Effect kinetic isotope

Isotope effects can be divided into three categories primary, secondary, and solvent. Primary isotope effects are ones where bonds to the isotopic atom are made or broken during reaction. Secondary ones involve isotopic atoms where bonding changes during reaction, but no bonds are made or broken to them. Isotope effects can be normal or inverse normal isotope effects are ones where the rate is slower with the heavy isotope and inverse ones show faster rates with the heavier atom Solvent isotope effects result from mnning reactions in heavy water solvent isotope effects may also be primary and secondary. 

Non-station ary Methods of Enzyme Kinetics Titration of Active Sites 9.2.5.1 Determination of Concentration of Active Sites 

Meanwhile, reagents (and methods see Hsia, 1996) have been improved. A short series of titration experiments at different concentrations of electrophile should be conducted to determine the percentage of active enzyme (without nucleophile, so as not to start the reaction). The calculation of the true [E] (= [E] ) is performed with [El after weighing in, with the factor ffrom the active-site titration experiment from Eq. (9.10). 

With [E]ttue the true kcat can be determined according to Eq. (9.11) (n = number of active sites per subunit of enzyme). 

Utility of the Elucidation of Mechanism Transition-State Analog Inhibitors 

What are the criteria for regarding a compound as a TS analog The observation that the binding affinity of an inhibitor is greater than that of a substrate, i.e., X, XM, is insufficient as many potent inhibitors bind differently to an enzyme than the substrate examples are methotraxate, inhibiting dihydrofolate reductase (DHFR) X] = 0.15 pM (Werkheiser, 1961), and sulfonyl urea herbicides, inhibiting acetolactate synthase (ALS) at picomolar levels. 

Studies of the kinetic effects of isotopic substitutions can provide support for a certain type of mechanism. The kie can be most helpful to settle whether a particular bond to hydrogen or another light element is broken in the activation process. 

Imagine that there is such a bond between group R and an attached atom A. The question is, by how much do the rates differ between R-A and R-A (the latter being 

consider the case A = H, A = D. This is the first one considered, because it is one of the few in which the effect is substantial and thus the case that has been of most use in practice. Since /Mr mH for most molecular fragments R, to a very good approximation the reduced masses are 

Since the force constant [A of Eq. (9-90)] is independent of the isotope, it is easy to show that the ratio of the zero-point vibrational frequencies is 

The difference in the activation energies is taken to be that between the ground states because the transition states, where no R-H or R-D bond remains, are at the same energy. That is. 

The quantisation of the vibrational degrees of freedom offers a method of calcnlating the effect of isotopic substitution on the rate constants, because isotopes differ in their masses, hence in their ZPEs, but not in their electronic potential energies. 

The naive approximation described above is in conflict with the TST, because the reactive bond is never completely broken at the transition state. The existence of a bonding interaction in A- -B- -C is the reason why the transition state can be defined in the first place, and the ZPEs of the C-H or C-D bonds cannot be totally omitted. Thus, the observed KIE should always be smaller that the calculated maximum. 

Westheimer [9] pointed out a more consistent method to estimate the maximum KIE in a reaction of the type 

If the transition state is not perfectly symmetrical, the H atom will be closer to either A or B, and will move with the synunetric stretching. This movement will produce a ZPE difference between the hydrogenated and denterated species, which will partly offset the ZPE difference of the reactive bonds. Thus, a smaller KIE should be observed when H (or D) is closer to either A or B. In Chapter 7 we will see that in an exothermic reaction the structure of the transition state resembles more closely that of the reactants and in an endothermic 

Westheimer s interpretation of KIE is based on identical pre-exponential factors for H or D transfers, neglects the contribution of the bending vibrations, and assumes that classical mechanics can describe the movement along the reaction coordinate. It is, nevertheless, a useful approximation for mechanistic interpretations of KIE. For example, the observation of a sizeable KIE when a hydrogen atom is replaced by deuterium in a given compound indicates that the bond where the isotopic substitution was made is practically broken in the rate-determining step of the reaction. 

