# Explanation for bond lengths in trans-hexatriene

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.

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.