Category:Chemical shifts

Nuclei with spin I > 0 have magnetic dipole moments. When placed in an external magnetic field B_ext, they precess at a frequency ω_L proportional to B_ext:

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

where γ is the constant of proportionality, the gyromagnetic ratio of the nucleus.

The nucleus is surrounded by electrons. Since electrons are charged, the external magnetic field induces a current, causing the electrons to move. This current in turn induces an opposing magnetic field B_in, following the Biot-Savart law. B_in acts in opposition to B_ext, thereby reducing the field that at the nucleus. The electrons, i.e. the chemical environment, surrounding the nucleus have effectively shielded the nucleus from the full effect of B_ext. There is a linear relationship between B_ext and B_in given by the chemical shielding tensor σ_ij:

${\displaystyle \textbf{B}_{in}(\textbf{R}) = -\sigma(\textbf{R}) \textbf{B}_{ext}}$

where i and j are Cartesian axes.

The chemical shielding tensor can be calculated at each nucleus to determine information about the surrounding chemical environment. The absolute chemical shielding tensor is calculated but this cannot be measured by experiment. Instead, a reference chemical shielding must be taken as a standard, the chemical shift δ_ij:

${\displaystyle \delta_{ij}(\mathbf{R}) = \sigma_{ij}^{\mathrm{ref}} - \sigma_{ij}(\mathbf{R}) }$

LCHIMAG calculates the absolute chemical shieldings ^[1][2], as well as the magnetic susceptibility Χ. There are several supporting keywords:

• DQ is the step size for the finite difference k-space derivative.
• LBONE adds the small B-component to the chemical shift tensor ^[3].
• LVGVAPPL uses vGv orbital magnetic susceptibility when calculating the chemical shift anisotropy (CSA) tensor.
• LLRAUG calculates the two-center contributions to the chemical shielding tensor .
• ICHIBARE determines the order of the finite difference stencil used to calculate the magnetic susceptibility. Note that magnetic susceptibility is a bulk property, while chemical shift is for each nucleus ^[2].
• LVGVCALC uses the vGv expression when calculating the orbital magnetic susceptibility ^[4][5].

LHYPERFINE calculates the hyperfine coupling constant. The gyromagnetic ratios for each isotope are defined in NGYROMAG.

These are for individual atoms and exclude the contribution due to the augmentation currents in other PAW spheres. If two-center terms are important, e.g. for H, then they should be included using LLRAUG .

How to

• Chemical shifts:
  • Chemical shift tensors: LCHIMAG.
  • Hyperfine tensors: LHYPERFINE.