Topology of Quantum Mechanical Current Density Vector Fields Induced in a Molecule by Static Magnetic Perturbations

Abstract

It is shown that the quantum mechanical theory of static magnetic properties can be reformulated in terms of electronic current densities induced by an external magnetic field and permanent magnetic dipole moments at the nuclei. Theoretical relationships are reported to evaluate magnetizability, nuclear magnetic shielding and nuclear spin-spin coupling via the equations of classical electromagnetism, assuming that the current density is evaluated by quantum mechanical methods. Emphasis is placed on the advantage of the proposed formulation, as an alternative to procedures based on perturbation theory, as regards interpretation of response allowing for the ideas of current density tensor and current susceptibility vector. Visualisation of the electronic interaction with a magnetic field and intramolecular perturbations, e.g., nuclear magnetic dipoles, is made possible via current density maps, nuclear shielding density maps and plots of nuclear spin-spin coupling density. Topological analysis of the quantum mechanical current density in terms of Gomes stagnation graphs is shown to yield fundamental information for understanding magnetic response. Examples are given for a few archetypal molecules. A topological definition of delocalized electron currents is proposed.