Mno rule

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... 

Some examples illustrating the application of the mno rule are given in Table 13.4.4, which makes reference to the structures of compounds shown in Fig. 13.4.10. 

Table 13 4 4. Application of the mno rule for electron counting in some condensed polyhedral boranes and related compounds ...

Considering the fact that the number of polyaromatic compounds known is large, this result should be no surprise. Of course neither the mno rule nor the cluster-fusion rule by itself gives any insight on the synthesis of the compounds. But they do suggest many such fused systems should be possible to make and that is added justification for seeking their syntheses. 

Exercise 2.8. The structure of GaioR6 is shown below. Consider the cluster as made up of edge-fused octahedra and compare the observed eve with the calculated one. Now apply the mno rule to this fused cluster system and calculate the number of cluster electrons required from each of the bare Ga atoms in order to satisfy the rule. 

Answer. For two octahedral clusters fused on an edge, the eve count is (2 x 26 — 14) = 38 whereas the observed count is (10 Ga + 6 R) = 30 -I- 6 = 36. Thus, we cannot assume non-cluster bonding lone pairs on the bare Ga atoms. With the mno rule, m = 2, n = 10 and o = 0 giving m + n = 12 sep. Each of the two Ga atoms shared between the clusters contributes all three valence electrons. Hence, we have 6 RGa + 2 Ga(shared) + 2 Ga(unshared) = (12 + 6 + 2x)/2 = 12 sep, where x is the contribution of the unshared cluster Ga atoms. Clearly x = 3 in this cluster, which suggests there are no formal lone pairs on these two Ga vertices. Indeed, the structure shows the Ga-Ga distances between the apical RGa and Ga centers (broken lines in the drawing) are about 0.2 A shorter than the other Ga-Ga distances. Electron counting identifies the cluster bonding problem but does not solve it. We will have more to say about this cluster type below. 

Recently, an extension of Wade s rules has been described for electron counting in boranes, heteroboranes, metallaboranes, other clusters, and even metallocenes. This approach called the mno rule, states that for a closed cluster structure to be stable, there must be m + n + o skeletal electron pairs, where... 

Determine the number of skeletal electron pairs predicted by the mno rule for the following ... 

To facilitate electron counting in composite cluster systems such as these, in which two or more deltahedra share one, two, or three vertex atoms, Jemmis has devised an extended electron counting procedure (his mno rule) that takes account of the number of cages (zzi), vertices (n), and singlevertex shared atoms (o). 

Electronic Requirement of Condensed Polyhedral Boranes-mno Rule... 

Figure 5.21 Equivalence of Huckel 4n + 2 pi electron rule and the mno rule Huckel 4n + 2 rule can be viewed as a special case of the mno rule.

Cu(C2B9Hii)2 here, the mno rule demands 2 + 23 + 1 = 26 pairs, whereas 27 are available. The extra two electrons will occupy the ej MO and, as expected, Jahn-Tellar distortion takes place, reducing the antibonding interactions [32],... 

The mno rule can be applied to other clusters as well. Only a few examples are... 

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