Fullerenes closed

Fullerene closed hollow-cage molecule consisting solely ... 

An interesting correlation is found between the kinetic stabilities of the fullerenes ] to C70. as determined by simple Hiickel theory HOMO-LUMO energy separations, and the intensities of photoionisation signals from carbon clusters produced by laser vaporisation of graphite. This correlation provides further circumstantial evidence that the observed C34 to C70 clusters are indeed fullerenes, closed carbon cages containing only five- and six-membered rings. 

The discovery of perfect geodesic dome closed structures of carbon, such as C o has led to numerous studies of so-called Buckminster fullerene. Dislocations are important features of the structures of nested fullerenes also called onion skin, multilayered or Russian doll fullerenes. A recent theoretical study [118] shows that these defects serve to relieve large inherent strains in thick-walled nested fullerenes such that they can show faceted shapes. 

This behaviour also stands for functionalized [60]fullerene derivatives, with, however, a few striking differences. The most obvious parameter is the negative shift of the reduction potentials, which typically amounts to -100 mV. Secondly, the separation of the corresponding reduction potentials is clearly different. Wlrile the first two reduction steps follow closely the trend noted for pristine [60]fullerene, the remaining four steps display an enlianced separation. This has, again, a good resemblance to the ITOMO-LUMO calculations, namely, a cancellation of the degeneration for functionalized [60]fullerenes [31, 116, 117]. 

I he results of their calculations were summarised in two rules. The first rule states that at least one isomer C with a properly closed p shell (i.e. bonding HOMO, antibonding I. U.MO) exists for all n = 60 - - 6k (k = 0,2,3,..., but not 1). Thus Qg, C72, Cyg, etc., are in lhi-< group. The second rule is for carbon cylinders and states that a closed-shell structure is lound for n = 2p(7 - - 3fc) (for all k). C70 is the parent of this family. The calculations Were extended to cover different types of structure and fullerenes doped with metals. 

Fullerenes are a range of stable closed-shell carbon molecules and their derivatives, of which Qo is the archetype. The next highest stable member of the series is C70 which is found in small quantities with in arc electrode soot. C,o may be regarded as a Qo molecule with an extra belt of hexagons inserted at the... 

In addition to diamond and amorphous films, nanostructural forms of carbon may also be formed from the vapour phase. Here, stabilisation is achieved by the formation of closed shell structures that obviate the need for surface heteroatoms to stabilise danghng bonds, as is the case for bulk crystals of diamond and graphite. The now-classical example of closed-shell stabilisation of carbon nanostructures is the formation of C o molecules and other Fullerenes by electric arc evaporation of graphite [38] (Section 2.4). 

The most extensive calculations of the electronic structure of fullerenes so far have been done for Ceo- Representative results for the energy levels of the free Ceo molecule are shown in Fig. 5(a) [60]. Because of the molecular nature of solid C o, the electronic structure for the solid phase is expected to be closely related to that of the free molecule [61]. An LDA calculation for the crystalline phase is shown in Fig. 5(b) for the energy bands derived from the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) for Cgo, and the band gap between the LUMO and HOMO-derived energy bands is shown on the figure. The LDA calculations are one-electron treatments which tend to underestimate the actual bandgap. Nevertheless, such calculations are widely used in the fullerene literature to provide physical insights about many of the physical properties. 

For C70, molecular orbital calculations [60] reveal a large number of closely-spaced orbitals both above and below the HOMO-LUMO gap [60]. The large number of orbitals makes it difficult to assign particular groups of transitions to structure observed in the solution spectra of C70. UV-visible solution spectra for higher fullerenes (C n = 76,78,82,84,90,96) have also been reported [37, 39, 72]. 

As distinct from ihe ideal connection of Dunlap, we now describe the series of nanotubule knees (9 ,0)-(5m,5 ), with n an integer. We call this series the perfectly graphitizahle carbon nanotuhules because the difference of diameter between the two connected segments of each knee is constant for all knees of the series (Fig. 4). The two straight tubules connected to form the = 1 knee of that series are directly related to Cfio, the most perfect fullerene[15], as shown by the fact that the (9,0) tubule can be closed by 1/2 Qo cut at the equatorial plane perpendicular to its threefold rotation symmetry axis, while the (5,5) tubule can be closed by 1/2 Qo cut at the equatorial plane perpendicular to its fivefold rotation symmetry axis [Fig. 5(a)]. 

As a general rule, any knee of the series (9 ,0)-(5n,5 ) can be closed by 1/2 of the fullerene C((,o.,P>- Note that, for this multilayer series, there is a single axis going through the middle of the heptagons and pentagons of any arbitrary number of... 

The multi-shell fullerenes constitute the transition from fullerenes to macroscopic graphite. They present both the closed graphitic surface of fullerenes and the stacked layers interacting by van der Waals forces, as in graphite. 

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