# Elucidation of Reaction Mechanisms - Kinetic Isotope Effects

## Secondary Kinetic Isotope Effects - SKI

In contrast to primary kinetic isotope effects, an effect is called secondary kinetic isotope effect if the chemical bond varied by the isotopic exchange is not cleaved during the reaction. Depending on the distance between the isotope and the actual reaction center, the secondary kinetic isotope effects are called α, β, or γ (etc.) secondary kinetic isotope effect. Usually, they are smaller than primary kinetic isotope effects and exhibit kH/kD values of about 0.7 to 1.5. Consequently, secondary kinetic isotope effects cannot be differentiated from primary kinetic isotope effects merely by their values. The values of β secondary kinetic isotope effects are usually very similar to that of α secondary kinetic isotope effects. As far as γ or δ (and so on) secondary kinetic isotope effects are concerned, the increasing distance of the isotope from the reaction center usually leads to kH/kD values of nearly one - that is, these kinetic isotope effects are barely noticeable. Therefore, γ (and "higher") secondary kinetic isotope effects play only a minor role in the investigation of reaction mechanisms.

Secondary kinetic isotope effects are also caused by a change in the $Ea$ of the rate-determining step. However, the alteration of the activation energy $Ea$ by secondary kinetic isotope effects is the result of the different influence of hybridization and hyperconjugation on the energy of the X-H/X-D bond's zero-point vibration, according to the type of isotope. At this point, the connections between the activation energy $Ea$, hybridization, hyperconjugation, and the zero-point energy can not be explained in any further detail.

According to the dependence of the activation energy $Ea$ on the hybridization of the starting products' conversion into the transition state of the rate-determining step, the α secondary kinetic isotope effects can additionally be classified as:

• Normal α secondary kinetic isotope effect (kH/kD > 1): In the case of this effect, the reaction rate is reduced (kH/kD > 1) by exchanging an atom for one of its heavier isotopes (e.g. H for D). The normal α secondary kinetic isotope effect occurs when the degree of hybridization of the reaction center in the is lower than that in the starting product of the rate-determining step - that is, for instance, when the hybridization is converted from sp3 to sp2 or from sp2 to sp.
Fig.1
Normal α secondary kinetic isotope effect [1].
• Inverse α secondary kinetic isotope effect (kH/kD < 1): In the case of this effect, the reaction rate increases (kH/kD < 1) by exchanging an atom for one of its heavier isotopes (e.g. H for D). The inverse α secondary kinetic isotope effect occurs when the degree of hybridization of the reaction center in the transition state is higher than that in the starting product of the rate-determining step - that is, for instance, when the hybridization is converted from sp to sp2 or from sp2 to sp3.
Fig.2
Inverse α secondary kinetic isotope effect [2].

According to the facts and connections described above, some information about the rate-determining step and the structure of the transition state can be inferred not only from primary but also from secondary kinetic isotope effects.

### Literature

1. Shiner Jr., V.J., Rapp, M.W., Pinnick Jr., H.R., J. Am. Chem. Soc. 1970, 92, 232.
2. do Amaral, L., Bull, H.G., Cordes, E.H., J. Am. Chem. Soc. 1972, 7579.
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