Chemical shift

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Chemical shift is a variation of larmor frequency between the nuclei due to differences in the electronic structure local to the nuclei.

ω = − γ(B0Bi)

where B0 is the external magnetic field and Bi - induced magnetic field.

Bi is proportional to B0 with the constant of proportionality called nuclear shielding tensor (it's a tensor in the general case, because Bi may adopt direction that differs from the direction of B0.

Physically, changes in the larmor frequency arise due to the modification of magnetic field with a smaller field, induced in the electron clouds, when molecules experience an external magnetic field.

Chemical shift is measured in parts per million, i.e. (ν - νref)/νref x 106, where νref is larmor frequency of nucleus in the reference compound and ν - larmor frequency of a given nucleus. Chemical shift of the reference compound is assumed to be zero.

As explained above, chemical shift is a relative measure of the larmor frequency. A relative scale is used in the practice of NMR for two reasons. Firstly, use of absolute scale in Hertz is inconvenient, because differences in those frequencies due to variations of the chemical structure are often on the order of kilohertz of less, while the absolute value may be in the hundreds of megahertz (depending on the gyromagnetic ratio of a given nucleus).

The second argument in the favor of relative scale is that the value obtained from a ratio will be independent of the strength of the magnetic field, Bo, while difference in the larmor frequencies will be proportional to Bo.

Chemical shift values are almost always perfectly transfereable between the data obtained with say 9.4 Tesla (400MHz 1H frequency) and 18.8 Tesla (800 MHz 1H frequency), unless molecules become strongly oriented in the magnetic field and display strong anisotropy of the chemical shielding tensor (or chemical shift anisotropy).


Factors influence the chemical shift

Local factors

Molecular conformation.

Electric field

Aromatic rings or other π system

Hydrogen bonding

Changes in neighbouring isotopes

Global factors


Temperature Temperature dependent chemical shift


Pseudocontact chemical shift: it's a long range interaction that is caused by a paramagnetic center

Chemical shift in various systems

Chemical shift in proteins

Chemical Shift and Structure

Value of the chemical shift is affected by the arrangement of covalent bonds and molecular conformation.

The latter property can be exploited to determine the molecular conformation. For proteins algorithms implemented in software TALOS and NIH-XPLOR 13C chemical shifts are used to determine backbone dihedral angle restraints.

It could also be used to determine the cystein disulfide bonds.

Chemical Shift Calculation

Ring current calculation


Their are several software that allow to predict chemical shift in protein, for instance :





Chemical shift could also be computed with quantum mechanics calculation. Or by using tabulated values, depending on the local groups ( that's more used for the determination in small molecules, atoms connectivity )


  1. wikipedia article about chemical shift [wikipedia]
  2. discussion of chemical shift in Georgetown Univ. NMR course


  3. Sharma, D and Rajarathnam, K. 13C NMR chemical shifts can predict disulfide bond formation. Journal of Biomolecular NMR 18(2):165--171, 2000. BibTeX [sharma2000ncs]

  4. Baxter, NJ and Williamson, MP. Temperature dependence of 1 H chemical shifts in proteins. Journal of Biomolecular NMR 9(4):359--369, 1997. BibTeX [Baxter1997jbmr]

  5. Cavalli, A and Salvatella, X and Dobson, CM and Vendruscolo, M. Protein structure determination from NMR chemical shifts. Proceedings of the National Academy of Sciences 104(23):9615, 2007. BibTeX [cavalli2007psd]

  6. Fukui, L and Chen, Y. NvMap: automated analysis of NMR chemical shift perturbation data. Bioinformatics 23(3):378, 2007. BibTeX [fukui2007naa]

  7. Berjanskii, MV and Wishart, DS. A simple method to predict protein flexibility using secondary chemical shifts. J Am Chem Soc 127(43):14970--14971, 2005. BibTeX [berjanskii2005smp]

  8. Xu, XP and Case, DA. Automated prediction of 15N, 13C$\alpha$, 13C$\beta$ and 13C' chemical shifts in proteins using a density functional database. Journal of Biomolecular NMR 21(4):321--333, 2001. BibTeX [xu2001apa]

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