Relative Values for Deuterium and Tritium Isotope Effects The Swain-Schaad Relation

5 Relative Values for Deuterium and Tritium Isotope Effects The Swain-Schaad Relation 

We will use reaction 10.15 to illustrate two important concepts of kinetic isotope effect studies. The first concerns the relation between isotope effects of different isotopes of the same element, say D and T. We denote the rate constant of reaction 10.15 by kn and consider isotope effects when one hydrogen in the a-position is substituted by deuterium or tritium  

In reactions 10.16 and 10.17 we label the corresponding rate constants ko and kT, respectively. The relationship between kn/ko and kp/kr is approximately described by the Swain-Schaad equation 

In deriving Equation 10.18 one assumes that the motions of the H, D, and T can be treated in the ZPE approximation and the only important isotope sensitive motions are the RH, RD, or RT stretching modes which shift significantly on the transfer from reactant to transition state. In the ZPE approximation 

For harmonic oscillators recall that the ZPE s, (ZPE = (l/2)hc(//p,)1/2), and ZPE differences scale proportionally to (1/p-h) and (1/ jid), respectively. The q s are oscillator reduced masses and / is the isotope independent force constant. Thus, writing equations analogous to Equation 10.19 for tritium substitution, and taking the ratio, we obtain kH/kT = (kH/kD)x where x, the Swain-Schaad exponent in the harmonic approximation is expressed 

---