The rate of thermal rearrangement of...

The rate of thermal rearrangement of 3-aryl-2,2-dimethylmethylenecyclopropanes has been studied as a function of aryl substituents. Some of the data are given below. Examine the rate data for correlation with the Hammett $\sigma$-substituent constants. What conclusion do you draw about the mechanism?

Key Concepts

Hammett Equation

The Hammett equation relates the effect of substituents on the reactivity of aromatic compounds through their sigma constants. It allows one to correlate reaction rates or equilibrium constants with the electronic properties of substituents. In such studies, a linear free-energy relationship is sought between the log of the rate constant and the substituent constant, which indicates how changes in electron donation or withdrawal affect the reaction mechanism.

Substituent Effects

Substituent effects describe how different groups attached to a molecule can influence the rate or outcome of a reaction by altering electron density through inductive or resonance effects. In the context of rearrangements, electron-donating groups may stabilize developing positive charge in the transition state, while electron-withdrawing groups might destabilize it, leading to measurable changes in the observed reaction rates.

Transition State Charge Development

The correlation of reaction rates with Hammett sigma constants provides insight into what is happening in the transition state. A good correlation, especially with a significant reaction constant (?), indicates that charge is developing on the carbon attached to the aromatic ring. In this case, the data suggest that positive charge is being built up in the rate-determining step, as electron-donating substituents accelerate the reaction by stabilizing the developing cationic character.

Thermal Rearrangement Mechanism

In the thermal rearrangement of cyclopropane derivatives, the mechanism appears to involve a bond reorganization that results in a transition state with ionic (or partially ionic) character. The rate acceleration by electron-donating substituents, as revealed by their Hammett correlation, supports a mechanism where the formation of a cyclopropylcarbinyl cation-like transition state is rate-determining. This indicates a polar, concerted or stepwise rearrangement process rather than a fully concerted, non-polar pericyclic reaction.

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