Carbon-atom clusters

Another set of carbon allotropes, the fullerenes, consist of carbon atom clusters. These molecules are unusually stable and are an exciting area of research for chemists because of their potential use as superconductors. 

Fullerene consists of molecular balls made of 60 (termed C60) or more carbon atoms clusters linked together [74-76]. Each of the carbon atoms has two single bonds and one double bond that attach to other carbon atoms. This causes C60 to act more like a supeialkene and superaromatic [74-76]. 

Nanotube (Section 11 8) A form of elemental carbon com posed of a cyhndncal cluster of carbon atoms Neopentane (Section 2 10) The common name for 2 2 dimethylpropane (CH3)4C... 

Figure 2 illustrates a proposed growth process[3] of a polyhedral nanoparticle, along with a nanotube. First, carbon neutrals (C and C2) and ions (C )[16] deposit, and then coagulate with each other to form small clusters on the surface of the cathode. Through an accretion of carbon atoms and coalescence between clusters, clusters grow up to particles with the size fi-... 

In 1985 Car and Parrinello invented a method [111-113] in which molecular dynamics (MD) methods are combined with first-principles computations such that the interatomic forces due to the electronic degrees of freedom are computed by density functional theory [114-116] and the statistical properties by the MD method. This method and related ab initio simulations have been successfully applied to carbon [117], silicon [118-120], copper [121], surface reconstruction [122-128], atomic clusters [129-133], molecular crystals [134], the epitaxial growth of metals [135-140], and many other systems for a review see Ref. 113. 

Nanotube (Section 11.8) A form of elemental carbon composed of a cylindrical cluster of carbon atoms. 

Figure 24.9 Cluster carbonyls of rhenium containing an encapsulated carbon atom, (a) Octahedral [HjReeC-(C0)i8] . (b) Monocapped octahedral [Re7C(CO)2i] . (c) tran -bicapped octahedral [RegC-(CO)24] . (d) and (e) isomers of [Re7HC(CO)2i] differing in the position of their /r-H atom.

Large clusters of carbon atoms have been studied with ab initio calculations using basis sets of double-C quality. Planar, single-sheet graphite fragments with 6 - 54 atoms were investigated, as well as the spherical "Buckminsterfullerene ... 

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. 

Apparently, the cohesive energy of these clusters shows a very slow convergence with the size of the molecule. This should not be surprising, since the number of unsaturated valences "dangling bonds" per carbon atom is one in 1,1/2 in 2 and 1/3 in 3. 

Assuming an approximately constant cohesive energy per C-C bond, that trend is understandable. With clusters on the above general type, the number of carbon atoms is 6N, the number of dangling bonds is 6N, and the number of C-C bonds is 9N -3N. The energy per bond shows a smoother trend, the numbers being 71.0, 77.6 and 79.9 kcal/mol, respectively. Alternatively, the energies can be fitted to a two-parameter expression of the form... 

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