The Curtin–Hammett principle is a principle in
chemical kinetics
Chemical kinetics, also known as reaction kinetics, is the branch of physical chemistry that is concerned with understanding the rates of chemical reactions. It is to be contrasted with chemical thermodynamics, which deals with the direction in ...
proposed by
David Yarrow Curtin
David (; , "beloved one") (traditional spelling), , ''Dāwūd''; grc-koi, Δαυΐδ, Dauíd; la, Davidus, David; gez , ዳዊት, ''Dawit''; xcl, Դաւիթ, ''Dawitʿ''; cu, Давíдъ, ''Davidŭ''; possibly meaning "beloved one". w ...
and
Louis Plack Hammett
Louis Plack Hammett (April 7, 1894 – February 9, 1987) was an American physical chemist. He is known for the Hammett equation, which relates reaction rates to equilibrium constants for certain classes of organic reactions involving subs ...
. It states that, for a reaction that has a pair of
reactive intermediate
In chemistry, a reactive intermediate or an intermediate is a short-lived, high-energy, highly reactive molecule. When generated in a chemical reaction, it will quickly convert into a more stable molecule. Only in exceptional cases can these com ...
s or
reactant
In chemistry, a reagent ( ) or analytical reagent is a substance or compound added to a system to cause a chemical reaction, or test if one occurs. The terms ''reactant'' and ''reagent'' are often used interchangeably, but reactant specifies a ...
s that interconvert rapidly (as is usually the case for
conformational isomers), each going irreversibly to a different product, the
product
Product may refer to:
Business
* Product (business), an item that serves as a solution to a specific consumer problem.
* Product (project management), a deliverable or set of deliverables that contribute to a business solution
Mathematics
* Prod ...
ratio will depend both on the difference in energy between the two conformers ''and'' the energy barriers from each of the rapidly equilibrating isomers to their respective products. Stated another way, the product distribution reflects the difference in energy between the two rate-limiting transition states. 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 relationship between the (apparent) rate constants and equilibrium constant is known as the
Winstein-
Holness equation.
Definition
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 (
stereoisomer
In stereochemistry, stereoisomerism, or spatial isomerism, is a form of isomerism in which molecules have the same molecular formula and sequence of bonded atoms (constitution), but differ in the three-dimensional orientations of their atoms i ...
s,
constitutional isomer
In chemistry, a structural isomer (or constitutional isomer in the IUPAC nomenclature) of a compound is another compound whose molecule has the same number of atoms of each element, but with logically distinct bonds between them. The term met ...
s, 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:
:
\bf\ \it <- _\bf \it\ <=> []\ \bf\ \it-> [k_]\ \bf D
''K'' is the equilibrium constant between A and B, and ''k''
1 and ''k''
2 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 ''k''
1 or ''k''
2, then the Curtin–Hammett principle tells us that the C:D product ratio is not equal to the equilibrium A:B reactant ratio, but is instead determined by the relative energies of the transition states (i.e., difference in the absolute energies of the transition states). If reactants A and B were at identical energies, the product ratio would depend only on the activation barriers 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 equilibrium ratio of A to B ''and'' on the relative activation barriers going to the corresponding products C and D. Both factors are taken into account by the difference in the energies of the transition states (ΔΔ''G''
‡ in the figure below).
The
reaction coordinate
In chemistry, a reaction coordinate is an abstract one-dimensional coordinate which represents progress along a reaction pathway. It is usually a geometric parameter that changes during the conversion of one or more molecular entities. In molec ...
free energy profile of a typical reaction under Curtin-Hammett control is represented by the following figure:

The ratio of products only depends on the value labeled ΔΔ''G''
‡ in the figure: C will be the major product, because the energy of TS1 is lower than the energy of TS2. A common but false assertion is that the product distribution does not in any way reflect the relative free energies of substrates A and B; in fact, it reflects the relative free energies of the substrates ''and'' the relative activation energies.
This misunderstanding may stem from failing to appreciate the distinction between "the difference of energies of activation" and "the difference in transition state energies". Although these quantities may at first appear synonymous, the latter takes into account the equilibrium constant for interconversion of A and B, while the former does not.
Mathematically, the product ratio can be expressed as a function of ''K'', ''k''
1, and ''k''
2 or in terms of the corresponding energies Δ''G''°, Δ''G''
1‡, and Δ''G''
2‡. By combining terms, the product ratio can be rewritten in terms of the quantity ΔΔ''G''
‡ alone, where ΔΔ''G''
‡ = (Δ''G''
2‡ – Δ''G''
1‡) + Δ''G''°. Inspection of the energy diagram (shown above) makes it apparent that ΔΔ''G''
‡ is precisely the difference in transition state energies.
Derivation
A generic reaction under Curtin–Hammett can be described by the following parameters:
:
\bf\ \it <- _\bf \it\ <=> []\ \bf\ \it-> [k_]\ \bf D
In order for rapid equilibration to be a good assumption, the rate of conversion from the less stable of A or B to the product C or D must be at least 10 times slower than the rate of equilibration between A and B.
The
rate of formation for compound C from A is given as
: