Kinetic Isotope Effect - Secondary Isotope Effect

Secondary Isotope Effect

The secondary kinetic isotope effect (SKIE) arises in cases where the isotopic substitution is remote from the bond being broken. The remote atom, nonetheless, influences the internal vibrations of the system that via changes in the zero point energy (ZPE) affect the rates of chemical reactions. Such effects are expressed as ratios of rate for the light isotope to that of the heavy isotope and can be "normal" (ratio is greater than or equal to 1) or "inverse" (ratio is less than 1) effects. SKIE are defined as α,β (etc.) secondary isotope effects where such prefixes refer to the position of the isotopic substitution relative to the reaction center (see alpha and beta carbon). The prefix α refers to the isotope associated with the reaction center while the prefix β refers to the isotope associated with an atom neighboring the reaction center and so on.

In physical organic chemistry, SKIE is discussed in terms of electronic effects such as induction, bond hybridization, or hyperconjugation. These properties are determined by electron distribution, and depend upon vibrationally averaged bond length and angles that are not greatly affected by isotopic substitution. Thus, the use of the term "electronic isotope effect" while legitimate is discouraged from use as it can be misinterpreted to suggest that the isotope effect is electronic in nature rather than vibrational.

SKIE's can be explained in terms of changes in orbital hybridization. When the hybridization of a carbon atom changes from sp3 to sp2, a number of vibrational modes (stretches, in-plane and out-of-plane bending) are affected. The in-plane and out-of-plane bending in an sp3 hybridized carbon are similar in frequency due to the symmetry of an sp3 hybridized carbon. In an sp2 hybridized carbon the in-plane bend is much stiffer than the out-of-plane bending resulting in a large difference in the frequency, the ZPE and thus the SKIE (which exists when there is a difference in the ZPE of the reactant and transition state). The theoretical maximum change caused by the bending frequency difference has been calculated as 1.4.

When carbon undergoes a reaction that changes its hybridization from sp3 to sp2, the out of plane bending force constant at the transition state is weaker as it is developing sp2 character and a "normal" SKIE is observed with typical values of 1.1 to 1.2. Conversely, when carbon's hybridization changes from sp2 to sp3, the out of plane bending force constants at the transition state increase and an inverse SKIE is observed with typical values of 0.8 to 0.9.

More generally the SKIE for reversible reactions can be "normal" one way and "inverse" the other if bonding in the transition state is midway in stiffness between substrate and product, or they can be "normal" both ways if bonding is weaker in the transition state, or "inverse" both ways if bonding is stronger in the transition state than in either reactant.

An example of an "inverse" α secondary kinetic isotope effect can be seen in the work of Fitzpatrick and Kurtz who used such an effect to distinguish between two proposed pathways for the reaction of d-amino acid oxidase with nitroalkane anions. Path A involved a nucleophilic attack on the coenzyme FAD, while path B involves a free-radical intermediate. As path A results in the intermediate carbon changing hybridization from sp2 to sp3 an "inverse" a SKIE is expected. If path B occurs then no SKIE should be observed as the free radical intermediate does not change hybridization. An SKIE of 0.84 was observed and Path A verified as shown in the scheme below.

Another example of a SKIE is the oxidation of benzyl alcohols by dimethyldioxirane where three transition states for different mechanisms were proposed. Again, by considering how and if the hydrogen atoms were involved in each, researchers predicted whether or not they would expect an effect of isotopic substitution of them. Then, analysis of the experimental data for the reaction allowed them to choose which pathway was most likely based on the observed isotope effect.