Chemical and Magnetic Equivalence

Many students are unclear about the difference between chemical equivalence and magnetic equivalence. The clearest explanation I have seen on this is in Robin Harris' book, "Nuclear Magnetic Resonance Spectroscopy" (1983). Chemically equivalent nuclei behave the same as one another chemically but do not have the same NMR properties as one another, whereas magnetically equivalent nuclei are chemically equivalent and they have the same NMR properties. One can determine whether two nuclei are chemically or magnetically equivalent by considering the following:

If the nuclei under consideration are not isochronous (i.e. they do not have the same chemical shift) then they are neither chemically nor magnetically equivalent. All chemically or magnetically equivalent nuclei are isochronous however, isochronous nuclei need not be chemically or magnetically equivalent as their chemical shifts may be fortuitously identical.

If the two nuclei being considered are isochronous, one should consider how they couple to a third magnetic nucleus in the molecule which is not equivalent to them. If the coupling to the third magnetic nucleus is different for each of the nuclei being considered, then the nuclei are chemically but not magnetically equivalent to one another. If the coupling to the third magnetic nucleus is identical (and this is true for every magnetic nucleus other than those being considered) then the two nuclei are both magnetically and chemically equivalent.

This is illustrated in the figure below. (The examples from Harris' book were used here.) In the molecule on the left, the two protons are both chemically and magnetically equivalent as they both have the same coupling with the fluorine. In the molecule on the right, the two protons are chemically equivalent but not magnetically equivalent as they do not have the same coupling to each of the fluorines. Similarly, the two fluorines are chemically equivalent but not magnetically equivalent as they do not have the same coupling to each of the protons.

Spin-Spin Coupling Between Equivalent Nuclei

When many chemists are asked what is the ²J_H-H coupling for compounds like methane, acetone, methylene chloride, dimethyl ether or DMSO, they will often return a look of confusion. "There is no coupling," they will say, "the proton spectrum is a singlet". Indeed the proton spectrum is a singlet for these compounds but ²J_H-H is not equal to zero. The only reason that the coupling is not observed in the spectrum is because the chemical shifts of each proton are identical. The coupling can easily be measured by observing the spectrum of a partially deuterated isotopomer. The ²J_H-H coupling constant is equal to ²J_H-D multiplied by the ratio of the gyromagnetic ratios of ¹H to ²H. This is illustrated in the figure below for methylene chloride.In fact, ²J_H-H is -7.192 Hz not +7.192 Hz however, this cannot be determined simply by observing the spectrum. Both spectra were measured for dilute solutions with CDCl₃ as solvent. The residual protons of CDCl₃ were used as the chemical shift reference (7.26 ppm). The chemical shift difference between CH₂Cl₂ and CHDCl₂ is due to an isotope effect.