Valence Bond Theory Reveals Hidden Delocalized Diradical Character of Polyenes

The nature of the electronic-structure of polyenes, their delocalization features, and potential diradicaloid characters constitute a fundamental problem in chemistry. To address this problem, we used valence bond self-consistent field (VBSCF) calculations and modeling of polyenes, C_2nH_2n+2 (n = 2-10). The theoretical treatment shows that starting with n = 5, the polyene's wave function is mainly a shifting 1,4-diradicaloid, a character that increases as the chain length increases, while the contribution of the fundamental Lewis structure with alternating double and single bonds (1) decays quite fast and becomes minor relative to the diradicaloid pack. We show how, nevertheless, it is this wave function that predicts that polyenes will still exhibit alternating short/long CC bonds like the fundamental structure 1. Furthermore, despite the decay of the VB contribution of 1, it remains the single structure with the largest weight among all the individual structures. The mixing of all the 1,4-diradicaloid structures into 1 follows perturbation theory rules, with the result that the delocalization energy due to this mixing is additive and behaves as a linear function of the number of the double bonds, ΔE_del = -6.9 × n (kcal mol^-1). The VB modeling shows that while the conjugation stabilizes structure 1, this stabilization energy is energetically overridden by the Pauli repulsion between two adjacent double bonds. Nevertheless, unsubstituted polyenes remain planar; this observation is addressed. Potential manifestations of the diradicaloid nature of polyenes are discussed, and it is concluded that the diradicaloid character is clearly not a well-defined physical property as in real diradicals. Thus, we went full circle to realize that our philosophical question may not be strictly resolved. The localized/delocalized properties of polyenes seem to define a "chemical duality principle". This duality of molecular wave functions is a ubiquitous beguiling phenomenon.