Isotope effects continued

Kinetic Isotope Effects Continued Variational Transition State Theory and Tunneling... 

Figures 7-9 show the fractional conversion of methanol in the pulse as a function of temperature for the three catalysts and the three methanol feeds. Evidently the kinetic isotope effect is present on all three catalysts and over the complete temperature range, indicating that the rate limiting step is the breaking of a carbon-hydrogen bond under all conditions. From these experiments, the effect cannot be determined quantitatively as in the case of the continuous flow experiments, but to obtain the same conversion of CD,0D, the temperature needs to be 50-60° higher. This corresponds to a factor of about three in reaction rate. The difference in activity between PfoCL and Fe.(MoO.), is larger in the pulse experiments compared to tHe steady stateJ results.

The formulae given in Table 4.1 for the molecular partition functions enable us to write the partition function ratio qheavy/qiight or q2/qi where, by the usual convention, the subscript 2 refers to the heavy isotopomer and 1 refers to the light isotopomer if heavy and light are appropriate designations. Then, a ratio of such partition function ratios enables one to evaluate the isotope effect on a gas phase equilibrium constant, as pointed out above. Before continuing, it is appropriate to... 

To begin we are reminded that the basic theory of kinetic isotope effects (see Chapter 4) is based on the transition state model of reaction kinetics developed in the 1930s by Polanyi, Eyring and others. In spite of its many successes, however, modern theoretical approaches have shown that simple TST is inadequate for the proper description of reaction kinetics and KIE s. In this chapter we describe a more sophisticated approach known as variational transition state theory (VTST). Before continuing it should be pointed out that it is customary in publications in this area to use an assortment of alphabetical symbols (e.g. TST and VTST) as a short hand tool of notation for various theoretical methodologies. 

Fig. 10.1 (continued) (c) An H atom attacking D2 or a D atom attacking HD. The TST isotope effect is negative (inverse) because the zero point isotope effect in the ground state is negative)... 

Fig. 12.1 (continued) (c) Isotope effects on mean square amplitudes (upper curve) and root mean square amplitudes (lower curve) as a function of temperature for hypothetical nondissociating molecules. At low temperatures the molecules are in the ground state and the amplitude is nearly independent of temperature. At higher temperature the vibrational amplitudes increase due to excitation into upper levels (Fig. 12.1) but the ratios drop smoothly to the classical value of unity at very high temperature (Fig. 12.1)... 

Table 12.3 CDDR (continuous dilution differential refractometry) least squares parameters, molar volume isotope effects, and derived PIEs for some isotopomer solutions at 298.15K see Equation 12.15, AR/R = A + mv2 (Wieczorek, S. A., Urbanczyk, A. and Van Hook, W. A.,. /. Chem. Thermodyn. 28, 1009 (1996)) ...

Westaway and co-workers work on kinetic isotope effects (KIEs) has continued.-... 

The biochemical reduction of sulfate to sulfide by bacteria of the genus Desulfovibrio in anoxic waters is a significant process in terms of the chemistry of natural waters since sulfide participates in precipitation and redox reactions with other elements. Examples of these reactions are discussed later in this paper. It is appropriate now, however, to mention the enrichment of heavy isotopes of sulfur in lakes. Deevey and Nakai (13) observed a dramatic demonstration of the isotope effect in Green Lake, a meromictic lake near Syracuse, N. Y. Because the sulfur cycle in such a lake cannot be completed, depletion of 32S04, with respect to 34S04, continues without interruption, and 32S sulfide is never returned to the sulfate reservoir in the monimolimnion. Deevey and Nakai compared the lake to a reflux system. H2S-enriched 32S diffuses to the surface waters and is washed out of the lake, leaving a sulfur reservoir depleted in 32S. The result is an 34S value of +57.5% in the monimolimnion. 

Aldol reactions have continued to attract attention.28-39 hi order to determine the mechanism of addition of lithium pinacolone enolate [CH2=C(OLi)C(Me)3] to benzaldehyde the carbonyl-carbon KIE (xlk/nk = 1.019) and the substituent effects (p = 1.16 0.31) have been compared with those for other lithium reagents.28,29 The small positive KIE, which is larger than the equilibrium IE (nK/nK = 1.006) determined by ab initio MO calculations (HF/6—31 + G ), is in contrast with nk/l4k = 1.000 for MeLi addition which proceeds by the rate-determining ET mechanism, characterized by a much smaller p value. Since probe experiments showed no evidence of single electron transfer, it has been concluded that the significant isotope effect for reaction of lithium pinacolone enolate is indicative of rate-determining polar attack (PL) rather than radical coupling (RC) (Scheme 2). 

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