Bond stretching model

Isotope effects are used to probe chemical processes, as isotopic substitution generally alters only the mass of the reacting groups without changing the electronic properties of the reactants. In this fashion, isotope effects can be used as subtle probes of mechanism in chemical transformations. This section will discuss how to use isotope effects to probe for tunneling effects on enzymes. The basic criteria for tunneling are experimental isotope effects that have properties that deviate from those predicted within the semi-classical transition state model, which includes only zero-point energy effects (we refer to this as the bond stretch model ). 

The temperature dependence of primary kn/ko within the bond-stretch model arises from the zero-point energy differences of the X-H and X-D stretch. The magnitude of kn/ko is related to the difference in activation energy for X-H and X-D, as per Eq (10.7) [16],... 

A traditional use of the primary kn/kD ratio is to infer the transition-state structure for a reaction. Large primary kn/ko ratios are predicted for symmetric transition-states kn/kD ratios decrease for an early or a late transition state, as compensatory transition-state motions increase in these situations [18]. The simple bond-stretch model predicts a direct relationship between the symmetry of the transition-state structure and the magnitude of the observed primary kn/kD- As discussed bdow and in other sections, this view no longer holds in the context of significant hydrogen tunneling. 

The bond-stretch model provides an upper limit for kinetic isotope effects that arise solely from ground state zero-point energy effects. Observations that deviate from this model imply a nonclassical effect. Provided that potential artifacts are controlled, the observation of KlEs that disobey the bond-stretch predictions calls into question the basic theory. 

Theories for hydrogen transfer that treat hydrogen as a quantum mechanical particle have been presented [30-35] ho vever, most of these models are not fully developed with respect to KIE predictions. These models do agree with some of the basic conclusions taken from the bond-stretch model and the Bell correction, specifically that marked deviations of KlEs from predictions of the bond-stretch model occur when the quantum nature of hydrogen is pronounced. The basic criteria used to evaluate how closely a particular reaction obeys the bond-stretch KIE model and, by extension, a classical reaction model is presented below. In the subsequent sections of theory (Section 10.4) and experimental systems (Section 10.5), more detailed examples of nonclassical KlEs are presented. 

The bond-stretch model of KIEs results in predictable relationships between kn, ku, and kj due to the ZPEs of X-H, X-D, X-T, as first noted by Swain et al. in 1958 [56]. These Swain-Schaad relationships are historically expressed with X-H as the reference state, kn/kj = (kH/ko) ". Using X-T as the reference state leads to a similar relationship in which the exponent, S, is 3.26 kn/kj = (ko/kj), and facilitates experimental determinations of exponential breakdown [10, 50]. In mixed-label experiments, the rule of the geometric mean (RGM) is an additional factor, causing R to be included in the observed exponent (see Eq. (10.10) below). The experimental KIE exponent, RS is evaluated by Eq. (10.9) as a composite of the Swain-Schaad (S) and RGM (R) exponents. RS is a good indicator of turmeling when it exceeds 3.3 by a large margin, with an extreme semi-dassical upper-bound ofca. 5 [57]. 

Early experiments with DfM, that provided intrinsic primary and secondary KIEs for the C-H cleavage step, showed a puzzling discrepancy in the context of the bond-stretch model for hydrogen transfer. This discrepancy was that the primary KIE implied a symmetrical transition state while the secondary KIE indicated that the transition state was very product like [120]. The failure of multiple probes of transition state structure to converge on a consistent pattern of behavior is one of the criteria available for the diagnosis of tunneling (cf. Section 10.3.3.2). 

In Chapter 2, we proved the existence of the barrierless discharge of hydronium ions. The adsorbed hydrogen atom in this process is removed by activationless electrochemical desorption. In principle, activationless desorption may involve various proton donors, both H30 ions and water molecules. As was shown in section 2.1, in experiments on barrierless discharge a hydronium ion is the proton donor in a desorption reaction. Later, we shall show that this fact makes the bond stretching model improbable. 

Fig. 4.4. Potential energy curves for the discharge of an H3O ion at two different metals (bond stretching model). 1 - 0-H...

The results discussed above show that in acidic solutions the isotope separation factor considerably decreases with increasing electrode potential. This fact was established in [254,255,276,285, 288-291]. In the framework of the bond stretching model, such a nature of the dependence is explained by a decrease in the activation barrier height with increasing potential and hence by the favored proton tunneling[254,255]. This explanation remains valid if we consider two kinds of classical motion, viz. bond stretching and solvent reorganization. 

We can make a choice between the explanations given by the two models from a comparison of isotope effects in acidic and alkaline solutions. In the latter case a proton donor is a neutral water molecule which naturally is attracted electrostatically to the electrode much more weakly than the HaO" ion. The distance between the molecules and the electrode is practically independent of the potential, so in the model of Dogonadze et al., we should not expect a considerable potential dependence of the isotope effect[276]. On the contrary, in the 0-H bond stretching model there is no difference, in principle, between the discharges of HaO and H2O. In both cases the increase in the overpotential lowers the potential barrier, and we can expect an easier tunneling. 

It was shown in Chapter 4 (sections 4.3-4.5) that the relations characteristic of kinetic isotope effect in hydrogen evolution reactions are in good agreement with the predictions of the reorganization model, and in contradiction to the bond stretching model. The latter model, however, has so far been used to explain the main features of the kinetic isotope effect in homogeneous proton transfer reactions[256,443]. 

Thus, the above analysis shows that the regularities of the kinetic isotope effect in enzymatic hydrolysis reactions confirm the basic results of the quantum-mechanical theory of an elementary act and contradict the results of the bond-stretching model. The concepts of the quantum-mechanical theory are found to be useful for discussing some specific aspects of the action of enzymes. Hence it is important to discuss the general corollaries of the theory as applied to enzymatic reactions and other biological processes. Some aspects of this problem will be discussed in the following section. 

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