In the context of nuclear magnetic resonance (NMR), the term magnetic inequivalence refers to the distinction between magnetically active nuclear spins by their NMR signals, owing to a difference in either chemical shift (magnetic inequivalence by the chemical shift criterion) or spin–spin coupling (J-coupling) (magnetic inequivalence by the coupling criterion). Since chemically inequivalent spins (i.e. nuclei not related by symmetry) are expected to also be magnetically distinct (barring accidental overlap of signals), and since an observed difference in chemical shift makes their inequivalence clear, the term magnetic inequivalence most commonly refers solely to the latter type, i.e. to situations of chemically equivalent spins differing in their coupling relationships. This situation can arise in a number of ways and can give rise to complexities in the corresponding NMR signals (beyond what a first-order analysis would handle) that range from the unnoticeable to the dramatic.
Occurrence Two (or more) chemically equivalent (symmetry-related) spins will have the same chemical shift, but those that have a different coupling relationship to the same coupling partner are magnetically inequivalent by the coupling criterion. This occurs in molecules bearing two (or more) chemically distinct groups of symmetry-related nuclei, with just one element of symmetry relating them. Most commonly, two chemically inequivalent pairs of hydrogen nuclei (protons) are involved, although other magnetically active nuclei will also show this phenomenon, and the spin system is often labelled an AA′BB′ system. Additional coupling partners may also be present, but it is the two A/A′ and B/B′ signals (at different chemical shifts) that are said to show magnetic inequivalence between the symmetry-related A and A′ (or B and B′) pairs at the same chemical shift. If the chemical shift difference (νA−νB) is large compared to the largest coupling constant, the spin system may be designated AA′XX′.
Paired H-C-C-H fragments Magnetic inequivalence may occur with two symmetry-related HA-C-C-HB fragments (where the different subscripts indicate chemical inequivalence) that may or may not be contiguous. In order to distinguish the resulting coupling relationships, the symmetry-related pair would be labelled HA′-C-C-HB′.
ortho-Disubstituted benzenes
H-3 and H-6 in any 1,2-homodisubstituted benzene are related by a mirror plane of symmetry bisecting the 1,2 and 4,5 C-C bonds. They are therefore chemically equivalent (and magnetically equivalent by the chemical shift criterion) but, because they have different spatial and connectivity relations to H-4 (with 3-bond vs. 4-bond couplings of different strengths), they are magnetically inequivalent by the coupling criterion. The same is true with respect to their coupling relationships with H-5. Similarly, H-4 and H-5 are chemically equivalent but magnetically inequivalent owing to their different coupling relationships with H-3 (or H-6). A classic example showing highly complex splitting is that of 1,2-dichlorobenzene. The two signals are nearly mirror-symmetrical. In 1,2-diaminobenzene (ortho-phenylenediamine), the two signals have nearly the same chemical shift, so that the resultant signals form a complex multiplet.
para-Disubstituted benzenes
H-2 and H-6 in any 1,4-heterodisubstituted benzene are related by a mirror plane of symmetry passing through C-1 and C-4. They are therefore chemically equivalent (and magnetically equivalent by the chemical shift criterion) but, because they have different spatial and connectivity relations to H-3 (with 3-bond vs. 5-bond coupling constants of different strengths), they are magnetically inequivalent by the coupling criterion. The same is true with respect to their coupling relationships with H-5. Similarly, H-3 and H-5 are chemically equivalent but magnetically inequivalent owing to their different coupling relationships with H-2 (or H-6). An example is provided by 4-nitroaniline. Although each signal retains the gross doublet shape predicted by first-order analysis, a close-up view of each reveals additional peaks.
Other aromatics Any 4-substituted pyridine, pyridine itself, 1-substituted pyrazinium ion, diazine, 1-substituted or unsubstituted pyrrole and related aromatic heterocyclics (phospholes, furan, thiophene, etc.) as well as unsubstituted or 1-substituted cyclopentadienes and 1-substituted cyclopentadienides all have the same symmetry framework as para-disubstituted or ortho-homodisubstituted benzenes, and will present chemically equivalent but magnetically inequivalent pairs of protons. In heterocycles and in five-membered rings in general, however, 3J values can be significantly smaller than in benzenes and the manifestation of magnetic inequivalence may be subtle. The rarer seven-membered and higher ring systems may also show the same symmetry property, as can linked and fused aromatic ring systems such as biphenyls, naphthalenes and isoindoles. Similarly, 1-H benzimidazoles have the appropriate symmetry if N1-deprotonated or N3-protonated, or as a result of rapid tautomerization of the neutral form (for instance, in DMSO-d6) where the signals greatly resemble those of 1,2-dichlorobenzene.
Non-aromatic systems The occurrence of symmetry-related pairs of HA-C-C-HB fragments is not limited to aromatic systems. For instance, magnetic inequivalence is found in 1,4-homodisubstituted butadienes. It might be expected in a molecule such as a symmetrical 2,3,4,5-tetrasubstituted pyrrolidine, but less rigid and less flat sp3 frameworks tend to show very weak long-range couplings (through 4 or more bonds) so as to not manifest much sign of magnetic inequivalence. Reich gives several additional examples of magnetic inequivalence in non-aromatic H-C-C-H pairs.
H2C-CH2 fragments
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