The Sn2 reaction and the anomaly of carbon.

It was three years ago that I first blogged on the topic of the Sn2 reaction. Matthias Bickelhaupt had suggested that the Sn2 reaction involving displacement at a carbon atom was an anomaly; the true behaviour was in fact exhibited by the next element down in the series, silicon. The pentacoordinate species shown below (X=Si) is naturally a minimum, and the fact that for carbon (X=C) one gets instead a transition state resulting in a significant thermal barrier (~ 20 kcal/mol) was a manifestation of abnormal behaviour.

The argument was that carbon as an atom was too small to fit snugly into a box of width ~5Å defined by the positions of two e.g. bromine atoms at more or less their closest possible approach, and instead rattled around between the two halogens, needing to surmount a barrier at the midpoint of the box. Silicon on the other hand being larger, fitted nicely into this box at the centre, and thus being unable to rattle around represented instead a minimum in the potential energy surface. I note (parenthetically) that a similar reason is often used to explain why hydrogen bonds to F are both rare and weak, whereas those to O are common and strong.

As part of a project to create a library of reaction mechanism animations, I calculated the IRC for the reaction above (X=C). This one is slightly different from those one may find in the research literature and textbooks; the counter-ion (Y=Na⁺) is also included so as to create a neutral system overall. The method is the usual ωB97XD/6-311+G(d,p)/SCRF=water.

If you watch carefully, you will see that at the early and late stages of the reaction, the bromine moves, but during the middle part of the reaction both bromine atoms are absolutely stationary and it is the carbon now that adopts the motion, rattling between the two bromine atoms. This aspect can also be seen very clearly in the two plots below:

Note in particular how the gradient norm plot changes in character at IRC ± 3; the central region represents motion of carbon inside the “box”, the region outside of the box that of the bromine. I think its fascinating how such an apparently simple reaction can carry such insight into molecular behaviour.