The cis-hexatriene electrocyclization : Attempted calculation of the transition state geometry

A model has been developed to permit calculation of the energy changes associated with the electrocyclic reaction of cis-hexatriene to 1,3-cyclohexadiene. A novel method for solving the problems associated with calculations of the pi system energy and the energy of the forming single bond as the terminal carbons undergo rehybridization was developed. The result permits calculation of the total energy in terms of contributions from the forming sigma bond, the pi system, non-bonded interactions and bond energy changes resulting from rehybridization. The angle of rotation θ about the C₂C₃ and C₄C₅ bonds was used as an approximation to the reaction coordinate. Surprisingly the plot of energy vs θ showed no maximum for either the disrotatory or the conrotatory stereopath. Failure to produce a transition state was attributed to problems with assignment of a reasonable kcal equivalent to the Hückel gb, and an artificial device was proposed to solve the problem. The geometry of the disrotatory transition state achieved in this manner suggests that non-bonded interactions between hydrogens on the terminal carbon are not serious, but the dihedral angle between the p-orbitals at C₂C₃ (and C₄C₅) leads to a significant degree of isolation of C₂ and C₅ from the remainder of the pi system.