The isotope effect

This effect was also present in the harmonic oscillator. When becomes larger this picture is modified. The larger v, the larger the modification of the energies of the stationary states (see the last term in the formula for Ey). 

The two first curves are identical (Fig. 4.15 a and b) and illustrate the isotope effect. When calculating the energy levels in case of a (or b), the reduced mass of the proton (or deuteron) has been taken. As we can see in the deuteron case, the number of energy levels has increased (from 6 to 9), the levels lowered and have became closer, when compared to the proton case. 

ISOTOPE EFFECT (after substitution by a heavy isotope) 

21) shows that the ratio of the OD bond frequency to the OH bond frequency is equal to the square root of the inverse reduced masses of D-substituted 

The red shift vqd voh) in the IR spectrum represents one of the main characteristics of deuteration. The effect is used in spectroscopy to check whether a band is indeed the OH band. In such a case, the substance is dissolved in heavy water, and after a while the OH functional groups are replaced by OD functional groups. If the IR spectrum is registered again and compared with the previous one showing a red shift in agreement with (4.27), this proves that indeed we were concerned with an OH band. 

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The occurrence of a hydrogen isotope effect in an electrophilic substitution will certainly render nugatory any attempt to relate the reactivity of the electrophile with the effects of substituents. Such a situation occurs in mercuration in which the large isotope effect = 6) has been attributed to the weakness of the carbon-mercury bond relative to the carbon-hydrogen bond. The following scheme has been formulated for the reaction, and the occurrence of the isotope effect indicates that the magnitudes of A j and are comparable ... 

The azo coupling reaction proceeds by the electrophilic aromatic substitution mechanism. In the case of 4-chlorobenzenediazonium compound with l-naphthol-4-sulfonic acid [84-87-7] the reaction is not base-catalyzed, but that with l-naphthol-3-sulfonic acid and 2-naphthol-8-sulfonic acid [92-40-0] is moderately and strongly base-catalyzed, respectively. The different rates of reaction agree with kinetic studies of hydrogen isotope effects in coupling components. The magnitude of the isotope effect increases with increased steric hindrance at the coupler reaction site. The addition of bases, even if pH is not changed, can affect the reaction rate. In polar aprotic media, reaction rate is different with alkyl-ammonium ions. Cationic, anionic, and nonionic surfactants can also influence the reaction rate (27). 

Infrared Spectrophotometry. The isotope effect on the vibrational spectmm of D2O makes infrared spectrophotometry the method of choice for deuterium analysis. It is as rapid as mass spectrometry, does not suffer from memory effects, and requites less expensive laboratory equipment. Measurement at either the O—H fundamental vibration at 2.94 p.m (O—H) or 3.82 p.m (O—D) can be used. This method is equally appticable to low concentrations of D2O in H2O, or the reverse (86,87). Absorption in the near infrared can also be used (88,89) and this procedure is particularly useful (see Infrared and raman spectroscopy Spectroscopy). The D/H ratio in the nonexchangeable positions in organic compounds can be determined by a combination of exchange and spectrophotometric methods (90). 

The origin of the isotope effect is the dependence of coq and co on the reacting particle mass. Classically, this dependence comes about only via the prefactor coq [see (2.14)], and the ratio of the rate constants of transfer of isotopes with masses mj and m2 m2 > mj) is temperature-independent and equal to... 

That is, the exponential increase of the isotope effect with is determined by the difference of the zero-point energies. The cross-over temperature (1.7) depends on the mass by... 

In the H/D isotope effect case, m2/wi = 2, the interval of temperatures between re(H) and re(D) is wider than AT as predicted by (2.19), and in this interval the H atom tunnels while the D atom classically overcomes the barrier. For this reason the isotope effect becomes several orders larger than that described by (2.70). At 7" < 7 c(m2) the tunneling isotope effect becomes independent of the temperature. 

The Arrhenius plot of k(T) for H and D transfer is presented in fig. 15. Qualitatively, the conclusions about the isotope effect drawn here on the basis of the one-dimensional model remain correct for more dimensions, but turns out to depend more weakly on m than In k This... 

The measured dependence of kn(T) and T) consists of an Arrhenius region ( = 9.6 kcal/mol) going over to the low-temperature plateau below IlOK, where k 10 s . The isotope effect grows as the temperature drops, kn/ko — 20 at T = 100 K (fig. 15). Tunneling is promoted by the torsional vibrations of the OH and CH groups, as well as the oxy-group bending vibration. 

A mechanism for alkene arylation by palladium(II) is given below. The isotope effect was found to be 5 when benzene-dg was used. When styrene-/S,i5-d2 was used. 

Here Tq are coordinates in a reference volume Vq and r = potential energy of Ar crystals has been computed [288] as well as lattice constants, thermal expansion coefficients, and isotope effects in other Lennard-Jones solids. In Fig. 4 we show the kinetic and potential energy of an Ar crystal in the canonical ensemble versus temperature for different values of P we note that in the classical hmit (P = 1) the low temperature specific heat does not decrease to zero however, with increasing P values the quantum limit is approached. In Fig. 5 the isotope effect on the lattice constant (at / = 0) in a Lennard-Jones system with parameters suitable for Ne atoms is presented, and a comparison with experimental data is made. Please note that in a classical system no isotope effect can be observed, x "" and the deviations between simulations and experiments are mainly caused by non-optimized potential parameters. 

