Isotopic perturbation of equilibrium

Intro duction of a deuterium at the chelate proton position will clearly not give rise to a shift in the equilibrium, whereas introduction at the aldehyde carbon will. 

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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. 

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... 

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 study of equilibrium isotope effects has found widespread application in analyzing near degenerate equilibria, and in this context is referred to as the isotopic perturbation of equilibrium. This technique, as developed by Saunders, has proven to be a powerful tool for studying carbocations. It provides a very clever way to distinguish a rapid equilibrium from a single, symmetrical structure. The method is best described by considering some specific examples, shown in Figure 8.9. 

Isotopic perturbation of equilibrium. A. The 1,1,3,3-tetramethylcyclo-hexane system. See text for discussion. B. C NMR spectra used to study equilibria given in part A. C. An isotopic perturbation of equilibrium experiment for a prototype carbenium ion. D. Isotopic perturbation of resonance for a substituted allyl cation. The equilibrium arrows are hypothetical for sake of discussion in the text. It is really resonance, not an equilibrium. 

Eq. 8.7 allows us to relate the chemical shift separations we have discussed to the equilibrium constant for the process, K. For this case, inserting A = 9.03 ppm and S = 0.184 ppm gives K = 1.042 0.001. This corresponds to an energy difference of 0.024 kcal/mol The isotopic perturbation of equilibrium method has allowed us to measure a very small deviation of an equilibrium constant from a value of 1. 

We can see, then, that the isotopic perturbation of equilibrium method offers a way to distinguish a situation in which we have a rapidly equilibrating pair of cations from one in which we have a single static structure. As discussed in Chapters 1,2,11, and 14, this is a recurring issue in carbocation chemistry, and so the method has proven to be very useful. 

The NMR data support the bridged structure. Under stable ion conditions, the value of Av (Eq. 14.64) is 175 ppm. This is far below the usual range seen for conventional carbenium ions, although the deviation is not as dramatic as that seen for the Coates ion. The isotopic perturbation of equilibrium technique (Chapter 8) has also been applied. At very low temperatures, the Cl and C2 of norbornyl cation show a single, merged line in the C NMR spectrum. When a 2-deuterio precursor is used in an effort to break this degeneracy, a single. 

The d3uiamics of a (l,3-disilylallyl)lithium and TMEDA complex has also been studied by NMR. Isotopic perturbation of equilibrium revealed that the lithium salt is symmetrical and favors an exo-exo configuration. The corresponding allyl lithium salt was revealed to be unsymmetrical in similar studies, although allyl sodium and allyl potassium salts were found to be s)unmet-rical. 

One of the very elegant ways of disclosing tautomerism in symmetrical systems is the isotopic perturbation of equilibrium. This technique is based on the fact that CH bonds may have very different vibrational stretching frequencies. For a system like P-diketones this is illustrated in following text, exemplified by 2-phenylmalonaldehyde [28,29). For a symmetrical system, the deuterium has to be introduced in such a manner that the degeneracy is lifted as shown in Figure 3.19. 

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