Isotopic substitution, effect reaction

A starting point in the study of the effect of isotopic substitution on reaction rates must be furnished by a theoretical model of chemical reaction. The discovery by Arrhenius that experimental reaction rates may be expressed by forms the cornerstone... 

The earlier contributors to this symposium have outlined the basic theory of the interpretation of the effects of isotopic substitution on reaction rates originally developed independently by Bigeleisen and Mayer (2) and Melander. ( ) They showed that it is the geometrical structure, nuclear masses and, most importantly, the vibrational force fields of initial and transition states that determine the magnitude of isotope effects on reaction rates. 

A special type of substituent effect which has proved veiy valuable in the study of reaction mechanisms is the replacement of an atom by one of its isotopes. Isotopic substitution most often involves replacing protium by deuterium (or tritium) but is applicable to nuclei other than hydrogen. The quantitative differences are largest, however, for hydrogen, because its isotopes have the largest relative mass differences. Isotopic substitution usually has no effect on the qualitative chemical reactivity of the substrate, but often has an easily measured effect on the rate at which reaction occurs. Let us consider how this modification of the rate arises. Initially, the discussion will concern primary kinetic isotope effects, those in which a bond to the isotopically substituted atom is broken in the rate-determining step. We will use C—H bonds as the specific topic of discussion, but the same concepts apply for other elements. 

Predict whether normal or inverse isotope effects will be observed for each reaction below. Explain. Indicate any reactions in which you would expect > 2. The isotopically substituted hydrogens are marked with asterisks. 

For the reactions given below, predict the effect on the rate of the isotope substitution which is described. Explain the basis of your prediction. 

Consider a reactant molecule in which one atom is replaced by its isotope, for example, protium (H) by deuterium (D) or tritium (T), C by C, etc. The only change that has been made is in the mass of the nucleus, so that to a very good approximation the electronic structures of the two molecules are the same. This means that reaction will take place on the same potential energy surface for both molecules. Nevertheless, isotopic substitution can result in a rate change as a consequence of quantum effects. A rate change resulting from an isotopic substitution is called a kinetic isotope effect. Such effects can provide valuable insights into reaction mechanism. 

If the proton is not equidistant between A and B, it will undergo some movement in the symmetric stretching vibration. Isotopic substitution will, therefore, result in a change in transition state vibrational frequency, with the result that there will be a zero-point energy difference in the transition state. This will reduce the kinetic isotope effect below its maximal possible value. For this type of reaction, therefore, should be a maximum when the proton is midway between A and B in the transition state and should decrease as H lies closer to A or to B. 

Kinetic Isotope Effect. The change in reaction rate caused by isotopic substitution. 

The route from kinetic data to reaction mechanism entails several steps. The first step is to convert the concentration-time measurements to a differential rate equation that gives the rate as a function of one or more concentrations. Chapters 2 through 4 have dealt with this aspect of the problem. Once the concentration dependences are defined, one interprets the rate law to reveal the family of reactions that constitute the reaction scheme. This is the subject of this chapter. Finally, one seeks a chemical interpretation of the steps in the scheme, to understand each contributing step in as much detail as possible. The effects of the solvent and other constituents (Chapter 9) the effects of substituents, isotopic substitution, and others (Chapter 10) and the effects of pressure and temperature (Chapter 7) all aid in the resolution. 

A disadvantage of this technique is that isotopic labeling can cause unwanted perturbations to the competition between pathways through kinetic isotope effects. Whereas the Born-Oppenheimer potential energy surfaces are not affected by isotopic substitution, rotational and vibrational levels become more closely spaced with substitution of heavier isotopes. Consequently, the rate of reaction in competing pathways will be modified somewhat compared to the unlabeled reaction. This effect scales approximately as the square root of the ratio of the isotopic masses, and will be most pronounced for deuterium or... 

Both the 12C/13C primary KIE and the 14N/15N secondary KIE have been determined (Table 4-2) [19, 20], with the immediate adjacent atoms about the isotopic substitution site quantized as well. To our knowledge, we are not aware of any such simulations prior to our work for a condensed phase reaction with converged secondary heavy isotope effects. This demonstrates the applicability and accuracy of the PI-FEP/UM method. 

Effect of Isotope Substitution on Organic Reaction Rates. Nucleonics,... 

A complicating factor associated with experimental application of the Skell Hypothesis is that triplet carbenes abstract hydrogen atoms from many olefins more rapidly than they add to them. Also, in general, the two cyclopropanes that can be formed are diastereomers, and thus there is no reason to expect that they will be formed from an intermediate with equal efficiency. To allay these problems, stereospecifically deuteriated a-methyl-styrene has been employed as a probe for the multiplicity of the reacting carbene. In this case, one bond formation from the triplet carbene is expected to be rapid since it generates a particularly well-stabilized 1,3-biradical. Also, the two cyclopropane isomers differ only in isotopic substitution and this is anticipated to have only a small effect on the efficiencies of their formation. The expected non-stereospecific reaction of the triplet carbene is shown in (15) and its stereospecific counterpart in (16). 

Garret, B. C. and Truhlar, D. G. Generalized transition state theory. Quantum effects for collinear reactions of hydrogen molecules and isotopically substituted hydrogen molecules, JPhys.Chem., 83 (1979), 1079-1112... 

In the preceding sections, the bond to the isotopic atom is broken or formed in the rate-determining step of the reaction. In these cases, the change in rate is referred to as a primary kinetic isotope effect. Isotopic substitution at other sites in the molecule has much smaller effects on the rate. These small isotope effects are collectively referred to as secondary kinetic isotope effects. 

