Brpnsted plot

Kinetic data17 with both phenols and carboxylic acids used as catalysts in reaction (10-27) are summarized in Table 10-6. The Brpnsted plot is shown in Fig. 10-6. The slope of the line gives a, which is 0.54. 

As pointed out above, values of KTS are obtainable from rate data without making any assumptions about the reaction mechanism. Therefore, one may use KTs and its variation with structure as a criterion of mechanism, in the same way that physical organic chemists use variations in other kinetic parameters (Brpnsted plots, Hammett plots, etc.). For present purposes, the value of Kts can be useful for differentiating between the modes of binding in the S CD complex and the TS-CD transition state, between different modes of transition state binding, and hence between different types of catalysis (Tee, 1989). 

Connected with the determination of Brpnsted plots, some mathematical treatments have been recently developed attempting to yield structural information on the transition state. 

The nucleophilicity of the amine is another factor affecting reactivity, and changes in it have been sometimes responsible for the observed scattering in the Brpnsted plots. The Ritchie equation80 (equation 11) has been applied to a variety of reactions in which nucleophilic addition to, or combination with, an electrophilic center is rate-limiting. 

Figure 11. Brpnsted plots for the proton transfer reactions of Cu-triglycine and yu-tetraglycine complexes. Key , Cu(H, Gtf O, Cu(H.,G,) and , Cu- - G,) (numbers refer to the acids 1, CH COOH 2, HCOOH 3, ClCH,COOH 4, CUCHCOOH and 5, H,0 ).

Transition state imbalance in the deprotonation of substituted 2-tetralones by hydroxide ions has been described. A Brpnsted plot of logA versus substrate pAfa is linear, with slope —a) of —0.60 0.01 but the negative deviation of the point for the 6-nitro derivative suggests that delocalization of charge lags behind proton transfer. ... 

A change in mechanism [at pH pX of (9)] from ElcBi to ElcB is also believed to account for the biphasic Brpnsted plots (/3i 0.7, P2 0) and associated entropy... 

There are a number of limitations on the Brpnsted relationship. First of aU, the relation holds only for similar types of acids (or bases). For example, carboxylic acids may have a different a values compared to sulfonic acids or phenols. Because charge, and likewise solvation, can greatly influence the reaction rate, deviations of net charge from one catalyst to another can also influence Brpnsted plots. Another limitation on this relationship relates to temperature. Reaction rates and the corresponding dissociation constants for the acids must all be measured at the same temperature (and, most rigorously, in the same solvent). For some systems, this may prove infeasible. A third limitation is that the reaction must indeed be subject to general acid (or base) catalysis. For certain catalysts, deviations from a linear relationship may indicate other modes of action beyond general acid/... 

Rowlett and Silverman used a Brpnsted plot to examine the interaction of external buffers with human carbonic anhydrase II. The buffers act as proton acceptors in the removal of the proton generated by the enzyme-catalyzed reaction. The Brpnsted plot displays a plateau at a value of about 10 for the catalytic rate... 

Figure 2.8 A Brpnsted plot for the nucleophilic attack of primary and secondary amines of p-nitrophenyl acetate. Note that the a -effect nucleophiles—semicarbazide (SC), hydroxylamine, and hydrazine—are more reactive than would be expected from their pAT s. [From W. P. Jencks and M. Gilchrist, J. Am. Chem. Soc. 90,2622 (1968).]...

Figure 2.9 A Brpnsted plot for the attack of oxyanion nucleophiles onp-nitrophenyl acetate. As in Figure 2.8, the -effect nucleophiles ( ) are unusually reactive. Note how the linear plot breaks down with increasing pKa for the more reacdve nucleophiles. In general, the Brpnsted relationships hold only over a limited range of pk s in these reactions. The curvature is not often seen in practice because of the limited range of bases used.

The Brpnsted plot just represents the average change in energy of activation on mutation. The variations are seen from the individual Of values, most of which are between 0.2 and 0.5. The higher values tend to be for the formation of the a helix, especially at its N-terminus. The energetics imply a structure for the transition state that looks like an expanded version of the native structure. But the expansion is not uniform. It is as if there is a center located in the N-terminal part of the helix, and the structure becomes more expanded the farther away it is from the center.29,30 The structure, fleshed out by molecular dynamics, is described in section 6. 

Figure 19.5 Effects of destabilizing mutations on the Brpnsted plot for a reaction that proceeds along two parallel pathways (Figure 19.4) and one that has a single expanded transition state.

Homocysteine, HSCH2CH2CH(NH2)C02H, is a toxic amino acid that is thought to acylate lysine residues on proteins via its corresponding thiolactone (72) (Scheme 19). Now, for the first time, the kinetics have been studied of the aminolysis of (72) and of two model compounds, y-thiobutyrolactone (72 H instead of NH2) and N-trimethylamino homocysteine thiolactone (72 Me3N+ instead of NH2). A Brpnsted plot for homocysteine thiolactone (72) gave ft = 0.66. This and other data supported... 

Curvature of Brpnsted Plots and Medium Effects Rate Variations in DMSO as a Guide to Mechanism... 

The linear correlation between logXj and log at/ m is an example of linear correlation between AG° and AG of two different reactions. Huge amounts of such linear correlation data (e.g., Hammett plots or Brpnsted plots) are reported in the literature for various organic reactions (67). The correlation, however, does not mean that the transition state corresponding to AG resembles the species corresponding to AG°. The linear correlation observed with carboxypeptidase A, therefore, cannot be regarded as evidence for the mechanism of T (33). 

The Marcus equation is also examined in Chapter 9. As discussed previously regarding the Lewis chapter, the quadratic term of the Marcus equation leads to a dependency of rate on the square of pKa, so that Brpnsted plots would be expected to be curved. Bordwell and co-workers observe curvature in some of their Br0nsted plots but conclude that the curvature is too large to be a Marcus effect and actually results from a solvation effect for some heteroatom substituents. These workers suggest that the curvature observed for Brpnsted plots in water results from differential solvation. 

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