Magnetic field‐dependent nuclear spin–spin coupling

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Abstract
As the magnetic fields used in NMR spectrometers become greater, it is expected that a field dependence of nuclear spin–spin coupling will be observed. A part of this, which would be independent of temperature, is due to the contributions of higher terms in the Hamiltonian of the molecule in the external magnetic field and the two nuclear spin operators. Perturbation theory at second, third and fourth order is used to extract the general features of these higher order terms. Contributions are due (a) to diamagnetic and paramagnetic terms of each of the four familiar parts of the spin coupling— Fermi contact, spin–dipolar, and orbital paramagnetic and orbital diamagnetic, and (b) to cross‐terms determined by operators for the diamagnetic and paramagnetic shielding at the two coupled nuclei. Explicit expressions are presented for the more important contributions. It is estimated for strongly magnetic nuclei in large molecules that the coupling varies as 0.5 × 10−5 B2 Hz, so that a field of about 14 T should produce a change in the coupling of 0.001 Hz. These are, respectively, the field used in high‐field NMR spectrometers and the upper limit of precision in the measurement of spin–spin coupling constants at the present time.