Isotope inverse

An inverse isotope effect will occur if coordination at the reaction center increases in the transition state. The bending vibration will become more restricted. Entry 4 in Scheme 4.2 exenqilifies such a case involving conversion of a tricoordinate carbonyl group to a letravalent cyanohydrin. In this case the secondary isotope effect is 0.73. 

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. 

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. 

If it is assumed that ionization would result in complete randomization of the 0 label in the caihoxylate ion, is a measure of the rate of ionization with ion-pair return, and is a measure of the extent of racemization associated with ionization. The fact that the rate of isotope exchange exceeds that of racemization indicates that ion-pair collapse occurs with predominant retention of configuration. When a nucleophile is added to the system (0.14 Af NaN3), k y, is found to be imchanged, but no racemization of reactant is observed. Instead, the intermediate that would return with racemization is captured by azide ion and converted to substitution product with inversion of configuration. This must mean that the intimate ion pair returns to reactant more rapidly than it is captured by azide ion, whereas the solvent-separated ion pair is captured by azide ion faster than it returns to racemic reactant. 

Values of kH olki3. o tend to fall in the range 0.5 to 6. The direction of the effect, whether normal or inverse, can often be accounted for by combining a model of the transition state with vibrational frequencies, although quantitative calculation is not reliable. Because of the difficulty in applying rigorous theory to the solvent isotope effect, a phenomenological approach has been developed. We define <[), to be the ratio of D to H in site 1 of a reactant relative to the ratio of D to H in a solvent site. That is. 

Some of the important properties of the elements are given in Table 18.1. The imprecision of the atomic weights of Kr and Xe reflects the natural occurrence of several isotopes of these elements. For He, however, and to a lesser extent Ar, a single isotope predominates ( He, 99.999 863% " Ar, 99.600%) and much greater precision is possible. The natural preponderance of " Ar is indeed responsible for the well-known inversion of atomic weight order of Ar and K in the periodic table, and the position of Ar in front of K was only finally accepted when it was shown that the atomic weight of He placed it in front of Li. The second isotope of helium, He, has only been available in significant amounts since... 

The amino acid methionine is formed by a melhylation reaction of homo cysteine with iV-methyltetrahydrofolate. The stereochemistry of the reactior has been probed by carrying out the transformation using a donor with a "chiral methyl group" that contains protium (H), deuterium (D), and tritium (T isotopes of hydrogen. Does the methylation reaction occur with inversion oi retention of configuration ... 

The atomic weight increases regularly across the row except for the inversion at cobalt and nickel. We would expect the atomic weight of Ni to be higher than that of Co because there are more protons (28) in the Ni nucleus than in the Co nucleus (27). The reason for the inversion lies in the distribution of naturally occurring isotopes. Natural cobalt consists entirely of the isotope 2 Co natural nickel consists primarily of the isotopes Ni and Ni, the 58-isotope being about three times as abundant as the 60-isotope. 

The secondary isotope effects come out to be inverse, as they should be483, and likewise have a value of about 12 % per atom484. If these effects are neglected,... 

Since the rate was independent of acidity even over the range where H0 and pH differ, and the concentration of free amine is inversely proportional to the acidity function it follows that the rate of substitution is proportional to h0. If the substitution rate was proportional to [H30+] then a decrease in rate by a factor of 17 should be observed on changing [H+] from 0.05 to 6.0. This was not observed and the discrepancy is not a salt effect since chloride ion had no effect. Thus the rate of proton transfer from the medium depends on the acidity function, yet the mechanism of the reaction (confirmed by the isotope effect studies) is A-SE2, so that again correlation of rate with acidity function is not a satisfactory criterion of the A-l mechanism. 

As a general rule, in both equilibrium and kinetic studies, the process that forms the stronger bond is favored more for the heavier isotope. If the labeled atom is more firmly attached in the transition state, as it was for Eq. (9-100), then one can even find an inverse kie. One rule to remember Substitution with a heavier atom favors the stronger bond in any equilibrium, including the quasi-equilibrium of TST. 

Kezdy-Swinboume method, 26-27 Kinetic element effect, 110-111 Kinetic isotope effects (kie), 214-219 inverse, 217... 

The isotopic difference between the mean squares of the displacements in equation (7) can be calculated if the carbon-hydrogen oscillator is treated as a diatomic molecule. It is easily shown that for constant potential the mean square of the displacement from the equilibrium position of the harmonic oscillator will be inversely proportional to the square root of the reduced mass, /x, and hence... 

The molecules most profitably studied in connection with purely steric isotope effects have been isotopically substituted biphenyl derivatives. Mislow et al. (1964) reported the first more or less clearcut example of this kind in the isotope effect in the configurational inversion of optically active 9,10-dihydro-4,5-dimethylphenanthrene (7), for which an isotopic rate ratio ( d/ h) of 1-17 at 295-2°K in benzene solution was determined. The detailed conformation of the transition state is not certain in this case, as it involves the mutual passage of two methyl groups, and thus it is difficult to compare the experimental results with... 

The work of Melander and Carter (1964) on 2,2 -dibromo-4,4 -di-carboxybiphenyl-6,6 -d2 (1) has been referred to above in the introductory and theoretical sections, where it was pointed out that the availability of two detailed theoretical computations of the inversion barrier (Westheimer and Mayer, 1946, Westheimer, 1947 Hewlett, 1960) made this system especially attractive for the study of steric isotope efifects. Furthermore, in the preferred initial-state conformation the two bromines are probably in van der Waals contact (cf. Hampsoii and Weissberger, 1936 Bastiansen, 1950), and thus initial-state steric effects are unaffected by deuterium substitution in the 6 and 6 positions. The barrier calculations provided two different theoretical values for the non-bonded H Br distance in the transition state which, together with the corresponding H Br potential function, could be inserted in equation (10) to yield values for A AH. For... 

H H non-bonded interactions are of great importance in organic compoimds, and thus it was of interest to attempt to investigate H H non-bonded potential functions via the determination of a steric isotope effect in the configurational inversion of an unsubstituted biaryl. In view of the extensive work of Harris and her co-workers in the 1,1 -binaphthyl series (see, for example, Badar et al., 1965 Cooke and Harris, 1963), and since the parent compound is one of the simplest hydrocarbons that may be obtained in enantiomeric forms, the determination of the isotope effect in the inversion of l,l -binaphthyl-2,2 -d2 (9) was... 

Apart from a few studies (ref. 7), the use of deuterium kinetic isotope effects (kie s) appears to have had limited use in mechanistic studies of electrophilic bromination of olefins. Secondary alpha D-kie s have been reported for two cases, trans-stilbene fi and p-substituted a-d-styrenes 2, these giving relatively small inverse kie s of... 

---