Support for predicted effects has come from two major types of kinetic approach, namely the use of kinetic isotope effects and the application of linear free energy relationships. 

Primary kinetic isotope effects are predominantly due to differences in the masses of the isotopes and the resulting differences in the zero-point energies of the bonds . The larger the relative difference between the masses of the two isotopes, then the more pronounced are the isotope effects. Conse- 

According to absolute rate theory , the kinetic isotope effect is equal to the quotient of the equilibrium constants for the formation of the transition states in the labelled and unlabelled substrates, respectively, if symmetry factors are neglected and the transmission coefficients are independent of isotopic substitution (60). Substitution of equilibrium constants reduces the calculation to solving the complete partition functions (61). 

and Aa are the isotopic substrates and X, and Xj their corresponding activated complexes. 

Qe ec is isotopically independent and can therefore be neglected in the isotope ratio equation. Fundamental vibrational frequencies of the reactant can be estimated for simple molecules from analysis of the infrared and Raman spectra. Transition state vibrations must be calculated from an assumed model. Only in recent years with the advent of high-speed computers have complete calculations for any but the simplest molecules become feasible. More often, the equation is simplified by assuming particular models. 

Molecules that are chemically identical except for containing different isotopes react at different rates. For example, it is the difference in rates of electrolysis that allows D2O to be obtained by the electrolysis of water, even though the relative abundance of D compared to H is 1 6000. This phenomenon is known as the kinetic isotope effect. A primary kinetic isotope effect occurs when isotopic substitution has been accomplished so that the 

It is known that the greater the relative difference in the mass of two isotopes, the greater the kinetic isotope effect. Therefore, the effect wiU be greater when H is replaced by D (where there is a 100% mass increase) than when Br is replaced by Br. Suitable preparation and detection procedures must be available, and a radioactive isotope must have a suitable half-life for the isotopicaUy labeled materials to be employed. This limits somewhat the range of atoms that are useful in studying kinetic isotope effects on reaction rates. Other than studies involving isotopes of hydrogen, 

For a vibrating diatomic molecule A—B, the vibrational energy can be expressed as 

If the vibration takes place with the molecule behaving as a harmonic oscillator, the frequency is given by 

In a similar way, we can show that /x t (3/4)mH while for D2 the result is tfiii. Only in the case of the hydrogen isotopes is the relative mass effect this large. 

Determination of the KIE, that is, the difference in reaction rate observed upon introduction of a different isotope is a very useful mechanistic tool [5, 6]. In the following, we will limit ourselves to the use of deuterium as a substitute for hydrogen as that usually results in a relatively large difference that is easily observable. The relative rate of hydrogen versus deuterium k- lk-Q) is termed the kinetic isotope effect. In the simple scenario where the reaction proceeds through a single 

This is only true under the assumption of complete bond breakage in the TS and the absence of tunneling effects. In a catalytic reaction, the situation is somewhat more complicated and the measured KIE depends both on the type of measurement (direct competition vs reaction in separate flasks) and whether or not the step that involves the breakage of the C-H/D bond occurs before or after the rate-determining step. These scenarios have recently been reviewed thoroughly by Simmons and Hartwig [7]. In the following, we will review several case studies where the interpretation of the measured KIE was assisted by calculations of plausible reaction steps and/or entire catalytic cycles. 

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. 

This treatment is not very mathematical it is intended to provide a physical picture for the origin of isotope effects and to show some of their uses. More detailed discussions are available in reviews by Bell, Saunders, Ritchie, Carpenter, - and Drenth and Kwart.  

A special type of substituent effect that has proved very 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 it often has an easily measured effect on the rate, which is called a kinetic isotope effect (KIE). Let us consider how this modification of the rate arises. Initially, the discussion concerns primary kinetic isotope effects, those in which a bond to the isotopically substituted atom is broken in the rate-determining step. We use C-H bonds as the specific case for discussion but the same concepts apply for other elements. 

