Though recognized to occur in organic systems, the breadth of involvement of heavy-atom tunneling has not been established. Doubleday, Greer and coworkers have examined 13 simple organic reactions sampling pericyclic reactions, radical rearrangements and SN2 reactions for heavy-atom tunneling.1 A few of these reactions are shown below.

Reaction rates were obtained using the small curvature tunneling approximation (SCT), computed using Gaussrate. Reaction surfaces were computed at B3LYP/6-31G*. The tunneling correction to the rate was also estimated using the model developed by Bell: kBell = (u/2)/sin(u/2) where u = hν‡/RT and ν‡ is the imaginary frequency associated with the transition state. The temperature was chosen so as to give a common rate constant of 3 x 10-5 s-1. Interestingly, all of the examined reactions exhibited significant tunneling even at temperatures from 270-350 K (See Table 1). The tunneling effect estimated by Bell’s equation is very similar to that of the more computationally demanding SCT computation.

Table 1. Tunneling contribution to the rate constant

Reaction

% tunneling

95

35

17

28

CN– + CH3Cl → CH3CN + Cl– (aqueous)

45

This study points towards a much broader range of reactions that may be subject to quantum mechanical tunneling than previously considered.

(Note: The original post had swapped some of the values in Table 1. These have now been corrected. My thanks to Drs. Greer and Doubleday for bringing this to my attention.)

References

1. Doubleday, C.; Armas, R.; Walker, D.; Cosgriff, C. V.; Greer, E. M., "Heavy-Atom Tunneling Calculations in Thirteen Organic Reactions: Tunneling Contributions are Substantial, and Bell’s Formula Closely Approximates Multidimensional Tunneling at ≥250 K." Angew. Chem. Int. Ed. 2017, 56, 13099-13102, DOI: 10.1002/anie.201708489.