Pseudocontact chemical shift

From NMR Wiki

The pseudocontact chemical shift (PCS) is a contribution to chemical shift of the nucleus caused by the presence of centers with unpaired electrons, where the probability density of the unpaired electron at the site of nucleus is negligible. This perturbation is measurable when the magnitude of the magnetic moment of the unpaired electron depends on the molecular orientation with respect to the magnetic field vector.

1 Source of the pseudocontact shift
2 Applications
3 Practice of PCS determination
4 References

Source of the pseudocontact shift

The shift of nuclear larmor frequency is caused by the dipolar coupling between the magnetic moments of the nucleus and of the unpaired electron. This situation is somewhat similar to the case of j-coupling whre we would expect the NMR peak to split into a doublet due to the coupling with the magnetic moment of the unpaired electron.

The significant difference however lies in the fact that the rate of electron spin relaxation is much faster than the rate of nuclear spin relaxation. So the expected doublet won't be observed. Instead, there will be only one peak at the position corresponding to the average of the available populations of spin states of the free electron, the corresponding chemical shifts of the nucleus [1], in addition averaged over all possible molecular orientations (due to the fast molecular tumbling).

If the magnitude of the magnetic moment of the free electron center were independent on the orientation of the molecule, the value of dipolar coupling with the nucleus would average to zero. Therefore, for this kind of coupling/apparent peak shift to be observable, the magnitude of the electron magnetic moment must depend on the orientation, i.e. - must be anisotropic.

Name pseudocontact shift has been devised to discriminate this mechanism from another source of the chemical shift perturbation due to unpaired electrons - the Fermi contact shift. In the latter it is a non-zero delocalized electron density of the unpaired electron at the site of the nucleus that causes the shift perturbation. In the pseudocontact shift mechanism the free radical center is treated as a geometrical point.

Applications

Magnitude of the pseudocontact shift is proportional to $r - 3$ [1], where r is the distance between the free radical center and the nucleus. Inverse third power dependence allows observation of pseudocontact shifts for larger distance ranges, when compared to NOE.

In addition to the dependence on distance, pcs also depends on the orientation of the nucleus-free radical center vector in the frame of reference of the radical's magnetic moment anisotropy tensor.

All this information can be successfully exploited for the determination of three dimensional structure of the molecules [2, 3], as well as help locate the unpaired electron center.

Practice of PCS determination

In order to determine magnitude of PCS, two samples are required, one with the anisotropic free radical center and one without.

Paramagnetic centers enhance nuclear relaxation making NMR signals of atoms in the proximity of the paramagnetic center difficult or impossible to record.