A little while ago, I speculated (blogs are good for that sort of thing) about hexavalent carbon, and noted how one often needs to make (retrospectively) obvious connections between two different areas of chemistry. That post has attracted a number of comments in the two years its been up, along the lines: what about carboranes? So here I have decided to explore that portal into boron chemistry. The starting point is the reported crystal structure of a molecule containing a CH12B11– anion (DOI: 10.1021/ja00201a073). This differs from the molecule I previously reported in having not so much 5C-C + 1C-H bonds around a single carbon, but instead 5B-C + 1C-H bonds. The basic cluster is much in fashion (as B12Cl122-) for its properties as a non-coordinating counterion.
Above is the QTAIM topological analysis of the electron density (B3LYP/6-311G(d,p) calculation) which reveals all 11 borons and the single carbon atom as being surrounded by six bond critical points. ELF tells us how many electrons populate the synaptic basins. This clearly reveals that the bonding to the carbon and all the boron atoms is non-Lewis, i.e. that of the six bonds to each of the non-hydrogens, five are not of the Lewis two-electron pair type. The carbon for example is surrounded by five C-B basins, each of 1.02e, with its valence shell occupied by ~7.2e in total. The boron involved in each of the C-B bonds also has five bonds, with basins corresponding to 1.01, 2*0.95 and 2*0.73e. The boron directly opposite the carbon has five basins corresponding to five B-B two-centre bonds of 0.6e each, and a further five basins of 0.3e corresponding to 3-centre BBB bonds (shown as yellow spheres above). Arguably, that particular boron atom has eleven bonds to it!
This molecule reveals quite clearly how sterile the debate is about whether carbon can be hypervalent. If the Lewis definition of a bond as an electron pair is removed, then hypervalency exceeding four can easily be obtained. What is certainly sacrosanct is the valence shell octet for carbon (and boron).
Finally, I throw B12H122- in. This has the wonderful icosahedral symmetry, and as you might expect, each boron is defined by five two-centre B-B bonds (~0.66e) and five three-centre BBB bonds (~0.24e), as well as a conventional two-electron B-H bond. Each boron is undecavalent! Not seen that particular valency before!!