Molecular orbital theory of homoaromatic character

Abstract

Ab initio STO-2G geometry optimizations have been carried out for the homotropenylium cation (1) and the cyclooctatrienylium cation [planar ( C, ) and nonplanar (C8)]. The homoconjugate W a g e for the homotropenylium cation is found to be 1.578 A at this theoretical level. This brings the ab initio calculations for 1 into line with previous MIND0/3 studies, frontier molecular orbital theories (FMOs), and the Winstein picture of an open cyclopropane unit in the homotropenylium cation. Both the homotropenylium cation and the cyclooctatrienylium cation are found to be markedly nonplanar when fully optimized. STO-BG, STO-3G, and 4-31G calculations on the STO-2G potential minima indicate that the cyclooctatrienylium cation probably lies no more than 10 kcal/mol higher in energy than the homotropenylium cation. This finding requires a revision of the concept of the homoaromatization energy for 1 and implicates the cyclooctatrienylium cation as an intermediate in the bridge-flipping process which occurs in the homotropenylium cation. MINDO/3 calculations are reported for the homotropenylium and cyclooctatrienylium cations together with results for other ions of interest in the area of homoaromatic chemistry. Evidence for homoaromatic character is found for the homotropenylium cation, the homocyclopropenylium cation, and the homocyclooctatetraene dication. The final frontier-dihomoaromatic character-is illustrated with the aid of calculations on the dihomotropenylium cation which is also found to be nonplanar. The homoaromatic cations show a number of well-defined trends. In particular it is shown that nonplanarity in the basal plane, shortened bond lengths between polyenyl and bridge fragments, bond equalization in the polyenyl segment, and lengthening of the homoconjugate linkage operate in concert to confer homoaromatic character. The bicyclo[5.2.0]nonadienylium cation, in which the cyclopropane group of the homotropenylium cation is replaced by a cyclobutane ring, does not exhibit the above characteristics and is concluded to be nonhomoaromatic. These results are in excellent agreement with previous FMO theories of homoaromatic character.The calculations for the homocyclopentadienyl anion and the .homocycloodatetraene dianion provide some evidence for homoaromatic character, but in contrast to the cations, the results for the anions do not lend themselves to a straightforward interpretation. The full sets of canonical molecular orbitals from the cyclooctatrienylium cation and the homotropenylium cation have been transformed to localized molecular orbitals (LMOs). The three *-type LMOs for the cyclooctatrienylium cation accord well with the notion of a heptatrienylium cation conjugation scheme. The *-type LMOs for 1 are of an entirely different character and most clearly evoke the conjugation of a cyclopropane unit with a pentadienyl cation in which each component has essentially retained its integrity. On this basis it is argued that the homotropenylium cation should be regarded as a resonance hybrid between the ful...

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