Secondary isotope effects at the (3-position have been especially thoroughly studied in nucleophilic substitution reactions. When carbocations are involved as intermediates, substantial (3-isotope effects are observed because the hyperconjugative stabilization by the (3-hydrogens weakens the C-H bond. The observed secondary isotope effects are normal, as would be predicted since the bond is weakened. 

Detailed analysis of isotope effects reveals that there are many other factors that can contribute to the overall effect in addition to the dominant change in bond vibrations. There is not a sharp numerical division between primary and secondary effects, 

A new method for determining KIE using compounds of natural isotopic abundance has been developed.This method makes experimental data more readily available. The method is based on the principle that as the reaction proceeds, the amount of the slower reacting isotope, e.g., or is enriched in the remaining reactant. For example, an isotope effect of 1.05 leads to 25% enrichment of the less reactive isotope at 99% conversion. The extent of enrichment can be measured by 

For more complete discussion of isotope effects see W. H. Saunders, in Investigation of Rates and Mechanisms of Reactions, E. S. Lewis, ed., Techniques of Organic Chemistry, 3rd Edition, Vol. VI, Part 1, John Wiley Sons, New York, 1974, pp. 211-255 L. Melander and W. H. Saunders, Jr., Reaction Rates of Isotopic Molecules, Wiley, New York, 1980 W. H. Saunders, in Investigation of Rates and Mechanisms of Reactions, C. F. Bernasconi, ed.. Techniques of Organic Chemistry, 4th Edition, Vol. VI, Part 1, Interscience, New York, 1986, Chap. VIII. 

The deuterium KIE values are generally in the range expected for linear three-center hydrogen transfer reactions,44107 and they track nicely with the rate constants for the reactions with the faster, more exothermic reactions displaying smaller KIEs. The large KIE value for reaction of the benzyl radical is noteworthy in that it exceeds the theoretical maximum for the classical model in a manner apparently similar to that seen with tin hydride (see below). 

The deuterium KIEs for reactions of alkyl radicals with Bu3SnH at 27°C 

The reason for the iower ZPE of the deuterium-retaining species is found in its iower vibrationai frequencies due to the doubie mass of D as compared to H at aimost identicai binding forces. From ciassicai mechanics the vibrationai frequency Vd shouid therefore be iower by the inverse ratio of the square roots of their masses, i.e., Vd/vh = 1/1.41 0.71. [67] 

Example Isotopic labeling does not only reveal the original position of a rearranging atom, but can also reveal the rate-determining step of multi-step reactions by its marked influence on reaction rates. Thus, the examination of H/D and isotope effects led to the conclusion that the McLafferty rearrangement of aliphatic ketones (Chap. 6.7) rather proceeds stepwise than concerted. [68] 

Notes i) The isotope effects dealt with in mass spectrometry are usually intramolecular kinetic isotope ejfects, i.e., two competing fragmentations only differing in the isotopic composition of the products exhibit different rate constants k and k, . [69] ii) The kinetic isotope effect is called normal if k k, 1 and inverse if k ko 1. iii) Isotope effects can also be observed on KER, [52,70] e.g. the KER accompanying H2 loss from methylene immonium ion varies between 0.61 and 0.80 eV upon D labeling at various positions. [52] 

While the mass of H remarkably differs from that of D (2 u/1 u = 2), the relative increase in mass is much less for heavier elements such as carbon (13 u/12u = 1.08) [68] or nitrogen (15 u/14u = 1.07). As a result, kinetic isotope effects of those elements are particularly small and special attention has to be devoted in order for their proper determination. 

