The π-Electron-System of Monocyclic Polyenes C2nH2n with Alternating Single and Double Bonds

Abstract

On the basis of quantum chemical calculations and general theoretical arguments a discussion has been going on regarding the stability towards distortion of benzene and the monocyclic polyene C2nH2n in general. Also the polyene radicals C2n+1H2n+3, of which the allyl- radical is the first representative, are of interest. These molecules contain a {sigma}-skeleton and a {pi}-electron system with two main contributing and, in a symmetric geometry, equivalent resonance structures. The question asked is whether (in)stability towards distortion away from a symmetric geometry is a {pi}-electron property or, on the contrary, primarily connected to the {sigma}-skeleton. In this communication the question is answered firstly by means of simple molecular orbital and valence bond arguments in the case of the {pi}-electron system, and secondly with the characteristic difference between 2p{pi} - and 2p{sigma} overlap integrals for the discussion of the {sigma}-skeleton. The outcome is inescapable: notwithstanding the symmetrizing influence of resonance, the {pi}-electron system as a whole is unstable towards distortion.

Structures of Annulenes and Model Annulene Systems in the Ground and Lowest Excited States

“…In the π-electron approximation both the Hückel molecular orbital (HMO) method and the simple valence bond (VB) theory predict that displacing the planar cyclic structures from the bond equalized to the bond alternating configurations the ground state energy is lowered [38,39].…”

“…For instance, in the VB treatment of benzene [38] the two equivalent Kekule' structures K A and K B at the bond equalized D 6h geometry are degenerate with energy Q + (3/2)J o , Q and J o being the classical VB coulomb and exchange integrals [40], respectively. The interaction between the K A and K B functions split their energies by (9/10)J o and −(3/2)J o , thus giving origin to the ground and lowest excited states.…”

“…Nevertheless, the π energies are lower in the bond alternating than in the bond equalized configuration. In the Hückel theory the MO energies for monocycles C 2n H 2n with conjugated double/single bonds [41] were adapted to the bond alternation case [38] where β o < 0 is the resonance integral. In this expression the ± and j labels are combined to give rise to the 2n orbital energies.…”

“…Table 1. Valence bond (VB) and molecular orbital (MO) energies of cyclobutadiene and benzene [38,39]. Upper, VB theory: under K A , K B ; energies of the Kekule' structures at the most symmetrical geometries, D 4h for cyclobutadiene and D 6h for benzene; under G; E π (0) ground state π energy after K A , K B mixing at the undistorted geometries, D 4h and D 6h , respectively, ∆E π (δ) π energy change as a function of the displacement parameter δ; under Exc; the same quantities for the excited state.…”

A Different Story of π-DelocalizationThe Distortivity of π-Electrons and Its Chemical Manifestations

“…30 Two papers in The Journal of Chemical Education address the topic and show that π-distortivity of benzene and allyl radical is a property independent of the quality of the wave function used to describe the systems. 13,15 In 1995, we decided to stop further research on this topic because it seemed a philosophical idea that engages primarily theoreticians with little or no impact on experimental chemistry. That this was a premature decision became obvious at the end of 1995, when we learned from Haas and Zilberg 31 about the frequency exaltation of the bond alternating vibrational mode in the 1 1 B 2u excited state of benzene.…”