Category:Chemical shifts: Difference between revisions

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where ''γ'' is the constant of proportionality, the gyromagnetic ratio of the nucleus.  
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'''''<sub>in</sub>'', following the Biot-Savart law. '''B'''''<sub>in</sub>'' acts in opposition to '''B'''''<sub>ext</sub>'', 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'''''<sub>ext</sub>''. There is a linear relationship between '''B'''''<sub>ext</sub>'' and '''B'''''<sub>in</sub>'' given by the chemical shielding tensor ''σ<sub>ij</sub>'':
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'''''<sub>in</sub>'', following the Biot-Savart law. '''B'''''<sub>in</sub>'' acts in opposition to '''B'''''<sub>ext</sub>'', 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'''''<sub>ext</sub>''. There is a linear relationship between '''B'''''<sub>ext</sub>'' and '''B'''''<sub>in</sub>'' given by the chemical shielding tensor ''σ<sub>ij</sub>'' at position '''R''':


<math>\textbf{B}_{in}(\textbf{R}) = -\sigma(\textbf{R}) \textbf{B}_{ext}</math>
<math>\textbf{B}_{in}(\textbf{R}) = -\sigma(\textbf{R}) \textbf{B}_{ext}</math>
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</math>
</math>


The absolute chemical shieldings are calculated using {{TAG|LCHIMAG}} {{Cite|pickard:prb:2001}}{{Cite|yates:prb:2007}}. This tag also calculates the magnetic susceptibility ''&chi;''. There are several supporting keywords:
The absolute chemical shieldings are calculated using {{TAG|LCHIMAG}} {{Cite|pickard:prb:2001}}{{Cite|yates:prb:2007}}. This tag also calculates the magnetic susceptibility ''χ''. There are several supporting keywords:
*{{TAG|DQ}} is the step size for the finite difference k-space derivative.
*{{TAG|DQ}} is the step size for the finite difference k-space derivative.
*{{TAG|LBONE}} adds the small B-component to the chemical shift tensor {{Cite|dewijs:laskowski:jcp:2017}}.
*{{TAG|LBONE}} adds the small B-component to the chemical shift tensor {{Cite|dewijs:laskowski:jcp:2017}}.

Revision as of 15:45, 27 February 2025

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

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 Bin, following the Biot-Savart law. Bin acts in opposition to Bext, 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 Bext. There is a linear relationship between Bext and Bin given by the chemical shielding tensor σij at position R:

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 δij:

The absolute chemical shieldings are calculated using LCHIMAG [1][2]. This tag also calculates 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].

Two other tags are used for calculating the hyperfine coupling constant:

  • LHYPERFINE calculates the hyperfine coupling constant [6][7].
  • NGYROMAG defines the gyromagnetic ratios for each isotope.

How to

  1. ↑ C. J. Pickard and F. Mauri, All-electron magnetic response with pseudopotentials: NMR chemical shifts, Phys. Rev. B 63, 245101 (2001).
  2. ↑ a b J. R. Yates, C. J. Pickard, and F. Mauri, Calculation of NMR chemical shifts for extended systems using ultrasoft pseudopotentials, Phys. Rev. B 76, 024401 (2007).
  3. ↑ G. A. de Wijs, R. Laskowski, P. Blaha, R. W. A. Havenith, G. Kresse, and M. Marsman, NMR shieldings from density functional perturbation theory: GIPAW versus all-electron calculations, J. Chem. Phys. 146, 064115 (2017).
  4. ↑ M. d'Avezac, N. Marzari, and F. Mauri, Spin and orbital magnetic response in metals: Susceptibility and NMR shifts, Phys. Rev. B 76, 165122 (2007).
  5. ↑ G.A. de Wijs, G. Kresse, R. W. A. Havenith, and M. Marsman, Spin and orbital magnetic response in metals: Susceptibility and NMR shifts, J. Chem. Phys. 155, 234101 (2021).
  6. ↑ O. V. Yazyev, I. Tavernelli, L. Helm, and U. R. Roethlisberger, Core spin-polarization correction in pseudopotential-based electronic structure calculations, Phys. Rev. B 71, 115110 (2006).
  7. ↑ K. Szasz, T. Hornos, M. Marsman, and A. Gali, Hyperfine coupling of point defects in semiconductors by hybrid density functional calculations: The role of core spin polarization, Phys. Rev. B, 88, 075202 (2013).

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