Mass spectrometry measures the abundance of ions versus their m/z ratio, and it is common practice to use the ratio /mH//mD = kn/ku as a direct measure of the isotope effect. The typical procedure for determining isotope effects from intensity ratios 

The power of the catalyst may also be seen in the relative rate constants. The rate constant for the loss of ozone due to reaction with NO is five times the loss of ozone in the reaction with O atoms. The constant for loss of O atoms in the reaction with NO2 is nearly four orders of magnitude faster than that due to reaction with ozone. These numbers are brought out to indicate the very large range in the values for rate constants. This range results mainly from differences in activation energies and the steric requirements for the reactions. (Steric requirements define the orientations of atoms necessary to form the new bonds.) Although the concentrations of the catalytic species in this example are lower than the 

Photosynthesis begins with the transfer of COj into the cell from the atmosphere or water. Photosynthetic enzymes then transfer the inorganic carbon to a 5-carbon organic compound to form two 3-carbon carboxylic acid molecules. (This is the case for the C3 photosynthetic mechanism.) In these steps, reaction of occurs slightly faster than 

Isotope effects also play an important role in the distribution of sulfur isotopes. The common state of sulfur in the oceans is sulfate and the most prevalent sulfur isotopes are (95.0%) and (4.2%). Sulfur is involved in a wide range of biologically driven and abiotic processes that include at least three oxidation states [S(VI), S(0), and S(—II)]. Although sulfur isotope distributions are complex, it is possible to learn something of the processes that form sulfur compounds and the environment in which the compounds are formed. 

The zero point energy of a molecule corresponds to the energy 

In fact, almost since the discovery of deuterium, such reactions have been studied In an attempt to find evidence for tunneling In a chemical reaction (14). 

To find evidence for tunneling, one must first account for kinetic Isotope effects that do not depend on tunneling. The most direct method of doing this Is by means of activated complex theory, which leads to a formulation of the rate constant In terms of partition functions of the reactants and the activated complex. Arguments concerning the validity of activated complex theory are easy to provoke and difficult to settle, and I shall not consider this question here. It can then be shown (15,16) that the ratio of rate constants for two Isotopic forms of the same reactant (AX] and AX2) Is given by 

ACS Symposium Series American Chemical Society Washington, DC, 1975. 

Given the details of the relevant potential energy surface, or some empirical scheme for predicting the force constants needed to calculate the vibrational frequencies upon which the T s depend, one can evaluate q. (8) with or without the tunneling 

A good example of this approach Is provided by the gas-phase reaction systems 

So far we have considered reactions that are either one-step reactions or are multistep reactions in which the rate-limiting step is known. In many cases we may be able to propose a reasonable mechanism for a multistep reaction. 

Two steps in the oxidation of isopropyl alcohol by chromic acid. 

Formation of a chromate ester from isopropyl alcohol and chromic acid. 

Decomposition of the chromate ester with concurrent oxidation of the alcohol and reduction of the chromium. 

There is a kinetic method that can, in principle, tell us about bonding changes in the rate-limiting step of a reaction and that was used to answer the questions just posed. The technique is the study of kinetic isotope effects, in which the rate constant of a reaction varies when one isotope of an atom is replaced by a different (usually heavier) isotope. If there is a kinetic effect upon replacement of an atom to which a bond is broken, then we observe a primary (1°) kinetic isotope effect (PKIE). If the kinetic effect results from placing an isotope elsewhere in the reactant, then we observe a secondary (2°) kinetic isotope effect.  

A deuterium label in heavy water is indicated by writing [ H2]water or water-t/2, and similarly for other labelled compounds. The formula for heavy water can be written as H20 or D2O. 

Many fully or partially deuterated compounds are available commercially, and the extent of deuterium labelling can be determined by mass spectrometry, density measurements (after conversion into water) or IR spectroscopy. 

The separation of deuterium from naturally occurring hydrogen is achieved electrolytically with the isotope in the form of D2O. When an aqueous solution of NaOH (natural isotopic abundances) is electrolysed (eq. 10.5) using an Ni electrode, the separation factor defined in eq. 10.6 is 1 6. The choice of electrode is critical for optimizing this value. 

