One approach to reporting science which is perhaps better suited to the medium of a blog than a conventional journal article is the opportunity to follow ideas in unexpected, even unconventional directions. Thus my third attempt, like a dog worrying a bone, to explore hypervalency. I have, somewhat to my surprise, found myself contemplating the two molecules I8 and At8. Perhaps it might be better to write them as I(I)7 and At(At)7. This makes it easier to relate both to the known molecule I(F)7. What led to these (allotropes) of the halogens? Well, as I noted before, hypervalency is a concept rooted in covalency, albeit an excess of it! And bonds with the same atom at each end are less likely to be accused of ionicity. I earlier suggested that the nicely covalent IH7 was not hypervalent, with all the electrons which might contribute to hypervalency actually to be found in the H…H regions. The next candidate, I(CN)7 ultimately proved a little too ionic for comfort. So we arrive at II7. At the D5h geometry, it proves not to be a minimum, but a (degenerate) transition state for reductive elimination of I2 (I note parabolically that the 2010 Nobel prize for chemistry was awarded for reactions which involve similar reductive elimination of Pd and other metals to form covalent C-C bonds). Thus I8 is useful only as a thought experiment molecule, and not a species that could actually be made.
The Wiberg bond index (B3LYP/Def2-TZVPP basis+pseudopotential) of the central iodine comes out at 2.81; that of the two axial iodines is 1.05 and that of the five equatorial atoms is 1.50. Well, the axial iodines are clearly monovalent, the equatorial ones are higher because of I…I interactions around the 5-ring. The central iodine is clearly again, not hypervalent. The individual Wiberg bond orders radiating form the central atom are 0.47 for the axial and 0.374 for the equatorial atoms. The I…I bond orders between the five equatorial atoms are 0.336 for adjacent atoms. This latter observation matches with the frequency analysis, since any individual I-I bond is already 1/3 formed, just asking to be eliminated.
What of that other technique for finding electrons, ELF?
All the I-I bonds radiating from the centre have well-defined disynaptic basins (the same is NOT true for e.g. IF7by the way, which comes out as ionic in ELF). The two axial covalent bonds have basins integrating to 1.35 electrons, and the five equatorial covalent bonds 0.77. The central iodine has a total of 6.55 electrons in bonds surrounding it. The five equatorial iodines have 7.7 electrons in two lone pairs, whilst the two axial iodines have 8.05 electrons in five monosynaptic basins. In summary, all eight iodines in this compound exhibit valence shells filled with an octet of electrons. Now, beyond any ambiguity, we can say this is NOT hypervalent.
Oh, for good measure, At8. The Wiberg index at the central atom is 2.77, the bond index is 0.46 for axial and 0.37 for equatorial At. The ELF basin integrations are 0.65 for equatorial, and 1.61 for axial, the former decreasing and the latter increasing compared to iodine.