What do the azobenzene oligomer helixes have to do with the Golden Ratio?

Azobenzene (di-phenyl-diazene) is a widely-studied prototype for its photoisomerisation capability. Whereas the trans-azobenzene is perfectly planar, the cis conformer assumes an inherent helicity, caused by the steric hindrance of each of the two benzene rings. In this study we explore by first principle DFT calculations the structural, mechanical, and chiroptical properties (Electronic Circular Dichroism spectra, ECD) of n-(phenylazo)-azobenzenes (n=. 1-10) from a computational point of view. The idea is that these polymers may photo-switch from a "strip"-like conformation (when each monomer is trans) to a "spring"-like conformation (when each monomer is cis). By studying the mechanical properties of these photo-induced nano-springs, we surprisingly obtain a nexus between the geometrical and elastic parameters and the Golden Ratio.