Polyhedral molecules

Hoffmann R, Lipscomb WN. Theory of polyhedral molecules. I. Physical factorizations of the secular equation. J Chem Phys 1962 36 2179-89. 

The third and largest class of compounds comprises closed-cage polyhedral molecules in which the metal atom is held in the cage by 77-bonding to the borane fragment in a manner formally analogous to ferrocene. The first members of this class were reported in 1965 by Hawthorne et al. (10). This diverse, chemically stable class of compounds will comprise the subject of this review. 

Bonds between boron atoms occur in halides such as BgCl, B4CI4 and BgClg (p. 271). In B4CI4 the four boron atoms are arranged in a tetrahedron and the B-B bonds are of fractional order. In BgClg every boron atom is attached to three others in a polyhedral molecule. 

New carbon modifications, which consist of discrete polyhedral molecules, have been intensively investigated since the early 1990 s. The structures of these fullerenes range from the highly symmetrical buckminsterfullerenes, C50, to the chiral fullerenes, 7, to larger tubular or carbon particles built up of onionscale-shaped molecules. Possible applications, such as the manufacture of superconducting alkali metal-doped fullerenes or their utilization as a support for catalysts, are being developed, but are not yet market ripe. 

Polyhedral molecules and ions Cyclic molecules and ions Infinite linear molecules and ions Structures based on 3-connected nets the plane 6-gon net 3D nets... 

Structural studies have now been made of a number of polyhedral molecules and ions, and of these the largest class comprises the tetrahedral complexes. 

There are some interesting observations too concerning the structures of polyhedral molecules. Very often they are electron deficient in the sense that there are fewer than two electrons for each close contact. The heavy atoms forming the skeleton of the molecule may be either main group atoms (for example in the boranes and carboranes) or transition metal atoms (metal cluster compounds) or both (metallocarboranes). 50 shows the structures expected from Wade s rules for five atom polyhedral molecules with six, seven and eight pairs of skeletal electrons. There are a total of fifteen skeletal orbitals... 

The moments of inertia of a polyhedral molecule therefore contain information concerning its dimensions, shape, and the distribution of atoms on its surface. In the remainder of this review the applications of moments of inertia to... 

R. Hoffmann and W. N. Lipscomb, J. Chem. Phys., 36, 2179 (1962). Theory of Polyhedral Molecules. I. Physical Factorizations of the Secular Equation. R. Hoffmann,/. Chem. Phys., 39, 1397 (1963). An Extended Huckel Theory. 1. Hydrocarbons. 

Consideration of the properties of vertex groups leads to the following very simple rule to determine whether polygonal or polyhedral molecules exhibit delocalized bonding or edge-localized bonding ... 

The matching rule cited above implies that fully edge-localized bonding occurs in a polyhedral molecule in which all vertices have degree 3. Such is the case for the... 

The structure of cluster compounds of transition metals and the limits of applicability of the electron counting rules for polyhedral molecules. Y. L. Slovokhotov and Y. T. Struchkov, Russ. Chem. Rev. (Engl Transl), 1985, 54, 323 (150). 

Jemmis, E.D. (1982) Overlap control and stability of polyhedral molecules. Closo-Carboranes. J. Am. Chem. Soc.,... 

The genesis of the EH method [2] was the linear combination of atomic orbitals/molecular orbital (MO) study of polyhedral molecules by Hoffmann and... 

A structural perspective gave rise to predictions about reasonable rearrangement pathways for polyhedral molecules. He also measured isomerizations that confirmed the predictions. The calculations that describe the boron hydride structures also gave basis for predicting which atoms would be most reactive. These predictions stimulated much synthetic chemistry. 

Three-dimensional polyhedral molecules such as the borane anions, B Hn , are characterised by a total of n -I- 1 skeletal electron pairs or 4 n -I- 2 valence electrons in total [33]. The isolobal analogy between the BH and ML3 fragments has provided a theoretical relationship between the borane and the transition metal cluster compounds [34]. A detailed analysis of the molecular orbitals of deltahedral transition metal clusters showed that they also have a total of n -h 1 bonding skeletal molecular orbitals, which is the same as that in the borane clusters, and 6 n orbitals that are either non-bonding or involved in the metal-ligand bonding. Therefore, such clusters are characterised by 14 n -I- 2 valence electrons in total. 

In the area of polynuclear clusters, the stabilisation of triangular transition metal frameworks of the type M3L6 has been analysed theoretically, and reasons sought for the stability of cZoso-Mi,E2 clusters (M = metal atom in an ML3 local co-ordination and E = S, Te) which have 8 skeletal electron pairs instead of the expected 7. A theoretical analysis has been used to show how the MOs of three-connected polyhedral molecules differ from those of deltahedra, and a systematic investigation of the electronic requirements for structures based on... 

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