Secondary Swain-Schaad Relationship

Upper Semiclassical Limit for Secondary 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. 

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... 

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 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. 

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). 

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