Isomer combinatorics for acyclic conjugated polyenes: enumeration and beyond

A combinatorial approach to fully conjugated acyclic polyenes (C _N H _{N +2}) is considered with a view to the extension of standard enumeration techniques to treat a widened range of chemically interesting features. As a first step, enumerations are made respecting: placement of single and double bonds, the occurrence of cis/trans isomers, and the degree (and type) of “radicality” of such conjugated networks. As a further extension, several structural (graph-theoretic) invariants averaged over various types of isomer classes and sub-classes are made, and then these invariants are utilized to estimate several physicochemical properties averaged over these same classes or sub-classes. The properties currently so considered are heats of formation, indices of refraction, and magnetic susceptibilities. Finally, the asymptotic behaviors of isomer counts and isomer properties in the many-atom limit is elaborated. Received: 10 August 1998 / Accepted: 17 November 1998 / Published online: 16 March 1999