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1u state has two directions of negative curvature, one of them corresponding to the twisting deformation.
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We had previously encountered a case of a bisallylic radical cation, bicyclo-[3.3.0]octa-2.6-diene-4,8-diyl, with a similar CR transition involving the bonding and the antibonding combination of allyl-NBMOs (Bally, T.; Truttmann, L.; Dai, S.; Wang, J. T.; Williams, F. Chem. Phys. Lett. 1993, 212, 141). However, in that case, the molecular framework did not allow for a relaxation of the excited state to a new ground-state equilibrium structure with the same atomic connectivities but with a distinct electronic structure (instead, this species underwent photoinduced tautomerization).
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2 by 0.2). In ROHF, the preference for localized states is smaller, but this method is useless in the present context, because it ignores spin polarization and, in addition, shows pronounced symmetry breaking in the localized state. A way out of this impasse would be to use CASSCF (which models spin polarization through an admixture of singly excited states). We did indeed carry out such calculations, but they also invariably resulted in localized structures, in disagreement with experiment for the parent radical cation.
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The parent system is small enough that it could possibly be treated by coupled cluster methods, but even those methods would probably find it difficult to strike the right balance between the opposing forces, given the dubious quality of the one-electron wave functions on which they would have to be based in the present case.
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The difference in the endo/exo coupling constants predicted by B3LYP is usually too large, but the average value is predicted correctly within <0.1 mT in allylic radicals carrying methyl groups (Müller, B.; Bally, T. Unpublished results).
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