Houk and Vanderwal have examined the dyotropic rearrangement of an interesting class of polycyclic compounds using experimental and computational techniques.¹ The parent reaction takes the bicyclo[2.2.2]octadiene 1 into the bicyclo[3.2.1]octadiene 3. The M06-2X/6-311+G(d,p)/B3LYP/6-31G(d) (with CPCM simulating xylene) geometries and relative energies are shown in Figure 1. The calculations indicate a stepwise mechanism, with an intervening zwitterion intermediate. The second step is rate determining.

1 (0.0)	TS1 (35.6)
2 (21.9)	TS2 (40.1)
3 (-4.2)

Figure 1. B3LYP/6-31G(d) and relative energies (kcal mol^-1) at M06-2X/6-311+G(d,p).

Next they computed the activation barrier for the second TS for a series of substituted analogs of 1, with various electron withdrawing group as R₁ and electron donating groups as R₂, and compared them with the experimental rates.

Further analysis was done by relating the charge distribution in these TSs with the relative rates, and they find a nice linear relationship between the charge and ln(k_rel). This led to the prediction that a cyano substituent would significantly activate the reaction, which was then confirmed by experiment. Another prediction of a rate enhancement with Lewis acids was also confirmed by experiment.

A last set of computations addressed the question of whether a ketone or lactone would also undergo this dyotropic rearrangement. The lactam turns out to have the lowest activation barrier by far.

References

(1) Pham, H. V.; Karns, A. S.; Vanderwal, C. D.; Houk, K. N. "Computational and Experimental Investigations of the Formal Dyotropic Rearrangements of Himbert Arene/Allene Cycloadducts," J. Am. Chem. Soc. 2015, 137, 6956-6964, DOI: 10.1021/jacs.5b03718.

InChIs

1: InChI=1S/C11H11NO/c1-12-10(13)7-9-6-8-2-4-11(9,12)5-3-8/h2-5,7-8H,6H2,1H3
InChIKey=MNYYUIQDOAXLTK-UHFFFAOYSA-N

3: InChI=1S/C11H11NO/c1-12-10(13)6-9-3-2-8-4-5-11(9,12)7-8/h2-6,8H,7H2,1H3
InChIKey=OHEBSZKLNGLATD-UHFFFAOYSA-N