Entropy, cyclizations

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

It is interesting to note that although the first examples of template effects were observed in nitrogen macrocycles (see chapter 2) no template effect appears to operate in the synthesis of 72. Richman and Atkins note this in their original report . The authors replaced the sodium cation with tetramethylammonium cations and still obtained greater than 50% yield of tetra-N-tosyl-72. Shaw considered this problem and suggested that because of the bulky N-tosyl groups, .. . the loss of internal entropy on cyclization is small He offered this as an explanation for the apparent lack of a template effect in the cyclization. 

These groups will reduce the number of conformational degrees of freedom (such as bond rotation) in the reactants and/or intermediates. It is this reduction which is thought to facilitate cyclization relative to polymerization for these systems in essence, the enhancement of cyclization can be considered to be largely a consequence of favourable entropy effects. 

Further examples of catalytic antibodies that are presumed to control rotational entropy are AZ-28, which catalyses an oxy-Cope [3.3]-sigmatropic rearrangement (Appendix entry 13.1) (Braisted and Schultz, 1994 Ulrich et al, 1996) and 2E4, which catalyses a peptide bond isomerization (Appendix entry 13.3) (Gibbs et al., 1992b Liotta et al., 1995). Perhaps the area for the greatest opportunity for abzymes to achieve control of rotational entropy is in the area of cationic cyclization reactions (Li et al., 1997). The achievements of the Lerner group in this area (Appendix entries 15.1-15.4) will be discussed later in this article (Section 6). 

These authors conclude that the problem of internal solvation is still an experimental and theoretical challenge GB measurements for this type of molecules of low volatility are not always in good agreement194. Molecular orbital calculations may help to solve the difficult experimental problems, but they have to take into account conformational isomerisms and the prototropic tautomerisms of the amidine and guanidine moieties. In light of the above discussion, the proton affinities deduced from the experimental GB values should be based on accurate estimations of the entropy of cyclization 86. 

A scheme depicting general base catalysis is shown in Fig. 7.2,b. Because the HO anion is more nucleophilic than any base-activated H20 molecule, intermolecular general base catalysis (Fig. 7.2,bl) is all but impossible in water, except for highly reactive esters (see below). In contrast, entropy may greatly facilitate intramolecular general base catalysis (Fig. 7.2,b2) under conditions of very low HO anion concentrations. Alkaline ester hydrolysis is a particular case of intermolecular nucleophilic attack (Fig. 7.2,cl). Intramolecular nucleophilic attacks (Fig. 7.2,c2) are reactions of cyclization-elimination to be discussed in Chapt. 8. 

The entropy factor should also be considered since cyclization results in a more ordered structure. The C5 cyclization of n-hexane involves an entropy decrease of about 15-17 entropy units (e.u.). The corresponding values for cyclohexane and benzene formation are about 25 and 38-45 e.u., respectively. These values are comparable with calculated values of adsorption entropy (29). Thus, adsorption of a molecule to be cyclized may supply a considerable part of the entropy change in other words, adsorption should take place in a geometry favorable for cyclization. This is one of the main roles of the catalyst. 

Formation of 2//-azirines by thermal decomposition of vinyl azides has been shown to exhibit small entropy of activation and insensitivity to solvent polarity acyclic vinyl azides decompose more readily than analogous cyclic ones and it is advantageous to have a hydrogen atom cis to the azido group ( -are more reactive than Z-isomers). These results and the linear correlation found for ring-substiment effects on decomposition of a-styryl azides are consistent with a nonconcerted mechanism in which elimination of nitrogen and cyclization into a three-membered ring proceeds synchronously. 

A plausible alternative mechanism involves as a first step the formation of a linear dimer, XB=NR—BX=NR, according to the left part of Eq. (21). This linear dimer will be more stable in entropy but less stable in energy than the corresponding cyclodimer. The second step would be addition of iminoborane to the open-chain dimer giving the borazine in either a concerted or a two-step mechanism. The intramolecular cyclization of the open-chain dimer, according to the right-hand side of Eq. (21), would compete addition of an iminoborane. We cannot definitely exclude a mechanism via open-chain dimers. 

The corresponding reaction of 23 with dimethylamine and with cyclic secondary amines (piperidine and morpholine) is less facile and gives the thermodynamically more favored C-3 addition product (Equation 13) <1999RCB1150>. Using ethylenediamine, the cyclization product 29 is obtained in 80% yield (Scheme 12), although with 1,3-propane-diamine, 1,4-butanediamine, and 1,2-cyclohexanediamine the yields are reduced (70%, 25%, and 1%, respectively), consistent with the importance of entropy as a driving force for the second (intramolecular) amination. 

More quantitative chemical evidence for random coil configuration comes from cyclization equilibria in chain molecules (49). According to the random coil model there must be a very definite relationship among the concentrations of x-mer rings in an equilibrated system, since the cyclization equilibrium constant Kx should depend on configurational entropy and therefore on equilibrium chain and ring dimensions. Values of /Af deduced from experimental values on Kx for polydimethylsiloxane, both in bulk and in concentrated solution, agree very well with unperturbed dimensions deduced from dilute solution measurements(49). 

Bond formation a to the heteroatom is a common path to azetidines, oxetanes, thietanes and many oxo derivatives. Attack by the heteroatom on the 7-position is disfavored by the entropy factor the reaction rates for cyclization are about 100 times less than for attack on (3-positions. However, exounsaturation can change this relation drastically in dimethyl sulfoxide at 50°C, (3-bromopropionate ion cyclizes about 250 times more rapidly than bromoacetate. 

The proportion of the acyclic form also increases with increasing temperature this is true for aldoses and ketoses,16,31 as well as for simple hydroxyketones.74 This would be expected from considerations of entropy, as the acyclic form has a greater degree of freedom, but studies on y- and d-hydroxyketones show that change in enthalpy contributes even more to the changing position of the equilibrium with increasing temperature. Evidently, cyclization of hydroxyketones is exothermic, and is favored by lower temperatures.74... 

The formation of the transition state AB leads to the loss of translational and rotational entropy as described above, although there are some compensating gains in internal rotation and vibration. The intramolecular cyclization in equation 2.23 involves the loss of only some entropy of internal rotation. 

Cyclization of 1,3,5-hexatriene occurs only when the central double bond has the cis configuration. The reaction is reversible at elevated temperatures because of the gain in entropy on ring opening (see Section 4-4B). The cyclobutene-1,3-butadiene interconversion proceeds much less readily, even in the thermodynamically favorable direction of ring opening. However, substituted dienes and cyclobutenes often react more rapidly. 

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