Topological theory of the electronic currents in benzene

The Magnetic Shielding Function of Molecules and Pi-Electron Delocalization

“…This review covers the whole range of theoretical work from the early formulation of the method, the introduction of ring current models, semiempirical computations of ring currents and properties arising from ring currents, until it discusses in detail the more recent ab initio based current density approaches. The analysis of the global current density of a molecule induced by an external field goes back to Gomes' work in the 1980s. − Such studies became more popular after the introduction of the ipsocentric approach, based on a CSGT , or, similarly, on a CTOCD. , The latter has been the most popular method to compute current density maps. − In this approach, the gauge transformation problem is resolved by using a different gauge origin for each point for which the current density is calculated. Within the CTOCD-DZ variant, the gauge origin is identical to the point at which the current density is computed, , while in the CTOCD-PZ alternative the gauge origin is chosen such that the transverse component of the paramagnetic current density is annihilated. ,, The latter method has been applied recently to a large series of molecules by Steiner, Fowler, and co-workers. ,,− …”

“…The analysis of the global current density of a molecule induced by an external field goes back to Gomes' work in the 1980s. [142][143][144][145][146] Such studies became more popular after the introduction of the ipsocentric approach, based on a CSGT 25,147 or, similarly, on a CTOCD. 26,148 The latter has been the most popular method to compute current density maps.…”

“…Maps of magnetically induced current densities in molecules were first illustrated by Lipscomb and others. 3,[167][168][169] The topological analysis of the current density was proposed in 1983 by Gomes [142][143][144][145][146]170 and in more detail, including the evaluation of basins, 10 years later by Keith and Bader. 147 Before discussing the physics of the ring current density, we briefly recall what can be extracted from a topological analysis of the electron density (see Figure 3).…”

“…The presence of such a stagnation point is necessary for establishing a ring current, but there are several other possibilities of density distributions than ring currents. For a complete mathematical description of this topic, the reader is referred to the milestone papers in the literature [142][143][144]146,147,170 and two review articles, which deal with this the topological analysis of ring current densities. 84,98 Whether a region of current flow is diamagnetic or paramagnetic depends on the curl of the current density ∇ B × j b(r b) at the stagnation point, also called its vorticity field, relative to the atomic shell structure.…”

Description of Electron Delocalization via the Analysis of Molecular Fields

“…When discussed considering relativistic influences, which are often necessary if an external vector potential is present, the four-component relativistic current density has to be used instead. , While for the relativistic case no topological analysis has been performed yet, the nonrelativistic induced current density has been discussed a few times in the literature. The relevant mathematical background has been developed by Gomes in the early 1980s, − and detailed reviews, including mathematical and physical background, were given at beginning of the millennium. , Most importantly, the stagnation points, (3, +1) critical points where the current density is zero, and stagnation lines, (2, 0) critical “axis”, are necessary for establishing a ring current effect, but also for other special positions of the current density.…”