Searching for Coulson’s lost theorem: Bond number in conjugated systems

The simplest description of conjugated hydrocarbons is Hückel Molecular Orbital (HMO) Theory, which is in essence a graph theoretical model. Eigenvectors and eigenvalues of the adjacency matrix of the molecular graph are used to model spatial distributions and energies of the mobile electrons that dominate the chemical and physical properties of these important unsaturated systems. Charles Alfred Coulson FRS (1910 – 1974) was a leading figure in the development and exploitation of HMO theory from the early 1940s all the way through to the 1970s. His work with Longuet-Higgins defined key concepts that still shape chemical thinking about benzenoids and have found new applications with the many forms of carbon that have emerged in the decades since his death. This talk will discuss a claim that surfaced in Coulson’s early work, is part of the folklore of HMO theory apparently believed by all chemists, but until recently had no complete published proof, despite tantalising hints sprinkled through 70 years of primary literature and textbooks.

This talk is based on J. Chem. Phys. 151 (2019) 151101, doi:10.1063/1.5128624 but also covers some more recent developments.

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