a regressed branch cell. Many of these errors (mutations) are found to be generation dependent. In any case, these errors may be routinely appraised as a function of generation by mass spectroscopy, electrophoresis and... 

Water clusters containing simple ions are another area of current experimental and theoretical interest. Accordingly, they are also the subject of EA studies. Chaudhury et al. [113] have used EA methods on empirical potentials to obtain optimized structures of halide ions in water clusters, which they then subjected to AMI calculations for simulation of spectra. EA applications to alkali cations in TIP4P water clusters [114,115] have led to explanations of experimental mass-spectroscopic signatures of these systems, in particular the lack of magic numbers for the sodium case and some of the typical magic numbers of the potassium and cesium cases, and the role of dodecahedral clathrate structures in these species. 

The study of bare metal clusters is central to the understanding of the links between solid state chemistry and that of discrete molecular species. Alkali metal clusters have been studied in molecular beams [12, 13], and the theoretical models proposed have attempted to interpret the abundances observed in the mass spectra of these clusters. These spectra show large abundances for specific numbers of metal atoms (N), the so-called magic numbers . Neutral alkali metal mass spectra show peaks at N = 2, 8, 20,40, 58, whereas cationic species show large abundances at N = 19, 21, 35, 41. The theoretical study of alkali metal clusters is simplified by the presence of only 1 valence electron per atom. 

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... 

The addition of the next four He atoms therefore occurs with very comparable binding energies (between 22 and 30 meV) that are already one order of magnitude smaller than in the case of the 1st shell. Furthermore, we see that beyond the n = 6 structure of label (2,4,0) we observe a marked reduction of binding energy the presence of a magic number for the species suggested by the experiments [8,9] is... 

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