A more recent isotope study has been conducted with the use of the actual Noyori catalyst by Casey and Johnson [41], They studied the kinetic isotope effect by H NMR spectroscopy at -10 to -30 °C for the reaction of d, d-i (CH/OD and CD/OH), < s isotopically substituted propan-2-ol and 4-phenylbut-3-yn-2-none. The catalyst and the reaction are shown in Figure 4.31. 

Obviously these considerations carry over to the isotope effects on the equilibrium constant. Thus, using subscripts 1 and 2 to refer to the lighter and heavier isotopi-cally substituted equilibrium reaction, one obtains... 

Choosing a method to determine isotope effects on rate constants, and selecting a particular set of techniques and instrumentation, will very much depend on the rate and kind of reaction to be studied, (i.e. does the reaction occur in the gas, liquid, or solid phase , is it 1st or 2nd order , fast or slow , very fast or very slow , etc.), as well as on the kind and position of the isotopic label, the level of enrichment (which may vary from trace amounts, through natural abundance, to full isotopic substitution). Also, does the isotopic substitution employ stable isotopes or radioactive ones, etc. With such a variety of possibilities it is useless to attempt to generate methods that apply to all reactions. Instead we will resort to discussing a few examples of commonly encountered strategies used to study kinetic isotope effects. 

These reactions proceed through symmetrical transition states [H H H] and with rate constants kn,HH and kH,DH, respectively. The ratio of rate constants, kH,HH/kH,DH> defines a primary hydrogen kinetic isotope effect. More precisely it should be regarded as a primary deuterium kinetic isotope effect because for hydrogen there is also the possibility of a tritium isotope effect. The term primary indicates that bonds at the site of isotopic substitution the isotopic atom are being made or broken in the course of reaction. Within the limits of TST such isotope effects are typically in the range of 4 to 8 (i.e. 4 < kH,HH/kH,DH < 8). 

Note in comparing reactions 10.1 and 10.3 the isotope effect should also be called primary, since the bond to the isotopically substituted atom is being broken, just as it was in Equation 10.2. However in Equation 10.3 the magnitude of the isotope effect... 

In reaction (10.11) the deuterium isotope effect is a secondary isotope effect, that is one in which the bonding to the isotopically substituted atom is not broken or formed during the course of the reaction. Secondary deuterium isotope effects are generally much smaller than primary ones. 

Secondary hydrogen kinetic isotope effects are further classified as alpha, beta, etc. depending on the distance of the isotopically substituted atom from the bond(s) that is (are) being made or broken (a = 1 bond, 3 = 2 bonds, etc.). Consider the simple Sn2 reaction between hypochlorite anion and ethyl chloride ... 

It is not always possible to determine intrinsic isotope effects. However, other useful information about the reaction can still be obtained. Above we assumed a single rate determining step sensitive to each isotope substitution. More frequently, however, the isotope sensitivity is found in different steps. Studies with multiple isotope effects can be used to determine the sequence of steps. To illustrate, a more complicated reaction scheme is needed ... 

It is reasonable to expect that isotopic substitution on solvent molecules will affect both equilibrium and rate constants. This is especially true for reactions in aqueous media, many of which are acid or base catalyzed and therefore sensitive to pH or pD. Furthermore H/D aqueous solvent isotope effects often display significant nonlinearity when plotted against isotope fraction of the solvent. The analysis of this effect can yield mechanistic information. The study of aqueous solvent isotope effects is particularly important in enzyme chemistry because enzyme reactions universally occur in aqueous media and are generally pH sensitive. 

In reactions 14.32 and 14.33 the hydrogen atoms are not involved in any bonds that are being made or being broken in the reaction. The isotope effect is therefore referred to as a secondary a-deuterium isotope effect since the position of isotopic substitution is a to the bond being broken in the rate limiting step (see Chapter 10 for discussion of secondary isotope effects). 

The formalism for treating primary isotope effects on unimolecular processes follows analogously to the development above, once due account is taken of the difference in zero point energies on isotope substitution at the reaction site (which is reflected in an isotopic difference in the threshold energy Eo). For thermal activation the rate ratio in the high pressure limit is straightforwardly obtained from Equation 14.25. For H/D effects... 

The title indicates the scope of the text. The term isotope effects is used rather than applications of isotopes to indicate clearly that it deals with differences in the properties of isotopically substituted molecules, for example differences in the chemical and physical properties of water and the heavy waters (H2O, HDO, D2O, HTO, etc.). Thus H20, HDO and D2O have different thermodynamic properties. Also reactions in solvent mixtures of light and heavy water proceed at different rates than they do in pure H2O. On the other hand, the differences are not large and consequently, to the extent the difference in properties can be ignored, HDO or HTO can be used as tracers for H2O. An important point, however, is that this book does not deal with isotopes as tracers in spite of the widespread importance of tracer studies, particularly in the bio and medical sciences. Also the title specifically does not mention physics which would necessarily have been included if the term Physical Sciences had been used. Thus the text does not deal with differences in the nuclear properties of isotopic atoms. Such differences are in the realm of nuclear physics and will not be discussed. 

Isotope substitution aims to ascertain whether a bond labeled with an isotope takes part in a given reaction. One then either looks at the products, noting the label distribution, or attempts to determine the kinetic isotope effect. The latter can be detected as the change in the rate constant of the reaction by using an isotope in the place of an atom taking part in the reaction of interest. 

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