Carbon clusters geometrical structure

A conglomerate of three hexagons contains one central atom and 12 atoms around it. A conglomerate of seven hexahedrons comprises 12 external and 12 internal (common) atoms. In these two cases geometric centers of hybridized molecular orbitals of each hexahedron are equidistant from such nearest centers of a conglomerate. This, apparently, explains the experimental fact that polyhedrons of carbon clusters represent an icosahedron - 12-apex crystalline structure each apex of which is connected with five other apexes. 

A characteristic feature of the carbon modifications obtained by the method developed by us is their fractal structure (Fig. 1), which manifests itself by various geometric forms. In the electrochemical cell used by us, the initiation of the benzene dehydrogenation and polycondensation process is associated with the occurrence of short local discharges at the metal electrode surface. Further development of the chain process may take place spontaneously or accompanied with individual discharges of different duration and intensity, or in arc breakdown mode. The conduction channels that appear in the dielectric medium may be due to the formation of various percolation carbon clusters. 

With respect to the thermodynamic stability of metal clusters, there is a plethora of results which support the spherical Jellium model for the alkalis as well as for other metals, like copper. This appears to be the case for cluster reactivity, at least for etching reactions, where electronic structure dominates reactivity and minor anomalies are attributable to geometric influence. These cases, however, illustrate a situation where significant addition or diminution of valence electron density occurs via loss or gain of metal atoms. A small molecule, like carbon monoxide,... 

The existence of the carbon monoxide dimer is currently accepted as a weakly bound molecular complex [CO CO] [124], Besides, it has been found that weakly bound molecular clusters of carbon monoxide dimers and cyclic trimers, confined in zeolite cavities and channels, are stabilized under the zeolite framework cationic field [125], These structures are similar in geometric configuration to those reported in Figure 9.14 however these are not covalently bonded, but are only weakly bound. 

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... 

Due to the development of methods for the production of cold cluster beams containing species up to C200, spectroscopic data on all-carbon molecules are now widely available. No direct structural or energetic information is available experimentally, and this has stimulated the application of computational methods in order to evaluate the geometric and electronic structures of these molecules, as well as to predict properties such as ionization potentials and vibrational frequencies. 

We described boratiranes and boriranes with one boron substituent at each ring carbon atom. The geometrical distortions found experimentally in the X-ray structures as well as by model computations can be understood in terms of variably strong hyperconjugation between a(C-B) bonds and the formally empty p-orbitals of more or less electron deficient boron atoms. Two electron reduction of an oxatriborabicyclohexane leads to ex-treme distortion of the bicyclic to a cluster structure by formation of a 3c,2e-BBB-bond. 

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