Density Functional Study of the Oxy‐Cope Rearrangement

With the goal of explaining the very large rate acceleration in the anion‐assisted Cope rearrangement, the behavior of the prototypes of the Cope rearrangements, namely hexa‐1,5‐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 reliability of DFT/B3LYP‐computed energies can not be taken for granted, we first performed model computations on the experimentally well‐studied bridged homotropylidenes 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‐vinylbicyclo2.2.2]oct‐5‐en‐2‐exo‐ol ( 11 ), and (1S,2R)‐2‐hydroxy‐1‐methyl‐2‐vinylbicyclo4.4.0]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 furnished already important contributions to the discussion of the character of the Cope rearrangement. The computation of ΔG^≠ for a given temperature allowed to calculate the rate constants at that temperature for the different rearrangements and to compare them with the experimental data. In the cases of the neutral and anionic oxy‐Cope rearrangements, the equation ΔΔG^≠=2.3026⋅RT⋅ΔpK_a suggested a correlation between the difference in the pK_a values of the pair of reactants and the pair of transition states and the change of the two free energies of activation.