Origin of kinetic isotope effects

1 Origin of kinetic isotope effects. By virtue of the Born-Oppenheimer approximation, which states that the motions of electrons and of nuclei can be considered separately, the potential energy surface of a molecule does not vary with the isotopic nature of nuclei moving on it. This makes isotopic substitution a uniquely valuable probe of mechanism, since, unlike electronic substituent effects, the probe does not alter what is being investigated. 

In general isotopic substitution alters reaction rate according to the Bigeleisen 

Zero point energy kinetic isotope effects lie exclusively in the energy of activation, so that rate-ratios have the form of equation 1.13, where AA(ZPE) is 

With the further approximation that the rest of the molecule is heavy compared to the hydron, it is seen that the zero point energy of a deuterated species is 1/ 2, and that of a tritiated species 1/ 3, that of a protiated species. Consequently, at ordinary temperatures, the Swain-Schaad relation (equation 1.15) holds. 

The foregoing applies to both primary kinetic isotope effects, where the bond to the site of isotopic substitution is made or broken, and secondary isotope effects, where it is weakened or strengthened. 

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The simplest version of the origin of kinetic isotope effects holds that, say A h/A d will given by ... 

Fig. 2.16. Origin of kinetic isotope effects. [4,5,66] The change in vibrational frequencies, and thus in density of states causes somewhat higher activation energy and consequently smaller excess energy for the reaction of the deuterated bond, and thus reduces kxj.

You have seen how isotopes have different physical properties—their nuclear spin, for example, which affects how they behave in an NMR machine. We also showed you in Chapter 3 how IR stretching frequencies depend on mass, and there you saw that C-D bonds have lower stretching frequencies than C-H bonds. That fact Is highly relevant to the explanation we are about to give you for the origin of kinetic Isotope effects. 

The original experimental evidence for concerted acid-base catalysis of the mutarotation in benzene is now considered unsound133 134 and concerted acid-base catalysis has been difficult to prove for nonenzy-matic reactions in aqueous solution. However, measurements of kinetic isotope effects seem to support Swain and Brown s interpretation.135 Concerted acid-base catalysis by acetic acid and acetate ions may have been observed for the enolization of acetone136 and it may be employed by enzymes.1363... 

Equilibrium isotope effects serve as an empirical calibration of kinetic isotope effects. P-Secondary deuterium isotope effects in equilibrating carbo-cations have been used especially to prove the interpretation of the hyper-conjugative origin and the dihedral angle dependence of P-kinetic deuterium isotope effects in nucleophilic substitution. 

NMR spectroscopy is one among many probes that have been reported for the evaluation of kinetic isotope effects. Several NMR methods, as analogs of previous proton inventory techniques involving classical kinetic methods were reported, involving line-shap>e analyses and polarization transfer experiments on the exchanging protons or deuterons and/ or on the remote spins as functions of the deuterium atom fraction n in the mobile proton sites. Moreover, the kinetic isotope effects and the number of transferred protons originating from... 

The Westheimer effect and its implications form the main subject of this chapter, and no attempt is made to consider for example the more traditional application of primary isotope effects to the study of reaction mechanisms. However, a further point that is emphasized is that interpretations of isotope effects may be appreciated without resort to calculations, and before discussing kinetic effects some time is spent in considering, from a qualitative standpoint, the origins of hydrogen isotope effects and the isotopic properties of stable molecules and equilibria. In this preliminary review previous accounts of hydrogen isotope effects are extensively used [2-9] and among these... 

When one of the ortho hydrogens is replaced by deuterium, the rate drops from 1.53 X 10 " s to 1.38 X lO s. What is the kinetic isotope effect The product from such a reaction contains 60% of the original deuterium. Give a mechanism for this reaction that is consistent with both the kinetic isotope effect and the deuterium retention data. 

Support for such an interaction of the H—C bonds with the carbon atom carrying the positive charge is provided by substituting H by D in the original halide, the rate of formation of the ion pair is then found to be slowed down by 10% per deuterium atom incorporated a result compatible only with the H—C bonds being involved in the ionisation. This is known as a secondary kinetic isotope effect, secondary... 

Isotope Effects in C-H Bond Activation Reactions by Transition Metals (225) were reviewed, and some pitfalls in interpreting kinetic isotope were pointed out. The interpretation of the kinetic isotope effects offered by the authors of the original reports (75,76,85) on the system shown in Schemes 15,16 was criticized. 

The electrophile E+ attacks the unhindered side of the still unsubstituted second aromatic ring. A proton (deuteron) is transferred from this ring to the second, originally substituted ring, from which it leaves the molecule. Thus, the electrophile enters, and the proton (deuteron) leaves the [2.2]paracyclophane system by the least hindered paths. Some migration of deuterium could be detected in the bromination of 4-methyl[2.2]paracyclophane (79). The proposed mechanism is supported by the kinetic isotope effects ( h/ d) found for bromination of p-protio and p-deuterio-4-methyl[2.2]paracyclophanes in various solvents these isotope effects demonstrate that proton loss from the a complex is the slowest step. 

The kinetic isotope effect has its origin in force constant changes occurring at an isotopically substituted position as the react2mt is converted into an activated complex. Hence it provides information about the transition state in the solvolysis reaction, but not necessarily about the stmcture of possible intermediates. This limits the utility of information drawn from isotope studies in resolving the structure of ions under stabilizing conditions. 

Nearly all kinetic isotope effects (KIE) have their origin in the difference of isotopic mass due to the explicit occurrence of nuclear mass in the Schrodinger equation. In the nonrelativistic Bom-Oppenheimer approximation, isotopic substitution affects only the nuclear part of the Hamiltonian and causes shifts in the rotational, vibrational, and translational eigenvalues and eigenfunctions. In general, reasonable predictions of the effects of these shifts on various kinetic processes can be made from fairly elementary considerations using simple dynamical models. 

Repeated deprotonation of 278 removed due to a high H/D kinetic isotope effect the 1-proton, forming the dideuterio compound 279 with low diastereoselectivity . It is quite likely that a dynamic thermodynamic resolution is the origin. Intermediate 277 is configurationally labile, enabling an equilibration of the diastereomeric ion pairs 277 and epi-211. Similar studies were undertaken with 1-phenyl-l-pyrid-2-ylethane (280) and l-(4-chlorophenyl)-l-(pyrid-2-yl)-3-(dimethylamino)propane (281) (50% eef. An improvement of the achieved enantiomeric excesses resulted when external chiral proton sources, such as 282 or 283, were applied (84% ee for 280 with 283 and 75% ee for 281). 

These results, as well as rate studies " and kinetic isotope effects ", support a concerted, 5ptra-structured oxenoid-type transition state for the CH oxidations". The original oxygen-rebound mechanism has been discounted (see the computational work in Section I.D). Recently, however, the stepwise radical mechanism was revived in terms of the so-called molecule-induced homolysis , but such radical-type reactivity was severely criticized on the basis of experimental" and theoretical grounds. 

We have examined the proton transfer reaction AH-B A -H+B in liquid methyl chloride, where the AH-B complex corresponds to phenol-amine. The intermolecular and the complex-solvent potentials have a Lennard-Jones and a Coulomb component as described in detail in the original papers. There have been other quantum studies of this system. Azzouz and Borgis performed two calculations one based on centroid theory and another on the Landau-Zener theory. The two methods gave similar results. Hammes-Schiffer and Tully used a mixed quantum-classical method and predicted a rate that is one order of magnitude larger and a kinetic isotope effect that is one order of magnitude smaller than the Azzouz-Borgis results. 

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