The Curtin-Hammett Principle

SECTION 4.4. BASIC MECHANISTIC CONCEPTS KINETIC VERSUS THERMODYNAMIC CONTROL, HAMMOND S POSTULATE, THE CURTE4-HAMMETT PRINCIPLE 

The product ratio is therefore determined not by AG but by the relative energy of the two transition states A and B. Although the rate of the formation of the products is dependent upon the relative concentration of the two conformers, since AG is decreased relative to Ag to the extent of the difference in the two conformational energies, the conformational preequilibrium is established rapidly, relative to the two competing product-forming steps.The position of the conformational equilibrium cannot control the product ratio. The reaction may proceed through a minor conformation if it is the one that provides access to the lowest-energy transition state. The conclusion that the ratio of products formed from conformational isomers is not determined by the conformation population ratio is known as the Curtin-Hammett principle.  

For a more complete discussion of the relationship between conformational equilibria and reactivity, see J. I. Seeman, Chem. Rev. 83 83 (1983). 

Curtin, Rec. Chem. Prog. 15 111 (1954) E. L. Eliel, Stereochemistry of Carbon Compounds, McGraw-Hill, New York, 1962, pp. 151 152, 237-238. 

CHAPTER 4 STUDY AND DESCIUPTION OF ORGANIC REACTION MECHANISMS 

The product ratio is therefore not determined by AG but instead primarily on the relative energy of the two transition states leading to A and B. 

The same arguments can be applied to other energetically facile interconversions of two potential reactants. For example, many organic molecules undergo rapid proton shifts (tautomerism) and the chemical reactivity of the two isomers may be quite different. It is not valid, however, to deduce the ratio of two tautomers on the basis of subsequent reactions which have activation energies greater than that of the tautomerism. Just as in the case of conformational isomeri, the ratio of products formed in subsequent reactions will not primarily be controlled by the position of the facile equilibrium. 

In the 1940s the idea was prevalent among chemists that the conformation of a reactant could be determined from the structure of a reaction product, i.e. the major conformer would yield the major product. This assumption was shown to be incorrect by Curtin and Hammett in the 1950s [32]. 

For a reaction in which a starting material A is an equilibrium mixture of two conformers (or diastereomers, tautomers, rotamers, etc.) A1 and A2 (Eq. 1.1), two extreme situations can be considered - one in which equilibration of A1 and A2 is slow if compared with their reaction with B (k1, k2 kc, kD), and one in which equilibration of A1 and A2 is much faster than their reaction with B (k1, k2 kc, kD). 

If equilibration of A1 and A2 is slow, the product ratio [C]/[D] will be equal to the ratio of conformers of the starting material A ([ A11/ A21) and independent of the ratio kc/kD. If equilibration is rapid, however, the amount of C and D formed will depend both on the ratio of starting materials ([A /jA2]) and on the ratio of the two reaction rate constants kc and kD [D]/[C] = [A /jA1] x kD/kc [32], 

The main implication of these derivations is that if equilibration is rapid, the product ratio cannot always be intuitively predicted if the reaction rates kc and fcD are unknown. Because energy-rich conformers, present in low concentrations only, are often more reactive than more stable conformers, it is not unusual for the main product of a reaction to result from a minor conformer which cannot even be observed. 

To conclude, the Curtin-Hammett principle states that the relative amounts of products formed from two interconverting conformers depend on the reactivity of these two conformers if the interconversion of these conformers is rapid, and cannot always be intuitively predicted. 

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Basic Mechanistic Concepts Kinetic versus Thermodynamic Control, Hammond s Postulate, the Curtin-Hammett Principle... 

In a simple statement of the Curtin-Hammett principle, we know that the rate will depend not only on the separate reactivities of the two pathways, but also on the relative populations of the catalyst species. In the following table we highlight the parameters referring to reactivity and to the population. 

Does the Curtin-Hammett principle apply to photoelectrocyclic reactions when more than one conformation of reactant is present in solution Why ... 

