Nuclear Shielding and Biomolecular Structure

Abstract

The origin of the chemical shift is easily understood in qualitative terms (Jardetzky and Roberts 1981; Harris 1983). Since electrons are moving charges, they are subject to the laws of electromagnetic induction. The net effect of the magnetic field is to superimpose a motion of electrons around the field axis on the orbital motion of the electron. In addition, the applied field will polarize the electron cloud. The motion of the electron generates a local magnetic field at the nucleus opposing the external induction field. The magnitude of the induced field will be proportional to the imposed field B₀ so that the effective field B_eff at the nucleus will be:

$$ {B_{{eff}}} = {B_{o}}(1 - \sigma ) $$

(1)

The nucleus is said to be shielded, the extend of shielding being given by the shielding constant a. This scalar shielding constant represents the isotropic part of the chemical shift tensor a:

$$ \sigma = \frac{1}{3}{\mkern 1mu} Trace{\mkern 1mu} (\sigma ) $$

(2)

The anisotropic components of a are averaged by fast reorientational motions. The non zero scalar shielding constant is often defined as the sum of contributions from a diamagnetic, a^d, and a paramagnetic, a^p, term:

$$ \sigma = {\sigma ^{d}} + {\sigma ^{p}} $$

(3)

The diamagnetic part relates to the concept of the free electron rotation about the nucleus and involves only the ground state electronic wave function of the molecule. In molecules the presence of the other nuclei hinders rotation of the electron cloud about the nucleus whose shielding is being considered.