Primary Swain-Schaad Relationship

Thus the primary and secondary isotope eifects are all within the semiclassical limits and their relationship is in full accord with the semiclassical Swain-Schaad relationship. There is no indication from the magnitudes of the secondary isotope elfects in particular of any coupling between motion at the secondary center and the reaction-coordinate for hydride transfer. Thus the sole evidence taken to indicate tunneling is the rigorous temperature-independence of the primary isotope elfects. 

Finally the temperature dependence of the primary isotope effects was determined. Here the traditional expectations of Chart 3 were fully met the results translate into AH/AD = 1.1 0.1, aD — aH = 0.8 kcal/mol. Thus the amount of tunneling present, adequate to produce the observed exaltation of secondary isotope effects, violations of the Swain-Schaad relationship, and violations of the Rule of the Geometric Mean in the neighborhood of room temperature, does not lead to anomalies in either the ratio of isotopic pre-exponential factors nor the isotopic activation energy difference over the temperature range studied (approximately 0-40 °C). As will be seen later, the temperature dependence of isotope effects for reactions that include tunneling is in general a complex, unresolved issue. 

The Swain Schaad relationship which yields boundaries for the ratios of the rate constants for the primary kinetic isotope effects for H, D and T with deviations being interpreted as evidence of tunneling. 

Several investigators examined this relationship under extreme temperatures (20-1000 K), and as a probe for tunneling [26-28]. This isotopic relationship was also used in experimental and theoretical studies to suggest coupled motion between primary and secondary hydrogens for hydride transfer reactions, such as elimination in the gas phase, and in organic solvents [29, 30]. The power of the Swain-Schaad relationship is that it appears independent of the details of the reaction s potential surface and thus can be used to relate unknown KIEs (see Section 12.3.2). 

The primary exponential relationship comes from a comparison of the primary (kH/kx)2 H primary (kD/kx)2oD isotope effects. It has been shown that primary exponents are not susceptible to large Swain-Schaad deviations, even in the event of fairly extensive tunneling [59] furthermore, primary exponents are not susceptible to large RGM deviations [52], and consequently, the composite exponent RS should remain close to 3.3 in the absence of kinetic complexity. This is a useful control, as the magnitude of the primary exponent is reduced when chemistry is only partially rate limiting (i.e., it can be use to establish that H-transfer has been kinetically isolated) [60]. 

The exponents described by Saunders, sometimes called mixed isotopic exponents , are shown in Eq. (11.17). The exponent describes the relationship between the H/T isotope effect from substitution at site one (determined when protium is at site two), and the site-one D/T isotope effect (determined when deuterium is at site two). If the two sites are distinguished as giving primary and secondary isotope effects, the first exponent in Eq. (11.17) resembles the single-site Swain-Schaad exponent Eq. (11.9) for a primary isotope effect, and the second exponent in Eq. (11.17) resembles a single-site secondary Swain-Schaad exponent. However, the mixed isotopic exponents necessarily involve isotopic substitution at two sites and should not be confused with single-site Swain-Schaad exponents. 

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

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