Disrotation calculations

SD(Q)-CI/6-31G //(2/2)CASSCF/6-31G calculations confirmed the qualitative expectation that coupled disrotation should be preferred to both conrotation and monorotation in the stereomutation of 9a. In addition, unlike the case in 8a, the calculations found that the preference for coupled rotation was enhanced by the addition of methyl groups to the terminal carbons of 10a. Hyperconjugative electron donation from the methyl groups in 10b and 10c enhances electron donation from the symmetric combination of 2p-n AOs on the terminal carbons into the antibonding orbitals of the C—F bonds at C2. 

Synthetically, the reaction is useless because complex mixtures generally result. In agreement with theoretical calculations a preferred outward disrotation in this rearrangement has been implicated however, experimental results are not clearcut due to configurational instability of allylic radicals under the rearrangement conditions. 

Primes with the AO basis of the product are used to denote the fact that the corresponding atomic orbitals x can differ from the AO basis of the reactant, for example because of different spatial orientation. This distinction between the AO bases of the reactant and the product is very important since it is just precisely from here that the possibility arises to exploit the formalism for the discrimination between the forbidden and the allowed mechanisms, i.e., in our case, between the conrotation and the disrotation. The basis of this discrimination are the so-called assigning tables, the physical meaning of which is just in providing the detailed specification of the mutual transformation between bases % and x. which is the necessary prerequisite for the calculation of the overlap integral S p. The same problem was encountered also by Trindle [33], and his mapping analysis failed to find broader use only because of considerable numerical complexity. On the other hand, the overlap determinant method solves this problem much more simply and its use is really a matter of seconds using only pen and paper. 

The preferred mode of ring-opening in the anion radicals (527) has been shown to be conrotatory, although the HOMO in the product is symmetrical and would predict disrotation. INDO MO calculations on the parent cyclobutene and buta-1,3-diene anion radicals, however, do predict the conrotatory mode. 

Like Hoffmann s EH calculations, the reaction dynamics calculations predict that double rotation should be favored over single rotation. However, the dynamics calculations predict that double rotation in cyclopropane should consist of a mixture of both conrotation and disrotation, with the former being favored over the latter by a factor of only about two. Unfortunately, the experiments on cyclopropane-rf2 can distinguish single from double rotation but cannot distinguish conrotation from disrotation or from a mixture of these two modes of double rotation. 

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