Equivalence accidental

As we have already seen, accidental equivalence could be responsible for the theoretically nonequivalent protons of an AB system presenting as a singlet and for the more complex ABX system presenting as a simple doublet and triplet. But occasionally, even more interesting manifestation of accidental equivalence can be observed. Consider the molecule below (Structure 6.10) and its spectrum (Spectrum 6.6) which shows only the regions of interest to us - expanded and with the intervening region removed. 

The complex multiplet centred at 5.04 ppm results from the overlap of the methine and -OH protons (i.e., they are accidentally equivalent ) whilst the equally complex methyl signal is centred at 1.48 ppm. Because of this overlap, their lines are indistinguishable and so the -OH is said to be virtually coupled to the methyl group. Virtual coupling is another potential consequence of non-first order behaviour. 

And for a final example, consider the molecule in Structure 6.11 and Spectrum 6.7. Please note Spectrum 6.7 has been simulated on account of no compound being available at the time of writing. The 

Now that we have an idea of what to expect, we can proceed to the next chapter and examine some actual NMR spectra. 

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The N-benzyl protons are accidentally equivalent, presenting as a singlet at 3.59 ppm and overlap with the two protons alpha to the chlorine atom which present as the heavily roofed AB part of an ABX system (i.e., eight lines) centred at 3.55 ppm. 

Each ifi nucleus is shielded or screened by the electrons that surround it. Consequently each nucleus feels the influence of the main magnetic field to a different extent, depending on the efficiency with which it is screened. Each nucleus with a different chemical environment has a slightly different shielding and hence a different chemical shift in the H NMR spectrum. Conversely, the number of different signals in the iff NMR spectrum reflects the number of chemically distinct environments for iff in the molecule. Unless two iff environments are precisely identical (by symmetry) their chemical shifts must be different. When two nuclei have identical molecular environments and hence the same chemical shift, they are termed chemically equivalent or isochronous nuclei. Non-equivalent nuclei that fortuitously have chemical shifts that are so close that their signals are indistinguishable are termed accidentally equivalent nuclei. 

Note here that in some instances, even when the molecule has lower symmetry, the value of E can be so small as to be indistinguishable from zero, especially with a randomly oriented sample. In that case again, only four of the expected six lines may be observed. With this caution in mind, we can see that a non-zero E value may be interpreted confidently as indicative of a carrier with low symmetry, but the converse, an approximately zero value, could be due to true symmetry, or to an accidental equivalence of two axes. We return to this point in the discussion... 

Nuclear magnetic resonance chemical shift differences can serve as an indicator of molecular symmetry. If two groups have the same chemical shift, they are isochronous. Isochrony is a property of homotopic groups and of enantiotopic groups under achiral conditions. Diastereotopic or constitutionally heterotopic groups will have different chemical shifts (be anisochronous), except by accidental equivalence and/or lack of sufficient resolution. 

Proton NMR spectrum of o-xylene. There are three types of protons in o-xylene, but only two absorptions are seen in the spectrum. The aromatic protons Hb and Hc are accidentally equivalent, producing a broadened peak at 8 7.1. 

Nuclei that are not chemically equivalent, yet absorb at nearly the same chemical shift and are not resolved. Nuclei that absorb at the same chemical shift cannot split each other, whether they are chemically equivalent or accidentally equivalent, (p. 577)... 

Bonded to a group that withdraws part of the electron density from around the nucleus. The absorptions of deshielded nuclei are moved downfield, resulting in larger chemical shifts, (p. 568) Nuclei that occupy diastereomeric positions. The replacement test for diastereotopic atoms gives diastereomers. Diastereotopic nuclei can be distinguished by NMR, and they can split each other unless they are accidentally equivalent, (p. 592)... 

Nuclei that are not symmetry equivalent but nonetheless precess at the same frequency are described as accidentally equivalent. 

Although the signal positions will spread out (when measured in hertz), the chemical shifts (8) should remain unaffected. Relative intensities might vary a little because of different pulse parameters. But, by and large, the spectra should not change significantly, since there are no accidental equivalencies to resolve. 

For example, the 60-MHz H spectrum of cyclopropane derivative 10-10 dissolved in carbon tetrachloride exhibits only one sharp signal at 8 1.45 ppm,9 indicating that the two sets of hydrogens (six methyl and two methylene) are accidentally equivalent (Section 4.4) ... 

Thus, when confronted with a case of accidental equivalence, it is worthwhile to see if changing the solvent resolves the signals. If not, try a lanthanide shift reagent. 

The remaining three nonprotonated carbons (recall that signal 10 represents two accidentally equivalent carbons) must be the connecting links between these three pieces. 

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