Either step could be rate determining. Study of many reactions has shown that most occur with a significant isotopic effect, but for some reactions the isotope effect is absent.If we apply the steady state approximation to the intermediate, this reaction scheme leads to... 

We now wish to generalize this to include the isotope effect in H2O/D2O mixtures. The equilibrium constant is defined... 

The deuterium isotope effect is thought to arise from the effect on the equilibrium position of this A-nitrosation. This is also the case for the diazotization of aniline, but the isotope effect is larger, because two deprotonations are involved in the kinetics. 

A large primary isotope effect kH/kD = 3.6 had also been found earlier by Ibne-Rasa122 in the nitrosation of 2,6-dibromophenol in the 4 position which was also shown to be base-catalysed. These values are not unexpected in view of the isotope effect found with diazonium coupling which involves a similarly unreactive electrophile, so that the rate-determining transition state will be displaced well towards products. Furthermore, the intermediate will have a quinonoid structure and will, therefore, be of low energy consequently, the energy barrier for the second step of the reaction will be high. 

For coupling with 2-naphthol-6,8-disulphonic-l-isotope effects (kK/kD) varied with the substituent in the benzenediazonium ion as follows 4-C1 (6.55) 3-C1 (5.48) 4-N02 (4.78), i.e. the reactivity of the ion was increased so that i correspondingly decreased. Base catalysis was observed127, 129, and there was a free energy relationship between this catalytic effect and the basicity of pyridine, 3- and 4-picoline. However, for 2-picoline and 2,6-lutidine, the catalysis was 3 times and 10 times less than expected from their basicities showing that, in this particular proton transfer, steric hindrance is important. 

A further effect of steric hindrance in the transition state was shown by comparing the isotope effects obtained in the reactions of the sulphonic acids (II-V)... 

A positive iodinating species was postulated to account for the kinetics and isotope effect observed in the iodination of some amines by iodine in aqueous potassium iodide (in some cases in the presence of acetate, lactate, or phosphate ion). The isotope effects (kH/kD values in parenthesis) for these compounds studied were 2,4,6-trideutero-m-dimethylaminobenzenesulphonate ion, 25 °C (1.0) 2,4,6-trideutero-m-dimethyIbenzoate ion, 30 °C (1.4) 2,4,6-trideutero-dimethylaniline, 30 °C, lactate (3.0) 2,4,6-trideuteromethylaniline, 25 °C, acetate (3.2) 2,4,6-trideuteroaniline, 25 °C (3.5), phosphate (4.0) 2,4,6-trideutero-metanilate ion, 35 °C (2.0) 2,4,6-trideutero-m-aminobenzoate ion, 30 °C (4.8), phosphate (3.0) 2,6-dideutero-l-dimethylaminobenzene-4-sulphonate ion, 25 °C, phosphate (1.0) 4-deutero-l-dimethylaminobenzene-3-sulphonate ion, 25 °C, phosphate (1.0). The kinetics of these reactions was given by... 

The values of kH/kD for the uncatalysed and catalysed reactions were 4.36 and 4.47 respectively, yet the isotope effect is not necessarily diminished on reducing the concentration of iodide ion to zero and by the arguments elaborated above (p. 95) this implies that molecular iodine is not the iodinating species and that this species is formed in some pre-equilibrium, the function of the base being to form the species and not to remove the proton. This argument assumes, as does the previous discussion of the effect of iodide ion concentration on isotope effects, that a minute concentration of I- is insufficient to compete effectively with the reaction involving proton loss. 

A kinetic isotope effect, kH/kD = 1.4, has been observed in the bromination of 3-bromo-l,2,4,5-tetramethylbenzene and its 6-deuterated isomer by bromine in nitromethane at 30 °C, and this has been attributed to steric hindrance to the electrophile causing kLx to become significant relative to k 2 (see p. 8)268. A more extensive subsequent investigation304 of the isotope effects obtained for reaction in acetic acid and in nitromethane (in parentheses) revealed the following values mesitylene, 1.1 pentamethylbenzene 1.2 3-methoxy-1,2,4,5-tetramethyl-benzene 1.5 5-t-butyl-1,2,3-trimethylbenzene 1.6 (2.7) 3-bromo-1,2,4,5-tetra-methylbenzene 1.4 and for 1,3,5-tri-f-butylbenzene in acetic acid-dioxan, with silver ion catalyst, kH/kD = 3.6. All of these isotope effects are obtained with hindered compounds, and the larger the steric hindrance, the greater the isotope... 

Variation of the isotope effect with bromide ion concentration has also been observed for the bromination of 4-methoxybenzenesulphonic acid and its ortho dideuterated derivative at 0 °C, the value of kH/kD changing from 1.0 with no Br to 1.31 at 2.0 M Br" 308. 

The theoretical difficulties encountered in attempting to relate the isotope effect in iodination with the occurrence of base catalysis are also apparent in bromina-tion, for Vainshtein and Shilov224 have shown that the isotope effects ArH/ArD are 1.0 (Br+), 2.6 (Br2) and 1.0 (HOBr) whereas the corresponding reactivities of the electrophiles in the systems used are > 1400 1.0 0.0015. 

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