Fullerenes Kekule structure

Figure 1.17 Schematic representation of [60-/h]fullerene with the lengths of the two different bonds in the moiecule and Schlegel diagram of the lowest energy Kekul structure.

In principle, 23 regioisomers of the dihydro fullerene CggH2 are possible. The formal addition of an A-B molecule, for example H2, to the externally Cgg sphere could proceed in three ways [30] (1) Addition to one double bond of the low-energy Kekule structure (Figure 5.3), which would leave all the other bonds unchanged ([6,6] double bonds and [5,6] single bonds) (2) conjugate addition of two atoms, which requires... 

Comparable alternations between the [6,6]- and [5,6]- bond lengths are observed in many fullerene adducts and higher fullerenes. Moreover, from the evaluation of many exohedral transformation of fullerenes, in particular Cjq, an important principle of fullerene chemistry can be deduced, namely minimization of[5,6]-douhle bonds in the lowest energy Kekule structure. Minimization of [5,6]-double bonds is... 

It is therefore useful to look at a l,2-dihydro[60]fullerene as a stereoelectronically slightly perturbed Cjq. Introduction of a double bond into a five-membered ring costs about S.Skcalmol (Figure 14.10) [111]. In a 1,4-adduct (l,4-dihydro[60]-fullerene) one, and in a 1,6-adduct (l,16-dihydro[60]fullerene or 1,6- dihydro[60]-fuUerene) two, double bonds in five-membered rings are required for the corresponding lowest-energy Kekule structure. This VB consideration is also confirmed experimentally and by computations (Figure 14.8) [36],... 

For polycyclic Jt-systems, there is not always a correlation between aromatic character and the total number of tt-electrons, as is the case for monocyclic annulenes91. In fullerenes, which are not only polycyclic but also three-dimensional, such a correlation is even less apparent. These carbon alio tropes embody completely conjugated spheroidal it-systems, so die carbon skeletons are boundary-less, and large numbers of Kekule structures can be drawn92. The aromaticity of fullerenes has been investigated theoretically and substantiated experimentally by using NMR studies93. 

A possibility of encapsulation of small fullerenes inside carbon nanotubes (CNTs) was considered recently [1], It was shown that the armchair (8,8) nanotube is the smallest CNT which can encapsulate the fullerene C20 [1]. We use the semiempirical PM3 molecular orbital method with periodic boundary conditions along the nanotube axis [2] to study the structure and properties of the system C2o (8,8) CNT. The PM3 method [3] was used previously to study the fullerene C20 [4] and to calculate the Kekule structure of the ground state of the (5,5) CNT [5]. To explore the relative motion of C20 inside the (8,8) CNT we additionally implemented molecular mechanics (MM+) calculations [6]. 

In order to minimize effects of nanotube edges in our molecular mechanics calculations we have chosen five unit cells (480 carbon atoms total) of (8,8) CNT. The calculated dependence of the interaction energy between the fullerene C20 and the (8,8) CNT on the fullerene displacement along the CNT axis is shown in Fig. 3. The calculated period of this dependence is a half of the translational period of the Kekule structure (Fig. 1). The small difference between two barriers in Fig. 3 is due to the edge effects. Correspondingly, the frequency of small oscillation of fullerene C20 along the CNT axis near the minimum of potential energy is v 60 GHz. 

Cash, G.G. (1998). A Simple Means of Computing the Kekule Structure Count for Toroidal Polyhex Fullerenes. J.Chem.lnf.Comput.Sci., 38, 58-61. 

Torrens also listed the numbers of Kekule structures of some larger IPR fullerenes with icosahedral symmetry, e.g., Cgo 140,625 Cigo ... 

The semiempirical method of molecular orbitals modified for onedimensional periodic structures [4] with PM3 parametrization of Hamiltonian [5] was used to calculate the formation enthalpy and geometry of (5,5) nanotube. The method has been applied previously to calculate the Kekule structure of the ground state of (5,5) nanotube [6]. The adequacy of the PM3 parametrization of Hamiltonian has been demonstrated [7] by calculation of bond lengths of C60 fullerene with Ih symmetry. The calculated bond lengths coincide with the experimental ones within the accuracy of IO-4 nm. 

In a treatise entitled "New Dimensions in Polynudear Aromatic Compounds", Herndon (1988) has described a number of polycyclic conjugated compounds, induding corannulene, a cydacene and CgQ buckminsterfullerene (Osawa 1970 Kroto et al. 1985 Kratschmer et al. 1990) see Fig. 10. The reader understands presumably very well that a full survey of the literature on this interesting molecule (and other fullerenes) is too voluminous (counting thousands of references) to be induded here. In the following small extract the number of Kekule structures K = 12500) for C q is reported (not necessarily as an original finding). 

A count of Kekule structures for all 1812 distinct fullerene isomers of Cjo shows that 20 isomers surpass the count of 12500 for icosahedral C q, and demonstrates the lack of correlation between molecular-orbital indices of stability and raw Kekule counts for fullerenes. Analysis of Kekule structures in terms of benzenoid, cyclopentenoid and cyclopentadienoid rings reveals the source of the stability of icosahedral C q in a localised model to be the fact that uniquely amongst the 1812 structural isomers it has a Fries Kekule structure where all hexagons contain three double bonds and all pentagons none. 

The discovery of fullerenes offered a new challenge in the field of the study of the aromaticity of Ti-conjugated systems. These carbon allotropes embody completely conjugated spheroidal 7r-systems, so the carbon skeletons are boundaryless and thus large numbers of Kekule structures can be drawn. 

The aromaticity of fullerenes has been investigated theoretically and substantiated experimentally by NMR [154]. The best experimental method for studying the aromaticity of fullerenes was devised by Saunders and Cross, who encapsulated helium atoms inside fullerenes and measured their NMR spectra [155]. He NMR measurements show that C o exhibits the least aromatic character whereas C70 has the highest, and that the aromaticity of higher fullerenes lies between these two extremes. This is in contradiction to the initial suggestion in 1985 that C o is covered by a sea of n electrons that make it aromatic [14a, 156], and to the assumption of high aromaticity due to the large number of possible Kekule structures [157]. The reduction of fullerenes is not expected to modify their shape or symme-... 

Characteristic polynomial and related, refs 950— 957 graph spectra and related, refs 958—960 automorphism, refs 961—966 enumerations of Kekule structures, refs 967, 968 enumeration of walks and related, ref 969 more on Kekule structures, refs 970— 977 Pauling bond orders, refs 978—980 more on Clar structures, refs 981—990 aromaticity, refs 991—994 and fullerenes, refs 995, 996. 

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