# NMR Interactions

When an atomic nucleus is placed in a magnetic field, the ground state will split into different energy levels proportional to the strength of the magnetic field. This effect is known as Zeeman splitting. While the Zeeman interaction is useful for identifying different types of nuclei placed in magnetic fields, structural and dynamic information may be obtained by considering other magnetic and electronic interactions coupling with the nucleus. These interactions are perturbations to the Zeeman interaction. The full NMR Hamiltonian may therefore be expressed as

$\hat{H}=\hat{H}_{Zeeman}+\hat{H}_{J}+\hat{H}_{CS}+\hat{H}_{DD}+\hat{H}_Q$

where HZeeman is the Zeeman interaction, HJ is the J coupling, HCS is the chemical shift coupling, HDD is the dipolar coupling, and HQ is the quadrupolar coupling. The relative magnitude of these interactions is shown in the table below. The Zeeman interaction is the largest, followed by the quadrupolar interactions which are on the order of MHz. The chemical shift and the dipolar coupling are on the order of kHz while the scalar coupling is the smallest which is only tens of Hz. Clearly, some of these interactions are more pronounced than others.

Interaction Magnitude (Hz)
Zeeman 108