The Benzidine rearrangement. Computed kinetic isotope effects.

Kinetic isotope effects have become something of a lost art when it comes to exploring reaction mechanisms. But in their heyday they were absolutely critical for establishing the mechanism of the benzidine rearrangement[1]. This classic mechanism proceeds via bisprotonation of diphenyl hydrazine, but what happens next was the crux. Does this species rearrange directly to the C-C coupled intermediate (a concerted [5,5] sigmatropic reaction) or does it instead form a π-complex, as famously first suggested by Michael Dewar[2] [via TS(NN] and only then in a second step [via TS(CC)] form the C-C bond? Here I explore the isotope effects measured and calculated for this exact system.


It boils down to the following. It was supposed that if the mechanism was a concerted [5,5] sigmatropic shift, then both the N-N and the C-C bonds would be breaking/forming at the transition state and both N and C isotope effects would be expected. However, if a π-complex were formed, then either TS(NN) OR TS(CC) would be the rate determining step, and so either a NN OR a CC isotope effect should manifest, but not BOTH. The experiment carried out by Henry Shine and colleagues was thus expected to be the definitive one.[3] The results (in aqueous ethanol, at 273K) revealed the following: k(2H/1H) = 0.962, k(14C/12C) = 1.013, k(13C/13C) = 1.013, k(15N/14N) = 1.041. This might have appeared to prove conclusively that the reaction was concerted, involving both the C-C and N-N bonds; in other words a [5,5] sigmatropic rearrangement.

The quantum mechanical (closed shell) surface reveals only two separate transition states, TS(NN) and TS(CC), and so at first sight seems to contradict the experimental isotope inference. But the experimental values are very unlikely to be wrong. So how can one reconcile these two methods? Well, the answer is not to give up, but to calculate the isotope effects for BOTH transition states, and see if either of them matches the experimental result. Here are these calculations:

TS k(2H/1H) k(14C/12C) k(13C/13C) k(15N/14N)
CC  0.946  1.050  1.050  1.032
NN  1.002  1.008  1.007  1.075
Expt  0.962  1.013  1.013  1.041

The match between experiment and theory for TS(CC) is reasonable (given the approximations in both the theory and the difficulty of the experiments and ensuring isotopic purities) but not so for TS(NN). But TS(CC) is a “stepwise-concerted” reaction as a closed shell singlet; as shown in the  IRC computed from TS(CC). 

Yamabe and co[4] have come to similar conclusions (their model used a dication rather than an ion-pair). In the latest twist, Ghigo et al[5] used the same model as here (HCl to provide protonation as an ion-pair) but identified biradical (radical-cation) character at the transition state. The latter group also calculated kinetic isotope effects[6] for the open shell biradical TS, finding an even better match with experiment than above.

So this see-saw mechanism has oscillated between a stepwise π-complex, then a direct [5,5] rearrangement and in more recent times using computational modelling, a concerted [5,5] sigmatropic proceeding via an initially formed π-complex, and (finally) via a multi-step mechanism proceeding through a biradical π-complex and involving radical coupling, which nevertheless appears to behave in some aspects as a concerted [5,5] rearrangement. It is fascinating that a simple diprotonation of a hydrazine could so readily induce biradical character, and that such an apparently simple reaction could have so many twists and turns!

For one 14C-12C pair.


  1. H.J. Shine, H. Zmuda, K.H. Park, H. Kwart, A.G. Horgan, and M. Brechbiel, "Benzidine rearrangements. 16. The use of heavy-atom kinetic isotope effects in solving the mechanism of the acid-catalyzed rearrangement of hydrazobenzene. The concerted pathway to benzidine and the nonconcerted pathway to diphenyline", Journal of the American Chemical Society, vol. 104, pp. 2501-2509, 1982.
  2. M. Dewar, and H. McNicoll, "Mechanism of the benzidine rearrangement", Tetrahedron Letters, vol. 1, pp. 22-23, 1959.
  3. W. Subotkowski, L. Kupczyk-Subotkowska, and H.J. Shine, "The benzidine and diphenyline rearrangements revisited. 1-14C and 1,1'-13C2 kinetic isotope effects, transition state differences, and coupled motion in a 10-atom sigmatropic rearrangement", Journal of the American Chemical Society, vol. 115, pp. 5073-5076, 1993.
  4. S. Yamabe, H. Nakata, and S. Yamazaki, "π Complexes in benzidine rearrangement", Organic & Biomolecular Chemistry, vol. 7, pp. 4631, 2009.
  5. G. Ghigo, A. Maranzana, and G. Tonachini, "A change from stepwise to concerted mechanism in the acid-catalysed benzidine rearrangement: a theoretical study", Tetrahedron, vol. 68, pp. 2161-2165, 2012.
  6. G. Ghigo, S. Osella, A. Maranzana, and G. Tonachini, "The Mechanism of the Acid‐Catalyzed Benzidine Rearrangement of Hydrazobenzene: A Theoretical Study", European Journal of Organic Chemistry, vol. 2011, pp. 2326-2333, 2011.

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One Response to “The Benzidine rearrangement. Computed kinetic isotope effects.”

  1. […] So, putting all this together, one might infer that armed with a computed transition state structure for the benzidine rearrangement, it is trivial to compute the kinetic isotope effects and hence to see if they correspond to those measured. You might expect a report on this in a future post here. […]

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