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
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.
Table 1. Magnitude of different NMR interactions
In the liquid state, the dipolar and anisotropic contribution to the chemical shift are averaged due to the molecular reorientation occurring in liquids. The averaging of these interactions gives the characteristically narrow isotropic peaks. Additionally, liquid state NMR primarily looks at spin 1/2 nuclei (13C, 1H) which eliminates any quadrupole interactions. Only the J coupling and isotropic part of the chemical shift remains. In the solid state, molecular reorientation does not occur and the solids may have a variety of bond lengths and angles of a given chemical site. These factors broaden in the NMR spectrum with the broadest peaks over 1MHz wide!
Contributors and Attributions
- Derrick Kaseman (UC Davis)