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Lecture 19 Electron count in cluster compounds 1) Electron count in boron cages. Wade’s and Mingos’s rules The cluster electron count in closo-polyboranes: BnHn (n = 5, … 12) have n+1 cluster bonding MO’s. As a result, the most stable electron configuration of these species is 2n+2 cluster electrons (1st Wade’s rule). Therefore, the closo-BnHn which has only 2n cluster electrons is expected to add 2 e’s to form stable dianion closo-BnHn2-. The total electron count in closo-polyboranes: each BH fragment contributes 3+1 = 4 electrons into the total electron count of BnHn. Therefore, BnHn itself has 4n electrons in total. The number of the bonding MO’s in it is n (BH bonds) + n+1 (cluster bonding MO’s) = 2n+1. Thus, to be stable the closo-BnHn should have the total electron count of 4n+2 (Mingos’s rule), which corresponds to dianionic closo-BnHn2-.

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**2) Electron count in boron cages. Wade’s and Mingos’s rules**

In the case of nido-polyboranes BmHm one vertex of the parent closo-BnHn is missing, m=n-1, but the number of the bonding core orbitals is m+2, the same as in the parent closo-BnHn (2nd Wade’s rule). nido-Polyboranes form stable tetraanions, BmHm4- and neutral BmH(m+4) with the total electron count of 4m+4 (2nd Mingos’s’ rule). arachno-Polyboranes BmHm with two vertices of the parent closo-BnHn missing, m=n-2, also have the same number of the cluster bonding MO’s, m+3, (3rd Wade’s rule) and form stable anions BmHm6- with the total electron count of 4m+6 (3rd Mingos’s rule).

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**3) Electron count in heteronuclear boron-based cages**

Using analogy with boron cages, it turned out to be possible to rationalize composition and shape of heteronuclear boron cages and some non-transition element clusters. Consider first some carboranes, where BH is substituted by CH. Each C contributes into the cage MO’s the same number of AO’s and one electron more than B. As a result, the charge of the related anion decreases by the number of CH groups present.

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**4) Electron count in main group element clusters**

So-called Zintl phases produced by reduction of Si, Ge, Sn or Pb with alkali metals contain cluster anions Si94-, Ge92-, Ge94-, Sn52-, Sn86-, Sn94-, Pb52-, Pb94-. Wade’s rule allows to rationalize their structure. Compare BH fragment which contributes 2 electrons into cage MO’s and Si, Ge, Sn or Pb which also contribute 2 electrons in it with 2 electrons remaining in their shell as a lone pair.

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