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Hexatriene is an unsaturated hydrocarbon with six carbon atoms and five carbon-carbon bonds, three of which are double bonds.

However, the bond lengths of the $\ce{C=C}$ bonds are not the same. The middle $\ce{C=C}$ bond has a length of 137 pm while the $\ce{C=C}$ bonds at the end of the molecule have lengths of 134 pm, the length of a standard $\ce{C=C}$ bond. The two carbon-carbon single bonds are 146 pm long, also off from the standard 154 pm length of carbon-carbon single bonds.

Bond lengths

Clayden's organic chemistry hints that the explanation has to do with the molecular orbits formed and the conjugation system in the molecule. However, I do not fully understand this explanation.

Why do these carbon-carbon bonds show this unusual bond length behavior? A thourough explanation using MO theory would be appreciated.

References

Clayden, J., Greeves, N., Warren, S. Organic chemistry, 2nd ed.; Oxford University Press: New York, 2012.

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If you derive the π-type molecular orbitals of hexatriene, the three lower-energy MOs which are filled would look something like this (image from p 33 of Fleming's Molecular Orbitals and Organic Chemical Reactions, Reference Edition):

Filled π MOs of hexatriene

I suspect what Clayden is getting at is that in the second MO, there is some antibonding character between C3 and C4, whereas the C1/C2 and C5/C6 interaction is purely bonding.

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  • $\begingroup$ And this antibonding interaction between C3 and C4 would cause the double bond to have slight single bond character, which would explain the longer than usual bond length for the C3=C4 bond? $\endgroup$ – Ethiopius Dec 27 '18 at 1:41
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    $\begingroup$ Yes, pretty much. So it is something like a 1.99-bond, if that makes any sense. (That number's made up, of course.) $\endgroup$ – orthocresol Dec 27 '18 at 1:43
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    $\begingroup$ You do not have to make it up. You can work out net pi bonding in each linkage by multiplying the coefficients on each pair of bonded atoms, doubling, and adding up the results for all orbital. This gives 0.87 pi bond between C-1 and C-2, 0.48 between C-2 and C-3, and 0.78 between C-3 and C-4. Other bonds are determined by symmetry. $\endgroup$ – Oscar Lanzi Dec 27 '18 at 12:09

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