Curtin-Hammett conditions

This system has its historical background in physical organic chemistry and the kinetic aspects are the subject of a detailed review by SeemarL In essence, this is a special application of the rapid-equilibrium assumption. The Curtin-Hammett conditions and their consequences also are relevant to inorganic systems, and this has been recognized especially in the area of stereoselective catalysis. 

If one takes the ratio of these rates and integrates over the limits [Z]q = [Y](, = 0 to [Z] and [Y], respectively, one obtains the product ratio at 

the Curtin-Harmnett conditions predict that the ratio of the product concentrations is constant at any time during the reaction. However, this ratio does not simply reflect the relative stabilities of the isomeric reactants, as determined by but also depends on kjk. Thus, a particular ratio might be obtained when [A] [B] (i.e. 

From transition-state theory (Section 1.6.2), the rate constants k and k are given as 

This shows that the product ratio is only dependent on the difference in the free energies of the transition states and is independent of the relative free energies of the reactants A and B, as long as the latter are in rapid equilibrium. 

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Case B is very common and can also be worked out easily. It is seen that the barriers for both the forward and backward reaction of (1) are much lower than the barrier for (2). We are dealing with a fast pre-equilibrium and a ratedetermining reaction (2) ki, k i k2 (concentrations omitted). It is also referred to as Curtin-Hammett conditions in U S. literature it refers to the kinetics of a system of a number of rapidly equilibrating species or conformations, each one of which might undeigo a different conversion, but all that counts is the global, lowest barrier, as that is the direction the system takes. 

The major intermediate observed in solution is the alkene complex, but it interchanges rapidly with the aldehyde complex. The product formed according to this scheme is allyl alcohol, because the overall barrier 2 is lower than barrier 1 (above we named this Curtin-Hammett conditions). Barrier 2 is also the ratedetermining step in this sequence. 

Quantitative data for the difference in complexation of ethene and CO to hydrocarbylpalladium(dppp)+ were reported by Brookhart and co-workers [15,33], The equilibrium between CO and ethene coordination amounts to about 104 at 25 °C. Multiplied by the concentrations of the two gases and the two individual rate constants for the insertion they calculated that the ratio of CO insertion versus ethene insertion is about 105 in an alkyl-palladium intermediate under Curtin-Hammett conditions, that is to say fast exchange of coordinated CO and ethene ligands compared to insertion reactions. Figure 12.9 summarises this. 

If the substrate contains two identical substituents at one terminus of the allylic position such as shown in Scheme 8E.26, the it-allyl intermediate can undergo enantioface exchange via the formation of a a-palladium species at that terminus. This process should occur faster than the nucleophilic addition, which is the enantio-determining step (fc, > 2[Nu ] and 2[Nu ]). Thus, enantioselection can be derived from the relative rate of the nucleophilic addition to each diastereomer the relative stabilities of the two diastereomeric complexes need not have a direct effect on the enantioselectivity (Curtin-Hammett conditions). Although the achiral allylic isomer 120 is expected to follow the same kinetic pathway as the racemic substrate 119, the difference between the results from the two systems often gives an indication as to the origin of enantioselection—complexation or ionization versus nucleophilic addition. 

The first scenario is relatively simple and relates to the previous example of group transfer. If interconversion of the diastereomeric olefin complexes I and T is slow, relative to the rates of conversion of the olefin complexes to product, the enantioselectivity-determining step is binding the prochiral olefin faces to the metal (Figure 14.12A). In contrast, if interconversion of the diastereomeric olefin complexes is significantly faster than their reaction to form product, the enantioselectivity-deternrining step will be the reaction to form product (Figure 14.12B). This latter scenario is stated to meet "Curtin-Hammett conditions."... 

Reaction coordinate diagrams illustrating reactions of diastereomeric olefin complexes. In scenario A, olefin binding is enantio-determining. In B, the diastereomeric olefin complexes are in rapid equilibrium and enantio-determination is the conversion of the olefin adducts to products. B is an example of Curtin-Hammett conditions. 

Two Examples of Reactions Under Curtin-Hammett Conditions... 

Mechanism of the asymmetric hydrogenation, iiiustrating a reaction meeting the Curtin-Hammett conditions. 

Energy diagram for the asymmetric hydrogenation reaction under Curtin-Hammett conditions. The enantioselectivity-determining step is the oxidative addition (OA) of hydrogen. 

Several experimental variables impact the relative rates of isomerization and nucleophilic attack in the allylic substitution reaction in Figure 14.15. For example, an increase in the rate of interconversion of the ir-allyl intermediates, such that the rate of this process is faster than nucleophilic attack, will change the enantioselectivity-determining step, because the diastereomeric complexes now equilibrate rapidly. Because isomerization of the diastereomeric ir-allyl complexes is a unimolecular process, but nucleophilic attack on the ir-allyl intermediates is a bimolecular process, reactions under dilute conditions will decrease the rate of nucleophilic attack, relative to the unimolecular ir-u-ir isomerization, and will help to achieve Curtin-Hammett conditions. 

Alternatively, additives can affect the rate of interconversions of diastereomeric intermediates, relative to the rate of formation of product from these intermediates, This affect of additives has been exploited to achieve Curtin-Hammett conditions in allylic alkylation. Halide ions are known to catalyze the ir-u-ir isomerization by the mechanism in Equation 14.15. Thus, the concentration of additives can affect enantio-selectivity by shifting the enantioselectivity-determining step from formation of the allyl intermediate to reaction of the allyl intermediates with the nucleophile. In fact, this affect of additives on the identity of the enantioselectivity-determining step can even cause reactions in the presence of additives to form the enantiomer that is the opposite of the one formed in the absence of additives. Even variation in temperature can cause a change in the enantioselectivity-determining step of a catalytic process and formation of opposite product enantiomers at low and high temperature. This effect has been observed in the asymmetric hydroformylation processes described in Chapter 17. ... 

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. 

Figure 8.5 Relationship between difference in activation free energy for the two pathways leading to opposite enantiomers and the resulting percentage of ee under Curtin-Hammett conditions.

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