Heavy-Atom Tunneling as the Dominant Pathway in a Solution-Phase Reaction? Bond Shift in Antiaromatic Annulenes

It is probably fair to say that many organic chemists view the concept of tunneling, even of hydrogen atoms, with some skepticism.' Heavy-atom tunneling is thus considered to be of negligible significance to chemical reactions.' The purpose of this communication is to point out that the bond shift reaction of [4n]annulenes could proceed by a mechanism that is primarily heavy-atom tunneling and that for cyclobutadiene in particular the tunneling process could constitute >97% of the total rate constant below 0 OC! The tunneling mechanism leads to the prediction of abnormally low activation entropies for the bond-shift reactions, in accord with experimental observation. The reaction coordinate for automerization of cyclobutadiene can be approximated by a single stretching motion. This is equivalent to treating cyclobutadiene as homonuclear diatomic molecule with the two pseudoatoms each having a massZ of 26 daltons (see Figure 1). The potential-energy profile for the bond-shifting reaction can be approximated as an intersection between two harmonic potential functions whose minima are separated on the reaction coordinate by a distance equal to the difference in length between the long and the short carbon-carbon bonds of cyclobutadiene. One could guess that this difference (AR) would be about 0.18 A, given typical lengths of 1.52 and 1.34 8, for the long (single) and short (double) bonds respectively. Recent molecular orbital calculat i o n ~ ~ ~ suggest that AR is about 0.198 8,. In the model used here the height of the potential-energy barrier is determined by AR and the force constant for the stretching vibration. If one assumes a plausible value of 1000 cm-* for the in-plane rectangular deformation6 (symmetry b,,), then the force constant for the pseudodiatomic molecule is calculated to be 1.532 X lo6 dyn/cm. This leads to a calculated potential barrier of 10.8 kcal/mol for the automerization reaction, which perhaps by co-