‘Ring-current’ and ‘pseudo-contact’ magnetic shielding by non-spherical molecules

Abstract

A multipolar susceptibility formalism for interpreting and mapping the isotropic magnetic shielding outside axially symmetric molecules is con¬structed. The method involves spheroidal harmonic expansions of the local magnetic fields outside molecules magnetized by the uniform magneto¬ static field of the nuclear magnetic resonance spectroscopy experiment. For ‘disk-shaped’ molecules with infinite axial symmetry the shielding at field points with oblate spheroidal coordinates (U, V, Ø) reduces to where the coefficient a L0 measure anisotropy in the molecular susceptibilities and the P L (V) and Q L (iU) are Legendre polynomials of the first and second kind. A similar result holds for prolate molecules like acetylene with cylindrical symmetry but additional terms appear for molecules like benzene with finite axial symmetry. The spheroidal expansions lead to more accurate descriptions of magnetic shielding outside non-spherical molecules than methods already available and are designed for interpreting experimental shieldings by both paramagnetic and diamagnetic molecules.