Polyhedral three-dimensional aromatic

Three-dimensional aromaticity in polyhedral boranes and related molecules 01CRV1119. 

Polyhedral clusters in which the electron count is less than Sn are electron-poor in the sense that the number of skeleton electrons is insufficient to form localized, 2c,2e bonds. Instead, models involving 3c,2e bonds or full global electron delocalization ( three-dimensional aromaticity) must be invoked to describe the bonding conditions. Electron-poor naked clusters are, as would be expected, formed by the early post-transition elements in groups 13 and 14. In addition, the cationic clusters of group 15 are electron-poor. Examples, derived from the compilation in Table 5, include the iso-electronic Pbg and Big " clusters and the 22-electron M5 species of thallium, tin, lead, antimony, and bismuth. 

King, R.B. (2001) Three-dimensional aromaticity in polyhedral boranes and related molecules. Chem. Rev., 101 (5), 1119-1152. 

Aihara J (1978) Three-dimensional aromaticity of polyhedral boranes. J Am Chem Soc 100 3339-3342... 

In contrast to the previously known boron hydrides, the polyhedral boron hydrides were shown to be exceptionally stable. One of the most striking features of the carboranes is the capability of the two carbon atoms and ten boron atoms to adopt the icosahedral geometry in which the carbon and boron atoms are hexacoordinated. This feature of carboranes gives rise to the unusual properties of these molecules and their carbon and boron derivatives. Due to these features of icosahedral carboranes, their chemistry has developed extensively, and the results obtained are summarized in R. Grimes monograph and review [5]. Investigation of the properties of polyhedral boron hydrides resulted in the conclusion that these compounds have aromatic properties. It was the first example of nonplanar three-dimensional aromatic compounds and resulted in the development of the eon-cept of three-dimensional aromaticity that is generally accepted at the present time [6,7]. 

In recent years the fundamental ideas of Huckel molecular orbital theory, the Huckel rule, and other aspects of aromaticity have been extended to polyhedral three-dimensional inorganic structures regarded as aromatic like the two-dimensional aromatic hydrocarbons. Such an extension of Huckel molecular orbital theory requires recognition of its topological foundations so that they can be applied to three-dimensional structures as well as two-dimensional structures. In this connection graph theoretical methods can be used to demonstrate the close analogy between the delocalized bonding in two-dimensional planar aromatic systems such as benzene and that in three-dimensional deltahedral boranes, and carboranes. Related ideas can be shown to be applicable for metal carbonyl clusters, bare post-transition metal clusters, and polyoxometallates. ... 

King, R. B. Three-Dimensional Aromaticity in Polyhedral Bo-ranes and Related Molecules. Chem. Rev. 2001, 101,1119-1152. 

Multicenter bonding is the key to understanding carboranes. The series [CB H i and C2B H 2 (Schemes 3.2-44) contain mainly polyhedral clusters (trigonal bipyramids 15 and 39, octahedral [CBsHg]- and C2B4H6, icosahedra [CB11 H,2 and C2B10H12) which are three-dimensional a aromatics, however, the... 

Scheme 3.2-44. From two-dimensional n aromatics (planar 2, C2BH3) to three-dimensional o aromatics (polyhedral 15, 39 and higher members of the series) via folded aromatics (3, 2 ) connecting both classes.

Here TV is the number of vertices in a graph (which corresponds to the number of atoms in a conjugated molecule), Xj are the roots of the characteristic polynomial of the aromatic system, and xf are the roots of the acyclic polynomial of the polyene-like reference system. In essence this corresponds to the procedure of the Hiickel method to solve for the eigenvalues Xj of the Hiickel matrix in units of Finally, gj is the orbital occupancy number. The method was applied to a large number of conjugated hydrocarbons - with results for TREPE that usually show a similar trend as the HSREPE values. Aiha-ra76.77 extended the concept to three-dimensional systems, in particular polyhedral boranes. However, soon afterward, controversial difficulties arose with this approach. ... 

Additionally, aromaticity has also been extended to three-dimensional systems and the term spherical aromaticity coined [25,26] for polyhedral hollow molecular structures with 2(n + 1), n e N, delocalized electrons. However, in this chapter we shall be concerned with aromaticity in planar n-manber all-metal ring-like clusters. 

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