Proton transfer, linear free energy relationship

Large numbers of reactions of interest to chemists only take place in strongly acidic or strongly basic media. Many, if not most, of these reactions involve proton transfer processes, and for a complete description of the reaction the acidities or basicities of the proton transfer sites have to be determined or estimated. These quantities are also of interest in their own right, for the information available from the numbers via linear free energy relationships (LFERs), and for other reasons. 

If a proton-transfer reaction is visualized as a three-body process (Bell, 1959b), a linear free energy relationship is predicted between the acid dissociation constant, Aha, and the catalytic coefficient for the proton-transfer reaction, HA. Figure I shows the relationships between ground-state energies and transition-state energies. This is a particular case of the Bronsted Catalysis Law (Bronsted and Pedersen, 1924) shown in equation (9). The quantities p and q are, respectively, the number of... 

The EVB potential was calibrated to reproduce experimental data for the uncatalyzed reference reaction in solution. In the case of proton transfer the difference in free energy between the two states, zlG° can be obtained from the difference in pK between the donor and acceptor. Once AG° is known the activation energy AG can be determined from a linear free energy relationship compiled by Eigen [50]. For the proton transfer described by 0,->[Pg.272]

Warshel, A., Hwang, J.K. and Aqvist, J. (1992). Computer simulations of enzymatic reactions examination of linear free-energy relationships and quantum-mechanical corrections in the initial proton-transfer step of carbonic anhydrase. Faraday Discuss 93, 225... 

Linear free energy relationships are particularly useful if it is necessary to have accurate knowledge of the pA of an intermediate which is unstable, or for which other experimental difficulties such as solubility prevent its experimental determination. Information about the values of putative intermediates is essential in mechanistic studies of reactions where proton transfers are involved. ... 

J., Computer Simulations of Enzymatic Reactions Examination of Linear Free-Energy Relationships and Quantum-Mechanical Corrections in the Initial Proton-transfer Step of Carbonic Anhydrase, Faraday Discuss. 1992, 93, 225. 

Heavy-atom isotope effects have been used to examine the transition state structures of the first phosphoryl transfer step, formation of the phosphocysteine intermediate, with the PTPs PTPl and YopH, and the DSP VHR (78). For each it was found that the transition state is very loose, resembling uncatalyzed phosphoryl transfer, and with full neutralization of the leaving group by proton transfer from the conserved aspartic acid. The transition state of the second chemical step, dephosphorylation of the intermediate, was probed in Stpl using linear free energy relationships and was found to proceed with little nucleophilic participation, suggesting that a loose transition state is operative for this reaction as well (79). 

A linear free-energy relationship between the composites = kikjk-i and the metal electrode potentials had a slope of 0.51 0.06, close to the theoretical Marcus value. Values for both iron(m) and ruthenium(m) fall on the same line, indicating that the outer-sphere reaction is little affected by the size of the metal f/-orbitals. It is suggested that the electron transfer takes place via the periphery of the polypyridyl ring. An isotope effect, kiiD oyk XHiO) = 2.7, can be accounted for by the (ki/A i) term indicative of electron transfer before loss of proton from the radical cation (8). 

Recall that Eqs. 8.48 and 8.50 are called BrDnsted linear free energy relationships. If an acid or base is involved in the rate-determining step of a reaction, the rate of that reaction should depend upon the strength of the acid or base. Hence, a Bronsted correlation is often found. Eqs. 8.51 and 8.52 relate the rate constants for an acid- or base-catalyzed reaction, respectively, to the pfC, of the acid or conjugate acid of the base. The sensitivity of an acid-catalyzed reaction to the strength of the acid is a, whereas the sensitivity of a base-catalyzed reaction to the strength of the base is p. The a and p reaction constants indicate the extent of proton transfer in the transition state. In Chapter 9 we explore the use of these two equations in much more detail, and we apply them in Chapters 10 and 11. 

Figure 13 Curvature in a free energy relationship due to a positive Hammond coefficient for the proton transfer from >ff,-dimethyl (9-fluorenyl)sulfonium tetrafluoroborate. The dashed line is fit of the data to a linear Bronsted equation...

Let us consider the proton transfer from acetone to a series of bases [3] and compare the logarithm of the rate constant with the pK of the conjugate acid of the base. A linear relationship is observed (Fig. 1) which is an example of a Bronsted correlation. If we had plotted log kf (a measure of the free-energy difference between ground and transition state) versus log k /kf (a measure of the free energy of the reaction) it is clear intuitively that the transition state would be product-like for a slope of unity and reactant-like for zero slope. It is difficult to measure equilibrium constants such as in Eqn. 1 but ionisation constants are easily estimated (using pH-titration equipment for example) so that the majority of comparisons are with these. Inspection of Eqns. 1 and 2 shows that the only identities are the base and the acid comparison of oxonium ion with acetone and water with the conjugate base of acetone is doubtful. 

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