Influence of Heavy-Atom Tunneling on Pericyclic Reactions in Biosynthesis: A Computational Study

Understanding the kinetics of reactions in biosynthetic pathways requires accounting for the contribution of quantum mechanical tunneling to the rates. Whereas hydrogen tunneling in biology is well established, the extent of heavy-atom tunneling in biochemical reactions has been very little studied. We report computational results (M06-2X/cc-pVDZ) on rate constants for electrocyclic ring closures and [3,3] sigmatropic shifts, processes dominated by heavy-atom motions, that are proposed steps in the biosynthesis of four representative natural products. Using direct dynamics and canonical variational transition state theory with and without the small curvature tunneling approximation, predicted rate constants suggest that heavy-atom tunneling contributes 21% to the electrocyclization step leading to (+)-occidentalol (3), and 28% to the Cope rearrangement leading to a close analogue of dictyoxepin (4), at 298 K. Key structural factors that lead to faster rates at a given temperature and higher tunneling percentages include tethers between the carbons forming a new σ bond and the release of ring strain from opening of a small ring. Computed ¹²C/¹³C kinetic isotope effects for cyclization to 3 provide a possible experimental test of the predictions.