Small Carbon Clusters

Fig. 2.16 Fragmentation energies for small silicon and carbon clusters as functions of cluster size, as calculated by Raghavachari. The dashed curve represents the fragmentation energies as a function of cluster size n for the reaction Si — Si i + Si. Note the most stable clusters are Si10, Si6 and Si4. The solid curve indicates the fragmentation energies of small carbon clusters as a function of cluster size n for the reaction C — + C. Odd number clusters are more...

R. D. Levine Prof. Neumark, your very detailed results on the excess energy dependence of the rate of delayed detachment of the electron from small carbon clusters should help test an ongoing discussion. 

Haufler, R. E. et al. 1991 Carbon arc generation of C60. Mater. Res. Soc. Proc. 206, 627-638. Heath, J. R. 1991 Synthesis of C60 from small carbon clusters a model based on experiment and theory. In Fullerenes synthesis, properties, and chemistry of large carbon clusters (ACS Symp. Ser., no. 481) (ed. G. S. Hammond V. J. Kuck), pp. 1-23. Washington, D.C. American Chemical... 

Carbon. -4.1.1 Small Carbon Clusters. IR data have been reported for a C3 molecule in a para-H2 matrix, with a value of 2035 cm-1 for v3 (12C3).167 Ab initio and DFT calculations have been made of vibrational wavenumbers for di-dodecahedral C5N30.168... 

Orden, A.V. Saykally, R.J. Small carbon clusters, spectroscopy, structure and energetics. Chem. Rev. 1998, 98. 2313-2357. 

We found that major products of Cgo suspended in hexane and methanol under laser ablation are graphite-like carbon. It probably arises from photodecomposition of fullerene network and photochemical and/or thermal isomerization from fullerene structure to graphite-like one. Another formation route of graphite-like carbon is clustering of small carbon clusters. 

M. Doverstal, B. Lindgren, U. Sassenberg, and H. Yu, Reaction of small carbon clusters with hydrogen during laser vaporization of graphite, Z. Phys. D, 1991, 19, 44" 449. 

Figure 20. Snapshots from reactive MD simulations of equilibrium configurations at temperature 3000 K and density (a) p=0.21 g/cm and (b) p=2.11 g/cm. A small carbon cluster can be seen for p= 2.11 g/cm in the top right comer of the figure.

In this section we shall summarize the results of certain systematic studies we have carried out to aid in the assessment of the performance of DFT methods on various chemical problems. First, computed results for geometries, dipole moments, vibrational frequencies and atomization energies of a set of small molecules will be presented and discussed, followed by an investigation of the reaction barriers of certain radical abstractions. The performance in the latter case is not nearly as good as in the former, and one possible means of improvement of the quality of the DFT barriers is examined. Finally, we give some additional examples of problematic cases, from studies on small carbon clusters important to fullerene chemistry, in which DFT methods were found to have difficulties. 

Relative stabilities of small carbon cluster isomers... 

The thermal decomposition of organic compounds can also be employed to generate small carbon clusters or atoms. The borderline with chemical vapor deposition (CVD) as presented in the next section is not really fix. In both cases, the method is based on the thermal decomposition of organic precursors. Processes both with and without catalyst have been reported. Contrary to the chemical vapor deposition, however, the catalyst (if applied) is not coated onto a substrate, but the substance or a precursor is added directly to the starting material ( floating catalyst ). The resulting mixture is then introduced into the reactor either in solid or in liquid state by a gas stream. From this point of view the HiPCo-process could also be considered a pyrolytic preparation of SWNT, but due to its importance it is usually regarded as autonomous method. 

The first MWNTs have been obtained as early as 1976 by iron-catalyzed pyrolysis of benzene. Apart from that, there is a number of methods to produce MWNT, which all of them differ in the way of generating small carbon clusters or atoms from the respective starting materials. They include arc discharge, laser ablation, chemical vapor deposition with and without plasma enhancement or the catalytic decomposition of various precursor compounds. It turned out that MWNTs from low-temperature syntheses bear more defects and, as a whole, are less ordered than those generated at high temperatures. However, these drawbacks can still be compensated by subsequent recuperation of defective samples at elevated temperatures. 

