Magnetically Induced Current Density Spatial Domains

Abstract

The pseudostagnation graphs of the current density induced by a magnetic field perpendicular to the plane of the carbon atoms of benzene and cyclopropane, chosen as archetypal of π- and σ-aromatic molecules, have been worked out. Saddle nodes forming the saddle stagnation lines of the pseudostagnation graph have been connected by means of trajectories of the current density, which delimit the border of four different sectors of flow around each saddle line. The merging of all such boundary trajectories provides local zero-flux surfaces in the pseudocurrent density, i.e., separatrices, which split the induced current density field in a number of three-dimensional domains of flow. As a result, a new partition scheme, corresponding to the physical flow that one could observe, has been obtained. For benzene and cyclopropane, by integration of the current density over the various spatial domains, the parallel component of the nuclear magnetic shielding and magnetizability tensors has been decomposed into contributions that are hard to reconcile with any atomic models of partition.

NICS – Past and Present

“…The main criticisms are (a) that current density (the integration of which is the ring current) is a vector field, which contains a lot of information. The representation as a single scalar number (NICS value) incurs a loss of information, sometime important, which can lead to wrong chemical conclusions . (b) The overinterpretation of NICS, especially when using improper NICS methods (see last section).…”

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

“…Previous works [22,65] have suggested using Newton-Raphson approaches to search for stagnation points, which occur at the nodes of the current density j. In particular, these optimization schemes only use first-order information to search the three-dimensional current-density vector field from a grid of arbitrarily chosen starting points [22].…”

“…in which the zeroth-order term is, by definition, zero. Taking only the first-order approximation, the current density in the region of the singular point can be described by the linear equation [54,[63][64][65][66][67]:…”

“…It can be shown that the local behaviour of the current may be characterized by the eigenvalues η i of the Jacobian matrix [51]. The number of non-zero eigenvalues of J is denoted by the rank r, whilst the excess of eigenvalues with a positive real component over those with a negative real component is denoted the signature s -together the ordered pair (r, s) can be used to characterize the stagnation point [22,[52][53][54]64,65]. Given that, at points where the current density is zero, the identity ∇ • j = 0 must be satisfied, the only possible (r, s) combinations for a three-dimensional vector field are (3, ±1), (2, 0) and (0, 0).…”

“…The resulting classifications are summarized in Table 1 and will be used throughout this work [22,54,[65][66][67].…”