Monocyclic Electrocyclic Transition States are Neither Favoured Nor Disfavoured if the Incipient Ring Bears More Than Two Odd Substituents

Abstract

A general case is presented that supports the conclusion that incipient π-bond orders, ^op_1,j, are approximately zero if the incipient alternant ring bears more than two odd substituents. Hence, corresponding electrocyclic transition states are neither favoured nor disfavoured. The case is made using permethylene polyenes. After presentation of the novel application of dense Sachs’ subgraphs to the problem of convenient, rapid access to permethylene polyene characteristic polynomials, permethylene polyenes are shown to belong to the newly defined Hückel symmetrenes. Employing novel expressions for permethylene polyene molecular orbital coefficients, a general relationship for pairs of terms that lead to π-bond orders, ^op_1,j, is obtained that, in turn, allows the key generalization to be made.