Heavy-Atom Tunneling Calculations in Thirteen Organic Reactions: Tunneling Contributions are Substantial, and Bell's Formula Closely Approximates Multidimensional Tunneling at ≥250 K.

Multidimensional tunneling calculations are carried out for 13 reactions, to test the scope of heavy-atom tunneling in organic chemistry, and to check the accuracy of one-dimensional tunneling models. The reactions include pericyclic, cycloaromatization, radical cyclization and ring opening, and SN 2. When compared at the temperatures that give the same effective rate constant of 3×10-5  s-1 , tunneling accounts for 25-95 % of the rate in 8 of the 13 reactions. Values of transmission coefficients predicted by Bell's formula, κBell  , agree well with multidimensional tunneling (canonical variational transition state theory with small curvature tunneling), κSCT . Mean unsigned deviations of κBell vs. κSCT are 0.08, 0.04, 0.02 at 250, 300 and 400 K. This suggests that κBell is a useful first choice for predicting transmission coefficients in heavy-atom tunnelling.