Basics of NMR of Molecules in Uniaxial Anisotropic Environments

Abstract

The NMR spectra of liquids are usually interpreted in terms of two types of scalar quantities: the chemical shifts (σ) and the indirect spin-spin couplings (J). Although σ and J in “normal” NMR appear as scalars, in truth they represent tensorial properties of the molecule. The Brownian movement of the molecule and the resulting isotropic tumbling leads to a situation where only the isotropic part of the tensorial properties is expressed. The Hamiltonian of NMR in isotropic liquids is given by:

$$H = - \frac{{{B_z}}}{{2\pi }}\sum\limits_i {{\gamma _i}\left( {1 - \sigma _i^{iso}} \right){I_{i,Z}} + \sum\limits_{i < j} {J_{ij}^{iso}\overrightarrow {{I_i} \cdot } \overrightarrow {{I_j}} .} }$$

((1.1))