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.

Topological analysis of functions on arbitrary grids: Applications to quantum chemistry

“…15. This stagnation graph exhibits the same features as a more detailed analysis at significantly reduced cost [32]. The graph is known to contain a stagnation line that bisects the molecule -this can be seen in Fig.…”

“…In any case, the approximate stagnation points determined via the present analysis on DFT grids can be used as a starting point for the derivative based optimization and refinement of the stagnation graph presented in Ref. [32]. Utilising the starting points from the algorithms in the present work can significantly reduce the cost of determining detailed stagnation graphs using the derivative based approaches.…”

The Oriented and Flux-Weighted Current Density Stagnation Graph of LiH

“…General procedures to compute stagnation points and stagnation lines have been published, as well, and are freely available. 11,12 Placing B parallel to the z axis and perpendicular to the Li -H bond (lying along the y direction) results in a J field that is composed of exactly two separate current vortices, each of which possessing a central stagnation line (see Fig. 1).…”

A natural scheme for the quantitative analysis of the magnetically induced molecular current density using an oriented flux-weighted stagnation graph. I. A minimal example for LiH

“…These surfaces are known as separatrix surfaces. Topological characterizations of the induced molecular current density field are fairly abundant in the literature 6,[8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] and analogies between the QTAIM analysis and the SG graph analysis have been discussed. 3 Unlike for bond paths in QTAIM, there are no established empirical rules or simple models of interpretation for the topology of the magnetically induced current density, yet.…”