Abstract
The interplay of radicality and resonance structures in conjugated π bonds is explored by graph theory. Radicality dominates substitution effect in polyenes. As a first step, non-radical and radical acyclic polyenes are sorted and enumerated through generating monosubstituted derivatives. The generating function is determined by the growth pattern of trees embedded in hexagonal lattice. Each substitution site of a polyene is characterized as either singly or doubly bonded. Doubly bonded sites are favored energetically. Growth pattern leads to the derivation of recurrence relations. The generating function consists of two parts intertwined, resulting in two coupled equations. Geometric and constitutional isomerisms of polyenes are treated. For the former, equations are solved either analytically or by iteration. For the latter, only numerical solution is obtained.
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Yeh, CY. A Mathematical Problem in Isomerism and Radicality of Acyclic Conjugated Polyenes. Journal of Mathematical Chemistry 34, 95–110 (2003). https://doi.org/10.1023/A:1025176529368
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DOI: https://doi.org/10.1023/A:1025176529368