Cyclization effective molarities

The stability of a trivial assembly is simply determined by the thermodynamic properties of the discrete intermolecular binding interactions involved. Cooperative assembly processes involve an intramolecular cyclization, and this leads to an enhanced thermodynamic stability compared with the trivial analogs. The increase in stability is quantified by the parameter EM, the effective molarity of the intramolecular process, as first introduced in the study of intramolecular covalent cyclization reactions (6,7). EM is defined as the ratio of the binding constant of the intramolecular interaction to the binding constant of the corresponding intermolecular interaction (Scheme 2). The former can be determined by measuring the stability of the self-assembled structure, and the latter value is determined using simple monofunctional reference compounds. 

In a few, but important, cases, EM s have been calculated not from rate constants but from product ratios. Where the effective molarity is low, competition between intramolecular and intermolecular reactions of the same compound may be observed, as in Freundlich s early work on the cyclization of w-bromoalkylamines (1) described by Salomon (1936). The inter-... 

The main tables are designated by a letter and a number (a full list is given in the Contents at the beginning of this chapter). Tables in the text, which mostly contain effective molarities taken from the main tables, are designated by a number only. Every individual reaction is identified by a reference letter and two numbers. Thus B.6.3 refers to the base-catalysed cyclization of cyclohexyl 2-hydroxyethyl phosphate which is the third entry in Table B.6. The EM for this reaction is given in Table 10 in the discussion of the effects of alkyl substitution on ring-closure, and the reference number quoted there. Full details of the calculation of the EM, the rate constant on which it is based, the conditions used and the authors concerned can then be found by consulting Table B.6. 

Similar explanations almost certainly account for the very large effective molarities found for lactonization of the hydroxy acids B.1.13, B.2.16 and B.2.25 (Table 12). All these compounds have the basic tetrasubstituted ethylene (here o-phenylene) structure found in the dialkylmaleic acid system further destabilized by substituents in the 3 and 6 positions of the benzene ring which also act to prevent bond angle spreading of the two inner substituents. (The effects of 3- and 6-substituents on this type of cyclization reaction are well known, and are shown for example by the range of EM s for compounds... 

From the second-order rate constant for imidazole-catalysed cyclization of the ethyl ester (34) (8 x 10 M s" ) and the rate constant for acylation of a-chy mo trypsin by N-acetyltyrosine ethyl ester (1600 s ), it can be calculated that, in order to attain a rate constant of the magnitude seen in the a-chymotrypsin reaction, a neighbouring imidazole would have to possess an effective molarity of 200,000 M. An effective concentration of this magnitude is not unreasonable, but it is probable that other factors are also important in the enzymatic reaction. 

Fig. 5. Profile of the effective molarity ( EM ) for the lactone formation from bromoalkanoates in DMSO (50 °C). The broken line shows the concentration at the start of the reaction (10 mol/l). Substrates drawn above the broken line react favourably under cyclization at the starting concentration given [102]...

Illuminati and Mandolini [101] explained the cesium effect from a physicochemical point of view solely in terms of ion pair effects. They introduced the term effective molarity ( EM ) to characterize the course of the cyclization reaction [101, 102], The effective molarity is definwi as the ratio of the velocity constants of the intramol mlar reaction (cyclization) Jind the intcrmolecular reaction (oligomerization) EM = kintra/ imer [mol/1]. EM therefore is the substrate concentration, at which the cyclization and oligomerization proceed with equal reaction rates. As a consequence, a concentration below the EM in the course of the reaction causes an intramolecular reaction path to be favored [102]. 

The rate of cyclization varies with ring size. Kinetic studies of cyclization of a series of anions derived from )V-tosyl-with ring size in the order S>3>6>7>4. First-order rate constants (Jbmtra) for cyclization have been translated into effective molarities (EM) with reference to the intermolecular alkylation (J imer) of (V-tosylbutylamine with butyl bromide (30-fold excess). The results are shown in Scheme 12. ... 

Table 19 Rate and equilibrium constants for the cyclization step through the ki k-i pathway of Scheme 9, intrinsic rate constants and effective molarities...

It is useful to consider some particular reactions within the framework presented above. It has been argued (35) that succinic acid, which does not even appear to have its reactive groups fully juxtaposed, should not exhibit the large effective molarities of 3 x 10 observed in its cyclization to the anhydride and similar reactions unless juxtaposition per se was the major factor. The two carboxylic acid groups of succinic acid are, however, more constrained than the simple approximated pair of Fig. 5. 

