The nature of the bridgehead-bridgehead bond in [1.1.1]propellane 1 poses an interesting quandary. The bond involves two inverted carbon atoms, whose hybrids should point away from each other. The internuclear region has in fact much less electron density than for an ordinary C-C bond. Nonetheless, the molecule is stable and the C-C bond is estimated to have a strength of about 6 kcal mol-1.
Shaik and Hiberty1 have now proposed that the central C-C bond of [1.1.1]propellane is a charge-shift bond. In classical valence bond theory, we have three configurations for a bond: the covalent structure A↑↓B ↔ A↓↑B, and the two ionic structures A↑↓ B and A B↑↓. The description of a typical covalent bond is dominated by the covalent VB structure with a little bit of the ionic structures mixed in. A charge-shift bond is one where the resonance energy due to the mixing of the covalent and ionic structures mostly accounts for the stabilization of the bond.2 Just such a case is found in the F-F bond, and also to for the central C-C bond of [1.1.1]propellane!
References
(1) Wu, W.; Gu, J.; Song, J.; Shaik, S.; Hiberty, P. C., "The Inverted Bond in [1.1.1]Propellane is a Charge-Shift Bond," Angew. Chem. Int. Ed., 2008, ASAP DOI: 10.1002/anie.200804965
(2) Shaik, S.; Danovich, D.; Silvi, B.; Lauvergnat, D. L.; Hiberty, P. C., "Charge-Shift Bonding – A Class of Electron-Pair Bonds That Emerges from Valence Bond Theory and Is Supported by the Electron Localization Function Approach," Chem. Eur. J., 2005, 11, 6358-6371, DOI: 10.1002/chem.200500265
InChI
1: InChI=1/C5H6/c1-4-2-5(1,4)3-4/h1-3H2
InChIKey=ZTXSPLGEGCABFL-UHFFFAOYAJ
Henry Rzepa responded on 15 Feb 2009 at 3:56 am #
Analysing the bonding in a molecule is always a fascinating exercise,
since it is susceptible to so many nuances and interpretations. I was
inspired by this example to do a simple AIM (Atoms-in-Molecules)
critical point analysis, and follow this up with an ELF (Electron
localization function) inspection of the so-called synaptic basins.
The results can be seen here.
This reveals there is indeed a bond critical point located along the
axis of the central C-C bond, but of course AIM does not
necessarily reveal how strong it is. Integration of the ELF basins
however does indeed confirm it is a very weak bond, amounting to only
0.16 electrons. But another nuance emerges from this analysis. The six
apparently normal C-C bonds to the three bridging methylene groups
are not apparently so. They are each revealed as corresponding to
trisynaptic basins, or in more familiar language,
three-center bonds. The three centers are the two axial carbons
and each in turn of the three bridging methylene groups. The
remaining basins are monosynaptic, correspoding in loose terms to lone
pairs at the end of each axial carbon, albeit with an integration of
only 1.4 electrons each.
So this molecule could be compared e.g. with the much better known
diborane, which of course links the two boron atoms with two
three-center bonds via the bridging hydrogens. There are of course
examples of such boron hydrides which exhibit three such bridges, and
propellane might be considered to belong to this class of molecule.
The weirdest bond of all? Laplacian isosurfaces for [1.1.1]Propellane. « Henry Rzepa responded on 21 Jul 2010 at 6:26 am #
[…] that it is merely a hydrocarbon). Its peculiarity is the region indicated by the dashed line below. It is a bond? If so, what kind, given that it would exist sandwiched between two inverted carbon […]
Computational Organic Chemistry » Structure of the propellane radical cation responded on 23 Feb 2011 at 8:47 am #
[…] 1, whose bridgehead-bridgehead bond has been a topic of an earlier post, has a HOMO that is largely outside of the bridgehead-bridgehead region. Thus, loss of an electron […]