Curtin-Hammett Principle

The Curtin-Hammett Principle

The Curtin-Hammett Principle is a key concept in physical organic chemistry that explains the product distribution in reactions where multiple conformational isomers of a reactant can interconvert rapidly, and the reaction proceeds through each conformer to a distinct product. This principle is particularly relevant when the interconversion of the conformers is faster than the rate of their reaction to form products. Importantly, the relative amounts of the products depend not on the equilibrium distribution of the conformers but on the difference in free energy between the transition states leading to the products.

Key Features of the Curtin-Hammett Principle

  1. Rapid Equilibration: The interconversion between conformers or reactants must be fast relative to the rate of product formation.

  2. Irreversible Product Formation: Once a product forms, it does not revert back to the reactant or conformers.

  3. Product Distribution: The product ratio is determined by the relative free energies of the transition states leading to each product, not the equilibrium ratio of the starting conformers.

  4. Kinetically Controlled Reaction: The principle operates under kinetic control, meaning the pathway with the lower activation energy dominates.

 

Curtin-Hammett Principle with Case Scenarios

Consider the equilibrium shown in Figure 1, where A and B are two conformations of a reactant, and C and D are two products formed from A and B, respectively. The Curtin-Hammett Principle applies when the energy barrier for the interconversion of A and B is much lower than the activation energies for their reactions to form C and D. The product distribution depends on the free energies of activation of the two reactions, and there are four possible scenarios:

Case I

The more stable conformation (A or B) leads to the major or exclusive product (C or D), provided the rate of reaction for the more stable conformation is higher than that of the less stable conformation.

An example of this is E2 elimination of 2-haloalkanes.

 

Case II

The less stable conformation leads to the major product, provided the rate of reaction for the less stable conformation is higher than that of the more stable conformation.

The alkylation of tropane with methyl iodide provides a classic example of this Curtin–Hammett scenario. In this reaction, the major product arises from a less stable conformation, where the methyl group adopts an axial position on the six-membered piperidine ring. This less stable conformer reacts through a more stable transition state, leading to the formation of the major product. As a result, the distribution of conformations in the ground state does not correspond to the product distribution.

Case III

The more stable conformation can lead to the major product even if the rates of reaction for the two conformations are comparable. This occurs when the stability of the more stable conformation compensates for the comparable reaction rates.

An example is the oxidation of piperidines.  The conformation with the methyl group equatorial position is more stable.  A product distribution of 95:5 indicates the more stable conformer is more reactive.

Case IV

When the two conformations are equally stable (i.e., equally populated in equilibrium), the major product will be derived from the conformation associated with the lower free energy of activation for its reaction pathway.

This scenario can be illustrated with trans-2-halocyclohexanol. The diequatorial conformer is stabilized by intramolecular hydrogen bonding, while the diaxial conformer benefits from the absence of electrostatic repulsion between the two dipoles. As a result, a balance is achieved, and the two conformers are nearly equally populated. However, when trans-2-halocyclohexanol is treated with base, only the trans-diaxial conformer undergoes epoxide formation due to the favorable conformational alignment (anti-periplanar) of the reacting groups.

Other Examples

Example 1: Epimerization in Sugars

Consider the epimerization of D-glucose to D-mannose in aqueous solution. The equilibrium mixture of glucose and mannose favors glucose because it is thermodynamically more stable. However, under certain reaction conditions, mannose may form preferentially due to a lower energy transition state for the reaction pathway leading to mannose.

Example 2: Alkene Isomerization

The isomerization of cis-2-butene and trans-2-butene to form distinct products can be described using the Curtin-Hammett Principle. Even if cis-2-butene is less stable, the pathway leading from cis-2-butene to a particular product may have a lower activation energy, resulting in the predominant formation of that product.

Example 3: Asymmetric Synthesis

In asymmetric synthesis, the Curtin-Hammett Principle is often invoked to explain enantioselectivity. For instance, consider a reaction where two conformers of a chiral substrate interconvert. Even if one conformer is less abundant, it may lead to a product via a more favorable transition state, thus dominating the product distribution.

Summary

The Curtin-Hammett Principle is a fundamental concept that provides insight into the kinetic control of product distributions. It emphasizes the role of transition state energies over reactant stability and is widely applicable across organic, biological, and industrial chemistry. Understanding and applying this principle allows chemists to predict and control reaction outcomes, making it a cornerstone of modern chemical theory.