Like in the preparation of single-walled carbon nanotubes, the chemical vapor deposition of MWNT consists in the generation of small carbon clusters or atoms from precursor compounds. The products precipitate in the shape of different carbon materials with the reaction conditions determining the specific stracture... 

Besides small carbon clusters generated in the reaction zone anyway, the presence of hydrogen further gives rise to light hydrocarbons that contribute to the deposition of DWNT as well. Hence, in principle, this is a floating catalyst CVD performed in situ. It has indeed been applied in a multitude of experiments for the deliberate production of double-walled nanotubes. Normally, acetylene is employed as carbon source because apparently it suits best to surround an existing nanotube with a second layer of amorphous carbon (refer to Section 3.3.6). 

The mechanism of nanotube formation in chemical vapor deposition features characteristics rather distinct from those found for the synthesis by arc discharge or laser ablation. Contrary to the latter, a solution of small carbon clusters in and subsequent diffusion through catalyst particles play a minor role in the deposition from the gas phase. The employed hydrocarbons decompose directly on the surface of the catalytic particle. The carbon, therefore, becomes immediately available for nanotube growth. 

Owing to a small number of dangling bonds and a favorable surface-volume ratio, carbon onions possibly represent the most stable form of small carbon clusters under conditions that favor high-energy structures. 

The very early history [22- 26] of carbon clusters starts with a mass-spectrometric observation of clusters up to C15 by Hahn and his co-workers [27] 60 years ago. In the 1950s and 1960s, experiments [28-30] could expand up to C33. At this stage, initial simple computations had also been performed on small carbon clusters by Pitzer and dementi [31,32], Hoffmann [33] and others [34,35]. Moreover, various qualitative estimations for larger carbon cages including Ceo were presented [36-40]. 

Already the MINDO/2 computations [34,202] of small carbon clusters C pointed out a simple, smooth dependency of the relative heats of formation AHf29sln on the number of carbons n. Later on, the curve was extended into the fullerene domain [51,86,203-206]... 

Vibrational studies on carbon clusters are highly important in interstellar and combustion research. An extensive review article on small carbon clusters (C , = 2-10) is available [1509]. Table 2.13 lists the structures and IR (antisym-metric stretching) frequencies observed in the gaseous phase and/or in inert gas matrices. 

TABLE 2.13. Structures and IR Frequencies of Small Carbon Clusters... 

Examples of specialized semiempirical methods include two MNDO variants for small carbon clusters [138] and for fullerenes [139]. Small carbon clusters (C2-C10) show many peculiar features and are difficult to handle by semiempirical or low-level ab initio calculations (e.g., with regard to the relative stabilities of isomers). A reparametrization [138] of the standard MNDO approach [19] (using experimental and high-level ab initio reference data for C3 and C4) leads to a much improved MNDO-... 

Mestres and Scuseria have combined semiempirical tight-binding potentials with a GA to find the global minima of small molecular clusters. Their chromosome is an adjacency matrix. The adjacency matrix element is equal to 1 if atoms i and / are neighbors, and 0 otherwise. A method is described to translate from the adjacency matrix representation to internal coordinates. Obviously, it is also important to restrict the number of Is in the chromosome to avoid making impossible structures. They successfully locate global minima for small carbon clusters. 

Van Orden, A., Saykally, R. Small Carbon Clusters Spectroscopy, Structure, and Energetics, Chem. Rev. 98(1998) 2313-2357. 

The small clusters of carbon, with a few added elements, can resemble any of these forms. Pure carbon clusters, up to ten atoms or so, are either linear or cyclic, most strongly resembling the graphite or polyyne forms. Larger cluster sizes, or impurity atoms, stabilize the diamond form. The graphite and polyyne forms have in common a conjugated tt electron system, so these small carbon clusters and their relatives may be cultivated into wires for nanometer-scale electronics. 

J. R. Heath and Saykally, The Structures and Vibrational Dynamics of Small Carbon Clusters, P. J. Reynolds (ed.), North-Holland, Amsterdam, 1993, pp 7-21. 

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