The electrolysis is continued until 90% of the liquid has been converted into O2 and H2. Most of the residual liquid is then neutralized with CO2, and the water distilled and 

In 1998, experiments were carried out in the US aimed at reproducing theoretical pnedictions that H2 would dissociate and form an alkali metal-fike lattice under pressures of 340 GPa. A diamond anvU cell was used to generate a pressure of 342 10 GPa, but there was no expterimental evidence for the formation of alkali metal-like hydrogen. In 2002, French physicists performed optical measurements on solid hydrogen up to 320 GPa pjressure. No structural changes were observed, but the darkening 

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It is clear, then, that the measurement of primary kinetic isotope effects will not give a wholly unambiguous clue to mechanism in the absence of other evidence. Nevertheless, the absence of a kinetic isotope effect is most easily understood in terms of the /S 2 mechanism... 

Melander first sought for a kinetic isotope effect in aromatic nitration he nitrated tritiobenzene, and several other compounds, in mixed acid and found the tritium to be replaced at the same rate as protium (table 6.1). Whilst the result shows only that the hydrogen is not appreciably loosened in the transition state of the rate-determining step, it is most easily understood in terms of the S 2 mechanism with... 

One way in which the step of the reaction in which the proton is lost might be slowed down, and perhaps made kinetically important (with i), would be to carry out nitration at high acidities. Nitration of pentadeuteronitrobenzene in 97-4% sulphuric acid failed to reveal such an effect. In fact, nitrations under a variety of conditions fail to show a kinetic isotope effect. 

The cases of pentamethylbenzene and anthracene reacting with nitronium tetrafluoroborate in sulpholan were mentioned above. Each compound forms a stable intermediate very rapidly, and the intermediate then decomposes slowly. It seems that here we have cases where the first stage of the two-step process is very rapid (reaction may even be occurring upon encounter), but the second stages are slow either because of steric factors or because of the feeble basicity of the solvent. The course of the subsequent slow decomposition of the intermediate from pentamethylbenzene is not yet fully understood, but it gives only a poor yield of pentamethylnitrobenzene. The intermediate from anthracene decomposes at a measurable speed to 9-nitroanthracene and the observations are compatible with a two-step mechanism in which k i k E and i[N02" ] > / i. There is a kinetic isotope effect (table 6.1), its value for the reaction in acetonitrile being near to the... 

By protodetritiation of the thiazolium salt (152) and of 2 tritiothiamine (153) Kemp and O Brien (432) measured a kinetic isotope effect, of 2.7 for (152). They evaluated the rate of protonation of the corresponding yiides and found that the enzyme-mediated reaction of thiamine with pyruvate is at least 10 times faster than the maximum rate possible with 152. The scale of this rate ratio establishes the presence within the enzyme of a higher concentration of thiamine ylide than can be realized in water. Thus a major role of the enzyme might be to change the relative thermodynamic stabilities of thiamine and its ylide (432). 

Kinetic isotope effects are an important factor in the biology of deuterium. Isotopic fractionation of hydrogen and deuterium in plants occurs in photosynthesis. The lighter isotope is preferentially incorporated from water into carbohydrates and tipids formed by photosynthesis. Hydrogen isotopic fractionation has thus become a valuable tool in the elucidation of plant biosynthetic pathways (42,43). 

In CLTST there appears a kinetic isotope effect owing to the difference in partition functions in the initial state [see eq.(2.12)], and at 2Pf < o > I5... 

Fig. 4.9. DifiBoing zero-point energies ofprotium- and deuterium-substituted molecules as the cause of primary kinetic isotope effects.

Scheme 4.2. Some Representative Kinetic Isotope Effects...