If it is assumed that the Curtin-Hammett principle applies, one need only to compare the energies of the minima on the solid and dashed curves to be able to predict the structure of the major product. These curves also allow a direct comparison of Cram s, Cornforth s, Karabatsos s and Felkin s model for 1,2 asymmetric induction. Both Figures show the Felkin transition states lying close to the minima. The Corn-forth transition states (Fig. 3) are more than 4 kcal/mol higher and should contribute little to the formation of the final products assuming a Boltzmann distribution for the transition states, less than one molecule, out of a thousand, goes through them. Similarly, Fig. 4 shows the Cram and Karabatsos transition states to lie more than 2.7 kcal/mol above the Felkin transition states, which means that they account for less than 1% of the total yield. 

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. 

The quaternization of amines is an extensively studied reaction in organic chemistry. The quaternization of piperidine can follow two distinct stereochemical pathways, axial or equatorial alkylation (70MI20700). Since the Curtin-Hammett principle is valid in this reacting system it is important to recognize that the product ratio of (87) to (89) does not directly reflect the ratio of (86) to (88). 

Because of the observation of a fast equilibrium between the C-titanium complexes 19A and 19C and the N-titanium ylides 19B, the reactivity model depicted in Scheme 1.3.16 was proposed in order to account for the regio- and diastereose-lectivity observed in the reaction of 19 with aldehydes. This model, which is based on the assumption of the operation of the Curtin-Hammett principle (that is, the reactions of 19A, 19B, and 19C with aldehydes are significantly slower than their isomerization), features the six-membered cyclic chair-like transition states... 

Application of the Curtin-Hammett Principle would suggest that the different ground state conformers have minimal influence on the product composition. It is the difference in activation energies for the two different isomers that controls the reaction, and the diastereomeric transition states would be attained from either ground state conformation. 

Owing to the Curtin-Hammett principle, the ratio of the iodonium intermediates 39 and 40 does not reflect the distribution of the conformers in 38 (5H4 4H5 = 95 5). Thus, both the 2-deoxy-2-iodo-ot-mannoside 50 and the 2-deoxy-2-iodo-P-glucoside 51 are formed in almost equimolar amounts. Similar results are observed in glycals with nitrile or carboxamide functions [11]. 

According to the Curtin-Hammett principle, the ratio of the distribution between two products depends only on their rates offormation (Figure 9.1). If the two products are conformers, the energy barrier between the two states tends to be small and the ratio between the two products is an indicator of the free enthalpies of the transition states. The Curtin-Hammett principle can be applied when two conformations, tautomers, or isomers of a starting material are in rapid equilibrium compared to the rate of a reaction. In this case, the product ratio provides no information about which conformation, tautomer, or isomer was present in the starting material. 

As a consequence of the Curtin-Hammett principle, one of the most useful means of investigating a mechanism is (not altogether unexpectedly) to measure the distribution of product(s). One prerequisite for measuring product distribution is a proper assay. 

Stereoelectronic effects can have a profound effect on the ground-state structure of molecules, and can often help to explain counter-intuitive conformational preferences or spectroscopic features. Their effect on the energy of transition states is, however, less straightforward to predict. As stated by the Curtin-Hammett principle [75] (Section 1.4), reactions will proceed via energetically unfavorable conformers if these are more reactive (as is often the case) than better stabilized conformers. In such instances ground-state stabilization of certain conformers or the weakening of bonds by hyperconjugation will not necessarily be predictive for the outcome of a reaction. 

Seeman, J. I. The Curtin-Hammett principle and the Winstein-Holness equation./. Chem. Educ. 1986, 63, 42-48. 

Assuming that the major conformation determines the product. In fact, in a mobile equilibrium the product ratio depends on the relative reactivities, not relative amounts, of the conformers (the Curtin-Hammett principle [35]). 

If one reactant of the pair yields several products (204), then any two products in this system may be compared in (209). This is the Curtin-Hammett principle, which states that the product ratio or the reaction-rate ratio depends only on the transition state energies, provided the equilibrium in (206) is maintained (Eliel et al., 1965). 

The anomeric outcome of these glycosylations can also be discussed in more general mechanistic terms. First, the product ratio is governed by competing rates of formation of the a and P glycoside and therefore the glycosylation is kinetically controlled. Second, the Curtin-Hammett principle describes that when two reactants are in fast equilibrium, the... 

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