Delocalization in Allyl Cation, Radical, and Anion

Abstract

Ab initio valence bond calculations are performed for the allyl cation, radical, and anion with 6-31G* basis set. Delocalized and hypothetically localized structures of these systems are thoroughly optimized and analyzed. The delocalization energies, defined as the energy difference between the delocalized structure and its hypothetically localized one, for the three allyl systems are −55.7, −28.4, and −52.3 kcal/mol, respectively. Our results clarify the recent debate on whether the allyl anion has little or comparable resonance stabilization with the allyl cation. The methylene rotation barriers of the allyl cation, radical, and anion are successfully explained in terms of resonance, hyperconjugation, and rehybridization. For the allyl radical, its resonance energy is only about half those of the allyl cation and anion; thus, it has the lowest rotation barrier. The twisted allyl cation, in which the rotating methylene group is perpendicular to the C−C−C plane, has the highest hyperconjugation energy (−6.8 kcal/mol), while, in its twisted form, the allyl anion has a negligible hyperconjugation effect. As the allyl anion assumes its twisted form, the carbon atom in the rotating methylene experiences a remarkable rehybridization from sp2 mode in the planar form to sp3 mode. This process decreases the total energy of the twisted allyl anion as much as 14.3 kcal/mol and eventually makes its rotation barrier smaller.

An Energetic Measure of Aromaticity and Antiaromaticity Based on the Pauling–Wheland Resonance Energies

“…The delocalization of the charge (no matter whether it is positive or negative) governs the stabilization of the acyclic systems. Thus, like the allyl ions, [33,37,48] the resonance energies of C 5 H 7 + and C 5 H 7 À are essentially identical. In contrast, the resonance energies of C 5 H 5 + and C 5 H 5 À differ considerably; the resonance stabilization of the cyclopentadienyl anion is almost three times greater than the cyclopentadienyl cation.…”

“…[17] However, in order to derive the wave function for a hypothetical localized 1,3,5-cyclohexatriene it is desirable to expand the bond functions in Equation (2) only in the basis space of the two bonded atoms. [40] When this is done, the three localized 1,3,5-cyclohexatriene double bonds do not mix and only interact in terms of electrostatic and Pauli exchange forms and thus should be comparable to the double bond of ethene. [19] To simplify the manipulation of HLSP functions, the bond functions are often represented by doubly occupied MO-like localized orbitals.…”

“…Both the BLW and the ab initio VB calculations in which electron correlations were taken into account resulted in very similar REs. [33,37,48] The computations reported here were carried out at the HF/6-311+G** level. The experimental heats of formation were taken from the latest NIST compilation.…”

“…[56] In other words, large variations of the CÀC single-bond lengths in organic molecules are due mostly to other factors such as electron delocalization, steric repulsion, and so forth, rather than to carbon hybridization. [40] The strong stabilization of benzene by p delocalization (57.5 kcal mol À1 , Figure 2) lengthens the double bonds by 0.07 and shortens the single bonds by 0.14 . The difference between VRE and ARE (E d = 34.8 kcal mol À1 ), the scompression energy, reflects the energy required to distort the optimal geometry of the benzene ring with a localized wave function and alternating bond lengths to the geometry with equal bond lengths (while maintaining the p-electron localization).…”

“…Van Lenthe et al adopted atomic orbitals for c i and c j , a treatment similar to the classical VB method. Our BLW bond functions are built with bond-distorted orbitals (BDOs), [40] as such bond functions correspond more closely to real bonds. As BDOs, both c i and c j are expanded with atomic orbitals centered on the two bonding atoms instead of only on one atom, as in Van Lenthes treatment.…”