Kinetic isotope effect. See

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. 

The rate-controlling step is the elementary reaction that has the largest control factor (CF) of all the steps. The control factor for any rate constant in a sequence of reactions is the partial derivative of In V (where v is the overall velocity) with respect to In k in which all other rate constants (kj) and equilibrium constants (Kj) are held constant. Thus, CF = (5 In v/d In ki)K kg. This definition is useful in interpreting kinetic isotope effects. See Rate-Determining Step Kinetic Isotope Effects... 

Each of the two isomeric organolithiums 63 and 64 could be formed selectively by using deuterium to block lithiation at the other site via the kinetic isotope effect (see below).43 The less stabilised a-lithio species 63 have a tendency to undergo dearomatising cyclisations,44 45 as described in section 7.2.4.6. 

Attempts to use intermolecular and intramolecular kinetic isotope effects (see section 2.2) to identify a complexation step during ortholithiation have so far been inconclusive. Both intramolecular and intermolecular KIE s for the deprotonation of 152 and 153 by s-BuLi at -78 °C have values too high to measure, perhaps because complexation is fast and reversible but deprotonation is slow.11... 

A rate-controlling step defined in the way recommended here has the advantage that it is directly related to the interpretation of kinetic isotope effects (see ISOTOPE EFFECT, KINETIC). 

The total annual input of methane from all sources to the atmosphere shown in Table 6.4 is 540 Mt, while the estimated output from atmosphere to sinks is 500 Mt. The potential inaccuracies in flux data can be seen by comparing the observed carbon isotopic signature of atmospheric methane of —47%o with that calculated from the data in Table 6.4 of c— 54%o (the latter is actually equivalent to —58%o upon correcting for the kinetic isotope effect (see Box 1.3) that operates during the hydroxyl abstraction reaction). There are clearly major gaps in our understanding of the pathways of methane into and out of the atmosphere and the fluxes involved, as there are for many anthropogenic substances (see Chapter 7). 

For a theoretical study of the relationship between the structure of Sn2 transition states cind secondary a-deuterium kinetic isotope effects, see Poirier, R. A. Wang, Y. Westaway, K. C. /. Am. 

Table 3. Kinetic ab initio and experimental data for the reaction CH4+ OH CH3+H2O, showing activation energies and kinetic isotope effects. (See bottom for references.)...

At temperatures above 1013 K the rates of hydrocarbon formation could be well described by Model 1, whereas at temperatures below 933 K the experimental values could be well described by Model 2 (see Figures 19a and b). Based on the above results and considering the kinetic models and the kinetic isotope effect (see Table 6), the rate determining step for hydrocarbon formation was suggested to be the formation of methyl radicals by reaction of molecular methane with an oxygen species as defined by Models 1 and 2 involving C-H bond rupture ... 

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