Electron-counting schemes

The many higher boranes such as B5H9 and BgH 2 are similarly electron deficient and cannot be described by a single Lewis structure. They can often be described in terms of a combination of two- and three-center bonds. Alternatively, their structures can be rationalized by electron-counting schemes such as those proposed by Wade. Analysis of the electron density of these molecules by the AIM method shows that there are bond paths between all adjacent pairs of atoms. So from the point of view of the AIM theory there are bonds between each adjacent pair of atoms, but these cannot all be regarded as Lewis two-center, two-electron bonds as is the case in B2H6. 

The electron-counting scheme which allows to understand this situation and which also works for the simpler clusters was developed from the MO theory for boron hydride polyhedra 389-393). It rests on the fact that a regular triangular faced polyhedron of n boron atoms in the molecule requires n + 1 bonding... 

A transition element has 5 additional valence orbitals, the 5d orbitals, and therefore 10 additional electrons are required per atom to fill the valence shell of each metal atom. A closo cluster consisting only of transition metal atoms should have a total of 14/i + 2 valence electrons. A capped cluster should have 14n, a nido cluster 14/i + 4, and an arachno cluster 14n+6. The combined formula 4/i+2 + 10m would represent the total electron count for a closo cluster, A mMm, of n atoms that contains m transition metal atoms and n -m main group atoms.Table 8.2 summarizes the main rules, and the following examples show how the total electron counting scheme is applied. 

In both [Fe4X4(N0)4](X = S or Se) and [Fe4S2(NO)4(NCMe3)2] the total valence electron count is 60. This is the number characteristic of tetrahedral tetranuclear metal clusters, such as [Ir4(CO)12], in the Wade and Mingos skeletal-electron counting schemes (76, 77) and, furthermore, each iron atom in these clusters obeys the 18-electron rule, provided that it forms single Fe-Fe bonds to each of the other iron atoms in the tetrahedron. 

A simplified electron-counting scheme (10) is also introduced in this module, providing a guide to likely products according to the 16- to 18-electron... 

Electron-counting scheme for macropolyhedral boranes mno rule... 

A generalized electron-counting scheme, known as the mno rule, is applicable to a wide range of polycondensed polyhedral boranes and heteroboranes, metal -laboranes, metallocenes, and any of their combinations. According to this mno rule, the number of electron pairs N necessary for a macropolyhedral system to be stable is... 

Allyl ligands have features common to metal-alkyl and metal-olefin complexes, and can act as three-electron donor ligands according to the electron counting scheme where total covalency is assumed. The metal ion in these complexes interacts with all three carbon atoms of the allyl functionality in an equivalent manner. 

For polyhedral clusters (sometimes called deltahedral, because the faces are all triangles resembling the Greek letter delta) the ancestor of all electron counting schemes is the correlation proposed by Wade between borane (or carborane) cages and metal carbonyl cages. Wade first drew attention to the similarity of a M(CO)3 unit and a BH (or CH) unit, a relationship that we would now call isolobality (Section 1-6). He then proposed that the 2n + 2 rule for closo boranes (Chapter 5) would also apply to closo metal cluster species such as [Os CO) ]2, and that 2n + 4 and 2n + 6 electron counts would, similarly, be appropriate for stable M clusters with nido and arachno structures. Hydrogen atoms are assumed to contribute one electron each, an interstitial carbon atom four electrons, and so on. 

A formal analogy is often drawn between the linear bonding modes of both ligands. NO" " is isoelectronic with CO therefore, in its bonding to metals, linear NO is considered by electron-counting scheme A as NO", a 2-electron donor. By the neutral ligand method (B), linear NO is counted as a 3-electron donor (it has one more electron than the 2-electron donor CO). 

The electron-counting schemes can be extended to isoelectronic species such as the carboranes (also known as carbaboranes). The CH" unit is isoelectronic with BH many compounds are known in which one or more BH groups have been replaced by CH (or by C, which also has the same number of electrons as BH). For example, replacement of two BH groups by CH" " in yields closo-C- Bayif, a neutral compound. 

Table 3-1 Electron Counting Schemes for Common Ligands...

Electron counting schemes Complexes containing p -cyclopentadienyl ligands... 

This example illustrates an important point about the use of such electron-counting schemes no information about the positions of the ligands can be obtained. Although Wade s rules rationahze why Rh4(CO)i2 and Ir4(CO)i2 both have tetrahedral cores, they say nothing about the fact that the ligand arrangements are different (Figures 23.11a and b). 

These are but three examples of the limitations of electron-counting schemes. As more clusters are structurally characterized, further exceptions arise providing yet more challenges for the theorist. 

An example of electron counting in a metal carbonyl cluster with an interstitial atom is illustrated by Ruf,C(CO)i7, which has the 14 skeletal electrons required for a globally delocalized octahedron by the following electron-counting scheme ... 

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