Curtin–Hammett principle

The Curtin–Hammett principle is a principle in chemical kinetics proposed by David Yarrow Curtin and Louis Plack Hammett. It states that, for a reaction that has a pair of reactive intermediates or reactants that interconvert rapidly (as is usually the case for conformational isomers), each going irreversibly to a different product, the product ratio will depend both on the difference in energy between the two conformers and the free energy of the transition state going to each product. As a result, the product distribution will not necessarily reflect the equilibrium distribution of the two intermediates. The Curtin–Hammett principle has been invoked to explain selectivity in a variety of stereo- and regioselective reactions.

The Curtin–Hammett principle applies to systems in which different products are formed from two substrates in equilibrium with one another. The rapidly interconverting reactants can have any relationship between themselves (stereoisomers, constitutional isomers, conformational isomers, etc.). Product formation must be irreversible, and the different products must be unable to interconvert.

For example, given species A and B that equilibrate rapidly while A turns irreversibly into C, and B turns irreversibly into D:

K is the equilibrium constant between A and B, and k₁ and k₂ are the rate constants for the formation of C and D, respectively. When the rate of interconversion between A and B is much faster than either k₁ or k₂, then the Curtin–Hammett principle tells us that the C:D product ratio is not equal to the A:B reactant ratio, but is instead determined by the relative energy of the transition states. If reactants A and B were at identical energies, the product ratio would depend only on the activation energy of the reactions leading to each respective product. However, in a real-world scenario, the two reactants are likely at somewhat different energy levels, although the barrier to their interconversion must be low for the Curtin–Hammett scenario to apply. In this case, the product distribution depends both on the relative quantity of A and B and on the relative activation barriers to the corresponding products C and D.

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