NMR Spectroscopy- Chemical Shift

NMR Spectroscopy- Chemical Shift

Fig: Distinct spectral line for different groups of the compound

The total magnetic field experienced by a nucleus in a sample kept in an applied magnetic field Bo is equal to the sum of the external applied field plus a induced microscopic field produced by the magnetic elements present in the sample. The resonance frequency of a particular nucleus is therefore determined not by the strength of the externally applied magnetic field (Bo), but by the local field (B_loc) experienced by the nucleus.

Let us consider a sample containing ¹H atoms present at different molecular sites of the sample making different electronic bond with different nuclei.  All ¹H nuclei within a chemical compound present at different molecular sites will not resonate at precisely the same frequency; differences in resonance frequency (called chemical shifts) exists depending upon the chemical nature of the molecule in which the particular nuclei reside. For ¹H these shifts are relatively small (on the order of a few hundred Hz at 1.5T) but are detectable. This chemical shift phenomena is observable for all kind of nuclei. Because of this chemical shift we able to see different distinguish peaks for same kind of nuclei present at different molecular site of any sample under observation.

Chemical shifts result from diamagnetism at the atomic/molecular level. This diamagnetism arises as a result of the response of matter to an external magnetic field. There are several reasons for the response of the matter to the external filed. 

Fig: When placed in an external magnetic field (B_o) a reactive response of the electron clouds around a nucleus produces an induced field (B_ind) that typically opposes the applied field. This is called "shielding". The resonant frequency of the nucleus depends on B_loc = B_o − B_ind.

 

For example, we can imagine that the electrons surrounding the nucleus is circulating around the nucleus. These circulating electrons generate a induced diamagnetism in the presence of the external field which opposes the applied external field. The electron cloud thus acts as a shield which reduces the effect of the external field on the nucleus. If the shielding factor is denoted by the symbol σ, where B_ind is the induced field produced in the presence of external field, then B_ind = σB_o. The local effective field experienced by the nucleus is therefore 

B_loc = B_o − B_ind = B_o (1 − σ)

Now the chemical shift (δ) defined as

δ = (f_samp − f_ref ) / f_ref

where, f_samp is the NMR frequency of the nuclear species under investigation and f_ref is the NMR frequency of a reference compound.

The frequency difference (f_samp − f_ref ) is usually of the order of a few hundred to a few thousand Hz, while the reference frequency (f_ref ) is measured in MHz. The chemical shift (δ) is therefore a small number, expressed in units of parts per million (ppm).

References
1. Spin Dynamics by Malcolm H. Levitt
2.Principles of Nuclear Magnetic Resonance in One and Two Dimensions, by Richard R. Ernst, et al.

3.Mehring M., 1983. High Resolution NMR in Solids, Springer.

4.Ramsey N.F., 1950. Magnetic Shielding of Nuclei in Molecules. Physical

Review 78, 699-703.