Thermal [1,5] Hydrogen Sigmatropic Shifts in cis,cis-1,3-Cyclononadienes Probed by Gas-Phase Kinetic Studies and Density Functional Theory Calculations

The kinetics of gas-phase thermal [1,5] hydrogen shifts interconverting the five isomeric mono-deuterium-labeled cis,cis-1,3-cyclononadienes have been followed at four temperatures from 240 to 287 °C. The activation parameters found were E a = 37.1 ± 0.8 kcal/mol, log A = 11.6 ± 0.3, ΔH ⧧ = 36.0 ± 0.8 kcal/mol, and ΔS ⧧ = −9.0 ± 0.3 eu. Density functional theory based calculations have provided geometries and energies for the ground-state cyclononadiene conformational isomers, for the transition states linking one to another, and for the transition states for [1,5] hydrogen shifts responsible for isomerizations among the five labeled dienes. A generalized formulation of the Winstein-Holness equation is presented and applied to the complex system, one that involves 11 ground-state conformers, 10 transition states separating them, and five transition states for [1,5] hydrogen shifts. The value for the empirical E a derived from calculated mole fractions of ground-state conformers and calculated energies for specific ground-state conformers and [1,5] hydrogen shift transition structures was 37.5 kcal/mol, in excellent agreement with the experimentally obtained activation energy. The significance of conformational options in various ground states and transition structures for the [1,5] hydrogen shifts is considerable, an inference that may well have general applicability.