A simple rationale for lowered stabilities of branched and cross-conjugated polyenes

The study is aimed at revealing the decisive factors for relative stabilities of acyclic pi-electron systems of polyenes, the carbon backbones of which are of different type of branching. The systems are modeled as sets of N weakly interacting double (C=C) bonds. The relevant total pi-electron energies are represented in the form of power series containing members of even orders with respect to the averaged resonance parameter of single (C-C) bonds. For distinct isomers of the same polyene, both zero-order energies and respective second-order corrections are shown to take uniform values. Relative stabilities of these isomers are then primarily determined by the fourth-order member of the series that, in turn, consists of two additive components of opposite signs, viz., of the stabilizing component expressible as a sum of transferable increments of individual triplets of linearly conjugated C=C bonds [i.e., of the three-membered conjugated paths (CPs)] and of the destabilizing component depending on overall adjacencies (connectivity) of C=C bonds. Lower stabilities of pi-electron systems of branched and/or cross-conjugated polyenes vs. the linear ones then follow from comparative analyses of the relevant fourth-order energies, and this destabilization is shown to originate either from (a) a reduced number of CPs or from (b) higher adjacencies of C=C bonds in the former isomers. An actual interplay of both factors (c) also is rather common. The three cases (a)-(c) are illustrated by specific examples. [GRAPHICS]