Cluster multicenter bonding

Multicenter bonding is the key to understanding carboranes. Classical multicenter n bonding gives rise to electron-precise structures characteristic of Hiickel aromatics, which are planar and have 4n + 2 n electrons. Clusters are defined here as ensembles of atoms connected by non-classical multicenter bonding , i.e., all... 

Classical aromatics like the electron-rich, cyclobutadiene dianion A or cydo-pentadienyl anion B and electron-precise hydrocarbons (e.g., benzene C, Figure 3.2-1) have pure n multicenter bonds and therefore are generally not regarded as clusters. 

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... 

Sn this is not so clear. The 22 valence electrons of the Sn ion could be accommodated in exact agreement with the octet rule according to the formula given in the margin. However, calculations with the electron localization function show that lone electron pairs are also present at the equatorial atoms therefore, only six electron pairs remain for the bonds. This corresponds to the number expected according to the Wade rules, as for bo-ranes ( + 1 multicenter bonds in a closo cluster with n = 5 vertices, cf. p. 144). We will deal with the bonding in such cluster compounds in Section 13.4. 

The structures and skeletal bond valences of Oss(CO)i6 and B5H52- are similar as a pair, as are also Fe5C(CO)is and B5H9. But the bonding types in the boranes and the metal clusters are not the same. Since every B atom in a polyhedral borane has three AO s for bonding of the BM skeleton, any vertex more than three-connected must involve multicenter bonds. In the transition-metal skeleton, the Mm atoms form either 2c-2e single bonds or 3c-2e multicenter bonds. 

The topological or graph-theoretical approaches attempt to define the bonding and antibonding orbitals available to a cluster in terms of a sort of valence-bond description, where hybridized atomic orbitals are directed in space to form either localized or multicenter functions. (See also Hybridization) The analysis of a complex structure involving delocalized bonding may, however, require some seemingly subjective decisions about how the atomic orbitals overlap, where the multicenter bonds should be formed, and so forth. 

Teo s topological approach also deserves mention in this section. It combines Euler s theorem with the idea of an effective atomic number rule for each cluster vertex, but involves a rather arbitrary parameter whose purpose is to correct for the formation of multicenter bonds. 

Although the Mulliken population analysis is useful for the discussion of two-center bonding, it is not sufficient for the description of the three- or four-center bonds that may exist in metal clusters. In order to elucidate the multicenter bonds, we examine contour maps of the charge densities of Na4 and Mg4 as typical tetramers of AM and AE, respectively. We use the differential charge density, Ap defined by eq. (3)., to express the charge redistribution on the formation of chemical bonds. 

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