Various Carbon to Carbon Bond Lengths Inter-related via the Golden   Ratio, and their Linear Dependence on Bond Energies
  This work presents the relations between the carbon to carbon bond lengths in the single, double and triple bonds and in graphite, butadiene and benzene. The Golden ratio, which was shown to divide the Bohr radius into two parts pertaining to the charged particles, the electron and proton, and to divide inter-atomic distances into their cationic and anionic radii, also plays a role in the carbon-carbon bonds and in the ionic/polar character of those in graphite, butadiene and benzene. Further, the bond energies of the various CC bonds are shown to vary linearly with the bond lengths. 
Raji Heyrovska