Paramagnetic electronic properties and nodal topology

Abstract

As Riess has showed, there exist restrictions on the nodal topology of electronic wavefunctions possessing permanent orbital paramagnetic moments. These supplement the well‐known requirement that such wavefunctions must be complex valued. They are identical to the conditions derived for the existence of quantized vortices. These nodal restrictions thus have nontrivial implications for the magnetic properties of atoms and molecules. Magnetic ’’anomalies’’ characteristic of the existence of orbital magnetic moments are expected to evince themselves in electronic systems capable of supporting vortices (e.g., electron beams, atoms and molecules in magnetic fields, and degenerate electronic states) under appropriate conditions. Indeed, the origins of paramagnetic ring currents and paramagnetic shielding are readily understood from this viewpoint. We briefly consider a few atomic and molecular systems to illustrate the value of this analysis. We demonstrate that, if an electronic system is of known nodal topology, very simple symmetry arguments permit the lowest order magnetic multipole moments to be deduced.