A Quantitative Metric for Conjugation in Polyene Hydrocarbons Having a Single Classical Structure

Abstract

A quantitative measure of the extent of conjugation is introduced. The number of Dewar resonance structures (DS) in a conjugated hydrocarbon quantitatively determines its extent of conjugation interaction. The greater the degree of conjugation the more stable is the conjugated hydrocarbon. The number of single bonds joining the exo-double bonds of a purely cross-conjugated hydrocarbon is equal to its number of Dewar resonance structures (DS). Polyene cross-conjugated hydrocarbons are minimally conjugated and possess only one classical structure with a succession of fixed single and exo-double bonds. There are three increasing levels of conjugation for systems with a single classical structure according to whether they are cross-conjugated, linear extended two-way conjugated, and ring-enhanced conjugated. Numerous analytical expressions have been derived. Our valence-bond (VB) approach involves studying the interrelationship of several well-known series of conjugated hydrocarbons having only a single classical structure, i.e., the number of Kekulé resonance structures is one (K = 1). This work provides a totally new perspective to the concept of conjugation.

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

“…Advantages of this (perturbational) perspective over the former (graphtheoretical) one are as follows: first, it is in line with the chemical way of thinking about an involved compound as consisting of quasi-transferable elementary fragments, as well as with the classical definition of conjugation as an interaction of unsaturated functional groups. Second, it is compatible with the observed bond length alternation [12,13] peculiar to polyenes of any size. Finally, application of alternating resonance parameters yields a proper chainlength dependence of the relevant excitation energies [22].…”

“…[12,13]) generally follow from experimental heats of formation (e.g. two ethene molecules serve as a reference system for 1,3-butadiene).…”

“…[15]), the vertices and edges of which represent atoms and bonds, respectively. The relevant studies of conjugation energies [4,13,[16][17][18][19][20] are carried out mostly by means of the chemical graph theory [15]. In particular, analysis of the principal Kekulé valence structure of polyene in terms of conjugated paths (CPs) of various lengths (i.e., of linear fragments consisting of C=C and C-C bonds alternately) [4,21] appears to be fruitful in this field.…”

“…In particular, analysis of the principal Kekulé valence structure of polyene in terms of conjugated paths (CPs) of various lengths (i.e., of linear fragments consisting of C=C and C-C bonds alternately) [4,21] appears to be fruitful in this field. An additional invoking of the main concepts of the valence bond (VB) theory (such as the Dewar resonance structures) also yields important conclusions concerning conjugation [13].…”

“…The reduced stabilities of fully cross-conjugated polyenes (dendralenes) vs. the respective linear isomers is a well-established fact [5,7,8,12,13,16,24]. The regular constitution of these chainlike systems allows the relevant p-electron energies to be expressed algebraically and analyzed in the general case without specifying the number of carbon atoms [13,16,17,24]. As a result, destabilization of dendralenes vs. linear polyenes has been traced back to unfavorable conditions for the so-called indirect delocalization in the cross-conjugated chain caused by specific orbital phase properties [24].…”