Topological Analysis of Magnetically Induced Current Densities in Strong Magnetic Fields Using Stagnation Graphs

Abstract

Stagnation graphs provide a useful tool to analyze the main topological features of the often complicated vector field associated with magnetically induced currents. Previously, these graphs have been constructed using response quantities appropriate for modest applied magnetic fields. We present an implementation capable of producing these graphs in arbitrarily strong magnetic fields, using current-density-functional theory. This enables us to study how the topology of the current vector field changes with the strength and orientation of the applied magnetic field. Applications to CH4, C2H2 and C2H4 are presented. In each case, we consider molecular geometries optimized in the presence of the magnetic field. The stagnation graphs reveal subtle changes to this vector field where the symmetry of the molecule remains constant. However, when the electronic state and symmetry of the corresponding equilibrium geometry changes with increasing field strength, the changes to the stagnation graph are extensive. We expect that the approach presented here will be helpful in interpreting changes in molecular structure and bonding in the strong-field regime.