Proton transfer, curvature

Figure 5-3. Active site and calculated PES properties for the reactions studied, with the transferring hydrogen labelled as Hp (a) hydride transfer in LADH, (b) proton transfer in MADH and (c) hydrogen atom transfer in SLO-1. (i) potential energy, (ii) vibrationally adiabatic potential energy, (iii) RTE at 300K and (iv) total reaction path curvature. Reproduced with permission from reference [81]. Copyright Elsevier 2002...

ApA < 1. In Fig. 2 the region of curvature is much broader and extends beyond — 4 < ApA < + 4. One explanation for the poor agreement between the predictions in Fig. 3 and the behaviour observed for ionisation of acetic acid is that in the region around ApA = 0, the proton-transfer step in mechanism (8) is kinetically significant. In order to test this hypothesis and attempt to fit (9) and (10) to experimental data, it is necessary to assume values for the rate coefficients for the formation and breakdown of the hydrogen-bonded complexes in mechanism (8) and to propose a suitable relationship between the rate coefficients of the proton-transfer step and the equilibrium constant for the reaction. There are various ways in which the latter can be achieved. Experimental data for proton-transfer reactions are usually fitted quite well by the Bronsted relation (17). In (17), GB is a... 

Eigen (1964) found that a plot of ApR against the rate constant for proton transfer between acetylacetone and a series of bases gave a curved plot. It should be noted, however, that Eigen s explanation for curvature is quite different from the one based on Marcus theory and the reactivity-selectivity principle. The curvature discussed by Eigen is attributed to a change from a rate-determining proton transfer to a diffusion controlled reaction which is independent of the catalyst p. 

It has been common practice to equate the value of )3 with the degree of proton transfer in the transition state /3 values close to 0 are taken to be indicative of reactant-like transition states and those close to 1 of product-like transition states. Any value outside these limits is inconsistent with this practice. Early investigators were only able to follow reactions within a limited rate constant range. With the development of fast reaction techniques (Eigen, 1964 Caldin, 1964) the predicted (Br nsted and Pedersen, 1923) curvature of the plots was fully established (cf. Bell and Lidwell, 1940). Pronounced curvature is in fact seen for fast proton transfers in DMSO (see p. 156). 

As stated on p. 151, curvature in Br nsted plots has become apparent from studies of fast proton transfer processes. Fundamental differences in Br nsted plots have been observed for reactions of... 

The curvature is large when the intrinsic barrier is low, which is in accord with the observation of curvature in fast reactions. The theory thus supports Kresge s (1973) statement that rapid proton transfers will give curved Br nsted plots and slow proton transfers will give linear plots, irrespective of the identity of the atoms involved. 

The Br0nsted plots (Fig. 3) give information on this point. The higher curvature of the plot for DMSO compared to methanol is indicative of a lower intrinsic barrier to proton transfer for the dipolar aprotic solvent. Since in the extended Marcus theory the solvent effect has already been taken into account, one would expect the intrinsic barrier for proton transfer to be identical in the two systems. This is not the case. Therefore it appears that separation of the mechanism into reagent positioning with concomitant solvent reorganization is not warranted. 

The first applications (230-234) concerned a study of the dependence of the tunneling effect on the curvature of the reaction path, of an energy transfer among different vibrational modes in the course of a reaction, and of the evaluation of microcanonical rate constants for study-case reactions, HCN - CNH, H2CO -> H2 + CO, H2CC -> HC=CH, and proton transfer in malonaldehyde. 

Furthermore, some knowledge of the approximate position of the proton on the reaction coordinate in the transition state as well as of the curvature of the barrier is needed for a calculation of the primary isotope effect in proton transfer reactions [93—96, 130]. 

Bronsted plots for other carbon acids may be curves but this is not detected because of the limited range of reactivity over which the reactions can be studied and the Bronsted relation is therefore a sufficiently good approximation. The demonstration of a sharply curved Bronsted plot for diazoacetate ion came shortly after a new rate-equilibrium equation for proton transfer reactions had been proposed by Marcus. This will be discussed fully in Sect. 5.2 but it should be noted here that with this new theory, Bronsted plot curvature is easily accounted for. 

Recently a new method has been developed for analysing rate-equilibrium data for proton transfer reactions (Marcus Theory) [200], Although the theory has not been tested extensively, it seems to have received fairly wide acceptance. This new treatment leads to various parameters which are useful in understanding results for carbon acids and offers an explanation for some anomalies in Bronsted plots such as curvature and Bronsted exponents outside the range 0 < a or j3 < 1. 

Curvature is most reliably detected in proton transfer reactions... 

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...

Figure 20 Marcus curvature for proton transfer between carbon acid and heteroatom bases...

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