Chemical Shift

From NMR Wiki

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

ω = − γ(B₀ − B_i)

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

B_i is proportional to B₀ with the constant of proportionality called nuclear shielding tensor (it's a tensor in the general case, because B_i 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 - ν_ref)/ν_ref x 10⁶, where ν_ref 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, B_o, while difference in the larmor frequencies will be proportional to B_o.

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).

Contents 1 Factors influence the chemical shift 1.1 Local factors 1.2 Global factors 2 Chemical shift in various systems 3 Chemical Shift and Structure 4 Chemical Shift Calculation 5 Ring current calculation 5.1 Software 6 References

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

Solvent

Temperature Temperature dependent chemical shift

pH

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

http://bouman.chem.georgetown.edu/nmr/interaction/chemshf.htm

Ring current calculation

Software

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

- SHIFTX2

- SHIFTX

- SHIFTY

- SHIFTS

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 )

References

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

   [georgetown]

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]