The details of proton-transfer processes can also be probed by examination of solvent isotope effects, for example, by comparing the rates of a reaction in H2O versus D2O. The solvent isotope effect can be either normal or inverse, depending on the nature of the proton-transfer process in the reaction mechanism. D3O+ is a stronger acid than H3O+. As a result, reactants in D2O solution are somewhat more extensively protonated than in H2O at identical acid concentration. A reaction that involves a rapid equilibrium protonation will proceed faster in D2O than in H2O because of the higher concentration of the protonated reactant. On the other hand, if proton transfer is part of the rate-determining step, the reaction will be faster in H2O than in D2O because of the normal primary kinetic isotope effect of the type considered in Section 4.5. 

A number of studies of the acid-catalyzed mechanism of enolization have been done. The case of cyclohexanone is illustrative. The reaction is catalyzed by various carboxylic acids and substituted ammonium ions. The effectiveness of these proton donors as catalysts correlates with their pK values. When plotted according to the Bronsted catalysis law (Section 4.8), the value of the slope a is 0.74. When deuterium or tritium is introduced in the a position, there is a marked decrease in the rate of acid-catalyzed enolization h/ d 5. This kinetic isotope effect indicates that the C—H bond cleavage is part of the rate-determining step. The generally accepted mechanism for acid-catalyzed enolization pictures the rate-determining step as deprotonation of the protonated ketone ... 

The distribution of a-bromoketones formed in the reaction of acetylcyclopentane with bromine was studied as a function of deuterium substitution. On the basis of the data given below, calculate the primaiy kinetic isotope effect for enolization of... 

Consider the kinetic isotope effect that would be observed in the reaction of semicarbazide with benzaldehyde ... 

Table 10.6. Kinetic Isotope Effects in Some Electrophilic Aromatic Substitution Reactions...

A substantial body of data, including reaction kinetics, isotope effects, and structure-reactivity relationships, has permitted a thorough understanding of the steps in aromatic nitration. As anticipated from the general mechanism for electrophilic substitution, there are three distinct steps ... 

Bromination has been shown not to exhibit a primary kinetic isotope effect in the case of benzene, bromobenzene, toluene, or methoxybenzene. There are several examples of substrates which do show significant isotope effects, including substituted anisoles, JV,iV-dimethylanilines, and 1,3,5-trialkylbenzenes. The observation of isotope effects in highly substituted systems seems to be the result of steric factors that can operate in two ways. There may be resistance to the bromine taking up a position coplanar with adjacent substituents in the aromatization step. This would favor return of the ff-complex to reactants. In addition, the steric bulk of several substituents may hinder solvent or other base from assisting in the proton removal. Either factor would allow deprotonation to become rate-controlling. 

Friedel-Crafts acylation sometimes shows a modest kinetic isotope effect. This observation suggests that the proton removal is not much faster than the formation of the (j-complex and that the formation of the n-complex may be reversible under some conditions. 

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. 

Indicate mechanisms that would account for the formation of each product. Show how the isotopic substitution could cause a change in product composition. Does your mechanism predict that the isotopic substitution would give rise to a primary or secondary deuterium kinetic isotope effect Calculate the magnitude of the kinetic isotope effect from the data given. 

We now carry the argument over to transition state theory. Suppose that in the transition state the bond has been completely broken then the foregoing argument applies. No real transition state will exist with the bond completely broken—this does not occur until the product state—so we are considering a limiting case. With this realization of the very approximate nature of the argument, we make estimates of the maximum kinetic isotope effect. We write the Arrhenius equation for the R-H and R-D reactions... 

A kinetic isotope effect that is a result of the breaking of the bond to the isotopic atom is called a primary kinetic isotope effect. Equation (6-88) is, therefore, a very simple and approximate relationship for the maximum primary kinetic isotope effect in a reaction in which only bond cleavage occurs. Table 6-5 shows the results obtained when typical vibrational frequencies are used in Eq. (6-88). Evidently the maximum isotope effect is predicted to be very substantial. 

Table 6-5. Calculated Hydrogen/Deuterium Primary Kinetic Isotope Effects" ...

A more rigorous theory of kinetic isotope effects begins with the transition state equation k = (kTlh)K. Writing this for and ito leads to... 

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