Ambimodal transition states in some organic reaction pathways

Question

In many computational studies, mechanisms appear to have so-called ambimodal transition states, i.e. a transition state which can lead to multiple products, in conflict to the common undergraduate idea of a reaction pathway.

To give an example, Houk, in Mechanisms and Origins of Periselectivity of the Ambimodal [6 + 4] Cycloadditions of Tropone to Dimethylfulvene,^[1] presents the following scheme:

^{Reaction pathway for [6 + 4] cycloadditions of Tropone to Dimethylfulvene. Taken from ref [1]}

In the scheme, TS-1 may either give 7 (the 'expected' product) or go directly to 6, completely skipping TS-Cope-1 (which would allow 7 and 6 to interconvert) — Houk describes this as an ambimodal transition state, that is one transition state that can lead to two possible products.

---

Although what he says makes sense, it seems to me that, given 6 is the lower energy product out of the two, it would be favoured thermodynamically anyway.

Upon further reading, I discovered the concept of valley ridge inflection, which appears to describe the phenomenon observed above, in which we completely 'miss' the intermediary transition state:

Why do these ambimodal transition states occur, and how does the situation differ from normal transition state theory?

---

Notes & References

^{[1]:Houk, K.N., J. Am. Chem. Soc. 2017, 139, 8251. DOI: 10.1021/jacs.7b02966}

Answer 1

Why do these ambimodal transition states occur?

I don't know that there is a general reason for that. Potential energy surfaces are complicated. Very often, there is an abundance of local minima, separated by potential energy barriers. It is similar to what happens with mountain chains and valleys, but with many dimensions.

One could argue that the opposite could be asked: why would there be a single minimum associated with each and every barrier? Why would there be exactly a single downhill valley behind each mountain chain, instead of, sometimes, two different valleys being similarly accessible, once you climb over the top of a hill?

How does the situation differ from normal transition state theory?

Transition state theory is a useful simplification, assuming a simple potential energy surface. It is useful because, at room temperature, the energy differences in the different possible paths are very often sufficient for a single reaction pathway to predominate, so that others effectively do not happen. When the temperature is comparable to the difference between the energies involved in different possible reaction pathways, the situation is more complicated.

Answer 2

ambimodal reaction path

The two different reaction trajectories from the 4+2 are both slightly lower in energy but they also are both energetically and geometrically relatively close to the Ea for the 4+2 reaction

For these pericyclic reactions ([4+2] vs [3,3],both pathways are "allowed". The cope rearrangement [3,3] has a lower Ea than the Diels-Alder, and the tajectory from the 4+2 Ts to the bifurcation for product formation is slightly energetically down hill from the 4+2 TS. Sigma bond formation is not complete, and thus its easy tor this reaction tajectory to slip down either side of this bifurcation.

It also interesting that if you execute the reverse reaction, you'll drop into the cope reaction, before you get the reverse Diels-Alder ( see Wooward-Katz)

RTP