Curtin-Hammett situation

A quantitative description of this behavior is given in Figure 4. Whereas the competition constant observed in presence of excess BCI3 can be derived from the known addition rate constants of the two carbenium ions (AAG " AGi - AG2 ), a Curtin Hammett situation is encountered in presence of catalytic amounts of Lewis acid. Now, the ratio of the two individual rate constants has to be multiplied with the equilibrium constant for the ionization (AAG AGj " - AG2 " + AAG ). 

The mechanism of this interconversion is known as apparent allyl rotation and results in a switching of the allylic termini in addition to the movement of the central allyl carbon from one side of the coordination plane to the other although, for situations with symmetrically substituted allyl units, only this latter change is noticeable As the name suggests, the process is non-trivial and, in reality, the mechanism is dependent on the specific conditions.1161 Nevertheless, in most cases, the interchange is rapid compared with the rate of nucleophilic attack and, therefore, the product outcome does not necessarily depend on the intermediate isomer ratio (Curtin-Hammett principle). 

In both of these situations, the reaction actually observed does not occur from the lowest-energy conformation of the reactants. That this need not be the case is a direct consequence the Curtin-Hammett principled This recognizes that some higher-energy reactive conformation , will be in rapid equilibrium with the global minimum and, assuming that any barriers which separate these conformations are much smaller than the barrier to reaction, will be replenished throughout the reaction. 

Reduction of C(5)-substituted 2-hydroxychromans selectively provides 2,4-cis-chromans using large silane RsSiH reductants and 2,4-frans-chromans using the smaller silane PhSiH3. The stereochemical outcome has been rationalized on the basis of a Curtin-Hammett kinetic situation arising from hydride delivery to two different conformations of an intermediate oxocarbenium ion.363... 

The synthesis of amino acid esters can be carried out enantioselectively when optically active EBTHI zirconaaziridines are used. After diastereomeric zir-conaaziridines are generated and allowed to equilibrate (recall Scheme 3), the stereochemistry of the chiral carbon center in the insertion product is determined by competition between the rate constants kSSR and ksss for the epimerization of zirconaaziridine diastereomers and the rate constants [EC] and ks[EC] for ethylene carbonate (EC) insertion (Eq. 31) [43]. When kR[EC] and ks[EC] are much greater than kSSR and ksss> the product ratio reflects the equilibrium ratio as shown in Eq. 32. However, the opposite limit, where epimerization is much faster than insertion, is a Curtin-Hammett kinetic situation [65] where the product ratio is given by Eq. 33. 

Note that the illustrated conformation has the acrolein oriented in an 5-cis conformation. This is in contrast to the usual 5-trans conformation of acroleins coordinated to a Lewis acid (Figure 6.13a), but it is supported by the fact that cyclo-pentadiene adds to the opposite face of acrolein itself [216]. It is likely that both s-cis and 5-trans dienophile conformers are present, and that the -cis conformer is more reactive. In other words, Curtin-Hammett kinetics [235] are operative. The rationale for this increased reactivity is as follows the j-trans conformation of 2-bromoacrolein would place the bromine above the indene ring. Cycloaddition to the top (Si) face of the 5-trans conformer would force the bromine into closer proximity to the indene as C2 rehybridizes from sp2 to sp3, a situation that is avoided in cycloaddition to the top (Re) face of the 5-cis conformer. 

Central to this argument is the assumption that reaction of the incipient carbocations is significantly faster than is rotation about carbon-carbon single bonds. As noted in Chapter 6, the Curtin-Hammett principle applies to situations in which conformational interconversion is faster than the rates of reaction of conformers. 

Consider the simplest situation where the diastereomers in energy minima A are in rapid equilibria (Curtin-Hammett conditions). Under these conditions, the reaction rates of the two diastereomers depend only on the difference in the diastereomeric transition state energies. 

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