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

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 S(N)2. When compared at the temperatures that give the same effective rate constant of 3 x 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, k(Bell), agree well with multidimensional tunneling (canonical variational transition state theory with small curvature tunneling), k(SCT). Mean unsigned deviations of k(Bell) vs. k(SCT) are 0.08, 0.04, 0.02 at 250, 300 and 400 K. This suggests that k(Bell) is a useful first choice for predicting transmission coefficients in heavy-atom tunnelling.