Various Carbon to Carbon Bond Lengths Inter-related via the Golden Ratio, and their Linear Dependence on Bond Energies

TL;DR

This paper explores the relationships between various carbon-carbon bond lengths and energies, revealing that bond lengths are related through the Golden Ratio and that bond energies vary linearly with bond lengths.

Contribution

It introduces a novel connection between the Golden Ratio and carbon-carbon bond lengths and demonstrates their linear dependence on bond energies.

Findings

Carbon-carbon bond lengths relate via the Golden Ratio.

Bond energies vary linearly with bond lengths.

Relations hold across different carbon allotropes and compounds.

Abstract

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.