The kinetics of templated cyclization reactions can be considered in the same way as for the linear coupling described in Section 1.4.2.1. There is one significant difference cyclization reactions are intramolecular, so they have characteristic effective molarities even in the absence of a template. 

Temp is the effective molarity for the cyclization of the substrate bound to the template and A/untemp is ths effective molarity for the cyclization of the free substrate. EMuntemp indicates the inherent tendency of the substrate to cyclize. 

Figure 1-11 Effective molarities and binding constants for cyclization of linear porphyrin oligomers, by Glaser coupling in dichloromethane.

Table 1-1 Effective molarities (M) for various metal cations used as templates for the cyclization of 68 y = 3, 4,5, 6,9, and 15) in Mc2SO at 25 °C.

Structure was determined by X-ray analysis. A detailed paper on the intramolecular acylation of long-chain >-(2-thienyl)alkanoic acids at the 5-position in acetonitrile solution in the presence of trifluoroacetic anhydride and catalytic amounts of H3PO4 has appeared. The ring-sizes of the resulting (2,5)thiophenophan-l-ones ranged from 12 to 21. Reliable rate data and effective molarities were obtained, for use in structure-reactivity correlations. This cyclization procedure was used for the preparation of a key intermediate in a five-step synthesis of //-muscone. ... 

Both rigid and flexible porphyrin sandwiches were studied by Hunter et aL [28,34]. A rigid bis-porphyrin, connected via naphthalene diimide (Fig. 12), theoreticaUy forms a number of complexes with DABCO, depending on the porphyrin to hgand ratio. To characterize the supramolecular system, and to find the optimum conditions for cyclization to form the sandwich complex, the effective molarity (EM) was determined by NMR and UV-vis titration experiments. The EM may represent a composite of the real effective molarity and cooperative effects (a), but it is nevertheless a useful parameter for predicting the stabihty of the sandwich complex. Here, the EM was determined to be 2 mM, which means that the macrocychc complex 14 is... 

Figure 3 Semi-logarithmic plot of entropic effective molarity, EMs, versus number of rotatable bonds, u, in the unsymmetrical bifunctional chain undergoing cyclization. Solid and dashed lines describe covalent and noncovalent interactions, respectively (see text for details).

Table 1 Entropic effective molarities and entropy cyclization of unsymmetrical bifunctional chains as the number of skeletal single bonds (v)...

The bicychc complex is foraied by two consecutive cyclizations, each characterized by its own microscopic effective molarity. Owing to the symmetry of the bicychc complex, it is reasonable to assume that the two EM values are equal. Then, the chelate cooperative factor jS is given by Eq. [49], where 1/9 is the statistical factor of the equilibrium shown in Fig. 16 ... 

Molecularity vs. Mechanism. Cyclization Reactions and Effective Molarity A useful illustration of the distinctions between mechanism, molecularity, and order arises in the analysis of intramolecular versions of typically intermolecular reactions. Consider a classic Sn2 reaction of an amine and an alkyl iodide. The reaction is second order (first order in both amine and alkyl iodide) and bimolecular (two molecules involved in the transition state that s what the "2" in "Sn2" Stands for). The mechanism involves the backside attack of the nucleophilic amine on the C, displacing the iodide in a single step. Now consider a long chain molecule i that terminates in an amine on one end and an alkyl iodide on the other. Now two types of Sn2 reactions are possible. If two different molecules react, we still have a second order, bimolecular, intermolecular reaction. The product would ultimately be a polymer, ii, and we will investigate this type of system further in Chapter 13. Alternatively, an intramolecular reaction could occur, in which the amine reacts with the iodide on the same molecule producing a cyclic product. Hi. This is still called an S 2 reaction, even though it will be first order and unimolecular. 

The differing kinetic orders of these two reaction pathways provide a simple means to select one product over another. The polymerization reaction depends on the square of the concentration of /, while the cyclization is first order in [i]. This states mathematically what we know intuitively. High concentrations favor the polymerization while low concentrations favor cyclization. When the cyclic product is desired, we simply run the reaction at high enough dilution that the polymerization reaction becomes implausibly slow. What is that concentration Let s set up the rate equations for the two reactions. Cyclization will be favored when reaction I is slower than reaction II—that is, when the ratio of rates is less than 1. The ratio of rate constants has the units of molarity, and it is a characteristic of the particular system known as the effective molarity (EM) (see Chapter 9 for another analysis). 

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