Bonding in boron icosahedra [closed]








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How do boron atoms make five bonds with other boron atoms even if the electron configuration of unbound boron atoms is [He]2s²2p¹, i.e. there is an insufficient number of outer electrons? Are the inner electrons ([He]) involved in binding?


[![enter image description here](https://i.stack.imgur.com/MtYSB.png)](https://i.stack.imgur.com/MtYSB.png)


$\ce{B12H12^2-}$, source: <https://commons.wikimedia.org/wiki/File:Dodecaborate(12)-dianion-from-xtal-3D-bs-17.png>




Boron makes not five but six bonds in compounds such as dodecaborate or boron carbide. Boron carbide is a semiconductor, so it has aspects of a metal and a non-metal. For actual metals such a elemental sodium, you have to explain twelve nearest neighbors with only 1 outer electron, so there is no way to describe it with covalent bonds. For boron carbide, you can get away with invoking 3 center 2 electron bonds, but it is not clear if there is much insight to be gained.


Roald Hoffmann wrote a detailed account of bonding in boron carbide [here](http://www.roaldhoffmann.com/sites/all/files/523.pdf). Even if all you get out of it is that boron makes beautiful intricate structures, and 2 electron bonds do not do justice to all compounds known, it is worthwhile taking a look.


[![enter image description here](https://i.stack.imgur.com/fUPUc.png)](https://i.stack.imgur.com/fUPUc.png)


I don't think any of the bonding models make use of the inner electrons.


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