Density functional study of the oxy-Cope rearrangement

With the goal of explaining the very large rate acceleration in the anion-a ssisted Cope rearrangement, the behavior of the prototypes of the Cope rear rangements, namely hexa-l,5-diene (4), hexa-1,5-dien-3-ol (5), and the oxy anion 6 of the latter were compared. For this purpose, two-dimensional DFT (hybrid B3LYP functionals with 6-31G* basis set) potential-energy surfaces (PESs) were computed, based on two interatomic distances. As the reliabilit y of DFT/B3LYP-computed energies can not be taken for granted, we first per formed model computations on the experimentally well-studied bridged homotr opylidenes 1-3. Then, the transition states of the Cope rearrangements of 3 -methylhexa-1,5-dien-3-ol (7), (2Z,4Z,7Z)-cyclonona-2,4,7-trien-1-ol (9), 1 -methoxy-2-endo-vinyibicyclo[2.2.2]oct-5-en-2-exo-ol (11), and (1S,2R)-2-hy droxy-1-methyl-2-vinylbicyclo[4.4.0]dec-6-en-8-one (arbitrary numbering, 13 ) and of their oxy anions 8, 10, 12, and 14, respectively, were computed by the same method. These examples were chosen because kinetic data have been measured for most of them (except for 13 and 14) and/or because they furni shed already important contributions to the discussion of the character of the Cope rearrangement. The computation of DeltaG(double dagger) for a give n temperature allowed to calculate the rate constants at that temperature f or the different rearrangements and to compare them with the experimental d ata. In the cases of the neutral and anionic oxy-Cope rearrangements, the e quation Delta DeltaG(double dagger) = 2.3026.RT.Delta pK(a) suggested a cor relation between the difference in the pK(a) values of the pair of reactant s and the pair of transition states and the change of the two free energies of activation.