Role of hyperconjugation in the 1,2-shift reactivity of bicyclo[2.1.0]pentane and cyclopropane radical cations: A computational study

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Hyperconjugation and its relationship with the 1,2-shift rearrangement reactivity in bicyclo[2.1.0]pentane and cyclopropane radical cations have been studied with density functional theory (PBE0/6-311G*). Hyperconjugation has been evaluated by calculating the 1H hyperfine coupling constants, atomic spin densities, and dihedral angles of β hydrogens with respect to the axes of the nearest p-orbitals bearing the main part of the localized spin density. The calculated hyperfine couplings are in good agreement with the experimental values, and the calculated couplings and angles satisfy the Heller-McConnell relationship, which validates our approach to measure hyperconjugation. Significantly, it is the endo β-hydrogen on the single methylene bridge of the housanes 1a, 1b, and 1d that has the largest hyperconjugative interaction, and this is also the migrating hydrogen in the 1,2-shift reaction leading to the rearrangement of these housanes to cyclopentene radical cations. As a result of this stereoelectronic preference, the migrating entity from the methylene bridge is the endo rather than the exo bond, irrespective of the nature of the substituent. Accordingly, for the 1a-1d housanes, the key role of hyperconjugation lowers the endo C-H or C-Me bond strength selectively, and thereby assists the preferred sigmatropic migration of the endo substituent to the bridgehead carbon. By comparison, the extent of hyperconjugation is found to be much reduced in the cyclopropane radical cations 2a-2d, and the latter species do not undergo the corresponding 1,2-shift rearrangement reaction. This absence of reactivity in 2a-2d is therefore attributed to the weaker hyperconjugative interaction as well as to the less favorable energetics for the overall reaction ​
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