Equilibrium, isotopic perturbation

Any observable effect of isotopic substitution on the rate or extent of a chemical/physical process. Equilibrium isotopic perturbation measurements can provide valuable information about kinetic isotope effects on enzymic catalysis. NMR shift difference measurements are also useful in detecting the effects of isotopic substitution on a fast (degenerate) equilibrium between two species differing only in their specific isotopic substitution . The... 

The deuterium isotope effects on chemical shift consists of intrinsic isotope effect (direct perturbation of the shielding of X atom) and equilibrium isotope effect (perturbation of the equilibrium caused by the isotopic substitution). The values of deuterium isotope effects are to some extent independent of chemical shifts and allow determination of the mole fraction of the forms in equilibrium. 

Perrin et al. probed the structures of 174 and 175 by using the 13C NMR method of isotopic perturbation of equilibrium <2001PCA11383>. The goal of this study was to measure the 13C NMR chemical-shift difference between C5 of a-deuterated molecule and C2-(5) of undeuterated molecule (see Equation 48). If 174 or 175 is a mixture of valence tautomers 180-r/ia and 180-r/]b or 181-equilibrium isotope shift (Aeq) will be observed in addition to the intrinsic isotope shift (5A0). In contrast, if 174 or 175 has C2v symmetry, then only (5A0) will contribute. 

The l3C NMR spectrum of the C4H7+ cation in superacid solution shows a single peak for the three methylene carbon atoms (72) This equivalence can be explained by a nonclassical single symmetric (three-fold) structure. However, studies on the solvolysis of labeled cyclopropylcarbinyl derivatives suggest a degenerate equilibrium among carbocations with lower symmetry, instead of the three-fold symmetrical species (13). A small temperature dependence of the l3C chemical shifts indicated the presence of two carbocations, one of them in small amounts but still in equilibrium with the major species (13). This conclusion was supported by isotope perturbation experiments performed by Saunders and Siehl (14). The classical cyclopropylcarbinyl cation and the nonclassical bicyclobutonium cation were considered as the most likely species participating in this equilibrium. 

The initially observed perturbation (or equilibrium isotope effect) will disappear as isotopic scrambling (or mixing) subsequently occurs. This is illustrated above for the malic enzyme note the initial displacement of the equilibrium toward malate, followed by readjustment of the system to its flnal equilibrium position. The magnitude of the initial perturbation provides information on the occurrence of kinetic isotope effects and the nature of the rate-limiting step in an enzymatic process. See also Kinetic Isotope Effect Solvent Isotope Effect... 

The ff-delocalized structures are nonplanar, although H NMR shows only one absorption for all the methylene protons. Saunders and Krause have given unequivocal evidence for the nonplanarity of the 1 -methylcyclobutyl cation based on the isotopic perturbation of the equilibrium among nonplanar structures using stereospecifically labeled a,/3,a -trideuteriated 1-methylcyclobutyl cation 11 (equation 17)44. The cation showed two peaks... 

Another important method, which is described in detail below in a separate subsection, is the isotopic perturbation technique invented by Saunders and coworkers. This allows discrimination between classical and nonclassical structures and accurate determination of equilibrium isotope effects. 

The small splitting is due to a change of averages over zeropoint motion which can be perturbed by isotopic substitution. In an equilibrium case the potential energy surface has two minima separated by a small barrier and the isotopic influence on their relative stability is observed. In isotopic perturbation of resonance there is only one minimum and the change in the single structure, averaged over a vibration, upon isotopic substitution is observed. 

Isotopic perturbation studied by Saunders and Siehl (1980) also indicates that the bicyclobutonium ion [34] is the main species present (cf. Section 4) and the rapid degenerate equilibrium has a barrier less than 3 kcal mol . The C-nmr spectrum of ion [106], prepared from 4,4-dideuteriocyclopropyl-carbinol [107] showed that the two nondeuterated methylene carbons were... 

To clarify the controversial nature of the /3-diketonates as 0,0-chelating symmetrical or not-symmetrical donor ligands in solution, the NMR method of isotopic perturbation of equilibrium has been used.62 A study successfully applied to the simplest dicarbonyl compounds, malonaldehyde and 2-phenylmalonaldehyde, showed the intrinsic asymmetric nature of several metal complexes containing these donor ligands even though, on the basis of NMR evidence, they appear to be symmetric chelates.63... 

Uvarov et al. demonstrated the suitability of the Saunders isotopic perturbation method, applied to vicinal C-D couplings, in order to measure the conformational equilibrium of deuterated cycloalkanes. To this end, the secondary isotope effect on "7(C,D) was determined as shown in Eq. (89), where I represents (Di)cyclohexane, and II represents (l,I-D2)cyclohexane. 

Saunders developed a very useful technique for studying equilibrium isotope effects on the proton nmr spectra of carbonium ions, which is known as isotopic perturbation of degeneracy. It is effective in problems where distinguishing symmetrical from fluxional unsymmetrical compounds is required. This effect is amplified in spectra " and has been used to distinguish fluxional 17 -cyclopentadienyl metal complexes from 17 -Cp complexes. 

The proton resonance for the CH2D group shows a pronounced temperature dependence. Lowering the temperature 95° changes the shift by 0.25 ppm to 5 - 3.72, whereas the CH3 resonance shifts only 0.02 ppm. This temperature dependence is an expected property of the perturbation of an equilibrium by an isotope effect and should always be verihed experimentally before an isotopic perturbation of degeneracy rationalization is invoked. 

By the study of 12 isotopomers of protoadamantane, the stereochemical dependence of isotope effects was also observed. A Karplus-type relationship similar to that for spin-spin coupling constants was proposed Recently, the first quantitative stereochemical dependence between isotope effects and dihedral angle was reported for a series of deuteriated norbornanes, as shown in Figure Observations of the influence of substitution with deuterium on conformational equilibria led to a new method in physical organic chemistry called isotopic perturbation of equilibrium. Details can be found in a recent review The effect was first observed for the chair-tO"Chair interconversion of deuteriated 1,3-dimethylcyclohexane 43 and later in 4-ethyl-l-methylcyclohexane " as well as in 1,1,4,4-tetramethylcyclohexane. In contrast, the isotope effect on conformational equilibrium in related systems turned out to be too small to be observable... 

The chemical shift method for the determination of equilibrium isotope effects is based on the chemical shift difference (the equilibrium isotope shift) between nmr signals for nuclei which are time-averaged to equivalence in the absence of the isotopic perturbation (Saunders, 1979). 

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