Kinetic Isotope Effect

The kinetic isotope effect (KIE) is the ratio of reaction rates of two different isotopically labeled molecules in a chemical reaction. It is also called "isotope fractionation," although this term is somewhat broader in meaning. A KIE involving hydrogen and deuterium is represented as:

with k_H and k_D are reaction rate constants.

An isotopic substitution can greatly modify the reaction rate when the isotopic replacement is in a chemical bond that is broken or formed in the rate limiting step. In such a case, the change is termed a primary isotope effect. When the substitution is not involved in the bond that is breaking or forming, a smaller rate change, termed a secondary isotope effect is observed. Thus, the magnitude of the kinetic isotope effect can be used to elucidate the reaction mechanism. If other steps are partially rate-determining, the effect of isotopic substitution will be masked. This masking of the intrinsic isotope effect has been referred to as 'kinetic complexity'.

Isotopic rate changes are most pronounced when the relative mass change is greatest, since the effect is related to vibrational frequencies of the affected bonds. For instance, changing a hydrogen atom to deuterium represents a 100% increase in mass, whereas in replacing carbon-12 with carbon-13, the mass increases by only 8%. The rate of a reaction involving a C-H bond is typically 6 to 10 times faster than the corresponding C-D bond, whereas a 12C reaction is only ~1.04 times faster than the corresponding 13C reaction (even though, in both cases, the isotope is one atomic mass unit heavier).

Isotopic substitution can modify the rate of reaction in a variety of ways. In many cases, the rate difference can be rationalized by noting that the mass of an atom affects the vibrational frequency of the chemical bond that it forms, even if the electron configuration is nearly identical. Heavier atoms will (classically) lead to lower vibration frequencies, or, viewed quantum mechanically, will have lower zero-point energy. With a lower zero-point energy, more energy must be supplied to break the bond, resulting in a higher activation energy for bond cleavage, which in turn lowers the measured rate (see, for example, the Arrhenius equation).

The Swain equation (also cited as the Swain-Schaad-Stivers equations) relate the intrinsic KIEs for the hydrogen isotopes to each other - i.e. using these relationships, one can extract the protium/tritium (H/T) KIE or the deuterium/tritium (D/T) KIE from the protium/deuterium KIE (H/D); similarly, if one of these KIEs is known, the other two can be extracted using the appropriate form of the Swain-Schaad equation.

The kinetic isotope effect leads to a specific distribution of deuterium isotopes in natural products, depending on the route they were synthesized in nature. By NMR spectroscopy, it is therefore easy to detect whether the alcohol in wine was fermented from glucose, or from illicitly added saccharose.

Isotopic effect expressed with Eq. (1) only refer to reactions that can be described with first-order kinetics. In all instances in which this is not possible, transient kinetic isotope effects should be taken into account using the GEBIK and GEBIF equations.