Category:NMR

Many nuclei have an inherent, non-zero spin I and therefore a magnetic dipole moment μ, conventionally along the z-axis:

${\displaystyle \mu_z = \gamma \textbf{I}_z }$

In the absence of a magnetic field, these are degenerate states. When an external magnetic field B_ext is applied, the energy difference between two states is given by the following equation:

${\displaystyle \Delta E = \gamma \hbar \textbf{B}_{ext} }$

Conventionally, the z-axis is chosen for the direction of B_ext. Along this axis, μ aligned with B_ext will be slightly more energetically favorable and so populated than μ opposed to B_ext. This is only signficant in the presence of strong magnetic fields.

In the presence of B_ext, μ precesses at its Larmor frequency ω_L, determined by the strength of the magnetic field and the nucleus' gyromagnetic ratio γ:

${\displaystyle \omega_L = \gamma \textbf{B} }$

A weak, oscillating magnetic field applied perpendicular (i.e. in the transverse frame) to B_ext (reference frame), e.g. using a radio-frequnecy (RF) pulse at frequnecy ω_rf, can causes μ to oscillate with the RF. If ω_rf is similar to ω_L, then resonance occurs, hence nuclear magnetic resonance (NMR). μ flips from the reference to the transverse frame and the relaxation of μ back to the reference frame creates a signal that is measured in NMR.

How to

• Chemical shift tensors: LCHIMAG.
• Hyperfine tensors: LHYPERFINE.
• Electric field gradient tensors: Electric Field Gradient. The main tags are:
  • LEFG to switch on the field gradient tensor calculation,
  • QUAD_EFG to specify the input nuclear quadrupole moments.