Curtin-Hammett principle

The Curtin-Hammett principle is a principle in chemica l kinetics that was 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 of conformers ) each going irreversibly to a different product, the product ratio will depend only on the difference in the free energy of the transition state going to each product, and not on the equilibrium constant between the intermediates.

Example

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

C

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 will not reflect K, but the relative energy of the transition states.

The reaction coordinate free energy profile can be represented by the following scheme:G

The ratio of products will depend only on the value labeled ………. in the figure: C will be the major product, because the energy of TSl is lower than the energy of TS2. It doesn't matter whether A is more stable than B or not, or by how much This can be understood qualitatively by thinking what would happen if the free energy of A were increased, while keeping everything else constant. On one hand, ………… would become smaller, which would make k1 larger, therefore favoring the formation of C. But on the other hand, the amount of A in equilibrium would decrease, because the change in …….would increase the value of K, favoring B. These

two effects cancel out, leading to the conclusion that the relative energies of A and B don't matter. This can also be proved algebraically as shown below.

DerivationThe rate of formation for compound C from A is given as

Application to stereo selective reactions

The Curtin-Hammett principle is used to explain the selectivity ratios for stereo selective reactions, such as in kinetic resolution. A typical example is the following: a prochiral molecule binds to a chiral catal y st, forming a pair of diastereomeric intermediates, depending on which face of the substrate was bound to the catalyst. These intermediates equilibrate rapidly (like A and B in the diagram above), and each one then leads to a different enantiomer of the product through the rate determinin g step.

Curtin-Hammett principleIn a chemical reaction that yields one product (X) from one conformationalIsomer (A') and a different product (Y) from another conformational isomer (A") (and provided these two isomers are rapidly interconvertibleRelative to the rate of product formation, whereas the products do notUndergo interconversion) the product composition is not in direct proportion to the relative concentrations of the conformational isomers in the substrate; it is controlled only by the difference in standard free energies …………. of the respective transition states.

It is also true that the product composition is formally related to the relative concentrations of the conformational isomers A' and A' '(i.e. the conformational equilibrium constant) and the respective rate constants of their reactions; these parameters are generally though not invariably unknown.

The diagram below represents the energetic situation for transformation of

interconverting isomers A and A' into products X and Y.

The Curtin-Hammett Principle

Consider a reaction in which two products C and D can be

Formed from A. A is in equilibrium with B. The Curtin-Hammett Principlestates that the position of the equilibrium between A and B does not control the product ratio of C and D. The activation energies to reach TS2 and TS3 are considerably larger than TS1. A and B interconvert rapidly.

In other words: If you have to climb the Alps the Black Forest is not going to stop you (approaching from the North). There are numerous applications of the Curtin-Hammett Principle, the most obvious one are conformational equilibrium in ring systems. The equilibrium between two conformers is established rapidly in comparison with the product-forming steps.