Swain-Schaad relation

Another criterion that has been used for detecting the presence of tunnelling is that the Swain-Schaad relation (55)... 

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

The observation of a primary tritium isotope effect (H/T) that is substantially larger than the value predicted on the basis of the semiclassical Swain-Schaad relation (Chart 3) from a heavy-hydrogen (DAT) isotope effect. The same information can be expressed in terms of a Swain-Schaad exponent required to relate the two isotope effects that is substantially larger than the semiclassical value of 3.26. 

Albery, W.J. and Knowles, J.R. (1977). The determination of the rate-limiting step in a proton-transfer reaction from the breakdown of the Swain-Schaad relation. J. Am. Chem. Soc. 99, 637-638... 

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)... 

Actually this equilibrium constant was measured for an analogous reaction involving a similar carbon acid (9-phenylfluorene). The value of KT /KD for (83) was calculated from Kr /KH with the Swain—Schaad relation. Using this analysis for the isotope exchange of triphenylmethane, a value of aT = 0.66 0.04 was obtained which is similar to the value deduced from other experiments for a closely related reaction [22]. However, the assumptions involved in the analysis may not be entirely valid and the derived values of a1 which measure the amount of internal return may not always be reliable. For the reaction of triphenylmethane the discrepancy between the measured value obs/ obs = 1-77 0.05 and the value 2.6 0.2 which is calculated for this isotope effect from the measured value of kobs/ obs = 1.34 0.03 using the Swain—Schaad relation is well outside experimental error. For the malononitriles discussed earlier in this section the experimental isotope effects for reaction in aqueous solution (Table 3) are well correlated by the Swain—Schaad relation which probably means that in these cases internal return is not important. 

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. 

A first significant point is that the adiabatic PT form in Eq. (10.24) has the same important feature as the standard picture, via Eq. (10.2) the Swain-Schaad relation is independent of temperature. We first examine the symmetric case AGrxn = 0, for which the adiabatic PT expression via Eq. (10.15) shows that the magnitude is related solely to the reactant and TS ZPE difference. These ZPE differences were shown to obey the same mass scaling used to derive the Swain-Schaad relations, cf Eq. (10.16) hence the Fig. 10.10(b) plot maximum is dose to the traditionally expected value. While Fig. 10.10(b) also shows that there is a small variation with reaction asymmetry, in the adiabatic PT perspective, of the Swain-Schaad slope. This has a minimal net effect, however, as discussed in Ref. 

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