Swain-Schaad equation

The secondary deuterium KIEs obtained by converting the secondary tritium KIEs found for the E2 reactions of several different 2-arylethyl substrates into secondary deuterium KIEs with the Swain-Schaad equation (Swain et al., 1958) are in Table 36. As discussed above, one would expect the secondary deuterium isotope effect to reflect the extent to which rehybridization of the /3-carbon from sp3 of the reactant to sp2 in the product has taken place in the transition state. According to this reasoning, the secondary tritium EIE should be a good estimate of the maximum secondary tritium KIE. Because these reactions were not reversible, the EIE could not be measured. However, one can estimate the EIE (the maximum expected secondary KIE) using Hartshorn and Shiner s (1972) fractionation factors. The predicted EIE (Kh/Kd) values were 1.117 at 40°C and 1.113 at 50°C. Seven of the reactions... 

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... 

There are two ways in which an enzymic reaction can fail to satisfy the Swain-Schaad relationship, one of which is if tunneling occurs. In order to use violations of this rule to diagnose the presence of tunneling, it is necessary to eliminate the other possible reason for a violation, namely, limitation of the rate by more than one step. The derivation of the Swain-Schaad equation in Chart 3 assumes that the step that produces the isotope effect is fully rate-limiting, and if this should be untrue, then the relationship should fail without any significance for tunneling. 

Griffiths and Gutsche (23) recently studied the interconversion of deuterated mandelaldehyde dimer and 2-hydroxyacetophenone in pyridine to obtain information concerning the glyceraldehyde-dihydroxy-acetone rearrangement. Their results support an enolization mechanism requiring a base and an acid catalyst. They found a deuterium isotope effect of ca. 1.3 for the transformation of the aldehyde to the ketone. When they corrected this for the apparently differing amounts of the aldehyde form in equilibrium with the proteo dimer and the deuterio dimer, they obtained a value of 3.9. By the Swain-Schaad equation (26) ... 

The relative importance of non-zero-point contributions to heavy atom effects also makes exact comparisons of results with different isotopes of the same element difficult. There is no counterpart of the Swain-Schaad equation (equation 1.15) for isotopes of hydrogen, although for isotopes of carbon, the intuitive expectation that effects would be around double effects was confirmed eqn (3.15) held for a series of effects, with 1.6[Pg.106]

The relationship between deuterium and tritium primary kinetic isotope effects is given by the Swain—Schaad equation ... 

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... 

The primary T and D KIEs for cacodylate-catalysed C -hydron transfer from racemic 458 (equation 270), ku/ky = 1.8 0.1, obey the Swain-Schaad relation515 and are consistent with incomplete proton transfer in the rate-limiting TS516,517. 

It is important to note that these equations are based on the Swain-Schaad relationship, which assumes that there is no tunnelling in any of the isotopic reactions (the KIEs are semiclassical) and that the relationship between the KIEs is determined only by the masses of the hydrogen, deuterium and tritium atoms. The secondary and kfyko KIEs calculated both with and... 

The observed rate coefficient for exchange (L = H, D, or T) is fe bs = k k2 /(kh. ] + k2)- If the primary isotope effect on k2 is different from that on k1 and k... j it is argued that the experimental isotope effects feob s tklb s and feobs/ ob s will not be related by the Swain—Schaad relation, kH/kT = (feH/feD)1442 which is derived with reference to a single-step proton transfer [115, 128]. The size of the discrepancy will depend upon the value of /e, /fe , the amount of internal return. In the analysis of isotope effects for triphenylmethane exchange it is assumed that k2=k2 = k2 since this represents a diffusion step. By introducing aT = k- i /k2 and Kl = k /k j eqns. (82) and (83) are obtained. A third equation (84)... 

With the further approximation that the rest of the molecule is heavy compared to the hydron, it is seen that the zero point energy of a deuterated species is 1/ 2, and that of a tritiated species 1/ 3, that of a protiated species. Consequently, at ordinary temperatures, the Swain-Schaad relation (equation 1.15) holds. 

Equation (94) assumes that in Eq. (84) either Cr = 0 or " /(eq = 1-0, and that k = the so-called Swain-Schaad relationship, which seems to hold... 

For C-H bond cleavage, Equation (4) predicts a KIE equal to kH/kD 7 at room temperature. In the limit where the semiclassical theory is valid, experimentalists measure the Schaad-Swain exponent, ln(kH/A T)/ln(kD/kT). In the special case that the pre-Arrhenius factor A is the same for all isotopes (which is not true in most cases) then semiclassical theory predicts for this exponent a value 3.26. Deviations from this value are often interpreted as signs of increased tunneling, but in our opinion this line of argument is based on an oversimplified model of quantum transfer in condensed phases. Note that in tunneling reactions where the ratio Au/AD l, the semiclassical theory predicts an exponent that is not equal to 3.26 and is temperature dependent. 

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